Direct simulation of hypersonic flows over blunt wedges
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Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitude only, whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire II vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura, who used gray-gas radiation model and thin-layer Navier-Stokes equations. Quite good agreement is obtained between the measured and computed values of radiative and convective heating from the VSL code in th medium-to-low altitude flight regime of the Fire II vehicle. At high altitudes, the Navier-Stokes calculations considerably overpredict the Fire II flight data for radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equilibrium assumption and precludes accounting for the collision-limiting phenomenon at high altitudes. Present Navier-Stokes calculations highlight the effect of these assumptions on radiative heating calculations for such conditions.
Detailed measurements of heat transfer and pressure distribution have been made in the present study of the aerothermal characteristics of regions of two-dimensional shock/shock interaction generated by the incidence of single and multiple shocks onto the bow shock ahead of a spanwise cylinder. For transitional flows, the measurements demonstrated a large increase in the aerothermal loads with increasing Mach number that cannot be predicted by simple phenomenological models. The studies with multiple incident shocks demonstrate that the largest aerothermal loads are generated on the cylinder when the shocks coalesce before they are incident on the bow shock.
Laminar nonequilibrium heat transfer to slender vehicles is discussed, with heating-rate results presented as a ratio of the noncatalytic to the corresponding fully catalytic value to illustrate the maximum potential for a heating reduction in dissociated nonequilibrium flow at a given flight condition. Larger blunted cone half-angles are shown to produce the most significant nonequilibrium effects at distances beyond 100 nose radii, except in the fore-cone region. Increasing nose bluntness is found to produce large reductions in the ratio for the smaller cone angles at relatively large downstream surface lengths. It is noted that the nose radius and freestream density are not independent scaling parameters in nonequilibrium flow.
Solutions of wind-tunnel and entry-flight flow around the vehicle are obtained from the Navier-Stokes equations coupled with the chemical species continuity equations if needed. The time-iterative method employs several techniques: shock fitting, chemistry-split ADI and an algebraic grid in conformal spherical-polar space. Sensitivities of the results to numerical parameters and to frozen, equilibrium and finite rate reactions are investigated in the forebody computation. Quantitative results are obtained for the shock layer and the near wake for the entire vehicle corresponding to both ground test and flight conditions. Complex flow characteristics are analyzed on the basis of the complete flowfield over the aerobrake and simplified afterbodies. The method is stable and cost effective, and has yielded shock locations and wall pressure distributions which are in good agreement with wind-tunnel data.
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Several models using different descriptions of high temperature air are used to compute the bow shock shapes on experimental model configurations. The test conditions result in nonequilibrium chemical reaction and thermal excitation of the gas which has a first-order effect on the shock shapes. The computed results are compared to experiment and demonstrate that the model using seven chemical species and six temperatures predicts the experimental shock shapes very well. The other gas models, including perfect gas, equilibrium gas and one-temperature chemical nonequilibrium models are less accurate. The results illustrate the necessity of including both thermal and chemical nonequilibrium in the description of the gas. The use of these experimental data makes it possible to verify aspects of current and future chemically reacting flow algorithms.
Results are obtained for the surface pressure, drag, heat-transfer, and skin-friction coefficients for hyperboloids and sphere cones. Body half angles from 5 to 22.5 degrees are considered for various low-density flow conditions. Recently obtained surface-slip and shock-slip equations are employed to account for the low-density effects. The method of solution employed for the viscous shock-layer (VSL) equations is a partially coupled spatial-marching implicit finite-difference technique. The flow cases analyzed include highly cooled long slender bodies in high Mach number flows. The present perfect-gas VSL calculations compare quite well with available experimental data. Results have also been obtained from the steady-state Navier-Stokes (NS) equations by successive approximations. Comparison between the NS and VSL results indicates that VSL equations even with body and shock-slip boundary conditions may not be adequate in the stagnation region at altitudes greater than about 75 km for the cases analyzed here.
In this paper, the extension of a multispecies TVD algorithm, second-order accurate for real-gas flows to a multitemperature formulation is described. The convection algorithm is coupled to internal relaxation processes, and the features of the coupling are examined. The first version consists of a three-temperature model, where translational-rotational, vibrational, and electronic energy modes are separately convected. Although several species are present, there is only one vibrational temperature in this model. The second version generalizes to a vibrational temperature for each molecular specie, with additional couplings between species. The algorithms are applied to a generic two-dimensional flow field, and results are compared with experimental observations.
Calculations using the direct simulation Monte Carlo (DSMC) method of Bird for flow past sharp cones in the near continuum to free molecule flow regime are presented and compared with experiment. It is found that results are sensitive to the grid and the interaction potential. Moreover, the time counter method was found to be as accurate as other methods when the solution is grid independent. Finally, the results show that the effects of the wake on the forebody surface properties are minimal.
A new simple and computationally efficient model was developed, describing the evolution of vibrational states during relaxation and dissociation. The model is based on dividing the nitrogen molecules into two types, those in the vibrational states at a lower level, whose vibrational energy is below a cutoff energy, and those in an upper level, with vibrational energy above the cutoff. Dissociation occurs at the upper level, and recombination returns molecules to the lower level. The model was applied to two flows of engineering interest, the flow through a normal Mach 15 shock wave at 60 km, and a supersonic quasi-one-dimensional flow in a nozzle. Results are compared to those obtained by existing translation-vibration-dissociation coupling models, with results indicating significant differences between the models.
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The optimum shape of a blunt forebody attached to a symmetric wedge or cone is determined. The length of the forebody, its semi-thickness or base radius, the nose radius and the radius of the fillet joining the forebody to the wedge or cone are specified. The optimum shape is composed of simple curves. Thus experimental models can be built readily to investigate the utilization of aerodynamic heating for boundary layer control. The optimum shape based on the modified Newtonian theory can also serve as the preliminary shape for the numerical solution of the optimum shape using the governing equations for a compressible inviscid or viscous flow.
Future space vehicles returning from distant missions or high earth orbits may enter the upper regions of the atmosphere and use aerodynamic drag to reduce their velocity before they skip out of the atmosphere and enter low earth orbit. The Aeroassist Flight Experiment (AFE) is designed to explore the special problems encountered in such entries. A computer code was developed to calculate the radiative transport along line-or-sight in the general 3-D flow field about an arbitrary entry vehicle, if the temperatures and species concentrations along the line-of-sight are known. The radiative heating calculation at the stagnation point of the AFE vehicle along the entry trajectory was performed, including a detailed line-by-line accounting of the radiative transport in the vacuum ultraviolet (below 200 nm) by the atomic N and O lines. A method was developed for making measurements of the haze particles in the Titan atmosphere above 200 km altitude. Several other tasks of a continuing nature, to improve the technical ability to calculate the nonequilibrium gas dynamic flow field and radiative heating of entry vehicles, were completed or advanced.
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A hybrid numerical technique, based on local application of continuum and particle methods, is applied to the one-dimensional normal shock structure in a monatomic gas. The methods are coupled iteratively via a flux boundary condition in a region where both are applicable. The validity of each method through the shock structure is quantified. The physical and numerical aspects of coupling are discussed and a variety of coupling methods are assessed. Results are presented to show the improvement in computational efficiency available via the hybrid approach.
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