Alireza Mazaheri

Study of Ablation-Flowfield Coupling Relevant to the Orion Heatshield

The coupled interaction between an ablating surface and the surrounding aerothermal environment is studied. An equilibrium ablation model is coupled to the LAURA flowfield solver, which allows the char ablation rate ṁ c to be computed as part of the flowfield solution. The wall temperature T w and pyrolysis ablation rate ṁ g may be specified by the user, obtained from the steady-state ablation approximation, or computed from a material response code. A 32-species thermochemical nonequilibrium flowfield model is applied, which permits the treatment of C, H, O, N, and Si-containing species. Coupled ablation cases relevant to NASAs Orion multipurpose crew vehicle heat shield are studied. These consist of diffusion-limited oxidation cases with Avcoat as the ablation material. The ṁ g values predicted from the developed coupled ablation analysis were compared with those obtained from a typical uncoupled ablation analysis. The coupled results were found to be as much as 50% greater than the uncoupled values in regions of turbulence. This is shown to be a result of the cumulative effect of the two fundamental approximations inherent in the uncoupled analysis.

Radiative Heating Uncertainty for Hyperbolic Earth Entry, Part 1: Flight Simulation Modeling and Uncertainty

This paper investigates the shock-layer radiative heating uncertainty for hyperbolic Earth entry, with the main focus being a Mars return. A baseline simulation approach involving the LAURA Navier–Stokes code with coupled ablation and radiation is presented, with the HARA radiation code being used for the radiation predictions. Flight cases representative of peak heatingMars or asteroid return are defined, and the strong influence of coupled ablation and radiation on their aerothermodynamic environments are shown. Structural uncertainties inherent in the baseline simulations are identified,with turbulencemodeling, precursor absorption, grid convergence, and radiation transport uncertainties combining for a 34 and 24% structural uncertainty on the radiative heating. A parametric uncertainty analysis, which assumes interval uncertainties, is presented. This analysis accounts for uncertainties in the radiation models, as well as heat of formation uncertainties in the flowfield model. Discussions and references are provided to support the uncertainty range chosen for each parameter. A parametric uncertainty of 47 and 28% is computed for the stagnation-point radiative heating for the 15 km=s Mars-return case. A breakdown of the largest individual uncertainty contributors is presented, which includes C3 Swings cross section, photoionization edge shift, and Opacity Project atomic lines. Combining the structural and parametric uncertainty components results in a total uncertainty of 81 and 52% for the Mars-return case.

Assessment of Radiative Heating Uncertainty for Hyperbolic Earth Entry

This paper investigates the shock-layer radiative heating uncertainty for hyperbolic Earth entry, with the main focus being a Mars return. In Part I of this work, a baseline simulation approach involving the LAURA Navier-Stokes code with coupled ablation and radiation is presented, with the HARA radiation code being used for the radiation predictions. Flight cases representative of peak-heating Mars or asteroid return are de ned and the strong influence of coupled ablation and radiation on their aerothermodynamic environments are shown. Structural uncertainties inherent in the baseline simulations are identified, with turbulence modeling, precursor absorption, grid convergence, and radiation transport uncertainties combining for a +34% and ..24% structural uncertainty on the radiative heating. A parametric uncertainty analysis, which assumes interval uncertainties, is presented. This analysis accounts for uncertainties in the radiation models as well as heat of formation uncertainties in the flow field model. Discussions and references are provided to support the uncertainty range chosen for each parameter. A parametric uncertainty of +47.3% and -28.3% is computed for the stagnation-point radiative heating for the 15 km/s Mars-return case. A breakdown of the largest individual uncertainty contributors is presented, which includes C3 Swings cross-section, photoionization edge shift, and Opacity Project atomic lines. Combining the structural and parametric uncertainty components results in a total uncertainty of +81.3% and ..52.3% for the Mars-return case. In Part II, the computational technique and uncertainty analysis presented in Part I are applied to 1960s era shock-tube and constricted-arc experimental cases. It is shown that experiments contain shock layer temperatures and radiative ux values relevant to the Mars-return cases of present interest. Comparisons between the predictions and measurements, accounting for the uncertainty in both, are made for a range of experiments. A measure of comparison quality is de ned, which consists of the percent overlap of the predicted uncertainty bar with the corresponding measurement uncertainty bar. For nearly all cases, this percent overlap is greater than zero, and for most of the higher temperature cases (T >13,000 K) it is greater than 50%. These favorable comparisons provide evidence that the baseline computational technique and uncertainty analysis presented in Part I are adequate for Mars-return simulations. In Part III, the computational technique and uncertainty analysis presented in Part I are applied to EAST shock-tube cases. These experimental cases contain wavelength dependent intensity measurements in a wavelength range that covers 60% of the radiative intensity for the 11 km/s, 5 m radius flight case studied in Part I. Comparisons between the predictions and EAST measurements are made for a range of experiments. The uncertainty analysis presented in Part I is applied to each prediction, and comparisons are made using the metrics defined in Part II. The agreement between predictions and measurements is excellent for velocities greater than 10.5 km/s. Both the wavelength dependent and wavelength integrated intensities agree within 30% for nearly all cases considered. This agreement provides confidence in the computational technique and uncertainty analysis presented in Part I, and provides further evidence that this approach is adequate for Mars-return simulations. Part IV of this paper reviews existing experimental data that include the influence of massive ablation on radiative heating. It is concluded that this existing data is not sufficient for the present uncertainty analysis. Experiments to capture the influence of massive ablation on radiation are suggested as future work, along with further studies of the radiative precursor and improvements in the radiation properties of ablation products.

