Nathan Mullenix

Spatially Developing Supersonic Turbulent Boundary Layer with a Body-Force-Based Method

A method to obtain a spatially developing equilibrium supersonic turbulent flat-plate boundary layer suitable for direct numerical simulations or large-eddy simulations of viscous/inviscid interactions is described. A steady counterflow actuator with properties based on a dielectric barrier discharge is employed to trip an incoming laminar boundary layer. The resulting unstable shear layer transitions rapidly and breaks down to generate the desired turbulent boundary layer. A fifth-order bandwidth and order optimized weighted essentially nonoscillatory scheme using Roe fluxes is used along with sixth-order viscous terms to simulate this process. The properties of the boundary layer are exhaustively analyzed on meshes of 65, 37, and 20 million grid points. The fine-grid solution agrees with the mean flow and statistical properties observed in the literature, and is used as a truth model to investigate results on smaller meshes. The medium-grid solution reproduces the fine-grid behavior with modest differen...

A Bandwidth and Order Optimized WENO Interpolation Scheme for Compressible Turbulent Flows

Weighted Essentially Non-Oscillatory schemes seek to maintain high order of accuracy away from discontinuities while eliminating oscillatory behavior near them. Attempts have been made to optimize these schemes for various properties, such as increasing the order of accuracy, or the bandwidth resolving efficiency. In this paper a fifth order scheme is developed that maintains the design order of accuracy of the underlying scheme while maximizing the bandwidth resolving efficiency. This scheme is compared to various other schemes, such as order or bandwidth optimized and a standard upwind biased scheme for a variety of test cases. A preliminary assessment for a controlled turbulent Mach 1.3 jet is also performed to show the ability of the new scheme to capture details of the flow in underresolved regions.

Analysis of Unsteady Behavior in Shock/Turbulent Boundary Layer Interactions with Large-Eddy Simulations

Various numerical and physical aspects of shock/turbulent boundary layer interactions (STBLI) are discussed in the context of Large-Eddy Simulations (LES). A spatially developing incoming equilibrium turbulent boundary layer is obtained with a force based tripping mechanism. Previous results are augmented with a detailed analysis of this procedure. In particular, it is shown that relatively coarser meshes may be employed if the strength of the trip is increased, together with an adjustment of the wall thermal condition for a short distance downstream of the trip. This approach yields both adiabatic as well as constant wall temperature results. Additionally, it is shown that precursor events provide estimates for the size of the trip with only a small portion of the domain in the vicinity of the trip, thus yielding an efficient technique. A simulation of a STBLI using this spatially developing incoming turbulent boundary layer confirms the low frequency signal observed in the STBLI by other approaches which use recycling techniques, and reproduces the particular unsteadiness shown in a reference experiment. A detailed analysis is performed of the evolution of the Reynolds stresses through the interaction. The amplification of turbulence energy is quantified, and the evolution of two point correlations is explored. The results indicate that the spanwise decorrelation distance first decreases and then increases through the interaction. A preliminary assessment of the effect of pulsed arc filament based actuators is provided. The results indicate a reduction in the separation length when pulsed at a St corresponding to the peak frequency near the reattachment point.

A Plasma-Actuator-Based Method to Generate a Supersonic Turbulent Boundary Layer Inflow Condition for Numerical Simulations

A method to obtain an equilibrium supersonic turbulent flat plate boundary layer suitable as an input to Direct Numerical Simulations or Implicit Large-Eddy Simulations is described. A steady counterflow actuator with properties based on Dielectric Barrier Discharges (DBD), which extends the span of the plate, is employed to trip an incoming laminar boundary layer of suitable properties. The DBD force field induces a small region of flow separation. The resulting unstable shear layer transitions rapidly and breaks down to generate the desired turbulent profile. A fifth order bandwidth and order optimized WENO scheme is used along with sixth order viscous terms to simulate this process. The properties of the boundary layer are exhaustively analyzed on two dierent meshes. The boundary layer on the fine mesh, comprised of 65 million points, displays the anticipated mean flow and statistical properties observed in the literature. The coarse mesh, comprised of 20 million points shows delayed transition and thus a smaller boundary layer thickness. On the coarse mesh, mean flow properties including the law of the wall, turbulent Prandtl number, and two-point correlations are reasonably well predicted while Reynolds stresses are over predicted and skin friction is under predicted. Coherent structures are shown to exist within the turbulent flow for both grids. For the domain dimensions chosen, the flow exhibits de-correlation of pertinent two-point statistics in the spanwise direction and is large enough in streamwise extent to yield a significant region of equilibrium turbulent boundary layer flow. The method displays no spurious frequency peaks and no artificial length scales are detected.

