urea melt pump design paper (1)
Post on 06-Apr-2018
218 Views
Preview:
TRANSCRIPT
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 1/24
Urea Melt Pump DesignFluid Mechanics of Turbomachinery
Dr. Ogut
Usman Asad
Ben Davidson
Jared Dodge
Hendra Novi
Figure 1: Actual Urea Melt Pump
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 2/24
2
ContentsABSTRACT ............................................................................................................................................... 3
INTRODUCTION ...................................................................................................................................... 3
DESIGN.................................................................................................................................................... 4
VELOCITY TRIANGLES ..................................................................................................................... 4
BASIC EQUATIONS FOR CENTRIFUGAL PUMP DESIGN ................................................................ 5
CAVITATION ...................................................................................................................................... 6
SYSTEM HEAD LOSSES ..................................................................................................................... 6
DESIGN ANALYSIS ................................................................................................................................... 8
INITIAL VALUES FOR DESIGN PARAMETERS ....................................................................................... 8
ESTIMATING PUMP LOSSES.............................................................................................................. 13
CONCLUSIONS ...................................................................................................................................... 19
APPENDICIES......................................................................................................................................... 20APPENDIX A: Performance Calculations........................................................................................... 20
APPENDIX B: Pipe Loss Calculations................................................................................................. 21
APPENDIX C: Equations and Iterations............................................................................................. 22
APPENDIX D: References .................................................................................................................. 23
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 3/24
3
ABSTRACT
The objective of this project was to design a urea melt pump that adequately met the
specifications of the piping system. The specific system in this case provided 125m of head, but designing
the pump with 10% factor of safety the system provided 137.5m of head. At a flow rate of 59.1 m3 /hr,
the pump provides 138.5m of head, uses 53kW at a 56% total efficiency. The final design was found
using an iterative design process altering β1, β2, r 1, r 2, b1, b2, nB,
INTRODUCTION
ω, and Q. By varying these parameters
and observing the results a pump design was found to meet the system specifications. The pump we
designed met these specifications thus the project yielded successful results.
The centrifugal pumps are by far the most commonly used type of pumps. Of all of the installed
pumps in a typical petroleum/petrochemical plant, about 80–90% are centrifugal pumps. Centrifugal
pumps are widely used because of their simplicity, high efficiency, wide range of capacity, head, smooth
flow rate, and ease of operation and maintenance. Basic components for centrifugal pump are the:
impeller, shaft, casing, and bearings. The others components are shown in Figure 2.
Figure 2: Centrifugal Pump Sectional Drawing The impeller is the main element in a centrifugal pump. Entire construction of a pump depends upon theimpeller. The fundamental equation of impeller, determines the head developed by the impeller with
respect to the increase in the momentum of the fluid flowing through the impeller i.e., to get a relation
between dynamic and kinematic parameters of impeller. The system is designed as seen in Figure 3:
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 4/24
4
Figure 3: Piping Layout
Pump performance can be found by ̇ = . This equation relates the power required to operate
the pump and the head provided by the pump. This is an ideal equation that can be corrected for real
life scenarios with slip factors and efficiencies.
DESIGN
VELOCITY TRIANGLESBase on impeller dimensions, fluids velocity across the impeller surface can be predicted, Figure 4 below
shows that relationship.
Figure 4: Velocity Triangles
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 5/24
5
The following symbols are used in drawing velocity triangles
U = Vane or blade tip velocity2160
C = (V) Absolute velocity of flow of fluid. (Velocity of the fluid with reference to the earth or any
non-moving object)
W = Relative velocity of the fluid in the blade passage. (The velocity of the fluid with reference tothe blade or impeller)
α = Absolute angle: the angle between the absolute velocity ‘C ’ or V and blade velocity ‘u’
β = Vane angle or blade angle—the angle between the relative velocity ‘w ’ and vane or blade
velocity ‘u’.
Cu = (Vu) Tangential velocity of V
Vm = (Cm) Radial velocity of V
Wu = Tangential velocity of W
Q = Flow Rate
b1 = Impeller suction side blade width
b2 = Impeller discharge side blade width
r1 = Impeller eye/suction side radius
r2
BASIC EQUATIONS FOR CENTRIFUGAL PUMP DESIGN
= Impeller discharge side radius
The Bernoulli equation shows the relationship between pressure, velocity and height that will always be
constant.
+2
2 + =
Based on the Bernoulli equation the total head can be determined.
=1
2 [(22 −12) + (22 − 12)− (2
2 −12)]
HE is theoretical head (Euler Head), is base on pump dimensions.
