dongfang bai - massachusetts institute of...
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A parallel solver for skirtliner lubrication
Dongfang Bai
Overview of skirtliner lubrication
• Characteristic of skirtliner interface:Thin film lubrication!
Lz~ 0.1m
Sliding: 10m/s
Exaggerated Piston
Liner
L ~ 10 microns
squeezing: 0.01m/s
OilPiston
Crankshaft
ConnectingRod
O
Pressure Force
Cylinder bore
Wrist pin
Governing equation• Reynolds' Equation
[ ∂∂ z hρ 3
12 μ∂ p∂ z ∂
∂ x hρ 3
12 μ∂ p∂ x ]= ∂
∂ z [ρ hW
2 ]∂ hρ ∂ t
• Limitation of Reynolds' equation: cavitationReynolds' equation fails when cavitation happens. When pressure drops to cavitation pressure, fluid will cavitate and separate into liquid and vapor. Thus fluid pressure will not drop below cavitation pressure, which is not guaranteed in Reynolds' equation.
How to handle cavitation• JFO cavitation assumption
Divide the computational domain into full film region and cavitation region. At full film region, use Reynolds' equation. At cavitation region, where there is partial film, assume pressure is constant and equals cavitation pressure, and assume the oil transport rate is determined by a linear velocity profile across the gap.
Algorithm overview• Finite volume method
A mass conserving finite volume method is used to discretize the governing equations and formulate the algebraic equations. For each control volume P, the mass flux into it across its four control surfaces are represented using the information (including height, pressure, and state, that is, whether local node is full film or cavitation) of P and its four neighbors. This way, for each node, we get an algebraic equation based on mass conservation.
• Using iterative method to handle cavitation
Parallel Implementation• PETSc
The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of largescale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all messagepassing communication.
• Grid and parallel decomposition
Parallel Implementation• Use DA to help manage parallel communicationDACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,Nx,Nz,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da);
• Use MPI standard to communicate between processorsSince each processor only have the local part of the overall information, when the information of 'ghost' points (the bordering portions of the grid that are owned by neighboring processes) are needed or need to be updated, MPI message is used.
Performance• Timing results on a quadcore computer: calculation time
Performance• Timing results on a quadcore computer: speed up
Performance• Timing results on a quadcore computer: parallel efficiency
Physical results• Comparison between the results of Reynolds' equation (cavitation not
considered) and the results when cavitation is considered.
Physical results• Effect of surface tooling marks.
Physical results• Results for a real measurement.
Conclusion• Necessity of including cavitation is validated.
• Parallel solver tested on a quadcore computer and good speed up is achieved.
• Future improvement considering other parallel linear system solver.