Lumped Parameter and Three-Dimensional CFD Simulation of a Variable Displacement Vane Pump for Engine Lubrication
- 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