Tangent Slab Approximation Research Articles

Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models

Accurate prediction of the aerothermal environment is of great significance to space exploration and return missions. The canonical Fire II trajectory points are simulated to investigate the radiative transfer in the shock layer for Earth reentry at hypervelocity above 10 km/s using a developed radiation–flowfield uncoupling method. The thermochemical nonequilibrium flow is solved by an in-house PHAROS Navier–Stokes code, while the nongray radiation is integrated by the tangent slab approximation, respectively, combined with the two-, five-, and eight-step models. For the convective heating, the present results agree well with the data of Anderson’s relation. For the radiative heating, the two-step model predicts the closest values with the results of Tauber and Sutton’s relationship, while the five- and eight-step models predict far greater. The three-step models all present the same order of magnitude of radiative heating of 1 MW/m2 and show a consistent tendency with the engineering estimation. The Planck-mean absorption coefficient is calculated to show the radiative transfer significantly occurs in the shock layer. By performing the steady simulation at each flight trajectory point, the present algorithm using a nongray step model with moderate efficiency and reasonable accuracy is promising to solve the real-time problem in engineering for predicting both convective and radiative heating to the atmospheric reentry vehicle in the future.

Investigation of Galileo Probe Entry Heating with Coupled Radiation and Ablation

This paper presents a trajectory-based heating and ablation study of the Galileo probe forebody flow and thermal protection system performance. The validity of modeling assumptions regarding diffusion, radiative heating, and ablation made in previous work, including preflight predictions, are addressed. The Navier–Stokes equations are solved assuming a one-temperature chemical nonequilibrium flowfield with coupled radiation and ablation. Geometric changes in the forebody due to ablation are accounted for. Solving the Stefan–Maxwell equations to compute the species mass diffusion in the flowfield, instead of assuming a constant Schmidt number as was done in previous studies, was found to significantly increase total predicted recession by about 10% on the flank, due to increased convective heating. Application of the high-fidelity ray-tracing approach resulted in a 10% reduction in the radiative heating along the forebody when compared with the heritage tangent-slab approximation. Additional modeling approaches, such as state-specific H modeling, application of ray-tracing for coupled flowfield radiative source terms, and including precursor absorption were considered but found to have a minimal impact on recession. The resulting nominal prediction was found to be nearly within the uncertainty of the flight data along the entire surface of the probe. This improved agreement relative to past studies is due to the notable impact of shape change, multicomponent diffusion, and ray-tracing radiative heating, most of which were not included in previous models. To provide uncertainty bounds for the present simulations, an uncertainty analysis was performed. Sources of uncertainty were identified in the ablation modeling, radiation modeling, flowfield kinetics, turbulence modeling, and thermodynamic properties of select species. When the impact of all considered uncertainties are combined, the stagnation point recession varies between and of the nominal value while a near constant uncertainty band exists on the flank.

Radiative Heating on the After-Body of Martian Entry Vehicles

The radiative heat flux imparted on the after-body of vehicles entering the Martian atmosphere is simulated. The radiation is dominated by bands emitting in the midwave infrared. This mechanism traditionally has not been considered in the design of past Mars entry vehicles. However, with recent analysis showing that radiative heating can exceed convective heating on after-body surfaces, and with several upcoming and proposed missions to Mars potentially affected, an investigation of this radiation is warranted. This paper aims to quantify and improve understanding of the impact of radiation to aerothermal heating predictions for Mars entry. The tangent-slab approximation is shown to be overly conservative, by as much as 58%, for most of the backshell compared with using a full angular integration method. However, due to the complexity of the wake flow, it is also shown that tangent slab does not always represent an upper limit for radiative heating. Furthermore, analysis shows that it is not possible to provide a general correction factor to convert tangent-slab results to those obtained using the more rigorous full integration method. Radiative heating on the after-body often exceeds convective heating and therefore must be included in thermal protection system design for future missions.

