| Computational Fluid Dynamics |
 Viscous Attenuation of a Detonation Wave Propagating in a Channel
P. Ravindran, R. Bellini, T.-H. Yi, Ph.D. and F.K. Lu, Ph.D. |
Motivation for Research |
Euler vs. Navier-Stokes |
- Detonation wave propogation in a tube similar to Sod shock tube problem
- Boundary layer growth due to viscosity has long been neglected due to complexity of the simulation
- Shock-Boundary layer interaction remains poorly understood
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- Faster computing power - preference of Navier Stokes equations over the Euler equations
- Transport processes such as viscosity can be included in the governing equations
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| Governing Equations |
Numerical Model |
- Governing equations are modeled by coupling thermodynamic processes, chemical reactions, and fluid dynamics
- Flow is assumed to be thermally perfect with non-equilibrium finite-rate chemistry
- Elementary reaction mechanism obtained from GRI-MECH database
- Viscosity, diffusion, and thermal conductivity obtained from classical kinetic theory
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- Discretization using Finite Volume formulation retaining integral form
- Convective fluxes approximated by
flow quantities left and right of a cell
- Viscous fluxes computed by averaged variables at a face
- Roe second order scheme for multi-species, thermally perfect gas
- Higher order approximations using
MUSCL approach
- Two-step Runge-Kutta scheme with
second order accuracy for temporal
discretization
- Transport terms are evaluated by Green’s theorem
- Evaluation of temperature at cell when species density is updated for thermally perfect gas
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| Results and Conclusions |
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- 50 cm long and 10 cm high channel
Domain discretized into 100X150 cells
- Grids are clustered near the walls to
capture BL
- Adiabatic wall conditions with inflow
supersonic
- Pressure at outlet set at 1 atm
- Premixed H2-Air at 2 atm and 500 K
with incoming Mach 2.0
- Mixture ignited by localized hot-spot at 30 atm and 3000 K located 0.1 m into channel at left end
- Results show wave propagation delayed for viscous case
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Parallel Algorithm for Detonation Wave Simulation |
| P. Ravindran and F. K. Lu, Ph.D. |
| Need for Parallel Computing |
Why MPI? |
- Increasing reliance on CFD to produce
time accurate simulations of physical
phenomenon
- Accurate simulations of complex phenomena such as detonations need immense computational requirements due to time constraints
- Expensive to build supercomputers, cost effective for parallel computers
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- MPI (Message Passing Interface) is used due to it language-independence, scalable nature and portability
- Provides virtual topology, synchronization and communication between processors
- Ability to initiate point-to-point communication without network overload
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| Simulation |
LONESTAR - DELL Cluster |
- Inviscid Euler model assuming thermally
perfect gas
- H2 – Air model with conditions 2 atm,
500K and incoming Mach number 2.0
- Localized hotspot of 30 atm and 3000 K Grid domain – 100X150 cells
- MPI 2.0 implementation with collective
communication
- Scaleup indicates good scalability with
memory usage increasing linearly with
increasing processors
- Bandwidth blockage noticed beyond 96
processors: higher the processors, more time spent in communication
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- Total no: of nodes – 1300
- Node – Dell Blade 1955, 4 cores/node
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