‘Investigation towards the efficiency of a multi-cyclone dust separator in biomass combustion’

Traineeship report

Author: Rob van Benthum Student number: 0531335 Rapport number: WPC 2007.10 Traineeship supervisors: Ir. Carlo de Best (TU Eindhoven) Dipl. –Ing. Josef Heinzle (Mawera)

Eindhoven, August 2007

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Table of contents:

Preface . . . . . . . . 1

1. Introduction . . . . . . . 2

2. Cyclone theory . . . . . . . 3 2.1 Flow characterisation . . . . . . 3 2.2 Geometric coupling . . . . . . 4 2.3 Characteristic particle size . . . . . 6 2.4 Characteristic dust loading factor . . . . 8 2.5 Fractional efficiency . . . . . . 9 2.6 Separation efficiency . . . . . . 10 2.7 Pressure drop . . . . . . . 11 2.8 Model build-up . . . . . . 15

3. Measurements . . . . . . . 16 3.1 Introduction dust measurements . . . . 16 3.2 Setup and Equipment . . . . . . 17 3.3 Filter pre- and after-treatment . . . . . 20 3.4 Device comparison . . . . . . 21 3.5 Measurement plan and execution . . . . 22

4. Analysis . . . . . . . . 23 4.1 Model verification . . . . . . 23 4.2 Uncertainties in the model . . . . . 25 4.3 Uncertainties in the measurements . . . . 27 4.4 Accuracy analysis . . . . . . 27 4.5 Geometrical parameter determination . . . . 32 4.6 Cyclone design comparison . . . . . 34

5. Recommendations on the multi-cyclone geometry . 37

6. Summary . . . . . . . 39 6.1 Conclusions . . . . . . . 39 6.2 Additional remarks . . . . . . 40

7. References . . . . . . . 41

Appendices . . . . . . . 43 A.1 The considered (multi)-cyclone and its dimensions . . 45 A.2 Measurement Rapport . . . . . 46 A.3 Calculation of flue gas density . . . . 47 A.4 Normalized conditions . . . . . 48 A.5 Moisture content . . . . . . 50 A.6 Determination of the friction coefficient . . . 51 A.7 Particle size distribution . . . . . 52 A.8 Determination of the total cyclone wall-gas contact surface area 54 A.9 Swirl coefficient . . . . . . 55

Symbolic declaration:(rapport)

Ai Cyclone inlet surface [ m2 ] Bi Cyclone inlet width [ m ] CD Friction coefficient [ - ] Ci Dust concentration [ kgm-3 ] Cin Dust concentration at multi cyclone entrance [ kgm-3 ] Cout Dust concentration at multi cyclone exit [ kgm-3 ] d Critical exhaust flow diameter [ m ] crdp Particle diameter [ m ] dp50% Characteristic particle diameter [ m ] Dc Outer diameter of the cyclone separation chamber [ m ] D0 Exhaust diameter of the cyclone separation chamber [ m ] Fs Total contact area between the gas and the wall [ m2 ] g Gravity acceleration [ ms-2 ] Hi Cyclone inlet width [ m ] kz Constant [ - ] ki Axial expansion loss correction coefficient [ - ] K Constant [ - ] K0 Constant [ - ] l Length of the cyclone outlet in the separation chamber [ m ] L Length of the cyclone separation chamber [ m ] mG Gaseous particle mass [ kg ] mp Solid particle mass [ kg ]

inm& Mass flow rate at multi cyclone entrance [ kgs-1 ]

outm& Mass flow rate at multi cyclone exit [ kgs-1 ] n Swirl exponent [ - ] Δp… Pressure loss [ Pa ] pdynamic Dynamic pressure [ Pa ] pstat, after Static pressure after multi –cyclone [ Pa ] pstat, front Static pressure in front of multi –cyclone [ Pa ] Q Volumetric flow [ m3s-1 ] r Trajectory radius [ m ] re Characteristic radius [ m ] ri Radius of entrance [ m ] ur Radial particle velocity [ ms-1 ] ut Tangential particle velocity [ ms-1 ]

0,axv Averaged axial velocity in the cyclone exhaust [ ms-1 ]

iv Average cyclone entrance velocity [ ms-1 ] vr Radial gas velocity [ ms-1 ] vt Tangential gas velocity [ ms-1 ]

0,tv Tangential velocity at the position r = Do / 2 [ ms-1 ]

ctv ,~ Dimensionless tangential velocity at position r = Dc / 2 [ - ] vTC Terminal velocity [ ms-1 ] Xgeo Dimensionless geometric parameter [ - ] Cy50 Rietema’s dimensionless parameter [ - ]

α Contraction coefficient for loss of angular momentum [ - ] ζ… Pressure loss factor [ - ] η Fractional efficiency [ - ] ηsep Separation efficiency [ - ] θ Angle [ rad ] λ Friction coefficient [ - ] λw Wall friction coefficient [ - ] μD Dust loading factor [ kgkg-1 ] μG Dynamic viscosity of the gas [ Pa s ] μGr Characteristic dust loading factor [ kgkg-1 ] ρG Gas density [ kgm-3 ] ρp Particle density [ kgm-3 ] Γsink Vortex strength of a sink component [ - ] Γvortex Vortex strength of a swirl component [ - ]

Preface: Mawera is an innovative company in small- and middle-scale biomass combustion plants for heat generation based in Austria with subsidiaries in Europe and Canada. They design and sell complete installations from fuel storage and supply systems to chimneys and all that is in between. Beside heat generation they are also involved in several projects for combined heat and power generation from biomass. The traineeship execution took place at the home company of Mawera in Hard am Bodensee in Austria, where approximately 150 employees are stationed. This report is about an investigation towards the efficiency of a multi cyclone dust separator. This multi cyclone is used in a first cleaning step for burned gasses of biomass combustion plants. It is meant to filter out small solid particles, down to approximately 1 μm, from the burned gas stream right after the combustion chamber. The cyclone under investigation is mostly adapted to biomass combustion plants up to 1 MW, running on non-contaminated biomass fuels. The main purpose of this report is the investigation of the separation efficiency of a given multi cyclone, for different number of single-cyclones and for different kind of flow rates. There should be found an optimum in separation, flow rate and pressure drop, for the current multi cyclone. The results are supported by measurements on a test facility, available at the home company of Mawera. First there will be given a detailed theoretical background on particle separation efficiency, starting with a force equilibrium method on a dust particle. This method is used to predict the dp50%; the diameter of a particles that are separated with a 50 percent probability. This part is followed by an investigation of the separation efficiency over the particle size and flow rate. After a discussion on pressure loss determination, the theoretical part is closed with a short introduction into the construction of a computer model. Furthermore the test facility, a measuring plan, the measurement equipment are discussed. In the third part the results of the measurements are compared to the prediction of the theoretical values. From the outcome of the comparison between the measurements and the theory, a fourth part arises where some changes towards the design of the multi-cyclone are proposed. This report is closed with a suggestion towards an optimal operating point and eventually an improvement on the geometry of the multi-cyclone.

1

1. Introduction The cyclone idea is first patented by Knickerbocker Co. Jackson, USA in 1886. The described device is a funnel (reversed cone) with a top cover and a collection chamber at the bottom. The top cover contains a cylinder in the centre functioning as an outlet. The device has a tangential inlet at the top of the funnel. This device was designed for filtering woodchips from an extractor flow in sawing processes. In the early thirties, it became clear and accepted that the cyclone has more potential. From there the development broadened to separation from thousands up to one micrometer [2]. As earlier mentioned a cyclone, see figure 1.2, is a particle separator, able to filter out small solid and liquid particles from a gas or liquid stream. The operating range is dependent on the cyclone geometry, flow rate and the density difference between the particles and the gas. The main strength of the cyclone is the absence of moving mechanical parts. The flow in a cyclone is illustrated in figure 1.1. The incoming gas stream is brought to a swirling flow via a tangential or spiral inlet or via a swirl generator in the axial case. This swirl causes centrifugal forces. These forces are density dependent and result in a move of the heavy particles towards the wall and the lighter gas stream towards the inside of the cyclone. Between the outlet entrance and the bottom of the cyclone the swirling flow is converted partly into a radial inward flow until the axial component turns. From this point a swirling flow of cleaned gas goes up in the centre of the cyclone and leaves the cyclone through the outlet. The collected particles at the wall are transported to the collection chamber via an axial flow at the wall, eventually supported by gravity.

figure 1.1: Schematic presentation of the flow in a cyclone. On the right the trajectory of a particle and the gas stream are illustrated. On the left the development of the gas stream is shown.

It can easily be seen that by increasing the flow, the separation efficiency goes up accompanied by a larger pressure drop. In order to run at higher flow rates, more cyclones can be used in a parallel setup [1],[12]. This is the main principle of a multi cyclone. See figure 1.2

2

2. Theory 2.1 Flow characterisation: Cyclones are complicated devices for flow calculations. The involvement of turbulence, the interaction between particles and the carrying gas, and the cyclone geometry makes it hard to solve the equations of motion [2]. Even though, in a first approximation these equations can be solved when some severe simplifications and assumptions are carried out. In a similar way as in [10] a start can be made at the equations of Newtonian motion of a particle in cylindrical coordinates:

Figure 2.1: Schematic presentation of the forces on a particle in centrifugal separation

( ) ( )

( ) ( )r

uumm

muvAC

dtdu

m

ru

mmm

uvACdt

dum

trpg

p

ttGDtp

tpg

p

rrGDrp

⋅⋅−+

−⋅⋅⋅⋅=⋅

⋅−+−⋅⋅⋅⋅

=⋅

2

22

5.0

5.0

ρ

ρ

(2.1)

The force change for both tangential and radial direction is a result of the change of the friction force, the buoyancy force and the centrifugal force, see figure 2.1. In expression (2.1) mp and mG are respectively the masses of the particle and the same particle but then gaseous in [kg], dp presents the particle diameter in [m], vt and ut are the tangential velocities of the gas and the particle in [ms-1], vr and ur are the radial velocities of the gas and the particle in [ms-1], r is the trajectory radius of the particle in [m], ρG is the gas density in [kgm-3] and CD is a friction coefficient. Under equilibrium condition, the particle moves in a circular orbit, meaning that its radial velocity, ur, and its radial acceleration, dtdur are zero. Under the above condition the tangential particle velocity is steady, so dtdut is zero. Substituting these assumptions into the equations of motion, results in the following:

( )p

ttGD

t

p

g

p

rGD

muvAC

ru

mm

mvAC

2

22

5.00

15.0

0

−⋅⋅⋅⋅=

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−+

⋅⋅⋅⋅=

ρ

ρ

(2.2)

So the particles have the same tangential velocity as the gaseous phase: . tt vu =Because the particle is in a steady orbit, and its radial velocity is zero, the radial velocity of the gas is per definition the terminal velocity, vTC, of the particle, since the terminal velocity represents the velocity of the particle seen from the gas.

3

4

If we now suppose that the radial inward gas flow is laminar and the particles are perfectly spherical, a so called Stokes flow can be assumed around the particle and the friction coefficient can then be presented as:

Re24

=DC G

TCpG vdμ

ρ ⋅⋅=Re (2.3)(2.4)

This expression for the drag coefficient holds for Reynolds numbers below one. Within the above expression the Reynolds number is given as equation (2.4). Herein presents μG the dynamic viscosity of the gas in [Pa s] and vTC the terminal velocity in ms-1. Combining equation (2.2) with (2.3) and (2.4) and replacing the masses by densities and particle size leads to a relation between the particle size, particle position and particle motion:

( )

rvd

vG

tpGpTC ⋅

−=

μρρ

18

22

(2.5)

In this expression ρp is the solid particle density in [kgm-3]. This expression can now be used for a cyclone model. 2.2 Geometric coupling: The working principle of a cyclone is based on its swirling flow inside, which causes centrifugal forces. According to ´Bart van Esch´,[1] and ´Cristóbal Cortés´,[11], the tangential component of the swirling flow can in a first approximation described in two parts: In the outer part of the cyclone the tangential velocity distribution is given by a (reduced) free vortex ( constant) whereas in the core flow a solid body rotation (

=⋅ rvt

=rvt constant) exists. The tangential velocity distribution is also shown in figure 2.2. As the particle concentration is sufficient low (no flow disturbance by particles) the particles can be assumed to behave in the same way as the gas flow. Furthermore it is assumed that there exists a particle with a diameter dp that has a trajectory on a steady radius r where it is theoretically neither separated nor let trough. Than potential flow theory can be used to express the tangential and radial gas velocity on the outside of the in terms of cyclone geometry. In combination with equation (2.5) the particle size versus the particles steady radius can be predicted.