Comparison of Hertz-Knudsen and Ytrehus Carbon Ablation Rates using a Reactive-Riemann Solver

A mathematical model for ablation via sublimation is developed that combines solid heat transfer, gas dynamics, and phase change processes into a unified set of equations. A Reactive-Riemann solver is developed to solve this system of equations. Two different methods for calculating the ablative mass flux, namely the Hertz-Knudsen equation and the method of Ytrehus, are compared for a simple one-di mensional test case. A two-dimensional axisymmetric case of ablation of a circular-tipped cone is then simulated using the Ytrehus method. A description of the parallel computing a lgorithm is also provided.

Implicit LES of a Shock Interaction with a Tripped Equilibrium Turbulent Boundary Layer

An Implicit Large Eddy Simulation of a Mach 2.33 re ected oblique shock/turbulent boundary layer interaction (Re = 3048, generated by a 9 wedge) is employed to understand the dynamics of the interaction. The boundary layer is generated with a new spatial approach that ensures the proper statistical and coherent structure dynamics, with no discernible time or length scales associated with the generation process. The dynamics of the interaction and its unsteadiness, are analyzed from the standpoint of the mean ow, statistical quantities such as Reynolds stresses, spectra of the unsteadiness and the e ect on coherent structures. The results are compared to ongoing experiments, and when scaled by the interaction length reproduce the key features including the low frequency unsteadiness. The shock ampli es the turbulence, and initially reduces the size of the largest length scales which is the behavior expected from the literature. Hairpin vortices are identi ed to be the large scale coherent structure present in the boundary layer before and after the interaction, with an increase in size found downstream. These results are then assimilated to initiate active ow control simulations with plasma actuators.

Modeling of Local Intense Ablation in Hypersonic Flight

Extensive research has been conducted in predicting the ablation rates of Thermal Protective Shield (TPS) due to hypersonic flow around aerospace vehicles. The majority of published ablation studies are limi ted to the set-up of uniformly distributed ablated mass flux that varies gradually along the TPS surface and does not cause separation of the boundary layer. Small s cale but high-intensity phenomena such as locally non-uniform mass transfer across an ablation front can greatly affect the overall flow field, transition t o turbulence, heat exchange, and overall ablation rate in a large-scale simulation. In the current study, small defects on the surface are used to induce localized high ab lation rates. To facilitate the research in non-uniform ablation, the parallelized Reactive-Riemann solver combined with the Ytrehus ablation rate has been developed in the current study.

Parallel implementation of a tightly coupled ablation prediction code using MPI

A parallel algorithm is developed for use with an ablation prediction code. The use of parallel computing is required due to the amount of computational time needed to simulate realistic physical times due to the small time steps demanded by explicit time schemes, and for the future use of the code to handle 3-D defects at the TPS surface. The details of a parallel algorithm using MPI are provided. The performance of this algorithm for a typical ablation problem is provided.

Hypersonic Ablation of Graphite Thermal Protection Systems with Surface Defects

The goal of this study is to analyze ablation of a thermal protection system with a small cavity-like surface defect. It is shown that, within the defect region, the ablation mechanism switches from the oxidation-dominated regime to the much faster sublimation-dominated regime. To accurately predict the ablation rate of graphite, several subprocesses must be accounted for, including high-temperature chemically reactive gas dynamics, heat transfer, and surface ablation mechanisms. In this study, a set of equations has been derived that intrinsically couple these subprocesses. A numerical methodology suitable for solving these equations has been developed, including modified finite-volume methods and a novel reactive-Riemann solver that treats the surface as another wave in the Riemann problem and its recession velocity as the wave speed. Numerical simulations have been carried out for the ablation of a graphite sphere–cone over a range of conditions with prevailing oxidation or sublimation. The results com...

Development of a Conjugate Heat Transfer Simulation Tool for Anisotropic Thermal Protection Systems

Novel materials intended for use in thermal protection systems in hypersonic vehicles, such as carbon foams, have highly anisotropic properties. These properties can be tuned in some ways during manufacture. Research is ongoing to develop a tightly coupled solver combining the gas dynamics of the surrounding gas with the mechanical and thermal response of these materials. Mature techniques are available to solve the dierent domains, such as finite element methods for the solid, and finite volume methods for the chemically reacting high speed gas dynamics. The dierent discretizations add complications to the coupling process. A set of tightly coupled integral conservation equations is derived that lends itself to solution via finite volume methods. A finite volume procedure is presented that is suitable for both the solid material and the surrounding gas. Results of representative test cases for anisotropic conduction are presented, and demonstrate that anisotropy can have a significant eect on the temperature distribution within the material.