=1 (22 − 11)
Slip factor is a correction factor to correct the assumption that the pump has infinite blades and include
the number of blades in the impeller.
µ = 1− 2 = 2′ 2
H i,s with slip, is the head that contains slip factor.
, = ( )()
Flow through the pump, inlet and outlet will always constant
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 6/24
6
= ( 11) = ( 22)
= (21)(1)(1) = (22)(2)(2)
Power required to pump the liquid will depend on flow rate and head
̇ = = = ̇ (22 − 11)
Specific speed is a number that characterizes the type of impeller in a unique and coherent manner.
Specific speed are determined independent of pump size and can be useful comparing different pump
designs. The specific speed identifies the geometrically similarity of pumps.
=0.5
0.75
CAVITATION
A low pressure condition at the suction side of a pump can cause the fluid to start boiling calledcavitation. Cavitation is a danger to the entire pump. Failure of pump components such as: rubbing in
wearing ring, shaft brake can occur if there is a cavitation. To avoid cavitation, number of net positive
suction head
NPSHA > NPSHR
NPSHR
The NPSHR is the required net positive suction head by the pump in order to prevent cavitation for safe.
The NPSHR for a particular pump generally determined experimentally by the pump manufacturer and is
part of the documentation of the pump.
NPSH A
The net positive suction head made available the suction system for the pump is often named NPSHA.
The NPSHA
SYSTEM HEAD LOSSES
can be determined during design and construction, or determined experimentally from the
actual physical system using the following equation.
= − − ℎ−
The head loss of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct
whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all
the components in the system. This can be expressed as
h loss = Σ hmajor_losses + Σ hminor_losses
where
h loss = total head loss in the pipe or duct system
hmajor_losses = major loss due to friction in the pipe or duct system
hminor_losses = minor loss due to the components in the system
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 7/24
7
System Head losses from Piping, elbow and Valve
ℎ = ℎ =
14
2
= = 142
= 2
2
= 2
2
Friction Coefficient - f
The friction coefficient depends on the flow - if it is laminar, transient or turbulent and the roughness of
the tube or duct. To determine the friction coefficient we first have to determine if the flow is laminar,
transient or turbulent - then use the proper formula or diagram, see Figure 5 for details.
The flow is
• laminar when Re < 2300
• transient when 2300 < Re < 4000
• turbulent when Re > 4000
=
Where
Re = Renould Number
V = Fluid Velocity
ρ = Fluid Density
µ = Dynamic or absolute viscosity
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 8/24
8
Figure 5: Moody Diagram DESIGN ANALYSIS
Our design approach is:
1. Select starting values for pump speed and all impeller geometry aspects.
2. Refine initial parameters so that the pump gives close to desired performance, in terms of flow and
head, at design point.
3. Use numerous techniques and assumptions to find approximate equations and values for all losses
and loss coefficients.
4. Combine loss factors and design parameters in Excel and use an iterative process to optimize design
parameters according to our system requirements.
INITIAL VALUES FOR DESIGN PARAMETERSConventionally, pump design is done on the experience basis. Manufacturers have extensive records of
existing performance data on families of pumps. Similarity analysis and non-dimensional groups areoften used to design new pumps based on existing pumps with known hydraulic and mechanical
performance. Such data for existing pumps has been compiled and plotted by numerous authors using
non-dimensional parameters. These parameters is used to give starting values of
The most important of these parameters is the Specific Speed (Ns) defined as:
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 9/24
9
= 0.50.75
Specific speed can be used to determine our pump type and efficiency as shown in figure below.
Figure 6: Pump efficiency and type against Specific Speed Ns
To meet our head and capacity requirement, first we need to select our pump speed. The pump speed
will depend on the type of driver we select. Our requirement is for a small size pump for constant
operation at non-fluctuating loads. Therefore a motor-driven pump meets our requirement and there is
no requirement for the added complexity and cost of a turbine driver. The rotational speed of motors
depend on the frequency of the electrical supply and number of poles as per below equation:
=120
where Nsynchronous is the synchronous speed of the motor in rpm
F is frequency of AC supply in Hz
P is number of motor poles.
Using a supply frequency of 50 Hz (Standard for Europe and Asia), our options for rotational speed are:
1500 Hz for 4 pole motor and 3000 Hz for 2 pole motor.
It is clear from Figure 6, that higher speed favors more efficient operation. So the driving speed including
motor slip is selected as 2900rpm, which is common for industrial motors.