Figure 2.2: Presentation of the velocity distributions in a cyclone. Right: the swirling flow. Left: 1: The radial speed. 2: axial velocity distribution. 3: tangential velocity distribution. ( Source: [1] )

5

The stream function for the flow in the outer part of the cyclone can be described as:

( ) ( )rr vortexk ln22

, sin

πθ

πθ

Γ−

Γ−=Ψ (2.6)

Herein ( )θ,rΨ represents the stream function, ksinΓ and vortexΓ give the strengths of the sink and the vortex component, and θ is an angle in [rad]. The resulting velocity expressions are depicted below:

rrv

rrv

vortext

kr

⋅Γ

≈∂Ψ∂

−=

⋅Γ

−=∂Ψ∂

=

π

πθ

2

21 sin

(2.7)

The unknown sink and vortex strengths can be derived from the cyclone geometry and the volumetric flow Q in [m3s-1], using a specific control area in radial and tangential direction:

( )

( ) ( 2

2

22 O

C

Dr

o

iiD

t

vlLD

Q

HBvQ

⋅−⋅⋅−=

⋅⋅=

π ) (2.8)

In equations (2.8) Dc presents the outer cyclone diameter in [m], Do the cyclone exit diameter in [m], L and l the total length of the separation chamber respectively the length of the exit duct in the separation chamber in [m] and Bi and Hi the inlet width and height in [m]. See also figure 2.3. In this way the vortex and sink strengths can be approximated and filled together with velocity expressions (2.7) into (2.5), when off coarse vr is used for the terminal velocity. The result is a relation between steady orbit particle position and the particle size:

( )( ) ( ) 2

2236

cGp

iiGp DlLQ

HBrd

−⋅⋅−⋅

=ρρπμ (2.9)

Figure 2.3: Schematic representation of the cyclone and its important dimensions.

6

2.3 Characteristic particle size: A major parameter for cyclones is the particle size of a particle which is separated with a 50 percent chance on a critical radius re. This characteristic particle size is called the dp50%. The main problem now is the definition of the value of the characteristic radius re. At this radius the axial velocity is assumed to be zero, as can be seen from figure 1.2. Within this radius, the particles are carried out of the cyclone. Particles outside this radius are carried to the wall, and transported to the downside of the cyclone due to the downwards axial velocity at the wall. In the most simple assumption according ‘Bart van Esch’ [1], 20Dre = .

( )( ) ( ) 2

22

%50,9

cGp

iioGp DlLQ

HBDd

−⋅⋅−⋅

=ρρπ

μ [1] (2.10)

In additional literature also other expressions can be found that are a variation on the derivation of (2.10). The following expression can be found in the book from ‘VDI Verlag’ [2]:

( )( ) ( )lLQ

HBr

Dd

Gp

iiG

n

ip −⋅⋅−

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

ρρπμ 22

0%50 2

9 [2] (2.11)

In this expression the proportionality between the cone and the tangential velocity is corrected with a swirl exponent n, which should take into account a correction for the ‘reduced’ free vortex. The value of n can vary approximately between 0.4 and 0.8 [11]. In this expression, ri represents the radius of the cyclone entrance in [m]. More exact, empirical relations of the swirl coefficient can be found in additional literature [7],[11]. These relations are shortly explained in appendix A.9. A third expression can be found in the book of ‘Prof. Dr.-Ing Wolfgang Fritz’ [3]:

( ) ( )lLQvv

DdGp

G

t

axp −⋅⋅−

⋅⋅=ρρπμπ 9

4 0,

0,20%50 [3] (2.12)

Herein 0,axv represent the averaged axial velocity in the exhaust duct of the cyclone in [ms-1] and the tangential velocity in the exhaust duct of the cyclone at radius D0,tv o/2 in [ms-1]. An often used relation between both velocities is derived from the angular momentum balance. This results in:

( )lL

rA

Dvv

i

iax

t

−+⋅

=λ

πα

22

0

0,

0, (2.13)

λ represents the dimensionless friction coefficient and is determined in appendix A.3. α Presents a dimensionless contraction coefficient for the loss of angular momentum due to the

cyclone inlet geometry and μD represents the dust loading factor in [kgm-3]. The latter two are expressed as:

Q

m

G

DD ⋅=ρ

μ&

ctc

ii

vDrv

,

2⋅⋅⋅

=α (2.14) (2.15)

In equations (2.14) represents the mass flow rate of dust at the cyclone entrance in [kgsDm& -1]. According [3], for a spiral cyclone inlet the dimensionless contraction coefficient from (2.15) can be approximated as:

i

i

Ar

λπα ⋅⋅+= 31 (2.16)

Equation (2.13) gives just an approximate value for the relation between the tangential and axial velocity in the exhaust duct, independent of the flow rate. It is quite reasonable to assume that this ratio differs for higher flow rates. Therefore, an empirical relation could be used for the tangential velocity in the separation chamber. Such an empirical relation is given in section 2.6, equation (2.31). Figure 2.4 compares the three expressions for particles, with a particle density of 800 [kgm-3]. As can be seen from figure 2.4, the three expressions give quite the same results:

0 50 100 150 200 250 300 350 400 450 5002

4

6

8

10

12

14

16

18

Flow in [m3/h]

dp50

% in

[um

]

Eq. (2.10)Eq. (2.11)Eq. (2.12)

Figure 2.4: Comparison of the three expressions for the dp50%. Herein particles in biomass exhaust gas are assumed. The particle density is put equal to 800 [kgm-3]. The biomass exhaust gas is assumed to be from combusted wood with a moisture content of 30 mass% (d.b.) at a temperature of 175 degrees Celsius and an absolute pressure of 857 mbar.

7

2.4 Characteristic dust load factor: The dust load in the gas stream is a very important parameter in the separation process. This dust load is normally given in the weight of dust per normal cubic meter of gas. According ‘Prof. Dr.-Ing Wolfgang Fritz’ [3] and ‘E. Weber’ [5] it is proven in earlier research that above a certain load factor µD spiral dust flows build up on the wall right after the cyclone entrance. This means that part of the dust is already separated at the entrance at these high dust loads. In practice these spirals have the advantageous effect of turbulence damping and flow stabilisation, resulting in a reduced pressure drop and better separation efficiency. This result can be explained by taking a closer look to the flow around a particle: When a particle enters a specific flow area, the total flow area is slightly decreased. This results in an increase of flow velocity directly around the particle, accompanied with a decrease in pressure. This lower pressure vanishes in a tail behind the particle. If another particle is close enough behind the first particle, it will be sucked into the lower pressure tail of the first one, meaning that the second particle follows roughly the trajectory of the first particle. So if the dust load is sufficiently high, the solid particles are close enough to follow each other. This dust load is approximated by a characteristic dust load factor µGr, expressed as:

( ) 578.022

410

23

0,

0,21

2 ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅⋅⋅=

oco

c

ax

t

i

c

o

inGr DD

lLDD

vv

rD

DA

παλμ [3] (2.17)

Equation (2.17) gives the characteristic dust load factor in [kgm-3]. The last number in this expression counts for the correction of the particle with a 50 percent separation chance. This is because this actual characteristic particle size is in most cases somewhat larger than the calculated one. Another expression for this characteristic parameter can be found in the book of ‘E. Weber’[5]:

( )2

20,

0,2

23

424

2

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅−

⋅⋅⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

⋅=

oax

t

ii

o

o

c

i

c

zGr D

Qvv

gAlL

AD

DD

rD

kπ

ππ

απ

λμ [5] (2.18)

Herein g presents the gravity acceleration in [ms-2] and kz is a constant, which is approximately

for average particle sizes of 10 micrometer. These two very complicated equations give only a rough approximation of this characteristic dust load. This difficulty of approximation is caused by the influence of many parameters on which the phenomena of dust-spiral-building depends, such as the different velocities and their fluctuations and relations to each other, the cyclone geometry, the wall friction, the particle distribution, etc. In most cases these equations are used to estimate the order of the characteristic value. For the cyclone under investigation the minimum value for which this phenomena can occur is about 0.02 [kgm

3102 −⋅

-3]. This is roughly a factor ten above the average dust load of primary exhaust gases from biomass combustion chambers.

8

2.5 Fractional efficiency: Fractional efficiency is very simply the separation chance for a certain particle size. Fractional efficiency is hard to calculate, since it depends on many parameters such as cyclone geometry, the flow characteristics and turbulence, dust load, particle distribution over the cyclone, etc. In theory a step function at the dp,50% -point could be the most simple model for the fractional efficiency. An expression of section 2.3 can then be used which includes the major geometrical and flow characteristics. Unfortunately this idea is of limited use because the split between separation and bypass is not fixed at a certain particle size but at a broad particle size area in which the separation chance rises from 0 to 100 percent. Furthermore the separation chance curve might not be symmetrical meaning that the dp50%-point is not in the center of this particle size area. Although if it is assumed that the concentration distribution over the cyclone separation chamber is homogeneous, a better approximation of fractional efficiency can be made using a comparison between a total and a fractional volume. The fractional volume is then defined by the radius of steady orbit for a certain particle size. The steady orbit radius of a particle defines the boarder between the position of a particle that is carried to the wall (separated) and the position of a particle with the same size that is carried to the core flow. The number off particles with the same size that are outside a cylindrical volume spanned by their steady orbit, divided by the number of particles with the same size in the total cyclone separation chamber volume gives an efficiency for a certain particle size. For a certain particle size range, this results in a fractional efficiency. An example of this method is given in figure 2.5 for Mawera’s cyclone.

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

effic

ienc

y

particle size [um]

`Bradley`volume-comparisonstep-function @ dp,50%

The main drawback of this approach is that a shortcut flow directly around the entrance of the exit duct is neglected. This shortcut flow is much stronger than the general radial flow in the cyclone separation chamber itself, resulting in a small amount of particles (of every size) that are directly carried out of the cyclone. This is why the resulting fractional efficiency goes steep to one. In reality the after the 50 percent fractional efficiency, the curve should become less steep because of this effect. Most expressions for particle efficiency are however derived on an empirical basis using experimental results and are related to the characteristic particle size. In ´Erik van Kemenade´ [12], such a relation is given according the method of Bradley:

( )( )( )b

X

bd

dX

p

p

−−

=

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−−−=

1log5.0loglog

exp1%50,

η

(2.19)

Bradley used for his S-curve: Figure 2.5: Bradley’s fractional efficiency (S-curve) given for a volumetric flow of 200 m3h-1. The step function (black line) gives the dp,50%-point.

b = 0.115 and X = 3. The S-curve for these values is given in figure 2.5.

9

2.6 Separation efficiency: The separation efficiency gives the rate between the amount of separated mass versus the amount of ingoing mass. This efficiency is very situation dependent, since it involves the particle size distribution in front of the cyclone. This separation efficiency can best be expressed as:

( )( ) ( )

( )∑∑∑ −

⋅=−

=

P

PP

dpin

dpout

dpin

in

outinsep dC

dCdCQ

mmmQ

&

&&η (2.20)

Herein present Cin and Cout the concentrations in front and after the cyclone in [kg/m3]. This can be further simplified in combination with the fractional efficiency, since the fractional efficiency is the link between the particle size distribution at the entrance and outlet of the cyclone. This is graphically presented in figure 2.6:

Figure 2.6: Graphical presentation of the relation between the fractional efficiency and the PSD at the cyclone entrance and outlet. The resulting expression is now given below:

( )( ) ( ) ( )( )

( )∑∑∑ ⋅−

⋅=

P

PP

dpin

dpinp

dpin

sep dC

dCQddCQQ

,ηη (2.21)

So to predict the cyclone separation efficiency, one needs to know both the particle density distribution in front of the cyclone and the fractional efficiency curve. This separation efficiency is also the main goal of the measurements, discussed in the next chapter.