Impact of Non-Tangent-Slab Radiative Transport on Flowfield–Radiation Coupling

For coupled flowfield–radiation simulations, required for Earth entry at velocities greater than , tangent-slab radiative transport is shown to sufficiently model the divergence of the radiative flux (this term couples the radiative energy to the flowfield energy equations). However, as shown in previous studies, the tangent-slab approximation does not sufficiently model the radiative flux reaching the surface (i.e., the radiative heating). These conclusions are reached through the development of a detailed ray-tracing approach capable of computing both the divergence of the radiative flux and the radiative heating. This approach is orders of magnitude more computationally expensive than the tangent-slab approximation. The ability of the tangent-slab approach to accurately model the divergence of the radiative flux, but not the radiative heating, is shown to be the result of a cancellation of errors during the angular integration. The current work shows that combining the tangent-slab approximation for the divergence of the radiative flux with the ray-tracing approach for the radiative heating (as a final step) provides sufficiently accurate results (radiative heating values within 1%), in an efficient manner, for coupled flowfield–radiation problems.

View-Factor Approach as a Radiation Model for the Reentry Flowfield

An accurate and efficient radiation transfer model, based on the view-factor approach, is proposed for the reentry flowfield. The radiation transfer equation is coupled to the gasdynamic system of equations in order to describe the energy transfer in the absorbing and emitting air plasma in two-dimensional axisymmetric and three-dimensional geometries. A newly derived semi-analytical expression for the radiative flux density dramatically simplifies the calculation of the spectral and integral characteristics of the radiation flowfield in the axisymmetric geometry. The comparison with the ray-tracing method and tangent slab approximation revealed an asymptotic accuracy of radiation flux density.

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 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.

Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.

Development of Coupled Particle Hypersonic Flowfield- Photon Monte Carlo Radiation Methods

DOI: 10.2514/1.44645 With its fast reentry speed, the Stardust vehicle generated a strong shock region ahead of its blunt body with a translational temperature in excess of 60,000 K. Such an extreme Mach number flow is sufficiently energetic to initiate gas ionization processes and thermal and chemical ablation processes. The generated charged species affect nonequilibrium atomic and molecular energy distributions and shock layer radiation. In this work, we present the first loosely coupled direct simulation Monte Carlosimulations with the particle-based photon Monte Carlo method to simulate high-Mach-number reentry flows in the near-continuum to transitional flow regimes. Eleven species including five ionization processes were modeled in direct simulation Monte Carlo, and the average ion velocity model was used to simulate the electron motion. The degree of ionization is predicted to be between 3–7% along the stagnation line for altitudes of 68.9 and 81 km, and the maximum translational and electron temperatures are approximately 60,000 and 20,000 K, respectively. To efficiently capture the nonequilibrium radiation generated by this flow, emission and absorption coefficient databases using the Nonequilibrium Air Radiation computational tool were generated. However, in contrast to the Nonequilibrium Air Radiation computational tool, radiative transport was modeled by the particle-based photon Monte Carlo method instead of the simplified one-dimensional tangentslab approximation. It was found that the atomic nitrogen emission is approximately 1 order of magnitude higher than the atomic oxygen emission along the stagnation line due to the higher concentration of atomic nitrogen at this altitude.Theradiationenergychangecalculatedbytheparticle-basedphotonMonteCarlomethodwascoupledwith the direct simulation Monte Carlo calculations, and it was found that although the atomic nitrogen and atomic oxygenatomicradiationdoesnothaveanimportantimpactonthe flowfieldat81km,thestrongerradiationmodified the flowfield and heat flux at the wall at an altitude close to peak heating.