Now, our system requirements are:
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 10/24
10
Flow
59.1
m3/hr
260.2
GPM
Head 137 m 449.5 ft
Speed
2900
rpm
303.7
rad/sTable 1: System Requirements
The specific speed (Ns) of our pump now comes out be roughly 500. Figure 6 shows our impeller will be
purely radial having efficiency in the range of 50-55%. Next, we select the blade number and discharge
blade angle. Our desired performance curve gives ~ 8% rise from BEP to shut-off head. Using Figure 7,
we select an initial value of 7 vanes with β2
Figure 7: Number of blades and discharge blade angle against Ns
Next, we determine the Head Constant K
of 27°.
u defined as :
=2
(2)0.5
Ku can be determined using Figure 8, which comes out to be around 0.95
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 11/24
11
Figure 8: Head constant against specific speed Ns
The Head constant is used to estimate, impeller tip diameter D2 by the following relation:
2 =(1860)0.5
Where H is required head in ft and N is speed in rpm.
This gives an initial value for D2 of 12.8 in or 325mm
Next, we determine the capacity coefficient Km2 defined as:
2 =
2
(2)
0.5
Km2
Figure 9: Capacity Constant vs. Specific Speed
comes out to be 0.06 using Figure 9
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 12/24
12
and Vm2 is evaluated using the relation:
2 = (2)(2)0.5
from here b2 can be evaluated as:
2 =0.321
�2(2 − )
Where Z is the number of blades and Su is the vane thickness (assumed to be 0.127mm)
This gives b2 ~ 6mm. Clearly, this value of b2 is perhaps too small. So a value of 10mm is chosen
Next, the eye diameter D s1
Figure 10: Diameter ratio against Specific Speed
Using D
is evaluated using Figure 10.
s1/D2 = 0.35, we get D s1 = 114 mm
A similar approach is used to find b1. Using Km1 which comes out to be ~ 0.08 at Ns = 500
and
1 = (1)(2)0.5
1 =11
which is evaluated to be ~12mm.
A summary of the starting values of impeller parameters are as follows:
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 13/24
13
Rotational Speed (ω) 2900 rpmImpeller tip radius (r2 324 mm)
Discharge blade angle (β2 27°)
Number of blades (Z) 7
Impeller inlet hub radius (rs1 113 mm)
Impeller inlet shroud radius (rh1 100 mm)
Discharge width (b2 13 mm)Table 2: Starting Values
Using these values, an excel sheet is developed which evaluates all pump velocities, Euler head, slip,
ideal head including slip, power consumed and plots these values against flow rate.
ESTIMATING PUMP LOSSESAs previously described, losses in centrifugal pumps may be classified as:
1. Leakage loss
2. Disk Friction
3. Mechanical loss
4. Hydraulic loss
Estimating these losses analytically is not practical considering the complexity of flows in pumps. In
order to estimate these losses, a mathematical model of the pump was created in Engineering EquationSolver (EES) initially using the previously determined impeller dimensions. Equations for all losses were
entered into the model and values for loss coefficients were estimated using numerous assumptions and
simplifications as detailed below for each category of losses. The complete set of equations for the
pump model is given in Appendix C.
a. Leakage Loss
Leakage losses in the wearing ring are given by:
=
∗ (2
)0.5
= + 1.50.5
A is the clearance area
HL is the head drop across the clearance.
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 14/24
14
A simplified empirical formula based on experimental measurements for H L is presented by Stepanoff
as:
∆=
ℎ − −(2
2 − 11)
8
Assuming a leakage loss of 4% of design flow at bep, and clearance area
A = 2πRh1 δ, where δ=0.5mm or 0.0005m, values for ΔH L and C were found as:
ΔHL
b. Disk Friction
=98m and C=0.1
Disk friction is normally considered a power loss, as it has a retarding effect on motor torque. It is
normally given as:
(ℎ) = 3
5
Where D is impeller diameter in feet, N is speed in rpm and K is an experimentally derived factor.
An alternative equation for power loss due to Disk friction is presented by Pfliederer as:
(ℎ) = 32
Where K is plotted against Reynolds number and ρ is the density of the fluid. A simpler chart is
presented by H. H. Anderson which relates impeller diameter and disc friction.