10

2.7 Pressure loss: Besides the characteristic particle size and separation efficiency of a specific cyclone, also the pressure drop is important. This is because a cyclone is simply and solely driven by the gas flow itself. In general the volumetric flow and the pressure drop to be conquered are coupled via the kinetic (and or potential) energy content of the flow. An increased pressure drop results in a decreasing volumetric flow, which then on its turn results in a worsening particle and separation efficiency. In the case of the biomass combustion plant design, an external fan is used after the cyclone to conquer the pressure losses in the exhaust system. The operating conditions and the maximum capacity and efficiency are thus dependent on the capacity of the fan. In a cyclone, the total pressure loss can be prescribed to three general sources [5]: 1) Pressure losses in the inlet region of the cyclone. These pressure losses occur because

of strong directional changes in velocity and due to changing inlet cross sections. 2) Pressure loss in the separation chamber of the cyclone due to wall friction and friction

in the flow. 3) Pressure losses in the cyclone core and in the exhaust duct of the cyclone, due to strong

velocity changes in magnitude and direction. In ‘VDI Verlag’ [2], ‘Prof. Dr.-Ing Wolfgang Fritz’ [3] and ‘E. Weber’ [5], an approach according “W. Barth” and “E. Muschelknautz” is used to predict the pressure drop in a pure gas driven cyclone. This method contains above three fractions of pressure loss separately. These three pressure losses can be determined via loss factors. For the total pressure drop the following equation can be set up:

( ) 0,0, 21

21

axgocspaxgocsp vvpppp ⋅⋅++=⋅⋅=Δ+Δ+Δ=Δ ρζζζρζ ( 2.22 )

Herein Δpsp is the pressure loss due to the spiral inlet geometry, Δpc is the pressure loss in the separation chamber and Δpo describes the pressure loss caused by the exhaust duct. All pressure losses are in [Pa].These loss factors are given as:

⎟⎠⎞

⎜⎝⎛ −⋅

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

+= 2

2

2 1142

4 απ

ππζ

o

i

o

ci

osp

DA

DDA

D ( 2.23 )

( )

2

0,

0,2

0,

0,

121

1⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅⋅−

=ax

t

oax

tc

oc v

v

DlL

vvD

D

λ

ζ ( 2.24 )

11

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅+⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛⋅=

0,

0,0

2

0,

0,34

0,

0, 1ax

t

ax

t

ax

to v

vK

vv

vv

Kζ ( 2.25 )

In expression (2.25) the constants K and K0 are equal to 4.4 respectively 2.0 for a sharp exhaust duct edge and 3.4 respectively 1.1 for a rounded exhaust duct edge. As can be seen in appendix A.1, the values for a sharp edge are applied for the involved cyclone. If the relation between the tangential and axial exhaust velocities is greater than one, the third term from equation (2.25) is cancelled. In the above expressions, equation (2.13) can be used for the relation between the tangential velocity at the radius Do/2 and the average axial velocity in the exhaust. Another possibility is to use an empirical relation such as equation (2.31) In this approach reference is made to the axial velocity in the exhaust duct, because the exhaust duct is the main and central component of the cyclone where major pressure losses occur. It has to be noted that in [5], it is stated that the calculation of the loss factor for the exhaust duct is determined in compliance with an amount of simplifications and assumptions. For this reason above method of predicting pressure drop is not always representative. Therefore a reference to experimental results for the loss factor is advised. A recent released and more accurate calculation (two to three orders of magnitude) of the pressure loss in a cyclone is given in a paper from ‘Jianyi Chen’ [6]. Herein the combination between loss factor, average inlet velocity and pressure loss is made in a same way using four loss factors: An expansion loss at the inlet causes a first loss factor for the inlet. A contraction loss at the entrance of the outlet tube results in an additional loss factor at the outlet. Then there is also a frictional loss in the separation chamber between the gas flow and the cyclone wall which gives the third loss factor. Finally there is a dissipation loss of gas dynamic energy in the outlet flow, resulting in the fourth loss factor. At the inlet of the cyclone the flow will expand both radially and axially. This results in a local pressure loss at the entrance. For a volute (spiral) inlet this loss is given as:

2

1 22

1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=oic

ii DBD

Bkζ ( 2.26 )

This pressure loss is only dependent on the flow and the geometry of the inlet. In equation (2.26), ki is a constant which corrects for the axial expansion loss. Its usual value is approximately 0.3. The second loss occurs at the entrance of the exhaust duct. This loss occurs because of an abrupt reduction of the flow area when the gases enter the exhaust tube from the separation chamber:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅=

2

42

2

2 3116

5.4c

o

c

i

DD

DA

πζ ( 2.27 )

The third expression is the swirling loss. Because of the friction between the gas and the cyclone wall due to gas viscosity, swirling energy is lost, appearing as an additional pressure loss. Because of this loss, the tangential flow in the cyclone is a combination of a quasi-free

12

13

and quasi-forced vortex. This can be expressed as an exponent in the free vortex relation: this exponent is called, as seen earlier, the swirl coefficient, and is explained in appendix A.6. It can be seen that this third loss factor is dependent on the tangential flow at the wall, the wall contact surface area and the friction coefficient:

n

o

cct

i

sw

DD

vAF

5.13

,3~

9.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

⋅⋅

=λ

ζ ( 2.28 )

Herein Fs is the total contact area between the gas and the wall in [m2]. A calculation of this surface area can be fount in appendix A.5. ctv ,

~ is the non dimensional tangential velocity ( )ict vv , at the wall, n is the swirl exponent and λw is the wall friction coefficient, determined in appendix A.4. The last loss factor considers the dissipation loss of the gas dynamic energy in the outlet flow.

( )2222

22

,416~

cro

i

n

c

o

c

crct

dD

ADD

Dd

v−

+⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

−

πζ ( 2.29 )

This is a complicated factor and it has the largest contribution to the total pressure loss. The determination of this loss is done using the fact that the axial flow is negligible in the vicinity of the core and is quite high in the outer region of the exhaust duct. Based on the axial flow profile, a quasi free vortex in the annular region and a quasi forced vortex in the core region of the exhaust duct, a critical diameter dcr can be determined, separating the two flow fields. This critical exhaust flow diameter, dcr expressed in [m], is used to determine the dissipation loss. Only the tangential velocity distribution and the critical exhaust flow radius are unknown, but can be determined according [7], using the correlations:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

2

5.038.0c

o

c

occr D

DDD

Dd ( 2.30 )

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅⋅+

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛⋅

==

−

c

o

i

cs

c

c

o

i

c

i

ctct

DD

AD

FD

DD

AD

vv

v2

2

06.016.021.02

,,

441

Re4

11.1~

ππ

λ

π

go

iig

DvA

μπρ4

Re = ( 2.31 )

In expression (2.31) Fs presents the total gas-wall contact surface in m2. The total pressure drop is now given as:

( ) ig vp ⋅⋅+++=Δ ρζζζζ21

4321 ( 2.32 )

Herein represents iv the average cyclone entrance velocity in [ms-1].

In above pressure drop calculation it is also possible to take in account the dust loading of the gas. Therefore, the density ρg needs to be replaced with ( )ig C+ρ in equations (2.26) and (2.32) and with { }( )isepg Cηρ −+ 1 in expressions (2.27) to (2.29) and (2.31) and (2.32). Herein Ci presents the dust concentration in [kgm-3]. If the cyclone separation efficiency ηsep is sufficiently high (suppose in the order of 90 to 100 percent), then the separation efficiency term term can be neglected and { }( )isepg Cηρ −+ 1 changes in ρg.

Not only is the density influenced by dust-loading, but also the wall friction. Therefore λw needs to be replaced by λ where the latter is determined in appendix A.4. The last concern is the tangential velocity at the wall. A new correlation or correction needs to be used in dust laden situations [7]:

27.0,

,

35.01

~~

⎟⎠⎞

⎜⎝⎛+

=′

g

i

ctct

C

vv

ρ

( 2.33 )

Using these equations, the following results can be viewed for the single cyclone where biomass combustion flue gas is used at a temperature of 175 degrees Celsius:

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

45

50

Flow in [m3/h]

pres

sure

dro

p in

[mba

r]

Chen & Chi Barth & Muschelknautz

figure 2.5: The pressure drop over the single cyclone for biomass combustion flue gas at a temperature of 175 degrees Celsius. The red (upper two) lines gives the method of ‘Barth and Muschelknautz’ according [2],[3] and [5]. The blue (lower two) lines gives the method of ‘Chen and Chi’ according [7]. The continuous lines are for the pure gas laden situation and the dashed lines are for a dust laden situation (water droplets) with a loading factor of 0.001 kg particles per kg flue gas. As in accordance with [7], the pressure drop decreases for small dust loadings.

14

2.8 Model build-up: In order to make a prediction of the separation efficiency of the multi cyclone under investigation, a numerical computer model of a single cyclone is set up in a mathematical environment, called Matlab. After parameter specification, a prediction is done of the characteristic particle size over the volumetric flow in the same way as described in section 2.3. In combination with the characteristic particle size a fractional efficiency is introduced for each flow rate, as described in equation 2.17 in section 2.5. This fractional efficiency is then combined with the assumed particle size distribution in front of the cyclone, introduced in appendix A.4. The separation efficiency for each flow rate is then equated according equation (2.19) in section 2.6. The second part of the model concerns the prediction of the pressure drop over a single cyclone. The pressure drop is also calculated for different flow rates over the cyclone, according the two methods in section 2.7. The results of this model are to be compared with measurements on the test facility. For the model a realistic cyclone operating condition of 175 degrees Celsius is taken with an atmospheric pressure of 960 mBar. The density of the flue gas is determined as given in appendix A.3. Herein an oxygen content of 13 Vol.% (related to dry flue gas) is assumed with perfect combustion. The particle density is set to 800 kg/m3. This is somewhat less than the usually used density of water since the particles are assumed to be porous.

15

3. Measurements: In order to support and verify the cyclone performance model, measurements where performed at the Mawera test facility . This test facility contains a multi-cyclone, just like the ones used on commercial scale biomass combustion plants from Mawera. The main purpose of these measurements is to determine the total fly ash concentration before and after the cyclone and the pressure drop over the cyclone for different volumetric flow rates over the cyclone at maximum performance (~350 kW) of the test facility. In this chapter, first a global overview of an absolute dust measurement is given. Next the combustion installation is shortly described, including the measurement setup. Thereafter the pre- and after-preparation of the used filters is discussed, followed by the method of data processing. This chapter ends with the results. 3.1 Introduction dust measurements: The measurements, done at the Mawera test facility, are absolute dust concentration measurements. The measurements are done according to the VDI guideline 2066, [9]. With a heated probe exhaust gasses are iso-kinetically extracted from the main flow for a period of at least 30 minutes. Isokinetic extraction means that the gas velocity in the probe inlet is equal to the gas velocity in the main flow. A changeable filter element is placed in the probe. This filter collects all dust particles from the flow trough the mouthpiece of the probe. It is important to note that we measure a total amount and not a distribution. It can be assumed that this filter captures particles down to approximately 1 µm. So only the aerosols pass this filter. Since we are only interested in the particle range that can be separated with the multi-cyclone (coarse fly ash particles), this is not a problem. Via the weight of the filter element before and after the measurement, the dust mass is determined. A combination of this dust mass with the time and the flow rate trough the probe, gives then the absolute dust concentration.

figure 3.1: Dust measurement setup according VDI 2066.

This absolute dust concentration is formally recalculated for normal conditions, dry flow and 13% O2 in the exhaust flow.

16

3.2 Setup and Equipment: In order to investigate the separation efficiency of the multi cyclone, dust, pressure and temperature are measured before and after the cyclone. The pressure measurements are done with a Prandtl-type Pitot tube. The dynamic pressure is then used to calculate the volumetric flow. The temperature and static pressure are used to calculate the volumetric flow under normalized conditions. The temperature measurements are done with Pt-100 thermo resistors. The dust measurement behind the cyclone is executed with a probe like measurement device, called a tubular filter device, described in VDI 2066, [9]. This device contains the filter bush, and is inserted completely into the flow. See picture 3.1 and 3.2. The flue gas is extracted by an external pump through the filter bush, some silica gel based filters and a gas meter. See also figure 3.4. The gas meter measures the dry volumetric flow, the under pressure and gas temperature. These values have to be read manually from the device. This is done at the beginning, the middle and the end of each measurement. The normalized extracted volume can be determined from these values. The timing is done manually for each measurement.

figure 3.2: The tubular filter device as mend in the VDI 2066 guideline. Left: a picture of the used device. Right: a cross section of the device. The area spanned by d2 and l3 is filled with filter material.

The mouthpiece of the tubular filter device is tuned to the average velocity of the flue gas. Since it is known that, in situ, the pump has a capacity of ~2 m3h-1 and the main flue gas velocity is at maximum performance approximately 7.5 ms-1, a mouthpiece of 10 millimeter diameter is used. The dust measurement in front of the cyclone is done with a lance like device. The device, the ´STMG40`, is fabricated by `Afriso Euro Index´. The filter is here mounted into a heated handle. The handle contains a ~50 cm long lance and a fixed mouthpiece of approximately 8 millimeter belonging to an inlet velocity of ~ 4 ms-1. This mouthpiece can not be changed. The lance is inserted into the flow. The gas suction device is a controlled device which has a regulated pump capacity of ~9L/h. Also here the gas is dried with silica gel based filters. This device is shown in figure 3.3:

17

18

The STMG 40 is standard equipped with a measuring time of 15 minutes. For these experiments 30 minutes are required. Therefore the measuring time is internally changed to 30 minutes. In order to validate the pump capacity, the flow rate of the device is measured with the gas meter of the tubular filter device. Via the pressure and temperature on the gas meter, normal conditions are derived. The results are depicted below in table 3.1: tabel 3.1: Result of the flow rate validation experiments. The values are derived from eight measurements,. In these measurements the pressure loss over the filter is simulated with a valve, so that in situ operation conditions are approached.

