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A very efficient direct particle simulation algorithm for hypersonic rarefied flows is presented and its implementation on a Connection Machine is described. The implementation simulates ideal diatomic Maxwell molecules with three translational and two rotational degrees of freedom. Results for a 2-D simulation of supersonic flow over a 30 deg wedge are presented and used for validation.
A hybrid numerical technique previously developed for one-dimensional rarefied gas flows is generalized to two dimensions. The method is based on the fact that the flowfield that develops near a body in a rarefied gas typically contains local regions of continuum, transitional and free-molecular flow. By utilizing the solution technique most appropriate for each region and coupling the techniques in an interface region where both are applicable, more computationally efficient solutions can be obtained, or equivalently, more complex flowfields can be analyzed. The present method combines finite difference solution of the Navier-Stokes equations in the continuum regions, with Direct Simulation Monte Carlo in the more rarefied regions. The two schemes are coupled interactively via a general conservative flux boundary condition. The method is tested by application to the model problem of pressure-driven rarefied flow through a slit. Results show the hybrid scheme offers a speedup of a factor of nearly two for the nominal conditions considered, due to the decrease in the size of the Direct Simulation domain.
The Direct Simulatiaon Monte Carlo method is used to study the hypersonic, rarefied flow interference effects on a flat plate caused by nearby surfaces. Calculations focus on shock-boundary-layer and shock-lip interactions in hypersonic inlets. Results are presented for geometries consisting of a flat plate with different leading-edge shapes over a flat lower wall and a blunt-edge flat plate over a 5-degree wedge. The problems simulated correspond to a typical entry flight condition of 7.5 km/s at altitudes of 75 to 90 km. The results show increases in predicted local heating rates for shock-boundary-layer and shock-lip interactions that are quantitatively similar to those observed experimentally at much higher densities.
Three-dimensional simulations of hypersonic rarefied flow about a delta wing are made using the direct simulation Monte Carlo (DSMC) method of Bird, and the results of the computations are compared with recent experimental data obtained in a vacuum wind tunnel at the DLR in Gottingen, Germany. The present study considers Mach 8.89 nitrogen flow for a range of conditions that include Knudsen numbers of 0.016 to 3.505 for an incidence angle of 30 deg, and angles of incidence of 15 to 60 deg for a constant Knudsen number of 0.389. The calculations provide details concerning the flowfield structure and surface quantities. Comparisons between the calculations and the available experimental measurements are made for aerodynamic and overall heat-transfer coefficients and recovery temperature. The agreement between the measured and calculated data are very good, well within the estimated measurement uncertainty. Comparisons are also made with modified Newtonian and free-molecule theories.
The data parallel implementation of a particle simulation for hypersonic rarefied flow described by Dagum associates a single parallel data element with each particle in the simulation. The simulated space is divided into discrete regions called cells containing a variable and constantly changing number of particles. The implementation requires a global sort of the parallel data elements so as to arrange them in an order that allows immediate access to the information associated with cells in the simulation. Described here is a very fast algorithm for performing the necessary ranking of the parallel data elements. The performance of the new algorithm is compared with that of the microcoded instruction for ranking on the Connection Machine.
Results of a numerical study using the direct simulation Monte Carlo method are presented for hypersonic rarefied flow past spheres. The flow conditions considered are those corresponding to low density wind tunnel test conditions. The set of the experimental conditions for the calculations encompasses the transitional to near-continuum flow regimes. Comparison of the calculated drag with experimental results shows good agreement to well within the experimental error. Particular attention is focused on the wake structure. Calculations show that the wake is very rarefied with considerable thermal nonequilibrium for all the cases considered. No flow separation is observed in the wake for the near-continuum case where a vortex has been predicted by Navier-Stokes type calculations.
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for hypersonic rarefied flow about a 1.6-m-diameter sphere. The flow conditions considered are those experienced by a typical satellite in orbit or by a space vehicle during entry. The altitude range considered is that from 90 to 200 km, which encompasses the near continuum, transitional and free-molecular flow regimes. A freestream velocity of 7.5 km/s is assumed in the simulations. The results show that transitional effects are significant at all altitudes below 200 km, but at 200 km the flow about the sphere attains the free-molecular limit. Very little chemical activity is present above 120 km. Both the stagnation point heat transfer and the sphere drag approach their respective free molecule values at 200 km. Results highlight the thermal and chemical nonequilibrium nature of the flowfield. Nonequilibrium effects on the surface heating and body drag are also investigated.
A summary of three-dimensional simulations on the hypersonic rarefied flows in an effort to understand the highly nonequilibrium flows about space vehicles entering the Earth's atmosphere for a realistic estimation of the aerothermal loads is presented. Calculations are performed using the direct simulation Monte Carlo method with a five-species reacting gas model, which accounts for rotational and vibrational internal energies. Results are obtained for the external flows about various bodies in the transitional flow regime. For the cases considered, convective heating, flowfield structure and overall aerodynamic coefficients are presented and comparisons are made with the available experimental data. The agreement between the calculated and measured results are very good.