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 15/24
15
Figure 11: Disk friction against Impeller Diameter for various speeds
Using this chart, power loss due to disk friction for our pump using 300mm diameter and 3000 rpm
comes out to be around 5 KW. This is a constant power loss of the pump.
c. Mechanical Efficiency
Mechanical efficiency for our model is simply assumed to be 94%.
d. Hydraulic Losses
Hydraulic losses can be separated into three types:
i. Incidence / Shock losses
ii. Diffusion Losses
iii. Friction
The general equation for friction loss is:
ℎ = ℎ2
2
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 16/24
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 17/24
17
Figure 13: Hydraulic losses and Actual Head vs Flow
The final performance curves from the Engineering Equation Solver (EES) model are shown below:
Figure 14: Flow vs. Efficiency, Head, and Power
Once initial starting values and loss coefficients were chosen, each dimension was individually isolated
and plotted across a range of values to evaluate the ranges that give the highest head and efficiency.
These plots were iterated until physically reasonable values were reached.
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 18/24
18
The above plot is from the last iteration, and shows the head and efficiency versus the outlet blade angle.
Figure 16: Outlet Blade Angle vs. Efficiency and Head
As seen, the inlet blade angle greatly affects head as long as we do not assume Vu1
Name
to be zero.
Symbol Value Units
Alternative
Units
Impeller Inlet radius r 0.0401 m
0
50
100
150
200
250
300
0 20 40 60 80 100
Head (m)
Efficiency (%)
β1 (degrees)
Head
Efficiency
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100
Head (m)Efficiency (%)
β2 (degrees)
Head
Efficiency
Figure 15: Outlet Blade Angle vs. Efficiency and Head
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 19/24
19
Impeller Outlet radius r 0.1252 m
Vane Inlet Width b 0.0101 m
Vane Oulet Width b 0.0102 m
Inlet Angle β 5.0001 ⁰ 0.087 rad
Outlet Angle β 30.0002 ⁰ 0.524 rad
Number of Blades n 8.000B
Angular Velocity ω 303.687 rad/s 2900.000 rpm
Volumetric Flow Rate Q 0.016 m3
59.100/s m3/h
Density ρ 1220.000 kg/m3
Figure 17: Final Pump Dimensions
Figure 18 shows the system performance curves for our designed pump.
Figure 18: Pump Performance Curves
CONCLUSIONSThe pump was designed for a system requiring urea melt to be pumped 100 m vertically. Head losses in
the pipes were estimated at 125 m and it was designed to provide a 10% buffer over what would be
needed, bringing the total pump head to 137.5 m. The final pump design provides 138.5 m of head at a
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120
Head (m)
Efficiency (%)
Power Required
(KW)
Volumetric Flow Rate (cubic meters per hour)
Pump Performance
Design Flow
System Head Required
Pump Head
Pump Efficiency
Power Required
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 20/24
20
design flow rate of 59.1 m3
/h. The pump requires 53 KW to run at its design flow rate and runs at a total
efficiency of 56%.
APPENDICIES APPENDIX A: Performance Calculations
See attached
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 21/24
21
APPENDIX B: Pipe Loss Calculations
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 22/24
22
Where is
Pa = Disharge Pressure (N/m2)
Pe = Suction Pressure (N/m2)
Ca=Vd = Fluid Discharge Velovity (m/s)
Ce=Vs = Fluid Suction Velocity (m/s)
Hvd = Total Loss form discharge side (m)
Hvs = Total Loss form suction side (m)
Za = Elevation of Discharge end
Ze = Elevation of Suction End
APPENDIX C: Equations and Iterations
See attached
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 23/24
23
APPENDIX D: References
Anderson, H.H. Centrifugal Pumps and Allied Machinery . 4th. Oxford, UK: Elsevier, 1994. Print.
8/2/2019 Urea Melt Pump Design Paper (1)
http://slidepdf.com/reader/full/urea-melt-pump-design-paper-1 24/24
24
Dixon, S.L., and C.A. Hall. Fluid Mechanics and Thermodynamics of Turbomachinery . 6th. Burlington
MA: Elsevier, 2010. Print.
Girhar, Paresh. Practical centrifugal pumps: design, operation and maintenance. 1. Burlington MA:
Elsevier, 2004. Print.
Kurokawa, J. "Simple formulae for hydraulic efficiency and mechanical efficiency of hydraulic
machinery." 3rd China-Japan Joint Conference. Kurokawa: Osaka, 1990. Print.
Lobanoff, Val, and Robert Ross.Centrifugal Pumps: Design and Application. 2nd. Gulf Professional,
1992.
"Moody Diagram." Graphic.Engineering Toolbox . First Last. 2011. Web. 10 Nov 2011.
<http://www.engineeringtoolbox.com/moody-diagram-d_618.html>.
Srinivasan, V.M. Rotodynamic Pumps. 1. New Deli,India: Newage International, 2008. Print.
Stepanoff, A.J. Centrifugal and Axial Flow Pumps. 2nd. 1993. Print.
top related