Average volume (30 minutes) Maximum deviation Standard deviation

0.2546 nm3

210860.1 −⋅ nm3

( 7.32 % )

210283.10 −⋅ nm3 ( 4.04 % )

figure 3.3: The STMG 40 dust measurement device. Left: the lance and handle. The filter is inserted into the white cylindrical part on the back of the handle. Right: The gas suction device is shown. The device is regulated at a flow rate of ~9 L/h.

figure 3.4 : Suction equipment of the tubular filter device. This equipment contains the water filters, the gas meter and the pump.

In figure 3.5 an overview is given of the experimental setup. The measurement position in front of the cyclone is between the boiler and the bend as can be seen from figure 3.4. The position after the cyclone is just in front of the suction fan, after two bends in the exhaust duct.

figure 3.5: The schematic presentation of the total measurement setup as built in the test facility at Mawera.

As mentioned earlier, the dust concentrations are calculated at 13 vol.% oxygen in dry flue gas. Therefore the volumetric flow trough the filter has to be corrected. This correction is given in appendix A.3. In order to do this correction, the actual volumetric fraction of oxygen in dry flue gas is measured with a gas analyzer (shown in figure 3.4). This fraction is stored via a computer in a data file. The average oxygen content can be calculated from this data file for each measurement. In the same way temperature and static and dynamic pressure are stored into the data file. From these values, the average the normalized flow rate of the flue gas can be calculated, just like the average pressure drop over the multi-cyclone for the duration of the measurement.

19

3.3 Filter pre- and after-treatment: In accordance with VDI guideline 2066, the filter element needs to be prepared before they are used. A filter element of the tubular filter element consists of a metal bush, a small grating and the filter material, which can be exchanged. A filter bush is shown in figure 3.6. The filter material, quartz wool, is obtained from the company Mercateo (1). The stepwise pre-measurement preparation of the filter bushes is stated below:

1) The filter bushes are numbered with a water proof pencil 2) The filter bush filled completely with quartz wool, while slightly pressed with the

thumbs 3) The quartz wool in the filter bush is saturated with tap water and pressed with the

thumbs into the bush until two third of the bush is filled with the filter material. 4) The filter bush is dried for at least 10 hours in a drying furnace at a temperature of 105

degrees Celsius. 5) The filter bush is mounted into the probe. Environmental air is sucked into the probe

trough the filter bush for at least 5 minutes to assure that broken most fibres are removed from the filter bush.

6) The filter bush is again dried in a drying furnace for at least one hour at a temperature of 105 degrees Celsius.

7) After drying the filter bush is cooled for at least 1.5 hours in a disiccator. This is a large closed bowl filled with silica gel.

The filter bushes are taken out of the disiccator just one to two hours before the measurement and straightaway weighted. The pre-measurement preparation of the filter elements of the STMG 40 is somewhat different. The filter element is a complete cartridge, obtained from: Bundesverband des Schornsteinfegerhandwerks-Zentralinnungsverband (2).

1) A new filter cartridge is put into an aluminium canister. All used canisters are numbered. The canister is closed with a corresponding aluminium lid during transport.

2) The cartridge taken out of the canister and is placed into the handle. Environmental air is sucked through the filter for a period of at least 5 minutes in order to reduce the fibre loss.

3) The filter is taken out of the device and is put into the canister again. The canister without lid is then placed into the drying furnace (105 degrees Celsius) for at least one hour.

4) The canister without lid is cooled into a dessicator for a period of at least 1.5 hours. A canister with cartridge is taken out of the dessicator just one to two hours before the measurement. They are straightaway weighted. The weight is determined from the canister with cartridge and without lid. After the measurement the filters have to be prepared again. This after-preparation concerns the last two steps of the pre-preparation for both filter types. The filters are again weighted. The weight difference gives the dust mass.

(1) Mercateo , www.mercateo.com , service@mercateo.com (2) Bundesverband des Schornsteinfegerhandwerks-Zentralinnungsverband , Westerwaldstraße 6 , Sankt Augustin (D)

20

21

3.4 Device comparison: Since the dust concentration measurements in front and after the cyclone are performed with different kind of devices, both devices are compared with each other. This comparison is split into two parts: The comparison of the sucked volume, and the comparison of the measured dust concentration. The comparison of the sucked volume is done by coupling the gas meter of the ´tubular filter device´ to the STMG40. The results from this volume comparison are given earlier in table 3.1. The comparison of the measured dust concentration is done by measuring the dust concentration after the cyclone with the two devices simultaneously. The measurement setup for device comparison is shown in figure 3.6. The distance between the two devices is approximately 50 centimeter. The results per measurement fluctuate quite a lot between the two devices. However, averaged over the measurements are the results approximately equal. The results are depicted below in table 3.2 and table 3.3: Tabel 3.2: Average measured dust concentration and corresponding standard deviation, averaged per device and per measurement. All values are related to 13 Vol.% oxygen and dry flue gas. Tubular filter device STMG40 Average value 40,02 mg/nm3

41,30 mg/nm3

Standard deviation 12,17 mg/nm3 12,78 mg/nm3

Tabel 3.3: Average difference in concentration, and corresponding maximum and standard deviation, between the two devices, averaged per measurement. All values are related to 13 Vol.% oxygen and dry flue gas.

Average difference 9,4 mg/nm3

Standard deviation 2,56 mg/nm3

Maximum difference 14,1 mg/nm3

Figure 3.6: A picture of the device comparison measurement. The left device (blue handle) is the heated probe from the gas analyzer. The distance between the STMG 40 (yellow handle) and the tubular filter

device (lance on right of picture) is approximately 50 cm.

3.5 Measurement plan and execution: As mentioned earlier three important parameters are to be measured: the pressure drop, volumetric flow rate and the total dust concentrations before and after the multi-cyclone. The first two are measured with the Prandtl tubes, and the last one with the devices described in section 3.2. To achieve different flow rates over a single cyclone, the number of single cyclones in the multi-cyclone is changed. This is done in such a way that three quite reasonable divided flow rates are obtained. The test facility is calculated at a maximum flue gas flow rate of approximately 1400 m3 per hour. The multi-cyclone in the test facility is originally equipped with 10 single cyclones. To keep the same setup of single cyclones in the multi-cyclone, there is chosen to remove two times three cyclones from the multi-cyclone. The setup in the multi-cyclone and the belonging flow rate per single cyclone is given in figure 3.7:

Figure 3.7: Layout of single cyclones in the multi-cyclone, for the three experiments. The depicted flow rate is the flow rate over a single cyclone.

It is difficult to determine the required number of measurements per number of cyclones, because one does not know the fluctuation in the data on forehand. Just one day later, after processing and evaluating all data, it becomes clear if more measurements are required. Since the dust concentration measurements are the most error sensitive due to their manual execution, the smallest number of demanded correct dust concentration measurements (in front and after the cyclone simultaneously for determining separation efficiency) is set on forehand to 7. This number proved to be sufficient for reliable and reproducible results. To accept or reject a measurement, three criteria are handled: First the operating power during a measurement must be in the range of full-power (~350 kW). Second the dust concentrations must be of realistic order. From external data, originating from earlier tests at the Mawera test facility, acquired via the University of Technology of Graz (Austria),[13], it becomes clear that the dust concentration in front of the cyclone should be in the order of 100 to 300 [mg/nm3, 13%O2]. The concentration behind the cyclone is expected to be somewhere in the range of 10 to 30 percent of the ingoing dust concentration according the theoretical model. Finally both dust concentration measurements have to be within their realistic range for deriving separation efficiency. If a measurement satisfies these three criteria, then it is called a properly executed measurement and can be used for calculation separation efficiency. After each measurement, data is processed, and all dust concentrations and flow rates are normalized as explained in appendix A.3.

22

4. Analysis: In this section the results from the measurements are to be compared with the theoretical results from the model. The comparison is followed by a clarification of possible error sources and uncertainties in the measurements and the model. Furthermore, a cyclone specific geometrical parameter is introduced for comparison with other cyclone designs. Finally the cost-efficiency for the current multi-cyclone is characterised by comparing the pressure prop over the separation efficiency. 4.1 Model verification: Below the results are presented from the model and the measurements. Figure 4.1 gives the separation efficiency over the volumetric flow. Figure 4.2 gives the pressure drop over the volumetric flow. All the measurements were done with wood chips as fuel and with a moisture content of approximately 30 Vol.%.(w.b.). Since the pressure and temperature fluctuate over time, all volumetric parameters are recalculated to the model condition of 175 degrees Celsius and an absolute pressure of 960 mBar. This is done to compare the measurements with the theoretical results of the model.

0 50 100 150 200 250 300 350 400 450 50070

75

80

85

90

95

100

Flow in [m3/h]

Ren

dem

ent i

n [%

]

model (PSD from fig A.2) measurements mean per number of cyclones model (PSD from fig 4.3)

Figure 4.1: Comparison of the measured separation efficiency, with the theoretical results from the model. The measurements are done with 4, 7 and 10 single cyclones in the multi-cyclone. The triangles give the mean point of the measurements for a certain number of single cyclones.

23

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

45

50

Flow in [m3/h]

pres

sure

dro

p in

[mba

r]Chen & Chi Barth & Muschelknautz measurement dataEmperical relation eq.(4.1)

figure 4.2: Comparison of the calculated pressure loss with the measured pressure loss. The variation over the flow rate is also here realized by the number of single cyclones in the multi-cyclone. From figure 4.2 it can be seen that the pressure drop prediction is in accordance with the experimental results. Pressure losses for cyclones are often related to the inlet velocity with the use of a pressure drop coefficient. (as explained in section 2.7). This pressure drop coefficient can empirically be related to the inlet Reynolds number in a same way as described in ‘Erik van Kemenade´ [12]. For the cyclone under investigation the following expression is derived:

( ) { } 20545.0Re3469.18 igistatic vp ρ−⋅=Δ ; Rei > 500 ; μ

ρ ig

ii

DAQ ⋅⋅=Re (4.1)(4.2)

This relation is given in figure 4.2 with the black dotted line. Above expression gives the static pressure loss, in [Pa]. ( )staticpΔ Somewhat different holds for the measured separation efficiency. From figure 4.1 it can be seen that the measured values are quite below the predicted curve. It is quite assumable that this difference is caused by two very important assumptions in the model which are explained below.

24

4.2 Uncertainties in the model: As stated above, the main uncertainty comes probably from the two major assumptions in the model: 1) The supposed particle size distribution in front of the cyclone as given in appendix A.6 2) The supposed shape of the fractional efficiency; the S-curve. The exact particle size distribution on the measurement position in front of the cyclone is not known, since no particle size measurements were done. Because a particle size distribution is necessary to predict the separation efficiency, one is assumed on data from other measurements (as explained in appendix A.6) Particle size distributions in biomass combustion are very dependent on combustion unit geometry, the kind of fuel and its composition, the moisture content, the degree of operating power, furnace temperature, the amount of excess air, etc. Therefore it is obvious that the assumed particle size distribution might not suit the actual particle size distribution in the test facility of Mawera at the time of the measurements.

10-3

10-2

10-1

100

101

102

103

0

50

100

150

Aerodynamic Particle size [ um ]

Con

cent

ratio

n [ m

g/nm

3 ]

In the assumption of the particle size distribution (appendix A.6), aerosols are neglected since it was assumed that aerosols (particles smaller than 1 µm) pass the filters from the dust measurement devices anyway. So the distribution below one micron is not included in the model. There is however a possibility that the filters do catch (some part of) the aerosol peak, so the assumption has certainly an influence on the inaccuracy of the model. From ´Aerosol Technology´,[15] it can be found that most particle density distributions can best be described by a log-normal distribution. In [14] a graphical presentation of a complete bimodal particle size distribution for wood, chips, bark and waste wood can be found. The distribution for wood chips can be approximated with the summation of a log-normal distribution for aerosols and a lognormal distribution for coarse fly ash. The corresponding values of the mean and standard deviation are given in table 4.1. From [13] it can be seen that for wood chips, the fraction of total aerosol concentration is approximately 5 percent of the total coarse fly ash concentration. The resulting particle size distribution is shown in figure 4.3.

Figure 4.3: The bimodal distribution of the particle size mass which is used in the model to show the effect of aerosols on the separation efficiency in figure 4.1.

