MODELLING: AERODYNAMICS
around an obstacle without breaking up into turbulent swirls and eddies. You can describe such turbulent flow as dominated by the fluid’s inertia – the tendency of each portion of fluid to follow a path determined by its own momentum. If a flow appears to be random, how can you
study it? Not very easily. George Papanicolaou, mathematics professor at Stanford University [1], explains: ‘Simply put, turbulence is very hard. Every hard problem in classical physics finds itself embedded in turbulence. It is nonlinear, chaotic, stochastic. And there is no separation of scales – you must deal with a very large number of scales of irregularities. It’s just a mess. In most other physics problems, you can get control by reducing them to simpler problems that you can understand. You can separate scales, for instance, and determine that certain scales are not important. You can limit the phenomena. Or perhaps the inhomogeneity, the chaotic behaviour, is not there all the time, so you can somehow approach it. In turbulence all these things happen at once, and you don’t know how to separate them out.’
handle various conditions. Many of these are incorporated in different packages, many of which contain similar sets of models. Users tend to compare Package A with Package B and ask, ‘why don’t you have Turbulence Model X?’ This motivates uniformity in the market. Thus, many packages have common basic models that are well known to all, but there are many more models that are not included in these packages. These are the ones that are more difficult to incorporate into the software, make the software unwieldy and are more difficult to solve; the result is that a software house doesn’t want to include them and get a reputation for unstable models that don’t converge. Another point Leschziner makes is
that you can’t make definitive statements about which model is the best one to use. The software reveals trends, so you can try different models to see their sensitivity and how they vary with each other. In every situation, models are influential, but not decisive. He adds, however, that users often simply choose one and just cross their fingers. It’s quite difficult to make a rational
‘One supplier commented that all vendors provide basically the same capabilities, and the differences are in the software’s usability and technical support’
How CFD handles turbulence
Despite this statement, any CFD (computational flow dynamics) software must include some way to handle turbulent flow. Getting vendors to discuss their offerings, however, isn’t always easy. One supplier commented that all vendors provide basically the same capabilities, and the differences are in the software’s usability and technical support. ‘There is some truth to this statement,’ comments Professor Michael Leschziner, who heads the Turbulent Flow Modelling and Simulation Group at Imperial College London. He adds that everyone is solving the same basic equations, and numerical modelling has nothing to do with the core physics, but instead works with the underlying partial differential equations. There are differences, however, in the numerical machinery in how various software approaches the solution method and in the solvers they use. Leschziner adds that there are roughly 120 different turbulence models in existence to
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decision as to which one to use. He believes that to understand turbulence to this degree requires a decade of experience. Along these lines, Leschziner points to
one of the best resources he is aware of, one of the few documents targeting people who are users but not turbulence experts. It comes from ERCOFTAC (the European Research Community on Flow Turbulence and Combustion), and it consists of two Best Practice Guidelines, one for single-phase flows and another for dispersed multi-phase flows. (Both are available at
www.ercoftac. org).
Several major classes
Even so, it’s instructive to recognise that simulation and modelling approaches can be broken down into several major classes (Figure 1). Much of this breakdown is based on the fact that turbulence involves a wide range of turbulence eddy sizes. With DNS (direct numerical solution), the software is expected to solve the actual Navier-
Fig. 1: Major classes of turbulence simulations and models (courtesy of Ansys)
Stokes flow equations and resolve all scales and frequencies. Because of the massive computations required, this approach is possible only for simple cases; otherwise, simulation times could run into the months or years, even with today’s hardware. It’s just not practical for real industrial applications. To cut down on computation times, the
other approaches vary in which turbulence eddy sizes are actually calculated directly and which are modelled with time averages of turbulent structures that produce mean values. At the other end of the class chart is RANS, Reynolds Averaged Navier-Stokes simulations, where all the turbulence eddies are examined in a time-averaged fashion. In between are a wide range of models that solve larger eddies directly but handle the remaining smaller ones in a time-averaged fashion. There are, of course, a multitude of approaches for deciding how to split up the work (Figure 2), and these options help account for the many turbulence models found in various software packages and even more in the literature. Even so, there are many possible selections
of turbulence models in today’s CFD software, which can be daunting. To help users, says André Braune, customer support team leader for power generation and turbomachinery, Ansys has released a handful of stable, validated and broadly applicable turbulence models in its CFD software. When guiding customers to select among them, Ansys puts the models in the following hierarchy, going from simplest (and often less accurate) to most complex (and most accurate): l Zero-equation models, for instance when constant eddy viscosity is applied throughout the entire domain; l 1-equation models, e.g. for external flows of wings;
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