Kinetic Energy Methods

Problems in which turbulent flow fields dominate form a major portion of engineering fluid mechanics and heat transfer work. In principle, the calculation of these flows involves the solution of the time-dependent Navier-Stokes equations. But these equations cannot be solved without recourse to numerical methods, which must divide the flow field into a finite number of calculation points. The fundamental problem in the computation of turbulent flows then becomes the fact that turbulence introduces motions on a scale far smaller than the distances between the calculation points on the smallest practical numerical solution grid. Indeed, even if it were possible to compute the velocity field in a turbulent flow down to the smallest scale of motion of interest, another problem would be encountered. Because the velocity field in a turbulent flow fluctuates randomly, the variables of engineering interest in the flow are in general time or ensemble averages of the fluctuating quantities. In order to predict these averages, it would be necessary to repeat a detailed computation a great number of times, each with a slightly different initial condition, and ensemble-average the results. For these reasons, a direct assault on the problem of the computation of turbulent flows is impractical.