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256 Computational Fluid Dynamics and Heat Transfer
size of 10
5
is an indicator of the main memory performance for each architecture.
Figure 6.13 shows one aspect of the equation that governs time to solution. The
other effect that needs to be considered in designing an optimal block size is its
effectonnumberofiterationstoconvergence.Typicallyastheblocksizedecreases,
convergenceslowsandthenumberofiterationsincrease.Thisiscounteredbyusing
a two-level method in which a coarse level is implemented with a granularity of
one coarse node per substructured block.A typicalV-cycle between the two levels
works much like in multigrid, in which the solution is relaxed individually in each
block, thenrestrictingthe block-integrated residues on to the coarse level followed
by an iterative smoothing of a correction, and finally a prolongation of the correc-
tion back to the blocks to be distributed across all nodes contained in the block.
The additive Schwarz preconditioner provided the following benefits (Wang and
Tafti [82]):
•
ReducedthenumberofiterationsforconvergenceintheKrylovsolverbyafactor
of 2 to 3, hence reducing the number of global inner products and matrix-vector
products.
•
Increased floating point performance by a factor of 2 to 3.
•
Decreased the overall CPU time by nearly an order of magnitude.
6.10 Parallelization Strategies
It would not be an overstatement to say that much of the gains in the widespread
use of steady and time-dependent CFD has been facilitated by the exponential
increase in computational power over the past two decades. Not only have pro-
cessors become more powerful, but the ability to harness their collective power in
parallel has also increased. While single-processor performance is dependent on
the efficient useof fast cache,parallelperformanceisdependent onhowefficiently
a code parallelizes on a given architecture. Three distinct brands of parallel archi-
tectureshaveemerged–shared, distributed,anddistributed-sharedmemory(DSM)
architectures. In the shared memory architecture, multiple processors have access
to the same shared memory through cache-coherent nonuniform memory accesses
(cc-NUMA), whereas in the distributed memory architecture, the processors are
distributed across a network with each processor only having access to its own
memory. Hence, explicit messages are required to transfer data from one mem-
ory to the other. The DSM architecture combines the two architectures by having
multiple shared memory nodes distributed across a network.
Barring recent research efforts in the computer science community, two dis-
tinct programming methods have evolved for parallel computing. One method
takes advantage of the shared memory architecture by using compiler directives
for parallelization, and the other uses explicit message passing libraries to move
information between distributed memories. In the former the OpenMP API has
evolved as the standard, whereas distributed memory programming has become
synonymous with MPI (now Open MPI). The OpenMP API is a set of compiler
Sunden CH006.tex 10/9/2010 15: 39 Page 257
Time-accurate techniques for turbulent heat transfer analysis 257
Processor
domain
Global
domain
Grid
Block
Cache
blocks
Figure 6.14. Data structure and mapping to processors and cache memory.
directives that instruct the code atruntime to perform certain operations in parallel
acrosssharedmemoryandcanbeimplementedincrementally. Buildingparallelism
into a serial code with MPI on the other handrequiresthatthe mode of parallelism
be decideda prioriwithin a single-program multipledata (SPMD)framework such
that for the most part the same operations are repeated on all processors. For CFD
applications, that usuallytranslates to a decomposition of the spatial grid into con-
tiguous pieces mapped to different processors with explicit message passing calls
through MPI for transferring data from one processor to another for global syn-
chronicity, andrequiresamajorrewriteofthecode.WhereasOpenMPissimplerto
implement and more flexible by being able to accommodate both different modes
of parallelism and adaptation of parallelism [85, 86], it does not scale as well as
codes written in MPI for these same reasons. There is merit in combining the two
on DSM architectures to reap the benefits of both modes of parallelism (Tafti and
Wang [87]).
The multiblock framework provides a natural framework for parallelization.
Figure 6.14 illustrates the data structure and the multiple levels of parallelism that
can be extracted. Depending on the total number of mesh blocks and the degree of
parallelismsought, eachprocessorcanhavemultipleblocksresidingonitas shown
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258 Computational Fluid Dynamics and Heat Transfer
Number of processors
Gflop/s
1
0.01
0.1
1
10
100
1000
10 100 1000
10
4
MPI-OpenMP (ASCI Red)
MPI-OpenMP (ASCI Blue)
MPI (ASCI BLUE)
ASCI Blue Orgin-MIPS 250 MHz
ASCI Red Pentium Pro 200 MHz
Figure 6.15. Parallel scalability ofASPCG on two pastASCI platforms with MPI
and MPI-OpenMP.
inFigure 6.14.The processordomain inFigure 6.14is thesame asan MPIprocess.