25

26

Tabel 4.1: Values corresponding to the log-normal distribution as an approximation for the complete particle size distribution of wood chips. 1) The standard deviation and the mean particle size in the log-normal distribution are the logarithms of the values in the table. A further explanation of the log-normal distribution is given in appendix A.6. Aerosols Coarse fly ashes Mean particle size 1)

0.015 µm 37 µm Standard deviation 1)

2.75 µm 2.25 µm The effect of expanding the PSD with the aerosol-peak, on the prediction of the separation efficiency is shown with the black dotted line in figure 4.1. As can be seen, the influence of the ignorance of the aerosol peak is quite small, so the ignorance of the aerosol peak is verified. Therefore it might be expected that the distribution of the coarse fly ash peak was somewhat broader during the measurements, which also result in a flatter separation efficiency curve. The fractional efficiency on the other hand is a very cyclone-geometry and flow rate dependent function. There are several possibilities to calculate this fractional efficiency theoretically, but, as stated earlier, the methods are not always representative. Therefore usually simple relations for the S-curve are derived from measurements, which are specific per cyclone geometry and corresponding operating conditions. For the cyclone under investigation this S-curve is unknown. Therefore a model is needed for this S-curve. The separation efficiency model uses the expression of Bradley for an S-curve. However, the parameters b and X in this expression are still unknown for the cyclone under investigation and are certainly not the same has the ones from Bradley’s design. This brings again an uncertainty in the model. Figure 4.4 shows the effect of different S-curve shapes on the separation efficiency. One might conclude from figure 4.4 that for the cyclone under investigation, a quite flat S-curve (like the dashed green line in figure 4.4) is more appropriate. A major improvement can be achieved on these two problems if the particle density distributions in front and after the cyclone are measured (for example with an impactor) for different flow rates over the cyclones. In this way one knows the exact particle size distribution in front of the cyclone. The exact fractional efficiency can then be determined via the particle size distribution after the cyclone. The dp50%-point can then be determined exactly and used for comparison with other cyclone designs. This comparison will be explained in section 5.4.

Figure 4.4: Effects of different fractional efficiencies on the separation efficiency of a cyclone. On the right: the different fractional efficiencies with their corresponding parameters b and X (see also equation 2.17). On the left: the predicted separation efficiency and the experimental values.

Another less important but not negligible point which introduces an uncertainty is the knowledge of some physical properties of biomass combustion gases and the particles in this flue gas. For the particles in flue gas from wood chips combustion, a density of 800 kg/m3 is assumed. The flue gas density is approximated on a basis of ideal combustion as given in appendix A.3. The viscosity is assumed to be equal to normal air. This causes some deviations from the real situation. 4.3 Uncertainties in the measurements: The difference between the predicted and measured values for the separation efficiency might not only be caused by uncertainties in the model, but also by faults and uncertainties in the measurements. A dust concentration measurement is a very complex manual measurement. First one needs to prepare a filter for the measurements. After pre-preparation, the filters are weighted. After a measurement, a filter is prepared again (as described in section 3.3) and then again weighted. Every contact between the filters and the environment (like during the assembly and disassembly of the filters in the devices) between the two weight determinations, can have influence on the weight difference of the filter. If a filter falls over in the drying furnace, the disiccator or on the balance, the measurement can be assumed to be lost, because of the (possible) spoiled dust. These cases are however excluded from the final data. Then off course one needs a perfect, faultless, measurement in front and after the cyclone simultaneously for a determination of the separation efficiency. If not, a measurement is assumed to be inappropriate for separation efficiency determination. For calculation of the normalised vacuumed volume over the filter during a dust concentration measurement, one needs to read out the gas temperature and the under pressure of the gas manually. This is done three times during the measurement. So the average value might not correspond with the real average. Then off course one can make a mistake during manual read out of the vacuumed volume, temperature and pressure. Other possible deviation sources are for example the position of the Prandtl tube compared to the centre of the flow, the accuracy of the Pt-100 temperature sensors and the calibration offset between sensors of the same type. 4.4 Accuracy analysis: The uncertainties described above are caused mainly by the measurement procedure or availability of the physical properties. Off course the measurement devices self have also their accuracy and the measured values fluctuate over time. Therefore it might be better to look at the best and worst case per parameter which occur in the measurements. From this, one can finally determine approximately a best and worst case for the measured pressure drop and separation efficiency. The dust concentration is calculated via the weight difference of the filter and the pumped volume. For normalisation the oxygen content of the dry flue gas is also involved. For the tubular filter device the pumped volume is calculated from the gas meter and the temperature and pressure at the gas meter. The weight is determined on a balance with an accuracy of 0.0001 g. Since the balance is calibrated before each weight determination, it can be assumed that there is just a negligible

27

deviation from the real weight. Therefore the influence of the deviation in the weight determination is neglected. The readout on the gas meter goes at an accuracy of 0.0002 m3. According to Mawera this gas meter is calibrated. The influence of the deviation in the pumped volume (which is in the order of 1 m3) can therefore also be ignored. The pressure and temperature at the gas meter are manually read three times (start, middle, end) during each measurement. For each measurement the standard deviations can be calculated from these three values. The maximum positive and negative deviations in percent (from the average value) can also be determined for each measurement. The lower limit can be taken as the minimum value of the negative deviation from all measurements. The upper limit can be taken as the maximum value of the positive deviation from all measurements. The real value shall be somewhere between these two limits.

Absolute pressure

Temperature (in K)

Standard deviation 15,1 mBar ( 2,28 % )

0.24 oC ( 0.08 % )

Minimum deviation ( lower limit ) 9,9 % 0,7 %

Maximum deviation ( upper limit ) 10,2 % 0,7 %

Table 4.2: Characteristics of the measured parameters for the determination of the dust concentration. The percentages are related to the average values

From these limits, the maximum positive and negative deviations in dust concentration can be derived for the tubular filter device For the STMG40 dust measuring device, the characteristics of the pumped volume are already presented in section 3.2. However, they are determined with the gas meter from the tubular filter device. This means that the characteristics from table 4.2 also influence the limits of the measured pumped volume. Therefore a correction is needed with above parameters. The minimum and maximum deviation limits for dust determination in front and after the cyclone is given in table 4.3: Tabel 4.3: Best and worse case in the deviation around the calculated dust concentrations. The deviation is given in percent of the mean dust concentration. Note that this involves the dust concentration that is not jet normalised to 13Vol.% O2.

STMG40 (in front of cyclone)

Tubular filter device (behind cyclone)

minimum deviation ( ) %0.16%10012.101007.0100

32.7100100

≈⋅−+−

+ %6.10%1001

2.101007.0100

≈⋅−+−

maximum deviation ( ) %6.20%10019.91007.0100

32.7100100

≈⋅−−+

− %8.11%1001

9.91007.0100

≈⋅−−+

The limits from table 4.3 can be used to estimate the best and worst case in separation efficiency measurements. This is allowed since the oxygen fraction in the flue gas duct changes hardly, and can said to be equal before and after the cyclone. Therefore the fraction between the concentrations in front and after the cyclone does not change after correction to 13 Vol.% oxygen at dry flue gas. The area between the best and worst case defines the region in which it is plausible to find the real values of the measured separation efficiency. The best case (highest efficiency) is defined by the smallest dust concentration behind the cyclone, and the largest dust concentration before of the cyclone. The worst case is defined in the opposite way. The resulting two limits are expressed in table 4.4 on the next page.

28

29

Tabel 4.4: Best and worst case separation efficiency as follows from the measurement data. Worst case:

in

out

in

outsep C

CCC

33.117.01002.10100

10032.7100

9.91007.01001 −≈

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛

−+

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛

−+

−=η

Best case:

in

out

in

outsep C

CCC

75.017.01009.9100

10032.7100

2.101007.01001 −≈

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛

+−

⎟⎠⎞

⎜⎝⎛ −⎟⎠⎞

⎜⎝⎛

+−

−=η

Next to the dust concentrations, the temperatures and dynamic and static pressures in front and after the cyclone are measured, in order to determine the flow rate in normal conditions and the pressure drop over the cyclone. The flow and pressure drop measurements are done automatically with a computer. For these measurements it is not useful to look at the fluctuations around the measured value, since the influence from the sensor-disturbance fluctuation is negligible compared to the influence from fluctuations in the combustion unit. Therefore the average flow rate and pressure drop are determined over 30 minutes (simultaneously with the dust measurements). One can now take a look at the sensor accuracy instead of fluctuation characterisation, since information on sensor accuracy is known for these sensors. The temperature sensors are of the type Pt100 and are manufactured by ´Jumo´. According the user manual [17], the sensors are of accuracy class B (norm: DIN EN 60 751). Class B gives an accuracy of +(0.30 + 0.005T )oC. The average temperature before the cyclone is from the order of 185 oC and after the cyclone in the order of 150 oC. This gives accuracies of Tfront + 1.23 oC and Tafter + 1.05 oC. The pressure sensors are manufactured by ´Huba Control´. They are pressure difference sensors, type: 698. From the manufacturers website a technical datasheet is obtained from these devices [18]. In this datasheet one can find the linearity and hysteresis error in percent from the full scale. For the dynamic pressure, devices up to 5 mBar were used. For the static pressure behind the cyclone a 50 mBar device was used and before the cyclone a 10 mBar device. The resulting measurement errors for above devices are given in table 4.5.

Accuracy % Accuracy mBar pstat , after ( )fs%6.0± + 0.3 mBar

pstat , front ( )fs%5.0± + 0.05 mBar

Pdynamic ( )fs%9.0± + 0.045 mBar

Table 4.2: The deviations from the real values for the pressure loss measurements.

Next to the pressure sensors, also the influence of the position and direction of the Prandtl tubes are involved in the flow rate determination. From the user manual [19] error estimation can be done according the two graphs of figure 4.5.

Figure 4.5: The influence of the Prandtl tube direction on the error (left) and the error over the measured air velocity at standard conditions. (right). The error (deviation) in percent is given on the vertical axis. Left the rotation angle (direction) is given in degrees on the horizontal axis. Right the velocity is given on the horizontal axis. ( Source: [19] ) The used Prandtl tubes had diameters of 2.5 mm and the flow fluctuated from 4 to 10 ms-1. From figure 4.5 it can be concluded that the derived velocity (derived from the measured dynamic pressure) contains a deviation of -0.5 to 0.4 percent from the real value, depending on the fact that the angle between tube and flow direction is always smaller than 10 degrees. From the determined deviations around the real value one can determine again a range around the measured value, in which the real value is certainly expected. This range has limits at plus and minus two times the deviation around the measured value, which can approximated as given in table 4.4 Tabel 4.4: Best and worse case in the deviation around the normalized volumetric flow and the pressure drop. The deviation is given in percent of the measured value. Note that this involves the volumetric flow rate that is not jet normalised to 13Vol.% O2.

Minimum deviation Maximum deviation 12.7% 10.6%

The above accuracy analysis produces rectangles (uncertainty windows) around the measurement points, in which the width and the height are determined by the above approximated deviations of the volumetric flow rate and the separation efficiency or the pressure drop. One can now say that the ‘real’ value of the measured point is certainly situated in this window. The uncertainty windows are depicted in figures 4.6 and 4.7.

30

31

0 50 100 150 200 250 300 350 400 450 50060

65

70

75

80

85

90

95

100

Flow in [m3/h]

Ren

dem

ent i

n [%

]

model (PSD from fig A.2) measurements mean per number of cyclones

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

45

Flow in [m3/h]

pres

sure

dro

p in

[mba

r]

Emperical relation eq.(4.1) Measurement data

Figure 4.6: The uncertainty windows for the separation efficiency measurements. The present single measurement points, the triangles are the mean over the measurements on a certain number of single cyclones. The dashed boxes give the uncertainty window

for every measurement point.

Figure 4.7: The uncertainty windows for the pressure drop measurements. The dots are the measurement points. The dashed boxes give the uncertainty window for every measurement point.

32

4.5 Geometrical parameter determination: The characteristic particle size is a very important parameter in cyclone design and performance, since a small characteristic particle size means a high performance. Therefore it is useful to compare this parameter from the cyclone under investigation with the ones from other cyclone designs. For such a comparison it is usual to rewrite the expression of the characteristic particle size in a parameter group containing only geometric parameters and a parameter group containing only physical parameters. The geometrical parameter group is then called the geometrical parameter. This parameter is characteristic for a certain cyclone design, and is expressed as Xgeo in equation (4.3). [12]. By comparing this geometrical parameter, one can compare the performance of different cyclone designs, independent of their physical environment.

