15-10-2012, 01:10 PM
Using Computational Fluid Dynamics for Aerodynamics
Using Computational Fluid.pdf (Size: 851.45 KB / Downloads: 137)
In this white paper we survey the use of computational simulation for aerodynamics, focusing on
applications in Aerospace and Turbomachinery. We present some representative problems to
illustrate the range of complexity in fluid simulations and the associated computational
requirements. We also examine the design process in current industrial practice, and the role
played by computational fluid dynamics (CFD). Measured against this backdrop we assess the
potential role and market for supercomputing in an environment of ubiquitous computing on the
desktop. We also address some algorithmic and architectural issues, exemplified in Stanford’s
project to develop a new system using stream processors.
In a 1986 report from the National Research Council on “Current Capabilities and Future
Directions in Computational Fluid Dynamics”, it was stated “computational fluid dynamics is
capable of simulating flow in complex geometries with simple physics or flow with simple
geometries with more complex physics”. This is not true anymore thanks to progress in
computers and algorithm developments. 3D Euler calculations of flows for complex geometries
that were “state of the art” in 1986 for both the hardware and software requirements, can now be
carried out on laptops. CFD is widely accepted as a key tool for aerodynamic design. Reynolds
Average Navier-Stokes (RANS) solutions are a common tool, and methodologies like Large
Eddy Simulation (LES) that were once confined to simple canonical flows (isotropic turbulence
in a box, channel flow), are moving to complex engineering applications. For example, the Center
for Integrated Turbulence Simulations here at Stanford is using LES to simulate the reacting flow
in a real combustor chamber of a jet engine.
The complexity of fluid flows.
The complexity of fluid flow is well illustrated in Van Dyke’s Album of Fluid Motion. Many
critical phenomena of fluid flow, such as shock waves and turbulence, are essentially nonlinear
and the disparity of scales can be extreme. The flows of interest for industrial applications are
almost invariantly turbulent. The length scale of the smallest persisting eddies in a turbulent flow
can be estimated as of order of 1/Re3/4 in comparison with the macroscopic length scale. In order
to resolve such scales in all three spatial dimensions, a computational grid with the order of Re9/4
cells would be required. Considering that Reynolds numbers of interest for airplanes are in the
range of 10 to 100 million, while for submarines they are in the range of 109, the number of cells
can easily overwhelm any foreseeable supercomputer. Moin and Kim reported that for an airplane
with 50-meter-long fuselage and wings with a chord length of 5 meters, cruising at 250 m/s at an
altitude of 10,000 meters, about 10 quadrillions (1016) grid points are required to simulate the
turbulence near the surface with reasonable details. They estimate that even with a sustained
performance of 1 Teraflops, it would take several thousand years to simulate each second of flight
time. Spalart has estimated that if computer performance continues to increase at the present rate,
the Direct Numerical Simulation (DNS) for an aircraft will be feasible in 2075.
Computational costs
In external aerodynamics most of the flows to be simulated are steady, at least at the macroscopic
scale. Computational costs vary drastically with the choice of mathematical model. Studies of the
dependency of the result on mesh refinement, performed by this author and others, have
demonstrated that inviscid transonic potential flow or Euler solutions for an airfoil can be
accurately calculated on a mesh with 160 cells around the section, and 32 cells normal to the
section. Using a new non-linear symmetric Gauss-Siedel (SGS) algorithm (Jameson and Caugley,
2001), which has demonstrated “text book” multigrid convergence (in 5 cycles), two-dimensional
calculations of this kind can be completed in 0.5 seconds on a laptop computer (with a 2Ghz
processor). A three dimensional simulation of the transonic flow over a swept wing on a
192x32x32 mesh (196,608 cells) takes 18 seconds on the same laptop. Moreover it is possible to
carry out an automatic redesign of an airfoil to minimize its shock drag in 6.25 seconds, and to
redesign the wing of a Boeing 747 in 330 seconds.
The role of CFD in the design process
The actual use of CFD by Aerospace companies is a consequence of the trade-off between
perceived benefits and costs. While the benefits are widely recognized, computational costs can
not be allowed to swamp the design process. The need for rapid turnaround, including the setup
time, is also crucial.
In current industrial practice, the design process can generally be divided into three phases:
conceptual design, preliminary design, and final detailed design, as illustrated in Figure 2. The
conceptual design stage, typically carried out by a staff of 15-30 engineers, defines the mission in
the light of anticipated market requirements, and determines a general preliminary configuration,
together with first estimates of size, weight and performance. The costs of this phase are in the
range of 6-12 million dollars.
In the preliminary design stage the aerodynamic shape and structural skeleton progress to the
point where detailed performance estimates can be made and guaranteed to potential customers,
who can then, in turn, formally sign binding contracts for the purchase of a certain number of
aircraft. A staff of 100-300 engineers is generally employed for up to 2 years, at a cost of 60-120
million dollars. Initial aerodynamic performance is explored by computational simulations and
through wind tunnel tests. While the costs are still fairly moderate, decisions made at this stage
essentially determine both the final performance and the development costs.
CFD algorithms and software
Commercial CFD software is widely available, and now amounts to an industry with annual
revenues in the range of $200 million. The best known examples (CFX, Fluent and Star-CD) all
had their origin in England. Commercial software, however, has yet to gain acceptance as a
design tool in the Aerospace Industry, which continues to use community codes, many of them
developed by government agencies such as NASA, ONERA and the DLR. Once a code has been
adopted, users are very reluctant to switch to a new code because of the large investment in
familiarization and validation. Accordingly software tends to have a much longer operational life
than hardware. For example, FLO22, written by Jameson and Caughey in 1975, has continued to
be extensively used to the present day.