Positive Displacement Pump Element
Positive Displacement Pump General Description & Quick Guide
The Positive Displacement pump element routine simulates only for Incompressible Liquids. In Principle the Positive displacement pump behaves like a Fixed Flow element where the flow gets calculated from volumetric displacement provided by manufacturer for the specific pump. The PD pump model is based on a nondimensional loss coefficient model developed by Wilson. (Ref: Wilson, W. “Performance criteria for positive displacement pumps and fluid motors”, ASME Semiannual Meeting, paper No. 48SA14, 1948.
Positive Displacement Pump Element Inputs
Table of the inputs for the Positive Displacement Element.
Element Specific Positive Displacement Pump Element Input Variables  

Index  Field  Description 
1  Pump Type (SUBTYPE) 
Positive displacement pump subtypes. (No Meaning) Default =1 
2  Speed (SPEED)  Pump shaft rotation speed in revolutions per minute 
3  Volumetric Displacement (VOL_DISP)  Maximum Volumetric Displacement per cycle 
4  Pump Leakage Coefficient (LEAK_COEFF)  The leakage coefficient characterizes the leakage flow which occurs within the pump. (Unitless) 
5  Coulomb Friction Coefficient (COULOMB_COEFF)  Coulomb Friction Coefficient is the friction between the moving part (gear, vane, or piston) on the stationary part (casing or cylinder). (Unitless) 
6  Viscous Friction Coefficient (VISCOUS_COEFF)  Viscous Friction Coefficient is the friction between the moving fluid and the casing or cylinder wall (Unitless) 
7  Flow Efficiency Option (LEAK_OPT) 
There are two ways to specify flow efficiency: 1: Fixed Leakage Coefficient 2: Leakage Coefficient vs. Speed 3: Leakage Coefficient vs. Delta.P vs. Speed 11: Fixed Volumetric Efficiency 12: Volumetric Efficiency vs. Speed 13: Volumetric Efficiency vs. Delta.P vs. Speed 
8  Volumetric Efficiency  Fixed Volumetric Efficiency 
10  Exit Area (EXIT_AREA)  Area at the pump’s exit. This input helps to account for dynamic pressure exiting the pump. 
11  Portion of Ustrm Chamb. Dyn. Head Lost (DQ_IN)  Inlet dynamic head loss. Refer General solver theory sections for more details about this input 
12  Element Inlet Orientation: Tangential Angle (THETA) 
Angle between the element centerline at the entrance of the element and the reference direction. If the element is rotating or directly connected to one or more rotating elements, the reference direction is defined as parallel to the engine centerline and the angle is the projected angle in the tangential direction. Otherwise, the reference direction is arbitrary but assumed to be the same as the reference direction for all other elements attached to the upstream chamber.
THETA for an element downstream of a plenum chamber has no impact on the solution except to set the default value of THETA_EX. (See also THETA_EX) 
13  Element Inlet Orientation: Radial Angle (PHI) 
Angle between the element centerline at the entrance of the element and the THETA direction. (spherical coordinate system)
PHI for an element downstream of a plenum chamber has no impact on the solution except to set the default value of PHI_EX. (See also PHI_EX) 
14  Element Exit Orientation: Tangential Angle (THETA_EX) 
Angle between the orifice exit centerline and the reference direction. THETA_EX is an optional variable to be used if the orientation of the element exit differs from that of the element inlet.
The default value (THETA_EX = 999) will result in the assumption that THETA_EX = THETA.
Other values will be interpreted in the manner presented in the description of THETA. 
15  Element Exit Orientation: Radial Angle (PHI_EX) 
Angle between the orifice exit centerline and the THETA_EX direction.
PHI_EX is an optional variable to be used if the orientation of the element exit differs from that of the element inlet.
The default (PHI_EX = 999) will result in the assumption that PHI_EX = PHI.
Other values will be interpreted in the manner presented in the description of PHI. 
16  Fluid Compressibility Mode (FLUID_MODE) 
The user can choose which solution algorithm to use. By Default, 2: Incompressible Liquid 
17  Mechanical Efficiency Option (MECH_EFF_OPT) 
Ways to specify Mechanical efficiency: 0: Friction Coefficients 11: Fixed Mechanical Efficiency 12: Mechanical Efficiency vs. Speed 13: Mechanical Efficiency vs. Delta.P vs. Speed 
18  Mechanical Efficiency (MECH_EFF)  Fixed Mechanical Efficiency 
19  TBL1_RPM/ TBL2_RPM/ TBL3_SPEED/ TBL4_SPEED 
Independent variable curve for shaft speed Should be in ascending order 
20  TBL1_LEAK_COEFF/ TBL2_LEAK_COEFF 
Dependent variable curve for leakage coefficient Unitless 
21  TBL2_DELTAP/ TBL4_DELTAP  Independent variable curve Delta Pressure Rise across Pump 
22  TBL3_VOL_EFF /TBL4_VOL_EFF  Dependent variable curve Volumetric Efficiency Table 
Positive Displacement Theory Manual
Mass Flow rate Calculation
The Flow rate for a give pump is given by
If Leakage Coefficient is provided
If Volumetric Efficiency is provided
Addition to this the efficiencies & torque across the pump is also calculated.
Additional Momentum Loss
For Additional Momentum loss, Portion of Upstream Dynamic Head loss, refer Solver General theory section.
Positive Displacement Element Outputs
The following listing provides details about conventional orifice output variables.
Name  Description  Units 

