Pramod K. Subbareddy

Unstructured grid approaches for accurate aeroheating simulations

The use of tetrahedral, prismatic, and hybrid hexahedral-prismatic-tetrahedral grids for the accurate prediction of aerodynamic heating at hypersonic conditions is investigated. We find that tetrahedral grids introduce significant error in the vicinity of strong shock waves, which results in unacceptable aeroheating predictions. The source of this error is studied with an idealized model, and it is found that a large spurious component of post-shock velocity is generated by triangular and tetrahedral elements. This type error is much smaller and easier to control on quadrilateral or hexahedral grids. Thus, we are very skeptical about the utility of tetrahedral grids for accurate hypersonic aeroheating predictions. Several comparisons of heating predictions for a three-dimensional sphere are made, and it is found that the stagnation region results are very sensitive to the grid design. Based on this work and our experience, we advocate the use of unstructured hexahedral grids which increase the grid design space, reduce the element count for many geometries, and result in accurate aeroheating predictions.

Numerical simulations of roughness induced instability in the Purdue Mach 6 wind tunnel

Results are presented from dns of Mach 6 flow around an isolated roughness element. The conditions correspond to experiments conducted at the Purdue Mach 6 quiet wind tunnel. Solutions are obtained on fairly large grids using a high order, low dissipation scheme that is capable of resolving the very small scales in the flow. The computations explore the creation of disturbances upstream of the protuberance and follow their growth as they travel downstream. The three cases correspond to Reynolds numbers in the range 45000-55000 and transition to turbulent flow occurs in the highest Reynolds number case.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota / NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

Advances in Computational Fluid Dynamics Methods for Hypersonic Flows

Over the past two decades or so, there have been many advances in the numerical simulation of hypersonic flows, with most effort focused on the development of upwind methods to produce accurate hea...

Roughness-Induced Instabilities at Mach 6: A Combined Numerical and Experimental Study

To develop improved methods of transition prediction for isolated roughness based on the growth of disturbances in the roughness wake, the underlying instability mechanisms must first be understood. This paper presents a direct comparison of experimentallyobserved and computed instabilities due to a cylindrical roughness in a boundary layer at Mach 6, to identify the dominant mechanism for transition. Direct numerical simulations allow a detailed analysis of the entire flow field, while experimental measurements discover the real flow physics and confirm the findings of the computations. For a large roughness height of 10.2 mm, an instability with a frequency near 21 kHz originates in the separation region upstream of the roughness. Unstable shear layers and horseshoe vortices appear to cause transition downstream of the roughness for this case. As the roughness height is reduced, there appears to be a change in the dominant instability mechanism.

Decoupled implicit method for aerothermodynamics and reacting flows

We propose a new implicit computational fluid dynamics method for steady-state compressible reacting flows. The concept is to decouple the total mass, momentum, and energy conservation equations from the species mass and internal energy equations and to solve the two equation sets sequentially. With certain approximations to the implicit system, it is possible to dramatically reduce the cost of the solution with little to no penalty on the convergence properties. Importantly, the cost of the decoupled implicit problem scales linearly with the number of species, as opposed to the quadratic scaling for the conventional fully coupled method. Furthermore, the new approach reduces the memory requirements by a significant factor. The decoupled implicit method shows promise for the application to aerothermodynamics problems and reacting flows.

DES investigations of transverse injection into supersonic crossflow using a hybrid unstructured solver

Numerical simulations of transverse injection through low-angled injector ports into a supersonic freestream are performed using a hybrid, unstructured solver. Two cases are investigated: air injected into a M=2.9 air freestream with a 25 injection angle, and heated helium injected into a M=4.0 air freestream with a 30 injection angle. Simulations were run in RANS and DES modes. A set of the DES simulations were run with an unsteady inflow boundary layer, where the perturbations are a statistically meaningful representation of a series of randomly placed hairpin eddies. This boundary condition was fed periodically into the domain, and was reused multiple times over the course of a simulation. The RANS and DES simulations are found to capture the salient features of the flow, though discrepancies with experimental data are found. While the DES simulations were found to give steady-state solutions for the flow fields, the addition of the unsteady inflow boundary layer was found to greatly impact the downstream flow field and to improve the overall agreement with experiment. In the case of the helium injection, it was found that the predicted mass fraction distributions of the DES simulations with the unsteady inflow boundary layer was far less dependent on the value of the turbulent Schmidt number. This result shows that the mixing found in DES simulation with the unsteady inflow boundary layer is a result of the large-scale turbulent motion of the flow, rather than because of the gradient diusion term. However, the ‘box of eddies’ used to create the unsteady inflow boundary layers were not long enough to ensure that no bias was introduced into the flow field, and future simulations will be run with larger boxes. The results of the study show a great deal of promise for the use of DES simulations in conjunction with unsteady inflow boundary layers for simulation of SCRAMjet fuel injection.

A synthetic inflow generation method using the attached eddy hypothesis

The attached eddy hypothesis is used to develop a means of generating synthetic turbulent boundary layers. Fluctuating velocity fields are created from simple vortex shapes using the Biot-Savart law. These are superposed with mean velocity profiles from experiment or RANS to create boxes of data which can be fed in through the inflow plane of a simulation. This provides realistic time varying inflow data. The method is computationally inexpensive compared with other synthetic inflow generation methods. Two flows are investigated using this approach. In the first, detached eddy simulation is used to compute normal and angled injection of helium into supersonic turbulent crossflows at Mach numbers 3 and 4 respectively. The diameter of the injector in each case is comparable to the boundary layer thickness of the crossflow and it is to be expected that fluctuations in the turbulent boundary layer play an important role in the dynamics of the jet. A comparison of the helium mass fraction in the flow field is made with experimental data and the results are encouraging. The second case considered is a supersonic turbulent mixing layer with ac onvective Mach number of0.46 and a Reynolds number of 12 × 10 6 /m (based on the velocity difference and average ρ and µ). The two streams are brought together across a thin splitter plate and the boundary layers on both sides are turbulent. Simulations are performed with steady inflow conditions and with the synthetic turbulent flow fields. The DES methodology is used for subgrid modelling and results are compared with the experiments of Goebel and Dutton. With unsteady inflow, the comparison with experiment was found to be very good.

Scalar conservation in large eddy simulations of reacting flows

Large eddy simulation is the most viable approach for the accurate simulation of turbulent reacting flows. With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. Furthermore, when higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. species mass fractions or progress variable). In this paper, we propose a numerical method that mitigates this issue.

Detached Eddy Simulations of Flush Wall Injection Into a Supersonic Freestream

Three cases of flush wall injection of helium into supersonic freestreams are simulated using detached eddy simulation with a synthetic inflow boundary layer used to provide a time-varying boundary condition. The synthetic inflow boundary layer only resolves the largest structures of the boundary layer and provides statistically meaningful perturbations to the jet plume. Reynolds-averaged Navier-Stokes simulations of each case are used for comparison. Two of the cases involve low-angled injection into a Mach 4.0 freestream, one being a single, circular cross section injector and the other being an array of four circular cross section injectors. The injection in the third case takes place through a circular cross section that is normal to the Mach 3.0 freestream. For the two Mach 4.0 cases, the DES with the synthetic boundary layer is found to reproduce the width of the jet plume well, but overpredict the jet plume height. Mean helium mass fraction contours are compared with experiment at two downstream data planes for the normal injection. At both data stations the DES overpredicts the mean height of the core of the jet plume (location of maximum helium concentration), but captures the overall plume height better than RANS. The DES and RANS are found to predict significantly dierent