Three-Dimensional Radiation Ray-Tracing for Shock-Layer Radiative Heating Simulations

A three-dimensional ray-tracing algorithm is developed for shock-layer radiative heating predictions. When coupled with a tangent slab approximate code, such as the HARA radiation code, this algorithm provides an efficient approach for computing the radiative heating and allows the commonly applied tangent slab approximation to be removed. Application to several Earth- and Mars-entry conditions show that the ray-tracing approach predicts up to 15% lower radiative heating values than the tangent slab approximation at the stagnation point, which is consistent with the results of previous studies. In the afterbody region of Mars entry vehicles, where radiative heating from the CO2 molecule may be larger than convective heating, a 70% reduction from the tangent-slab result is seen, indicating the inadequacy of the tangent slab approximation in such regions.

Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids

In this paper, we construct second- and third-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the accuracy of the second-order hyperbolic schemes in J. Comput. Phys. 227 (2007) 315-352 and J. Comput. Phys. 229 (2010) 3989-4016 can be greatly improved by requiring the scheme to preserve exact quadratic solutions. The improved second-order scheme can be easily extended to a third-order scheme by further requiring the exactness for cubic solutions. These schemes are constructed based on the SUPG methodology formulated in the framework of the residual-distribution method, and thus can be considered as economical and powerful alternatives to high-order finite-element methods. For both second- and third-order schemes, we construct a fully implicit solver by the exact residual Jacobian of the proposed second-order scheme, and demonstrate rapid convergence, typically with no more than 10-15 Newton iterations (and about 200-800 linear relaxations per Newton iteration), to reduce the residuals by ten orders of magnitude. We also demonstrate that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids even for a curved boundary problem, without introducing curved elements. A quadratic reconstruction of the curved boundary normals and a high-order integration technique on curved boundaries are also provided in details.

A Study of Ablation-Flowfield Coupling Relevant to Orion Heatshield

The coupled interaction between an ablating surface and the surrounding aerothermal environment is studied. An equilibrium ablation model is coupled to the LAURA flowfield solver, which allows the char ablation rate (ṁc) to be computed as part of the flowfield solution. The wall temperature (Tw) and pyrolysis ablation rate (ṁg) may be specified by the user, obtained from the steady-state ablation approximation, or computed from a a material response code. A 32 species thermochemical nonequilibrium flowfield model is applied, which permits the treatment of C, H, O, N, and Si containing species. Coupled ablation cases relevant to the Orion heatshield are studied. These consist of diffusionlimited oxidation cases with Avcoat as the ablation material. The ṁc values predicted from the developed coupled ablation analysis were compared with those obtained from a typical uncoupled ablation analysis. The coupled results were found to be as much as 50% greater than the uncoupled values. This is shown to be a result of the cumulative effect of the two fundamental approximations inherent in the uncoupled analysis.

A first-order hyperbolic system approach for dispersion

We propose a new first-order hyperbolic system approach for dispersive partial differential equations.We apply a compact 4th-order RD scheme, and solve time dependent dispersive PDEs.We demonstrate the performance of the high-order RD schemes on the proposed hyperbolic system, including dispersive shock cases.We verify that the predicted solution, its gradient and Hessian have the same order of accuracy on randomly distributed nodes.

Heating Augmentation for Short Hypersonic Protuberances

Computational aeroheating analyses of the Space Shuttle Orbiter plug repair models are validated against data collected in the Calspan University of Buffalo Research Center (CUBRC) 48 inch shock tunnel. The comparison shows that the average difference between computed heat transfer results and the data is about 9.5%. Using CFD and Wind Tunnel (WT) data, an empirical correlation for estimating heating augmentation on short hypersonic protuberances (k/delta less than 0.3) is proposed. This proposed correlation is compared with several computed flight simulation cases and good agreement is achieved. Accordingly, this correlation is proposed for further investigation on other short hypersonic protuberances for estimating heating augmentation.

Efficient high-order discontinuous Galerkin schemes with first-order hyperbolic advection-diffusion system approach

We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time. We propose an efficient high-order discontinuous-Galerkin (DG) schemes with the first-order hyperbolic advection-diffusion formulation.The proposed DG-H schemes have the same DoF as classical DG schemes for the same accuracy without a second-order diffusion operator.DG-H ( P k ) is (k + 2)-order accurate for solution and (k + 1)-order accurate for gradients on irregular elements for advection problems.DG-H ( P k ) gives (k + 1)-order accurate for both solution and gradients on irregular elements for general advection-diffusion problems.The DG-H schemes are nearly as efficient as DG and IP schemes with relatively the same error for nearly similar CPU time.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

Abstract : In this paper, we construct high-order hyperbolic residual-distribution schemes for gen- eral advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second- order scheme can be easily extended to the third-order by further requiring the exact- ness for cubic solutions. We construct these schemes based on the Low-Diffusion-A and the Streamwise-Upwind-Petrov-Galerkin methodology formulated in the framework of the residual-distribution method. For both second- and third-orderschemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10 15 iterations to reduce the residuals by 10 orders of magnitude. We also demonstrate that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the con- struction of hyperbolic residual-distribution schemes for the compressible Navier- Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis per- formed on the constructed linear system and show that an underrelaxation parameter is needed for stabilization of Gauss-Seidel relaxation.