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T turbulence aming


Beth Harlen investigates why turbulence remains one


of the great unsolved physics problems


I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.’ A very similar observation has also been credited to Horace Lamb, a British mathematician. Te fundamental challenge where turbulence modelling is concerned is that turbulent flow appears to be random and chaotic. So how do you begin to model something as uncertain as turbulence with any degree of accuracy? Te answer is: with great difficulty, as there is no all-encompassing method. Rather, a range of models is required. One method for defining turbulence is with


A


the Reynolds number. Within fluid mechanics, this number characterises the different flow conditions. Laminar flow, which is smooth and constant, occurs at low Reynolds numbers. A large Reynolds number indicates turbulent flow, whereby inertial forces produce chaotic swirls and eddies as the fluid or air moves around an object. Known as laminar-turbulent transition, the process of laminar flow becoming turbulent is unpredictable and as such is yet to be fully understood. To work around this problem, said Doug


24 SCIENTIFIC COMPUTING WORLD


quote oſten attributed to the German physicist Werner Heisenberg captures the complexity of turbulence quite nicely. It states: ‘When I meet God,


Neill, vice president of product development at MSC Soſtware, aerospace companies have spent the past few decades tripping boundary layers on purpose in order to know that they are in a turbulent, attached state. Reshaping various surfaces on the aircraſt allows engineers to then direct the laminar and turbulent flows. By keeping the flow attached to the wing of a plane, for instance, engineers can ensure a greater level of predictability and stability.


Navier-Stokes equations and beyond Developed in the early 1800s, the Navier-Stokes equations attempt to describe the motion of fluid in a non-linear fashion. If these equations could be solved exactly, in principle there would be no need for turbulence modelling. However, the numerical solution of the Navier–Stokes equations for turbulent flow is extremely challenging and, therefore, a number of approaches have been developed. Reynolds averaged Navier-Stokes simulations (RANS), for example, refer to the fluid flow equations being solved, averaged in time. While this form of averaging in time enables


engineers to migrate using a steady assumption, meaning that how they arrive at the final answer is not critical as it doesn’t change with time, there are some significant drawbacks to this approach. Fred Mendonca, director of aeroacoustic applications at CD-adapco, explained: ‘By using RANS, you’re making some fairly fundamental assumptions about how turbulence behaves, which can deviate greatly from reality. Te most obvious deviation is that turbulence is not a steady phenomenon, and so cannot be treated as such.’ He added


that, because time variations are not taken into account, modelling on this basis will always be an approximation. Models based on a RANS approach will


accurately predict attached boundary layers, but they are known to struggle with large separations behind airfoils. ‘Te ideal solution would be to use large eddy simulations (LES), which is an approach that can potentially provide a significant increase in accuracy for the types of flows that RANS struggles with,’ said Brian Bell, lead technical services engineer at Ansys. ‘But for many years the problem with LES has been that the mesh requirements for realistic Reynolds numbers for aerospace applications simply mean that there’s no possibility of using it for problems with such a large number of grid points.’ LES does provide higher fidelity compared


to RANS, however, and so one approach is to use the information from the RANS model as the inflow conditions for a small region. By restricting the grid points, engineers can potentially use LES in small, critical areas. Bell added that the generation of turbulence inflow is a very active area of research as, although methods are good, there is still a lot of room for improvement. Te embedded LES model in Ansys’ Fluent solution has the ability to isolate a small piece of the computational domain. Outside that region, a RANS model with a relatively coarse grid can be used. Upcoming releases of the soſtware will offer the ability to combine transitional modelling capabilities with a scale-resolving approach. ‘Te industry is beginning to recognise


that transient modelling is the way forward as it makes no gross assumptions about the


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