A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

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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 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 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 flowfield 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 flux 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 defined, which consists of the percent overlap of the predicted uncertainty bar with the corresponding measurement uncertainty bar.

Radiative equilibrium surface temperatures and surface heating rates from a combined inviscid-boundary layer method are presented for the X-34 Reusable Launch V ehicle for several points along the hypersonic descent portion of its trajectory. I n viscid, perfect-gas solutions are generated with the Langley Aerothermodynamic Upwind Relaxation Algorithm LAURA and the Data-Parallel Lower-Upper Relaxation DPLUR code. Surface temperatures and heating rates are then computed using the Langley Approximate Three-Dimensional Convective Heating LATCH engineering code employing both laminar and turbulent ow models. The combined inviscid-boundary layer method provides accurate predictions of surface temperatures over most of the vehicle and requires much less computational e ort than a Navier-Stokes code. This enables the generation of a more thorough aerothermal database which is necessary to design the thermal protection system and specify the vehicle's ight limits. Research Engineer, Aerothermodynamics Branch, Aeroand Gas-Dynamics Division. Senior Member AIAA.