Modeling and simulation of wall-bounded turbulent flows with pressure-gradient and compressibility effects
Keywords: Mechanical Engineering.

Turbulent wall-bounded flows are ubiquitous in engineering and understanding and predicting their dynamics is necessary to address pressing grand challenges in aerospace, energy, and environmental science. For example, control and prediction of wall-bounded turbulence can lead to improved aerodynamic performance of air, land, and sea vehicles, increased efficiency of gas turbines used for electricity generation or propulsion, and accurate predictions of changes in the weather or climate. However, for most real applications, directly simulating the governing physics is intractably expensive even when the world's largest supercomputers are employed. The immense computational complexity of simulating turbulence is due to its multiscale nature; quantities of engineering interest, such as aerodynamic forces on a vehicle, manifest on the macroscale but they depend strongly on accurately predicting microscale phenomena such as turbulent kinetic energy dissipation. To address the high cost of direct simulations of turbulence, it is common to use physical modeling, which is the process of simplifying the governing equations and boundary conditions in order to obtain approximate variants that are computationally efficient to simulate. If the models are accurate, then the resulting solutions can be useful to make engineering design decisions at affordable cost. Specifically, this work focuses on the modeling of turbulent flows near solid boundaries since this is often the rate-limiting region which dominates the computational cost of a simulation. The direct impact of the models developed herein will be that advanced models can deliver accurate engineering predictions at reduced computational costs. To quantify this impact, we present detailed estimates of the grid-point and time-step requirements for simulations of incompressible and compressible wall-bounded flows. When paired with estimates for the growth of computational power over time, these estimates are useful for planning the types of simulations that will be tractable in the future. For the wall models developed in this work, it is assumed that the boundary-layer thickness can be computed reliably. However in complex flows, this is not trivial to define because of the inherent complexity of the background inviscid flow. In this work, a robust method for computing the boundary layer thickness is developed. The proposed method is based on estimating the inviscid base flow that leads to the actual observed viscous solution. Then, the wall-normal location of the departure of the viscous solution from the reconstructed inviscid one is labeled as the boundary layer thickness. This method is used throughout this work. Two models for the near-wall flow are presented for incompressible flows. The first model is for flows over complex geometries with strong streamwise pressure gradients. Lagrangian history effects are incorporating by introducing additional dependence of the wall model on the outer partial differential equation solver. The second model is designed for cases where computational resources are extremely limited and even the boundary layer is difficult to resolve (e.g., very high Reynolds number flows). The boundary layer wake is incorporated into the wall model to expand its domain of applicability. Both of these models are found to improve the prediction of the wall shear stress in a priori analysis. In applications with significant wall heat transfer, such as high-speed aerospace applications, wall-normal variations in density and viscosity can alter the structure of wall-bounded turbulent flows. In this work, a compressible velocity transformation is developed, which enables the mapping of a wide range of compressible velocity profiles to a single universal incompressible law of the wall. The proposed transformation is unique in that it is successful in collapsing data from channel and pipe flows and boundary layers with and without heat transfer. In addition, the inverse of this transformation is derived and applied as a wall model for large-eddy simulation. It is found that the model is significantly more accurate than the classical model, especially in applications with strong wall heat transfer