( )gp

cGgeop Q

DXd

ρρμ

−⋅⋅

= ⋅

3

%50, (4.3)

as the expression for the characteristic particle size was derived from force equilibrium, a theoretical expression for the geometrical parameter can be obtained. It is however more common to determine the geometrical parameter via the experimental determined ´real´ characteristic particle size. From the experimental data, shown in figures 4.1 and 4.2 it is not possible to derive the ´real´ characteristic particle size directly. There are however two methods to determine the geometrical parameter indirectly: The first method is based on the measured separation efficiency, and is already short described in the section above. If one knows the particle size distribution before the cyclone and the fractional efficiency as a function of the particle size and characteristic particle size, than the characteristic particle size can be determined by adjusting the characteristic particle size in the fractional efficiency expression in such a way that the predicted separation efficiency is the same as the measured one. In the current case, neither the real particle size distribution nor the real fractional efficiency is known. The ‘real’ characteristic particle size and corresponding value of the geometrical parameter can only approximated when a particle size distribution and fractional efficiency curve are assumed. This involves again the two major uncertainties which were described in section 4.2. The second method to determine the geometrical parameter is based on a theory from K. Rietema. With some basic simplifications, he was able to derive a cyclone correlation number which relates the total pressure difference over the cyclone to the characteristic particle size [16]. Equation (4.4) shows this expression:

( ) ( )

Qvp

Ld

Cyg

igstaticgpp

⋅

⋅+Δ⋅⋅

−⋅=

ρρ

μρρ 2

212

%50,50 (4.4)

33

Rietema stated that this cyclone number was only dependent on the geometry of a cyclone. He also showed experimentally that there exists a minimum cyclone correlation number of 3.5 for a maximum performance design. This design has ratios: 5=cDL , 34.0=co DD ,

28.0=cin DD , 4.0=cDl . Rietema presented the geometrical dependency of the cyclone correlation number in two graphs. These graphs are given in figure 4.5.

Figure 4.5: The geometrical dependency of the cyclone correlation number. The right graph springs from cyclones with a length over outer diameter ratio of 5. The left graph springs from cyclones with a fixed inlet diameter over outer diameter ratio of 0.20 and a fixed exhaust diameter over outer diameter ratio of 0.04. The red dot in the right graph presents the current cyclone under investigation. ( Source: [16] )

For the current cyclone under investigation the ratios hold: 57.3=cD

L , 55.0=c

o

DD

, 41.0=c

in

DD

.

Since the inlet of the current cyclone is square, the inlet diameter is approximated by the hydraulic diameter of the inlet: the ratio of four times the inlet surface over the length of the inlet contour. For these values, the position is shown in the right graph of figure 4.5. The reason that this dot is out of limit is that the current cyclone uses a square spiral inlet (entrance on a larger diameter than the outer cyclone diameter. Rietema used a round slot inlet for his experimental cyclones. From the figure it can be seen that it is suggested that the contours of constant cyclone correlation number are closed around the contour of Cy50 = 3.5. If this is true a value of 6 to 8 is approximated for the cyclone correlation number of the cyclone under investigation. Since the graph is representative for a L/Dc-ratio of 5 and the current L/Dc-ratio is smaller, the lower value of 6 is taken for the cyclone correlation parameter. Equations 4.1 till 4.4 can be combined with the cyclone number to express the geometrical parameter as a function of flow rate and pressure drop:

( )1

23

250

+⋅⋅⋅⋅

=ζLD

ACyX

c

igeo (4.5)

4.6 Cyclone design comparison: Now if one knows the pressure drop curve or one knows the particle size distributions and the fractional efficiency for different cyclone designs and sizes, one can compare their geometrical parameters on the basis of section 4.4. This parameter is, as stated earlier, only dependent on the design of the cyclone, and represents via the characteristic particle size in general the fractional efficiency. So the smaller this geometrical parameter, the better is its separation performance. This comparison is shown in figure 4.6 for the current design, the optimum design from Rietema and the cyclone design from Bradley. The last one has ratios: 85.6=cDL ,

20.0=co DD , 133.0=cin DD , 33.0=cDl , which corresponds with a cyclone number of approximately 8, according figure 4.4. A pressure loss correlation for this design can be found in [1]. In a first step, it is useful to look at the designs that have a same inlet diameter as the current design, since that corresponds to same Reynolds numbers for different designs. For the two above described design-types the geometric parameter curve is shown in figure 4.6. In figure 4.6, also the experimental values of the geometrical parameter are shown; calculated according the efficiency data (first method) and calculated according the pressure drop correlation(second method, equation 4.1):

0 50 100 150 200 250 300 350 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Flow in [m3/h]

Geo

met

ric p

aram

eter

Xge

o

Efficiency data fitMawera`s cycloneRietema (1)Bradley (1)

Figure 4.6: The geometric parameter for different cyclone designs. The curves correspond to designs with the same inlet area. The dots are determined via the fitting of the fractional efficiency (first method). The lines are determined via the pressure loss correlations, using the Theory of Rietema (second method)

34

35

Tabel 4.2: Measurements corresponding to the designs of Rietema and Bradley, belonging to the curves in figure 4.6. 1) Hydraulic diameter

Table 4.2 gives the corresponding measures for the different cyclone designs corresponding to the curves in figures 4.6, 4.7 and 4.8

diameter

Table 4.2 gives the corresponding measures for the different cyclone designs corresponding to the curves in figures 4.6, 4.7 and 4.8 From figure 4.6 it can be concluded that the Bradley design is the one with the optimum performance. However its dimensions are too large for application in biomass combustion units. Therefore it is possible to decrease the dimensions and volumetric flow rate by increasing the number of cyclones in the multi-cyclone. The design trajectory is however beyond the goal of this project, since the objective is to compare the different designs, to confirm the possibility of improvement.

From figure 4.6 it can be concluded that the Bradley design is the one with the optimum performance. However its dimensions are too large for application in biomass combustion units. Therefore it is possible to decrease the dimensions and volumetric flow rate by increasing the number of cyclones in the multi-cyclone. The design trajectory is however beyond the goal of this project, since the objective is to compare the different designs, to confirm the possibility of improvement. Optimal performance does not only mean maximal separation, but also the lowest operation costs, which are controlled by the dissipated power in the cyclone. This dissipated power is the product of the volumetric flow rate and the pressure loss over the cyclone.

Optimal performance does not only mean maximal separation, but also the lowest operation costs, which are controlled by the dissipated power in the cyclone. This dissipated power is the product of the volumetric flow rate and the pressure loss over the cyclone. So the optimal performance is defined as the best separation efficiency (smallest characteristic particle size) possible at the lowest possible dissipated power. So the optimal performance is defined as the best separation efficiency (smallest characteristic particle size) possible at the lowest possible dissipated power. Therefore drawback is made from geometric parameter to characteristic particle size again. Therefore drawback is made from geometric parameter to characteristic particle size again. In figure 4.7 and 4.8 the pressure drop and characteristic particle size are given for the three cyclone designs. In figure 4.7 and 4.8 the pressure drop and characteristic particle size are given for the three cyclone designs.

Figure 4.7: Characteristic particle size curves (left) and pressure drop curves (right) for the three different designs as given in table 4.2.

Mawera’s cyclone

Rietema (1)

Rietema (2)

Bradley (1)

Bradley (2)

Dc 150 270.3 200 569.1 200 Do 82.5 91.9 68 113.8 40 dc 80 49.2 56.0 617.5 217 L 536 1351.7 1000 3898.5 1370 l 176 108.1 800 187.8 66

di 62.1 1) 75.7 56 75.7 26.6

0 50 100 150 200 250 30010

-12

10-10

10-8

10-6

10-4

10-2

100

102

104

characteristic particle size [ um ]

diss

ipat

ed p

ower

by

pres

sure

loss

[ W

] Mawera`s cycloneRietema (1)Rietema (2)Bradley (1)Bradley (2)

Figure 4.8: The Cyclones dissipated power versus characteristic particle size for the different designs from table 4.2. The dotted lines give the cyclone designs with an outer diameter of 200 mm. The solid lines give the designs with same inlet area. The dashed line gives the current cyclone. The graphs from figure 4.7 can be combined to one graph of the dissipated power versus the characteristic particle size. This graph is given in figure 4.8. From figure 4.8 and table 4.2 it can be seen that the general trend is an improvement of costs versus performance for decreasing cyclone dimensions and other designs. Therefore the suspicion of a possible improvement of the separation efficiency at a decrease of pressure drop by changing the cyclone geometry is confirmed. If one goes a little further in the design process then one can find an improvement in characteristic particle size and pressure drop (resulting in separation efficiency rise) at reasonable dimensions. However one also needs to take in account the number cyclones needed in the multi cyclone to satisfy these conditions at a total maximum flue gas flow of the plant. From figure 4.7 and 4.8 and table 4.2 it can be seen every design is more efficient than the current design. So changing the design and dimensions of the cyclone can have a positive effect on dissipated power and separation efficiency, if one is not limited by space, material and the number of cyclones in the multi cyclone.

36

5. Recommendations on multi-cyclone geometry: During the experiments it was noted that a lot of dust was settled on the bottom, walls and in the corners in the entrance and exit room of the multi-cyclone. This is due turbulence and flow rotations, caused by the rectangular design of the multi-cyclone entrance and exit room and the positioning of the single-cyclones in the multi-cyclone. One could however realise a reduction in dust settling by some small practical changes on the current multi-cyclone design. A reduction in dust settling mostly means also a decrease in turbulent flow and flow rotations in the multi cyclone entrance room. Those rotations and turbulence consume power from the flow. So decreasing dust deposit should come together with a reduction in dissipated power. Some possible practical improvements are given below: 1) Cyclones on one side of the multi-cyclone could be replaced by cyclones from a mirrored type. In this way the single-cyclone entrances are better positioned behind the multi-cyclone inlet, resulting in a more equal performance over all cyclones. The disadvantage however is the rise of production costs due to the requirement of two single-cyclone designs instead of one in the current case.

2) Also the supporting floor of the multi-cyclone entrance room can be adapted in a way that less dust settling is possible. The single-cyclones are now supported by the entrance room floor at the residue exit (bottom of single-cyclone). The space between this supporting floor and the single-cyclone inlet acts as a deposition area for dust. By lifting the supporting floor up to the bottom of the single-cyclone inlet, this deposition area decreases enormously. This is shown in figure 5.2:

Figure 5.1: An improvement in dust deposit by using mirrored cyclone geometries on one side of the multi-cyclone

Figure 5.2: An improvement in dust deposit in the cyclone entrance room by raising the supporting floor up

to the single-cyclone inlets.

37

3) The inlet and exit duct of the multi cyclone are also quite small, compared to the multi-cyclone entrance and exit rooms. Therefore, the flow needs to bend around a sharp edge to reach the cyclones in the corners, which results in its turn in turbulence behind the edge. This has quite an influence on the dissipated power. So by widening the multi-cyclone inlet and outlet gradually to approximately the sizes of the cyclone entrance and exit room decreases this effect. This design improvement is shown in figure 5.3:

Figure 5.3: An improvement in dust deposit by changing the width of the multi-cyclone inlet and outlet.

5) One could also increase the efficiency of the inlet flow (and decreasing dust deposit) by an extension of the inlet ducts of the single cyclones towards the inlet of the multi-cyclone. In this way one could realize in a quite simple way a leak free inlet flow by adapting the multi-cyclone entrance towards the lengthened single cyclone inlets. This improvement also equalizes the length the mean effective flow path for all cyclones: This may be explained as follows. The single-cyclones in the first row have the longest outlet tubes, but have therefore a short length to the multi-cyclone inlet. The single-cyclones in the last row have short outlet tubes (because of the stepwise supporting floor) but have long a long length towards the multi-cyclone inlet. Equalized mean effective path means also a more equal pressure drop over all single-cyclones, which result in a more equal performance over all cyclones.

Figure 5.4: An improvement in performance, pressure drop and dust deposit by extention of the single-cyclone inlet channels towards the entrance of the multi-cyclone.

