urea melt pump design paper (1)

8/2/2019 Urea Melt Pump Design Paper (1)

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Urea Melt Pump DesignFluid Mechanics of Turbomachinery

Dr. Ogut

Usman Asad

Ben Davidson

Jared Dodge

Hendra Novi

Figure 1: Actual Urea Melt Pump



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



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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:



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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



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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



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= ( 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



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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



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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:



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= 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:



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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



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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



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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:



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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.



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A simplified empirical formula based on experimental measurements for H L is presented by Stepanoff

as:

∆=

ℎ − −(2

2 − 11)

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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.



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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



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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.



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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



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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



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



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APPENDIX B: Pipe Loss Calculations



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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



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APPENDIX D: References

Anderson, H.H. Centrifugal Pumps and Allied Machinery . 4th. Oxford, UK: Elsevier, 1994. Print.



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.

urea melt pump design paper (1)

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