1) Researchers developed lumped parameter and 3D CFD models of a variable displacement vane pump for engine lubrication. 2) Experimental testing was used to validate the models and tune parameters like discharge coefficients. 3) The lumped parameter model was improved by using FEM analysis to determine the equivalent stiffness of the cover for more accurate external leakage calculations.

1. Massimo Rundo and Giorgio Altare
ASME 2017 Fluids Engineering Division Summer Meeting
Waikoloa, Hawai‘i, August 2, 2017
LUMPED PARAMETER AND THREE-DIMENSIONAL
CFD SIMULATION OF A VARIABLE DISPLACEMENT
VANE PUMP FOR ENGINE LUBRICATION

2. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Summary
• Component description
• Experimental facility
• Lumped parameter model (LMS Amesim®)
• FEM model of the cover (ANSYS®)
• CFD model (Simerics PumpLinx®)
• Analysis of the results
2 / 17

3. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Lubricating vane pump
Hydraulic scheme
of the displacement control
(absolute pressure limiter)
3 / 17
B
A
valve
B
A
valve
p < p* max displacement
p = p* variable displacement
p
p*

4. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Layout of the test rig
Config. 1: steady-state tests
Config. 2: measurement of pressure ripple
Interface plate
4 / 17
Oil SAE 5W30
throttle
valve
flowmeter
electric
motor

5. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
0D model – Governing equations
dp dV
Q
dt V d



 
  
 

volume
flow rate angular
volume
derivative
oil bulk modulus
• pressure in each control volume:
• flow rates through port plate (turbulent):
shaft speed
2
d
p
Q C A



• leakage flows (laminar):
density
pressure
drop
flow area
discharge
coefficient
3
12
bh
Q p
L
 
viscosity length
width
clearance
5 / 17
To oil sump

6. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Chamber volume
chamber volume
rotor
stator
Eccentricity (e)
Volume and its derivative vs. shaft angle and eccentricity
Volume derivative: analytic evaluation
as function of vector ray lengths ρ and phases ψ
Chamber volume: numerical calculation of
the area ABCDEF enclosed by the chamber
contour and interpolation of look-up table
at max eccentricity
6 / 17

7. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Chamber flow area
Port plate contour Chamber contour
Minimum
volume
Max
volume
Numerical evaluation of the flow area
• Input: polylines – X,Y tables
• Numerical procedure for common area
• Interpolation of look-up tables
at max eccentricity
7 / 17
1) Discretization of common area
2) Count of “pixels” in common

8. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Critical issues
Stator
Rotor
Cover
Inlet
volume
Chamber
2
d
p
Q C A


• Evaluation of Cd for flow area inlet – chamber
(critical in defective filling conditions – high speed)
• Evaluation of real clearance due to cover deformation
(critical at high temperature)
External leakage Delivery
volume
3
12
b h
Q p
L
 
8 / 17

9. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
FEM model of the cover
Boundary condition: delivery pressure detail
Cover: 8x105 nodes
Entire model: 1.2x106 nodes
Shell-type cells
Grid sensitivity
analysis (cover)
9 / 17

10. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Correction of the axial clearance
casing
cover
rotorchamber
delivery volume (p)
nominal
clearance
additional
clearance
shaft housing
Total clearance = nominal + k * p
k = equivalent stiffness (m/Pa) Evaluated from the displacement of the monitoring points
Monitoring points
10 / 17
R
R

11. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
CFD model (PumpLinx)
• Imported CAD surfaces in STL format
• Fixed volumes: unstructured body-fitted Cartesian grid
• Variable chamber and leakages: structured hexahedral grid
• About 800 000 cells for mesh independent results
Use: Tuning of mean values of
discharge coefficients
11 / 17
Ducts in the
interface
plate
(config. 2)

12. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Lumped parameter model
1
1. Variable chambers
22
2. Variable flow areas
3 3
3. Leakages
4
4. Stator dynamics
5
5. Volume evaluation
6
6. Areas evaluation
7
7. Parameters
IN
OUT
VALVE
R
8
8. Cover deformation
9
9. Delivery line
12 / 17
B

13. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Steady-state flow-pressure curves
Intervention displacement control Oil temperature: 120 °C
Progressive reduction
of flow area of the load valve
Theoretical flow rate
 
3
12
leak
b h k p
Q p
L
 

Non-linear flow-pressure characteristic
due to the variable clearance
(deformation of the cover)
13 / 17
0D model with coefficients tuned on FEM and CFD

14. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Steady-state flow-speed curves
• Oil temperature: 40 °C
• Delivery pressure: 2 bar
• 3 displacements
(stator mechanically blocked)
100% - 76% - 53%
CFD tuning (on experimental):
total air volume fraction 6%
Incomplete chambers filling 0D tuning (on CFD):
discharge coefficients inlet side
(same flow rate at max speed)
14 / 17
A tuning only at max speed is enough

15. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Steady-state pressure-speed curve
Simulation of a real operating condition
Intervention
displacement
control
0D model tuning on CFD:
discharge coefficients
of the restrictors
T = 100 °C
Delivery volume
To tank
Fixed orifice
(simulates lubricating
circuit resistance)
15 / 17

16. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Pressure ripple
• Load: fixed orifice
• Temperature: 40 °C
9 vanes  angular pitch = 360°/9 = 40°
Partial displacement
Maximum displacement
Delivery line:
three-element distributed
parameter pipe
(resistive, capacitive
and inertia effects)
16 / 17

17. Politecnico di Torino
Dipartimento Energia
Fluid Power Research Laboratory
http://www.fprl.polito.it
Conclusions
Validated 0D and 3D models of a vane pump have been presented
• Integrated approach: a few focused simulations with high-time consuming
codes for tuning the 0D model (determination of critical coefficients)
• FEM model used for determining an equivalent stiffness of the cover
(improvement of the external leakages)
• CFD model used for tuning discharge coefficients
(only the operating condition at maximum speed can be simulated)
• Advantage of 0D tuned model: integration in a more complex model for
system-level studies
17 / 17

18. Fluid Power Research Laboratory
www.fprl.polito.it
Politecnico di Torino