The main advantages of this improvement are: the reduction in size of the entrance room (the room in which the inlets of the single cyclones are placed), the more equal performance over all cyclones, a better and more equal pressure drop over all cyclones, and less dust deposit in the multi-cyclone which result in a decreased need for cleaning. This idea is presented in figure 5.4:

38

6. Summary: 6.1 Conclusion: From the preface, one can find that the goals of this essay were to investigate the separation efficiency of the current multi-cyclone, to find an optimum in this the performance and to investigate the possibility of performance improvement by changing the design. Currently the multi cyclone is equipped with 10 cyclones at a flow rate of 140 normal cubic meters per hour per cyclone. From the model and the measurements this corresponds with separation efficiency of approximately 75 to 80 percent at a pressure drop of 3 to 4 millibar. The theoretical model and measurements show that separation efficiencies of 90 to 95 percent are reachable at realistic flow rates of 300 to 350 normal cubic meters per hour at a pressure drop of approximately 12 to 17 millibar. So an improvement in separation efficiency is possible. However from figures 4.1 and 4.2 it can be concluded that there exist no optimum for separation efficiency. The separation efficiency approaches the 100 percent for higher flow rates at a quadratic increase in pressure drop. The overall combustion unit is designed for a multi-cyclone pressure drop of approximately 7 millibar which belongs to a flow rate of 230 to 240 normal cubic meters per hour and per cyclone at a separation efficiency of approximately 85 to 90 percent. This means that the current number of single cyclones is too much. For the design-requirement 6 single cyclones are enough to digest the 1400 cubic normal meters per hour from the combustion unit. From accuracy investigation it can overall be seen that the exactness of the measured and predicted values are roughly within 20 to 25 percent for separation efficiency, within 10 to 12 percent for the flow rate measurements and 1 to 2 percent for the pressure drop prediction. In the second part it can be found that a proper change in single-cyclone geometry and design shall definitely result in a better performance at a smaller dissipated power. The overall trend for the designs is a decrease in dissipated power at increased performance (smaller characteristic particle size) for a decrease in single-cyclone dimensions. From the total essay the general conclusion can be drawn that the current design can be improved quit a lot by adaptation of the number of single cyclones, in combination with the practical improvements given in chapter 5. Further improvement and optimization is possible by adapting the single-cyclone geometry, but will require a complete re-design of the multi-cyclone.

39

6.2 Recommendations on future investigation: It is quite thinkable that the performance investigation on the current multi-cyclone is continued in the future. Therefore some critical notes and recommendations for future investigation are given below: 1) For an improvement of the theoretical prediction (model) one should gain more data on separation efficiency, flow rate and pressure drop. It is further advised to do simultaneously impactor measurements before and after the cyclone unit. In this way one gets insight in the actual particle size distributions. From these particle size distributions one can derive the exact fractional efficiency and finally better model for the ingoing particle size distribution. It is recommended to do this also for different kind of biomass fuels. 2) For future measurements it is also advised to use equal measurement devises before and after the cyclone in order to increase the accuracy of the measurements. This was not the case in the current investigation. Also automatic dust measurements with a computer will increase the accuracy of the separation efficiency measurements a lot. 2) Before a re-design is considered, some further investigation towards optimum single-cyclone geometry is recommended. One should also pay attention on the prevention of dust deposit, to guarantee long term performance. 3) There exist also a lot of other cyclone pressure drop reducing add-ons. These improvements are not included in this report. It might be useful to gain some information about these pressure drop reducing add-ons, before one starts a re-design.

40

7. References: [ 1 ] Bart van Esch, Erik van Kemenade. (2004). Procestechnische constructies I.

TU-Eindhoven (NL). (4A460) [ 2 ] VDI Verlag. (1996). Zyklonabscheider in der Energie- und Verfahrenstechnik. Düsseldorf (DE):VDI Verlag GmbH. (ISBN: 3-18-091290-1) [ 3 ] Prof. Dr.-Ing Wolfgang Fritz, Prof.Dipl.-Ing. Heinz Kern. (1990). Reinigung von

Abgasen. 2. Auflage. Würzburg (DE): Vogel Verlag und Druck KG. (ISBN: 3-8023-0244-3)

[ 4 ] Daniel Wagner, Thomas Nussbaumer. (1994). Messverfahren zur Erfassung des

Emissionsverhaltens von Holzfeuerungen. Zürich (CH): Ingenieursbüro Verenum [ 5 ] E. Weber, W. Brocke. (1973). Apparate und Verfahren der industriellen Gasreinigung

Band 1: Feststoffabscheidung. München (DE): R. Oldenbourg Verlag GmbH. [ 6 ] Jianyi Chen, Mingxian Shi. (2006). A universal model to calculate cyclone pressure

drop. www.sciencedirect.com. Elsevier. Powder technology 171(2007) p188-p191. [ 7 ] Excel file on Particle Size Distribution off coarse fly ash. (2005). Source: Joachim

Friesenbichler, Technical University Graz. The file contains the data from the PSD from figure 2-2-2 on page 16 of the BIO-Aerosols final rapport: ´Aerosols in fixed-bed biomass combustion – formation, growth, chemical composition, deposition, precipitation and separation from flue gas´.

[ 8 ] Comité Européen de Normalisation {CEN}. (2004). Solid biofuels – Methods for the

determination of moisture content – Oven dry method – Part 2: Total moisture – Simplified method. Brüssel (B): Management-center. Ref.Nr. CEN/TS 14774-2/2004D

[ 9 ] Verein Deutscher Ingenieure. (1993/1994). Manuelle Staubmessung in strömenden

Gasen . Gravimetrische Bestimmung der Staubbeladung. Filterkopfgeräte (4-12 m3/h). Düsseldorf (DE). VDI Handbuch Reinhaltung der Luft, Band 4

[ 10 ] R. Zhang , P. Basu. (2004). A simple model for prediction of solid collection efficiency

of a gas-solid separator. www.sciencedirect.com. Elsevier. Powder technology 147(2004) p86-p93.

[ 11 ] Cristóbal Cortés , Antonia Gil. (2007). Modelling the gas and particle flow inside

cyclone separators. www.sciencedirect.com. Elsevier. Progress in Energy and Combustion Science.

[ 12 ] Erik van Kemenade. Procestechnische constructies II. [ 13 ] Excel file on biomass flue gas characteristics. (2005). Source: Joachim Friesenbichler,

Technical University Graz. The file contains data on aerosol, fly ash and fuel characteristics. The data comes from pilot tests done at the Mawera test facility.

41

[ 14 ] Graz University of technology. (2003). BIO-Aerosols final rapport: ´Aerosols in fixed-bed biomass combustion – formation, growth, chemical composition, deposition, precipitation and separation from flue gas´.

[ 15 ] William C. Hinds. (1982). Aerosol Technology. 1. Edition. New-York (USA): Wiley-

Interscience.(ISBN: 0-471-08726-2) [ 16 ] K. Rietema. (1961). Performance and design of hydrocyclones II & III.

Koninklijke/Shell-Laboratorium, Amsterdam. Chemical Engineering science 1961 Vol.15 p303-p319.

[ 17 ] Jumo. Typeblatt 90.2424: Wärmezahler-Wiederstandsthermometer mit Anslusskopf,

PTB zugelassen. Source: Mawera. [ 18 ] Huba Control. 698 Pressure, vacuum and differential pressure module with or without

display 0 – 1/3/5/10/30/50 mbar. Source: www.hubacontrol.com [ 19 ] User Manual Prandtl tubes: AIRFLOW Mikromanometer-Prüfsätze und AIRFLOW-

Staurohre. Source: Mawera

42

Appendices:

43

44

Symbolic declaration:(appendices)

A Required oxygen content for stoichiometric combustion [ mol ] Ai Cyclone inlet surface [ m2 ] C(dp) Concentration distribution over particle size [ kgm-3 ] dp Particle diameter [ m ] d a.e. Aerodynamic particle diameter [ m ] Dc Outer diameter of the cyclone separation chamber [ m ] D0 Exhaust diameter of the cyclone separation chamber [ m ] E Average absolute error [ … ] 1)

Fs Total contact area between the gas and the wall [ m2 ] g Gravity constant [ ms-2 ] K Constant [ - ] L Length of the cyclone separation chamber [ m ] m Mass [ kg ] M… Molar mass [ kg mol-1 ] n Swirl coefficient [ - ] N Number of molecules [ mol ] p pressure [ Pa ] Q Volumetric flow [ m3s-1 ] R Radius [ m ] R Universal gas constant [ Jmol-1K-1 ] Ret Reynolds number for tangential flow [ - ] ReR Reynolds number for wall friction [ - ] RRm Specific gas constant [ Jkg K ] -1 -1

T Temperature [ K ] u Moisture content of the dry biomass fuel [ mass% ]

0,axv Average axial gas velocity [ ms-1 ] vt Tangential gas velocity [ ms-1 ]

0,tv Tangential velocity at the position r = Do / 2 [ ms-1 ] V Volume [ m3 ] Vm Molar Volume [ m3mol-1 ]

εw Fraction of the dust load at the wall [ - ] λw Wall friction coefficient [ - ] λs Additional friction coefficient [ - ] λ Friction coefficient [ - ] μ mean value [ … ] μD Total dust load [ kg kg-1 ] μG dynamic viscosity of the gas [ Pa s ] ρG Gas density [ kgm-3 ] ρp particle density [ kgm-3 ] σ Standard deviation [ … ] 1)

[..] Volumetric percentage [ Vol% ] 1) ...Dependent on the unit of the involved parameter

A.1 Cyclone dimensions:

45

46

A.2 Dust measurement rapport: Dust measurements on cyclone separation efficiency Measurement number Fuel Moisture content mass% d.b. / mass% w.b. Number of cyclones Time & Date Date dd:mm:yy

In front of cyclone Behind cyclone start end start end Time hh:mm :ss Environmental values: In front of cyclone Behind cyclone start end start end p environment mbar T environment o C Dust measurement : In front of cyclone Behind cyclone start end start end d probe inlet m Bush number - Bush weight g Q-meter score m3

Fixed average rate at: 0.5092 nm3/h p pump mbar T pump

o C C Oxygen , exhaust Vol.% p dyn. exhaust Pa p stat. exhaust Pa Q exhaust m3/h T exhaust

o C Q pump , norm , 13 %

O2

Nm3/h

Dust concentration Mg_

47

@ 13 Vol. % O2 Nm3

A.3 Calculation of the exhaust gas density:

reaction between biomass and air that occurs in biomass combustion can be depicted as:

The density of the exhaust gases for different kinds of biomass fuels can be calculated in a similar way as used in [4]. This calculation is based on the ideal gas law, assuming the involved gases are ideal. To make the calculation easier, some other assumptions are made. The general

( ) ( ) 2222

222

2179

21

10021

2179

100

2

2

NAOAOHMMumCOCO

NOAOHMMuOCH

OH

fuel

OH

fuelnm

⋅+⋅⎟⎠⎞

⎜⎝⎛ +−+⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛++⋅+⋅−

→⎟⎠⎞

⎜⎝⎛ +⋅+⋅+

λβλββ

λ

Herein air is assumed to be 20.4 Vol% O2 and 79.6 Vol% N2. A presents the oxygen

quirement in [mol] for stoichiometric combustion as: re

24

1 nmA −+= (A.1)

ed that b fuel co In a first approximation it can be assum iomass mpositions have all quite the same composition as ordinary wood: 44.1≈m and 66.0≈n so that 03.1≈A [mol]. It is possible to change this in a future stage. Further it is assumed that the combustion is perfect, so the factor β = 0 and soot and nitrogen oxide can be are neglected. Finally the fuel has a certain moisture content u ( mass% d.b.). Determination of this moisture content is explained in appendix A.4. Finally also the air humidity is neglected. The main thing to do is now to calculate the specific gas constant RR relation between the

ecific and universal gas constant can be derived from the ideal gas law:

m. Thesp

mRmT

VpRN ⋅=⋅

=⋅ → ( )Nm

In above expressions R and R

RRm = (A.2)

R

in [m ], N is the number of molecules in [mol], m is e mass in [kg] and p is the pressure in [Pa].

e also the same as the molar fractions. Fraction m/N in equation (A.2) can now be ritten as:

m are respectively the universal and specific gas constant in [Jmol K ] and [Jkg K ], V is a volume 3-1 -1 -1 -1

th So the fraction between the total exhaust gas mass m and the total molecules in the gas N gives the relation between the universal and specific case. Since it is generally known that the molar volume Vm ( given in [m3mol-1] ) is approximately constant for all gases, the volumetric fractions arw

⎟⎠⎞

⎜⎝⎛

Nm

[ ] [ ] [ ] [ ]100

2222

2222

22222222

2222 NOOHCO

NOOHCO

NNOOOHOHCOCO

MNMOMOHMCO

NNNNMNMNMNMN

⋅+⋅+⋅+⋅=

+++

+++=

(A.3)

48

Herein the brackets [..] stands for the real volumetric fraction in [Vol%] and M… for the molar

e measured for CO2 and ecific gas constant can be calculated according (A.4)

mass in [kgmol-1]. Now there are several possibilities. If the volumetric fractions can bH2O, the real sp

[ ] [ ] [ ] [ ] ( )2222

6.794.20100

100103145.8

2222

2

NOOHCO

m

MMOHCO

MOHMCOR

+⋅⎟⎠

⎞⎜⎝

⎛ −−+⋅+⋅

⋅= (A.4)

l. The actions can than be deduced from the assumed chemical reaction at the previous page:

In our case we prescribe the air excess ratio λ and the moisture content u of the fuefr

( )( )

( )( )222

2

2

2

4.206.791

1002

4.206.791

10021

3145.8

NOOHOH

FuelCO

OH

Fuel

m

MAMAMMMumM

AAMMum

R

⎟⎠⎞

⎜⎝⎛+−+⎟

⎟⎠

⎞⎜⎜⎝

⎛++

⎟⎠⎞

⎜⎝⎛+−+⎟

⎟⎠

⎞⎜⎜⎝

⎛++

⋅=

λλ

λλ (A.5)

ccording the ideal gas law the gas density can now be written as:

A

TRp

mG ⋅=ρ (A.6)

his calculation can now be implemented in the matlab model.