Further within each block, “virtual cache blocks” are used for preconditioning the
solution of linear systems. The “virtual” blocks are not explicitly reflected in the
data structure, butare used only inthe solutionof linearsystems.Hence embedded
in each MPI process are additional levels of parallelism across mesh blocks or
across cache blocks that can be exploited by OpenMP.
Figure 6.15 shows scalability studies on the ASCI Blue Origin 2000 cluster
at Los Alamos and ASCI Red Intel machine at Sandia for a model problem. The
domainsizeoneachprocessorismaintainedat1,024×1,024cells,with1,024sub-
domains of size 32×32 for cache performance. The number of relaxation sweeps
in the Jacobi smoother is kept at 40 in each block and 100 on the coarse level.
The calculations on the ASCI Blue are run across a cluster of Ori-
gins using only MPI (in and across Origins) or a combination of
MPI-OpenMP. In the hybrid MPI-OpenMP model, MPI processes are not only
used across Origins but within Origins as well. For each nproc (total number of
processorsused)in thefigure,themultipledatapointscorrespond todifferent com-
binationsofMPIandOpenMPthreadsexecutedacrossdifferentnumberofOrigins.
On the ASCI Red, OpenMP is used within each two-processor node. In all cases,
the scaled performance exhibits a perfect linear speedup showing the efficacy of
the architecture as well as the use of hybrid parallelism.
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Time-accurate techniques for turbulent heat transfer analysis 259
6.11 Applications
Thetheoryandmodelingtechniquesdescribedinthischapterhavebeenusedexten-
sivelyforLES([88–92])andDES([73–75,93–95])ofturbineinternalcoolingducts
with ribs with rotation and centrifugal buoyancy effects at Re=20,000 to 50,000
and LES of leading edge film cooling at Re=100,000 ([96–98]). A number of
investigations have also been performed in studying different fin configurations or
heat transfer enhancement techniques in compact heat exchangers, which mostly
operateinthetransitionalregimebetweenRe=100to2,000([99–103]).Adynamic
meshcapabilityispresentlybeingusedtoinvestigateflappingflightforapplications
to Micro-Air Vehicles (MAVs) at Reynolds numbers between 10,000 and 100,000
([104, 105]). A two-phase dispersed phase capability using Lagrangian particle
dynamics has been used with LES to model fouling of internal cooling channels
and film cooling holes ([106, 107]).
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Sunden CH007.tex 10/9/2010 16: 6 Page 265
7 On large eddy simulation of turbulent flow
and heat transfer in ribbed ducts
Bengt Sundén and Rongguang Jia
Lund University, Lund, Sweden
Abstract
This chapter presents some work on large eddy simulation (LES) for heat transfer
studies. Firstly, the numerical accuracy is validated with the simulation of the fully
developedpipeflowwiththedirectnumericalsimulation(DNS)data.Secondly,the
solverisusedtostudytheheattransferandfluidflowinrib-roughenedducts, where
theribs couldbe straightorV-shaped.Thisis primarily toclarifyacontradictionon
which pointing direction is the better for V-shaped ribs. Lastly, current status and
prospects of LES are presented.
Keywords: LES, Heat transfer, Ribs, Duct flow
7.1 Introduction
In order to allow the gas turbine designer to increase the turbine inlet temperature
whilemaintaining an acceptable materialtemperature, sophisticated cooling meth-
ods are essential. For the internal cooling of the blades, ribbed ducts are usually
used.The presence of ribs, also called roughness or turbulators, enhances the heat
transfer coefficients by redevelopment of the boundary layer after flow reattach-
ment between the ribs, and because of induced secondary flows. The rib layouts
and configurations can be varied and include 90-degree, 60-degree, and 45-degree
parallel ribs and 45-degree and 60-degreeV-shaped ribs.
It is essential to be able to accurately predict the enhancement of heat transfer
generatedbytheroughnesselements toensuregooddesigndecisions.Accordingly,
the heat transfer and fluid flow in ribbed ducts have been extensively studied both
experimentally and numerically. A summary is presented in Jia et al. [1], where
contradictions on experimental studies of V-shaped ribs have been identified. The
experimental studies of both Han et al. [2] and Olsson and Sundén [3] show that
square ducts roughened with upstream pointing V-shaped ribs perform better than
those pointing downstream. However, results on the contrary were obtained by
Taslim et al. [4] and Gao and Sundén [5]. The contradiction might be due to the