DQ_IN 
Portion of Ustrm Chamb. Dyn. Head Lost (Usually an echo of the user input unless modified inside Flow Simulator.) 
Flag 
Axial (K_EXIT_Z) Tangential (K_EXIT_U) Radial (K_EXIT_R) 
Exit K Loss (Usually an echo of the user input unless modified inside Flow Simulator.)

Unitless 
ELEMENT_THETA 
Tangential Angle (Usually an echo of the user input but converted to radians.) 
radians 
ELEMENT_PHI 
Radial Angle (Usually an echo of the user input but converted to radians.) 
radians 
REL_INLET_ANGLE  It is a relative inlet angle calculated based on upstream chamber velocity  Deg 
IDEAL_FLOW  (Total flow – Leakage flow)  Lbm/s, Kg/s 
SPPED 
Pump Speed (Usually an echo of the user input unless modified inside Flow Simulator.) 
RPM 
LEAKAGE_FLOW  Leakage Flow  Lbm/s, Kg/s^{} 
EXIT_AREA 
Exit area used for calculating exit conditions of the orifice element. This output is only printed when an exit area is used (EXIT_AREA>0). A default value of 0 has no effect on exit conditions. (Output is an echo of the user input.) 
inch^{2}, m^{2} 
VOL_EFFIC  Volumetric Efficiency  (Unitless) 
LEAKAGE_COEFF  Leakage Coefficient  (Unitless) 
MECH_EFFIC  Mechanical Efficiency  (Unitless) 
COULOMB_COEFF  Coulomb Friction Coefficient.  (Unitless) 
VISCOUS_COEFF  Viscous Friction Coefficient  (Unitless) 
HYDRAULIC_POWER  Hydraulic Power  HP 
SHAFT_HPOWER  Shaft Power  HP 
OVERALL_EFFIC  Overall Efficiency  (Unitless) 
TORQUE  Torque  Ftlbm, Nm 
PTS  Driving pressure relative to the rotational reference frame (i.e. rotor) at the restriction inlet.  psi, mPa 
PTEX  Total pressure relative to the rotational reference frame (i.e. rotor) at the restriction exit including supersonic effects.  psi, mPa 
PSEX 
Static pressure relative to the rotational reference frame (i.e. rotor) at the restriction exit. Limited by critical pressure ratio for supersonic flows. 
psi, mPa 
PSEB  Effective sink (static) pressure downstream of the restriction.  psi, mPa 
TTS  Total temperature of fluid relative to the rotational reference frame (i.e. rotor) at the restriction inlet.  deg F, K 