.4 Normalized conditions:

means that volumetric values are recalculated ith the universal gas law to normal conditions:

pn = 1013 millibar

ental equipment is sually dried. So measured volumes are then automatically considered dry.

tration varies when the air excess changes. Therefore reference is made to a certain air excess:

T A In order to compare the different measurements with each other, they have to be normalized to a specific condition. The normal condition: This w Tn = 273.14 Kelvin Biomass fuels have quite high moisture contents which can vary a lot between two fuels or even two batches of the same fuel. This means the volumetric fraction of water vapour in the flue gases varies which influences the actual concentrations of dust and other species. Therefore reference is made to the dry flue gas containing no water vapour. Since most measurement devices are sensitive to moisture, the flue gas used in experimu Biomass combustion happens always under conditions of air excess. This air excess varies over time and position and will be different for different fuel loads. When the air excess increases concentrations will decrease. This means that the dust concen

This excess is expressed as a fixed oxygen concentration in the flue gas. It is commonly to use a dry flue gas oxygen concentration of 13 % as a reference value for the excess air amount. With this, the total dry flue gas volume(rate) can be rescaled to 13 % oxygen, using the reaction equation from appendix A.2, expressing λ as oxygen available divided by oxygen required and assuming perfect combustion because of the air excess:

( )

( ) AA

AO

A

VV O

⎟⎠⎞

⎜⎝⎛

−+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

132121

211001

][2121

211001

2

%]13[

][ 2 (A.7)

In appendix A.2 it is stated that the stoichiometric oxygen requirement A is approximately 1.03. If this is filled into equation (A.7) one finds:

][21

1321

132110303.0

][2110303.0

2

2

%]13[

][ 2

OO

VV O

−−

≈⎟⎠⎞

⎜⎝⎛

−+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=⎟

⎟⎠

⎞⎜⎜⎝

⎛ (A.8)

This last expression is commonly used in most literature For example taking the dust concentration in mg nm-3:

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅==

%]13[

][

][,%13,%13,,

2

2VV

Vm

Vm

C O

onorm

dust

norm

dustnormdust

To complete the summarization of the normalized conditions: The Aerodynamic particle diameter according Hinds Aerosol technology [15]: Related to the particle diameter via:

( ) ( )eaTSppTS dVdV .,1000, == ρρ 2.

2 1000 eapp dd ⋅=⋅ρ

49

A.5 Moisture content: To calculate the flue gas density and to refer to dry flue gases in experiments, it is important to know the moisture content of the fuel. This moisture content is determined according to the CEN guideline CEN/TS 14774-2, [8]. This guideline gives the simplified method for determination of the moisture content, using a drying furnace and fuel samples. They refer to the moisture content of the wet basis. At Mawera these fuel samples are stored in visually clean and dried one litre canisters. First the empty dry and clean canister is weighted. The canister is then filled with at least 300 g of fuel, and is weighted directly. After weight determination, the sample is stored in a drying furnace at a temperature of 105 (+/- 2) degrees Celsius. The storing time depends on the kind of fuel and the amount of moisture. Normally a storing time of 24 hours should be satisfactory to gain constant dry weight. Since biofuels are very hygroscopic, they are weighted within 15 seconds after they are taken out of the drying furnace. The moisture content can now be calculated according equation (A.9):

%100⋅−−

=canisterwet

driedwet

mmmm

u (w.b.) (A.9)

50

A.6 Determination of the friction coefficient: For the calculation of the characteristic particle size and the characteristic dust load factor in chapter 2, a friction coefficient is needed. This friction coefficient depends on many factors, such as the dust load, wall friction and friction in the gas. In the book of ‘Apparate und Verfahren der industriellen gasreinigung’[5] a method is given to determine this friction coefficient. Herein the friction coefficient contains a contribution for the wall friction and a contribution for the friction caused by dust flows at the wall:

850, Re −⋅

⋅⋅⋅⋅⋅+= t

o

ax

p

gwDsw gD

vρρ

εμλλλ (A.7)

λw presents the wall friction coefficient, λs an additional friction coefficient, μD is the dust loading factor in [ kg kg-3 ], εw is the fraction of the dust load at the wall, ρG and ρp the gas and particle density in [ kgm-3 ],

0,axv the average axial velocity in [ ms-1 ] which can be calculated from the volumetric flow and the exhaust duct cross section. D0 is the exhaust diameter of the cyclone separation chamber in [ m ], g is the gravity constant in [ ms-2 ] and Ret is the tangential Reynolds number at the exhaust radius. As can be seen, the additional part is dependent on many parameters, such as flow conditions, densities, dust loading and separation efficiencies. According [3] and [5] equation (A.7) can be approximated with averaged values to:

( )Dw K μλλ ⋅+⋅≈ 1 (A.8) Herein the most used value for K is 3 and with very low dust loadings 2.

figure A.1: The wall friction as function of the Reynoldsnumbers and different relative wall roughness. Source: ‘Apparate und Verfahren in der industriellen Gasreinigung’

The wall friction coefficient is also dependent on a Reynolds number, and can be roughly determined using figure A.1. Herein the wall friction coefficient between a gas and a steel cyclone wall is given as function of a Reynolds number for different wall roughness. The Reynolds number for this figure is approximately given as:

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅

⋅⋅=

14Re 0,

2

o

cg

gtoR

DD

L

vD

μ

ρ

o

c

it D

DAQv ≈0, (A.9) (A.10)

51

52

10-1 100 101 102 1030

50

100

150

200

250

particle size in [ um ]

parti

cle

conc

entra

tion

in [

mg/

Nm

3 ]

Bark Spruce Waste wood Fibre Board

The tangential velocity can be approximated with the free vortex relation as is shown in equation (A.10). In above expressions μG presents the dynamic viscosity of the gas in [ Pa s ], L the length of the cyclone separation chamber in [ m ], Dc the outer diameter of the cyclonseparation chamber in [ m ], Q the volumetric flow in [ m

e 3s-1 ] and Ai the cyclone inlet surface

in [ m2 ]. If we now assume a very smooth cyclone wall and an average inlet flow of about 200 cubic meters per hour, the value of the mentioned Reynolds number ReR is about: . According figure A.1 this corresponds with a wall friction coefficient of about 0.005. For higher flows, the mentioned Reynolds number increases, but as can be seen from figure A.1, this has almost no influence on the wall friction coefficient.

R

3103 ⋅

A.7 Particle size distribution: To make an overview of the separation efficiency, the distribution of the dust concentration over the particle size is needed. Mostly these kinds of characteristics are given as the particle concentration in mass per normal volumetric unit over the aerodynamic particle diameter. These kinds of characteristics are often measured with an impactor. An impactor stores particles, isokenetically extracted from a gas flow, on different shells according particle size areas. The weight of these different shells, combined with the extracted volume, determines such a particle size distribution. According investigation towards biomass flue gases, [14], a bimodal particle density distribution holds for the flue gases This distribution contains a small peak below one micron (aerosols) and a peak around 30 micrometers (course fly ash). Since it is assumed particles below one micrometer pass the filters from the dust measurement device anyway, the first peak can be neglected. For the model, distributional data on coarse fly ash (> 1 µm) in biomass combustion gases is gained from the University of Graz [7]. This data contains the PSDs of four different fuels. The file contains distributional data from biomass combustion gases, right after the combustion chamber. The distributions from the data are shown in figure A.2:

Figure A.2: The particle size distribution of coarse fly ash for 4 different fuels. The interrupted lines give log-normal distributions as possible approximations. The distribution is corrected to 300 mg/nm3

53

50 100 150 200 250 300 350 4000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

number of steps in particle size range

abso

lute

ave

rage

err

or:

Erro

r / s

um(C

(dp)

) [ %

]

BarkSpruceWaste woodFibre Board

As can be seen from figure A.2, the distributions can be approximated with a distribution over the logarithm of the particle size, a log-normal distribution. Equation (A.11) expresses this distribution function:

( ) ( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −−⋅

⋅=

2

2log

exp2

1σ

μ

πσp

p

ddC (A.11)

The corresponding mean particle size and the standard deviations are given in table A.1: Tabel A.1: Values corresponding to the log-normal distribution as an approximation for the particle size distribution. 1) The standard deviation and the mean particle size in the log-normal distribution are the logarithms of the particle sizes in the table. Fuel Mean particle size 1)

Standard deviation 1)

Bark 22,4798 1,7942 spruce 44,9020 2,1288 waste wood 44,9020 1,7139 Fibre board 44,9020 2,0194 For use in a matlab model, this data is interpolated over its corresponding particle size, since this gives better results for the distribution than a log-normal distribution. In order to determine how many steps the interpolation requires, the average absolute error between the real and interpolated points is calculated. This average absolute error is given as:

%10012

⋅⋅=∑

i

E

UE i

i

D

(A.12)

Herein is Ei the difference between the value at a specific particle size and the corresponding value resulting from the interpolation at this particle size point, in [mg/nm3]. UD is the total dust load of the gas in [mg/nm3] and E is the average absolute error in percent. The result is shown in Figure A.3. From approximately 200 steps and more, the average absolute error does not decrease anymore, so 200 steps should satisfy for the interpolation of the PSD. For the model it is important that the total dust concentration, so the sum of the particle mass concentration over the particle size, equals the total dust concentration in front of the cyclone in the test facility. This total dust concentration is about 300 [mg/nm3]. After this correction it can be seen from the distributions in figure A.2, that with the exceptions of ´bark´ and ´waste wood´, the distributions are approximately the same. Therefore spruce is taken as the distribution which presents the wood chips, used at the experiments.

Figure A.3: Average absolute error, caused by the interpolation of the PSD-data. The error between the data and the interpolated function goes to a constant value for 200 steps or more

A.8 Determination of the total cyclone wall-gas contact surface area: For the calculation of the friction between the cyclone walls and the gas, in order to determine the pressure drop, the total contact area between gas and cyclone wall is needed. This area can be described by the geometry of the cyclone. In the case of a single cyclone, also the residue bunker is included, because the swirling core flow might also introduce a swirl in the bunker. In the case of a multi-cyclone, this effect is neglected because the several single cyclones have the same bunker, where multiple swirls damp each other. The different cyclone components which participate to the contact surface are:

- top cover ( )22

4 octop DDA −=π ( A.11 )

- exhaust cylinder lDA oexh π= ( A.12 ) - Outer cylinder (wall) cylccyl LDA π= ( A.13 )

- Conical part ( ) ( )42

22 cc

concccondD

LdDA−

+−=π ( A.14 )

- Dust bunker (eventually) In the above expressions Lcyl and Lcon are the lengths from the cylindrical and conical parts of the cyclone in [m]. dc is the residue exhaust diameter in [m]. The total gas – wall contact surface area can obviously be calculated from the summation: concylexhtops AAAAF +++= ( A.15 ) In combination with appendix A.1 this gives: mm861.234974≈sF 2

54

A.9 Swirl coefficient: As stated in the chapter about cyclone theory, the free vortex distribution of the tangential velocity annular region of cyclone the separation chamber is not a perfect free vortex, but a reduced free vortex. This reduce is introduced via an exponent, the swirl exponent n. This relation can be depicted as follows: constant instead of: =⋅ n

t rv =⋅ rvt constant For the general flow is a cyclone, n varies from one at the outer part of the flow in a cyclone, to minus one at the center flow of the cyclone (solid body rotation) [11]. For the general outer flow, n varies approximately between 0.4 and 0.8, and is very dependent on geometrical and physical properties. Therefore n is mostly derived empirically from experimental results. In [7] an empirical relation is given for this swirl exponent:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+−−=

− 5.0

12.0 1Re26.0exp1i

i

BHl

n go

iig

DvA

μπρ4

Re = ( A.16 )

Herein the swirl exponent is correlated to the Reynolds number and the cyclone inlet geometry. Another equation to approximate the swirl coefficient in the outer flow of the cyclone is given in [11], according ´Alexander RMCK´:

( )3.0

14.0

28367.011 ⎟

⎠⎞

⎜⎝⎛⋅−−=

TDn c (A.17)

In this last expression, T presents the gas temperature in [K].

55