The role of direct numerical simulations in validation and verification

Numerical modeling of practical problems is constrained by two major considerations: -Often the governing equations are not completely known, or include processes only poorly understood, and -Frequently the range of scales is so large that even when the governing equations are known it is not practical to resolve all time and length scales fully. This does not, of course, eliminate modeling as a viable prediction tool. Equations for the average large-scale behavior of systems ranging from turbulence in pipes to the evolution of the climate are routinely solved and used to predict industrial and natural processes. To account for unknown processes and unresolved behavior we resort to phenomenological modeling. For unknown physics, experimental correlations of observable quantities substitute for our lack of understanding of the underlying processes. For unresolved but known physics, such as the unsteady motion in turbulent flows, direct numerical simulations are increasingly providing an alternative to experimental measurements. DNS of turbulence go back over a quarter century and in the last decade and a half, DNS of multiphase flows have become increasingly common. The availability of DNS results where every flow variable is available for realistic - although small - systems, is already changing how we obtain closure for the average descriptions. Here we review recent progress for multiphase flow and discuss a couple of examples where DNS has led to a much-improved understanding. It has been well known for some time that the injection of a relatively small amount of bubbles into a turbulent boundary layer can result in a significant drag reduction. DNS results have shown that slightly deformable bubbles can lead to reduction of the wall drag by sliding over stream wise vortices and forcing them toward the wall, where they are cancelled by the wall bound vorticity of the opposite sign. Spherical bubbles, on the other hand, often reach into the viscous sub-layer where they are slowed down and lead to an increase in drag. This was a particularly successful study and demonstrated powerfully the ability of DNS to explain very subtle effects that could probably not be understood in any other way. Experiments in Delft have confirmed the computational predictions. In another study of nearly spherical buoyant bubbles in vertical channels, DNS have provided insight that allowed many aspects of the problem to be predicted analytically. The result showed that for nearly spherical bubbles the lateral migration of the bubbles due to lift results in two regions: A core where the void fraction is such that the weight of the liquid/bubble mixture balances the imposed pressure gradient (and the velocity is therefore constant) and a wall-layer that is free of bubbles for down-flow and bubble-rich for up-flow. The void fraction can be determined analytically for both up and down-flow and the velocity profile can be computed analytically for down-flow. Both of these studies suggested that our current models for bubbles near walls are inadequate and need to be updated to incorporate what we now know. Although most progress has been made for relatively simple flows of bubbles, drops, and particles, new methods are rapidly being developed for more complex flows such as those including boiling, mass transfer and chemical reactions, electric fields, and flow regime transitions. We review the status of such methods, results already obtained, and what can be expected in the near future. (authors)