Numerical Computation of Radiative Heating Environment for Huygens Probe Entry Flight

A trajectory-based analysis for obtaining aerodynamic heating environment for the Huygens probe is carried out using the thermochemical nonequilibrium computational fluid dynamics code. Radiative heat transfer is accounted for in computational fluid dynamics calculations where a modern multiband radiation model is employed. In this study, we first compare the radiative heat flux obtained by the ray-tracing approach in three-dimensional space with that given by the tangent-slab approximation, to determine how the difference in obtaining radiative heat flux can alter the overall aerodynamic heating environment. We then explore the radiative cooling effect on surface heat flux through radiation coupled computational fluid dynamics calculations. It is shown that the radiative heat flux value at the stagnation point obtained by the ray-tracing approach becomes about 17-19% smaller than that given by the tangent-slab approximation due to body curvature at all the chosen trajectory points. Furthermore, it is also shown that the radiative cooling effect can reduce the surface radiative heat flux by almost the same amount at the stagnation point when computational fluid dynamics calculation coupled with radiation is conducted. It is therefore confirmed that, even for the relatively lower radiative heating rate such as for the Huygens entry flight, we need to employ the ray-tracing approach instead of the tangent-slab approximation, and also need to account for radiative cooling effect through radiation coupled computational fluid dynamics calculation, to evaluate the surface heating condition accurately.

Heating Environments of a Venus Entry Capsule in a Trail Balloon Mission

A preliminary assessment of the heating environments during a hyperbolic entry to the planet Venus is conducted to investigate fundamental characteristics of flows in the shock layer and to predict the convective and radiative heat flux transferred to the entry capsule at the peak-heating point. Thermochemical nonequilibrium flows are calculated using two-dimensional Navier-Stokes equations in the axisymmetric geometry, taking into account oxidation and sublimation of the heatshield surface, and pyrolysis-gas injection. Radiative heat transfer coupled with the flow is computed by a line-by-line method with a tangent-slab approximation. Influences of uncertainties in the thermochemical models on the predicted heat flux are also examined.

Impact of Flowfield-Radiation Coupling on Aeroheating for Titan Aerocapture

A methodology is developed that enables fully coupled computation of three-dimensional flow fields including radiation, assuming an optically thin shock layer. The method can easily be incorporated into existing computational fluid dynamics codes and does not appreciably increase the cost or affect the robustness of the resulting simulations. Further improvements in the accuracy of radiative heating predictions in an optically thin gas can be achieved by using a view-factor method rather than the standard tangent slab approach. These techniques are applied to the Titan aerocapture aeroheating problem, which is dominated by strong radiative heating. For this application, neglecting the nonadiabatic effects caused by radiation coupling results in an overprediction of radiative heating levels by about a factor of 2. Radiative coupling effects also significantly lower predicted convective heating by reducing boundary-layer edge temperatures. In addition, it is shown that the tangent slab approximation overpredicts radiative heating levels by a minimum of 20% in the stagnation region for this application. Over an entire design trajectory, correctly modeling radiative heat transfer results in a more than a factor of 2 reduction in total stagnation-region heat load over an uncoupled analysis.

Stagnation-Point Heat Transfer Rates for Pioneer-Venus Probes

Summary The convective and radiative heat transfer rates are calculated for the stagnation region of the Pioneer- Venus Probe vehicles during their entry flights into the planet Venus. The nonequilibrium thermochemical state of the flow is calculated using a viscous shock layer method accounting for oxidation of heatshield surface by atomic oxygen and for pyrolysis-gas injection. Radiative transport along the stagnation streamline is calculated using a lineby-line technique and tangent-slab approximation. For both radiative and convective heating rates, the present results are substantially smaller than the earlier values obtained assuming equilibrium.

Effects of non-grey self-absorption and energy loss for blunt body flows

The effects of non-grey self-absorption and energy loss for blunt-body flows during superorbital reentry are considered. The air spectral absorption coefficients are represented approximately by a two-band (level) model and a six-band model. A tangent-slab approximation is used for radiation transport calculations. The solutions of the inviscid flow field for the stagnation and nonstagnation regions are formulated separately. A similarity solution is obtained for the stagnation region and a streamtube method is used for the nonstagnation region. Results obtained for typical superorbital reentry environmental conditions indicate that both non-grey self-absorption and energy loss have very significant effects on the flow field and wall heat fluxes.