An overview of the process for obtaining the Shuttle Orbiter rarefied-flow pitching moment from flight gyro data is presented. The extraction technique involves differentiation of the output of the pitch gyro after accounting for nonaerodynamic torques, such as those produced by gravity gradient and the Orbiter's auxiliary power unit and adjusting for drift biases. The overview of the extraction technique includes examples of results from each of the steps involved in the process, using the STS-32 mission as a typical sample case. The total pitching moment and moment coefficient (Cm) for that flight are calculated and compared with preflight predictions. The flight results show the anticipated decrease in Cm with increasing altitude. However, the total moment coefficient is less than predicted using preflight estimates.
Rarefied hypersonic flow model for sharp flat plate in strong interaction regimes, discussing inviscid and viscous shock and merged layers subregimes
This report presents a discussion of the analysis and the results of sensitive micro-g accelerometry measurements on the Shuttle Orbiter in the rarefied flow flight regime, that is, from altitudes of 60 km to 160 km. A brief description of the experimental apparatus called High Resolution Accelerometer Package (HiRAP) is given along with a description of the ground processing to obtain the lift-to-drag ratio (L/D) from the flight measurements. The flight results of L/D from six missions are presented and discussed. Comparisons are made with preflight wind tunnel data in the near continuum viscous interaction regime and preflight analytical estimates in the rarefied transition regime. Excellent agreement is obtained between flight and wind tunnel data in the viscous regime, but differences are noted between flight and preflight predictions in the transition regime. Free molecule flow F/D data are also obtained on each mission. Comparisons of flight data with classical theory show that complete diffuse reflection is not an appropriate model for rarefied aerodynamic coefficient calculations, and, for the Shuttle, some specular fraction is required. Surface reflection laws are explored to define the sensitivity of the L/D measurements to gas-surface molecule interactions.
This paper describes a method for doing direct simulation Monte Carlo (DSMC) calculations using parallel processing and presents some results of applying the method to several hypersonic, rarefied flow problems. The performance and efficiency of the parallel method are discussed. The applications described are the flow in a channel and the flow about a flat plate at incidence. The results show significant advantages of parallel processing over conventional scalar processing and demonstrate the scalability of the method to large problems.
Jet plume impingement forces acting on large flexible space structures may precipitate dynamically unstable behavior during space flights. Typical operating conditions in space involve rarefied gas flow regimes which are intrinsically distinct from continuum gas flow and are normally modeled using the kinetic theory of gas flow. Docking and undocking operations of the Space Shuttle with the Russian Mir space laboratory represent a scenario in which the stability boundaries of solar panels may be of interest. Extensive literature review of research work on the dynamic stability of rectangular panels in rarefied gas flow conditions indicated the lack of published reports dealing with this phenomenon. A recently completed preliminary study for NASA JSC dealing with the mathematical analysis of the stability of two-degree-of-freedom elastically supported rigid panels under the effect of rarefied gas flow was reviewed. A test plan outline is prepared for the purpose of conducting a series of experiments on four rectangular rigid test articles in a vacuum chamber under the effect of continuous and pulsating Nitrogen jet plumes. The purpose of the test plan is to gather enough data related to a number of key parameters to allow the validation of the two-degree-of-freedom mathematical model. The hardware required careful design to select a very lightweight material while satisfying rigidity and frequency requirements within the constraints of the test environment. The data to be obtained from the vacuum chamber tests can be compared with the predicted behavior of the theoretical two-degree-of-freedom model. Using the data obtained in this study, further research can identify the limitations of the mathematical model. In addition modifications to the mathematical model can be made, if warranted, to accurately predict the behavior of rigid panels under rarefied gas flow regimes.
A computational method is given for the prediction of local pressure and viscous shear stress on windward surfaces of bluff, convex, axisymmetric or quasi-axisymmetric, hypersonic bodies in the transitional, rarefied flow regime. Overall aerodynamic forces and moments are computed by integration of the local quantities. The method is based upon a correlation of local pressure and shear stress computed by the direct simulation Monte Carlo (DSMC) numerical technique for cold wall, real gas conditions and some supplemental data from low-density, hypersonic wind tunnels. The relative simplicity of the method makes it feasible to do the necessary calculations with a personal computer. Two-dimensional shapes and leeward surfaces are not included in the scope of the method as it is presented here. Results are compared with DSMC computations for both local and overall coefficients. The latter includes sphere and blunt cone drag as well as lift and pitching moment coefficients for the NASA AFE vehicle at various angles of attack. Very satisfactory agreement is shown.
Data obtained from multiple flights of sensitive accelerometers on the Space Shuttle Orbiter during reentry have been used to develop an improved aerodynamic model for the Orbiter normal- and axial-force coefficients in hypersonic rarefied flow. The lack of simultaneous atmospheric density measurements was overcome in part by using the ratio of normal-to-axial acceleration, in which density cancels, as a constraint. Differences between the preflight model and the flight-acceleration-derived model in the continuum regime are attributed primarily to real gas effects. New insights are gained into the variation of the force coefficients in the transition between the continuum regime and free molecule flow.
Rarefied gas dynamics - drag coefficient of circular cylinder - characterization of fluid momentum exchange
Rarefied gas dynamics - electron beam density, temperature probe and examination of electro- luminescence spectra
Rarefied gas dynamics, continuum mechanics, and molecular mechanics