The 2nd Russian-German Advanced Research Workshop on Computational Science and High Performance Computing Stuttgart, 2005 Parallel numerical modelling of gas-dynamic processes in airbag combustion chamber using different computing platforms A.D. Rychkov 1 , N. Shokina 1,2 , T. Bönisch 2 , M.M. Resch 2 , U. Küster 2 1 Institute of Computational Technologies SB RAS, Novosibirsk, Russia 2 High Performance Computing Center Stuttgart, Stuttgart, Germany Institute of Computational Technologies SB RAS High Performance Computing Center Stuttgart Slide 1
Introduction - 1 Principle of operation of airbag Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 2
Introduction - 2 Scheme of the airbag combustion chamber Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 3
Overview of the project: full mathematical modelling - 1 Main assumptions: – 3-D non-stationary flow – gas (combustion products) / burning hard material (fuel elements) as porous medium – friction force work, pressure force work, heat transfer between the fuel elements are neglected – booster particles have a spherical form, fuel granules have a cylindrical form – material of the fuel elements is homogeneous, booster particles contain incombustible part – combustion products consist of a mixture of the perfect gas with the constant adiabatic exponent and incombustible small solid particles – carrying gas is considered as two-phase equilibrium medium Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 4
Overview of the project: full mathematical modelling - 2 Main assumptions: – initiation of the booster particle ignition occurs due to the heat exchange between the ignitor combustion products, which enter the left boundary of the booster combustion chamber at the time moment t=0 – composition of the ignitor combustion products is identical to the composition of the carrying gas, but does not contain solid phase – temperature distribution inside a fuel element is determined from the solution of the non-stationary heat conduction equation for a sphere – combustion of a fuel element starts when its surface temperature reaches the given value T v – combustion rate depends on a local static pressure Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 5
Mathematical modelling Mathematical model: – 3-D Navier-Stokes equations for carrying gas, taking into account the volume, occupied by fuel elements – state equation for carrying gas – motion equation for fine-dyspersated particles suspended in the carrying gas – equation for calculational density of fuel elements – interphase resistance coefficient is calculated either by Ergun formula or as the resistance coefficient of a sphere – initial conditions – boundary conditions for gas Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 6
Scheme of airbag combustion chamber Initial and boundary conditions: inlet: ignitor work is modelled as the hot gas input thorough the left boundary of booster combustion chamber impermeable surfaces: no-slip conditions, heat insulation condition for the temperature outlet: if gas flow is subsonic - non-reflective boundary if gas flow is supersonic - no condition Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 7
Mathematical statement - 1 Solution methods: Temperature of fuel element surface: numerical solution of heat conduction equation for the sphere using implicit difference Cranck-Nicolson scheme of the second order Main equation system: second-order upwind LU difference scheme with TVD properties Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 8
Parallelization of calculations Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 9
Parallelization of calculations Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 10
Strider The CRAY Opteron cluster (strider) platform consists of one front node for interactive access (strider.hww.de) 125 nodes for execution of parallel programs and 2 I/O nodes. The cluster consists of 127AMD dual CPU nodes with 2GHz Opteron CPU's + 4GByte memory on each node and a 2way frontend node with 2 Opteron 2GHz CPU's + 8GBytememory. Additionally a RAID system with 2 TByte is available.The local disks of each node (26 GByte) serves as scratch disks. Features: • Cluster of 127 dual SMPs (AMD Opteron's) servers with 4GByte memory • Frontend node is a 2way (AMD Opteron) server with 8GByte memory\item Node-Node interconnect Myrinet 2000 Network • Disk 1000 GB home + 1000 GB scratch + 3250 GByte local scratch • Batchsystem: OpenPBS, Maui scheduler • PBSPro, CRAY Utils • Operating System: SuSE SLES 8 (AMD64) (United Linux 1.0) • PGI Compilers Main data: • Peak Performance: 1048 GFLOP/s • Processors: 256 • Memory: 516 GB • Shared Disk: 2000 GB (Raid5) • Distributed Disks: 3250 GB • Number of Nodes: 125 compute, 1 frontend, 2 I/O • Node-node data transfer rate: 250 MB/s Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 11
Calculation results for CRAY Opteron cluster (strider) computational speedup Number of processors Calculation acceleration 1 proc. 1 2 proc. 1,59040581 2 proc. on different nodes 1,71052254 4 proc. 2,9488004 8 proc. 5,28785594 Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 12
Calculation results Main data: T v – fuel element ignition temperature λ p – fuel element heat conductivity coefficient K sd – empirical sedimentation coefficient ( 0 K sd 1 ) Variant 1: λ = 3.25 Wt/(m K), K sd = 0 T v = 500 K, Variant 2: λ = 13 Wt/(m K), K sd = 0.25 T v = 500 K, Variant 3: λ = 3.25 Wt/(m K), K sd = 0.25 T v = 500 K, Variant 4: λ = 3.25 Wt/(m K), K sd = 0 T v = 650 K, Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 13
Gas pressure on the left boundary Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 14
Gas temperature on the left boundary Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 15
Field of gas temperature Time t=1 ms T 2200 2064.29 1928.57 0.03 Z 1792.86 1657.14 0.025 1521.43 1385.71 0.02 1250 1114.29 978.571 0.015 842.857 707.143 0.01 571.429 435.714 0.005 300 0 X 0.005 0 0 0.01 0.005 0.015 0.01 0.02 0.015 0.025 0.02 0.03 0.025 0.035 0.03 0.04 Y Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 16
Field of gas temperature Time t=3 ms T 2200 2064.29 1928.57 0.03 Z 1792.86 1657.14 0.025 1521.43 1385.71 0.02 1250 1114.29 978.571 0.015 842.857 707.143 0.01 571.429 435.714 0.005 300 0 X 0.005 0 0 0.01 0.005 0.015 0.01 0.02 0.015 0.025 0.02 0.03 0.025 0.035 0.03 0.04 Y Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart Slide 17
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