Parallel numerical modelling of gas-dynamic processes in airbag - - PowerPoint PPT Presentation

Slide 1

Institute of Computational Technologies SB RAS High Performance Computing Center Stuttgart

Parallel numerical modelling

• f gas-dynamic processes

in airbag combustion chamber using different computing platforms

A.D. Rychkov1, N. Shokina1,2, T. Bönisch2, M.M. Resch2, U. Küster2

1Institute of Computational Technologies SB RAS,

Novosibirsk, Russia

2High Performance Computing Center Stuttgart,

Stuttgart, Germany

The 2nd Russian-German Advanced Research Workshop

• n Computational Science and High Performance Computing

Stuttgart, 2005

Slide 2

Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Introduction - 1 Principle of operation of airbag

Slide 3

Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Introduction - 2 Scheme of the airbag combustion chamber

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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

Slide 5

Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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 Tv – combustion rate depends on a local static pressure

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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

Slide 7

Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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

• utlet:

if gas flow is subsonic - non-reflective boundary if gas flow is supersonic - no condition

Slide 8

Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Parallelization of calculations

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Parallelization of calculations

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

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

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Calculation results for CRAY Opteron cluster (strider)

computational speedup 2,9488004 4 proc. 1 1 proc. 1,59040581 2 proc. 1,71052254 2 proc. on different nodes 5,28785594 8 proc. Calculation acceleration Number of processors

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Calculation results Main data:

Tv – fuel element ignition temperature λp – fuel element heat conductivity coefficient Ksd – empirical sedimentation coefficient (0฀ Ksd ฀1)

Variant 1:

Tv = 500 K, λ= 3.25 Wt/(m K), Ksd = 0

Variant 2:

Tv = 500 K, λ= 13 Wt/(m K), Ksd = 0.25

Variant 3:

Tv = 500 K, λ= 3.25 Wt/(m K), Ksd = 0.25

Variant 4:

Tv = 650 K, λ= 3.25 Wt/(m K), Ksd = 0

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Gas pressure on the left boundary

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Gas temperature on the left boundary

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Field of gas temperature

Time t=1 ms

0.005 0.01 0.015 0.02 0.025 0.03

Z

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

X

0.005 0.01 0.015 0.02 0.025 0.03

Y

T 2200 2064.29 1928.57 1792.86 1657.14 1521.43 1385.71 1250 1114.29 978.571 842.857 707.143 571.429 435.714 300

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Институт Вычислительных Технологий СО РАН High Performance Computing Center Stuttgart

Field of gas temperature

Time t=3 ms

0.005 0.01 0.015 0.02 0.025 0.03

Z

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

X

0.005 0.01 0.015 0.02 0.025 0.03

Y

T 2200 2064.29 1928.57 1792.86 1657.14 1521.43 1385.71 1250 1114.29 978.571 842.857 707.143 571.429 435.714 300