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Comparison Between DSMC and CFD for Hypersonic Planetary Entry Simulations

Hypersonic planetary entry flows span a wide range of Knudsen numbers between rarefied and continuum flows. While computational fluid dynamics (CFD) techniques cannot provide an accurate solution for flows in the rarefied regime, the direct simulation Monte Carlo (DSMC) method is capable of providing accurate solutions for flows in both in the rarefied and continuum regimes but becomes prohibitively expensive as the Knudsen number decreases. For the purpose of thermal protection systems (TPS) design and post-flight reconstruction, various selected points along an entry trajectory are often solved using hypersonic solvers. The quantities of interest that are obtained from that exercise are generally surface quantities, such as pressure, heat flux and enthalpy. Then, material response solvers are used to either design the heat shield to an optimal thickness based on a choice of material, or to provide in-depth heating profiles through the material at various select locations, and compare with flight instrumentation such as the ones that flew on NASA’s two most recent Mars missions, MSL and Mars2020. While most of the heating is generally experienced during the continuum part of the entry, the heating within the rarefied regime is significant for some atmospheres, and hence the flow solutions need to be computed using the DSMC method. Ensuring consistency between hypersonic CFD and the DSMC is crucial so that reliable surface quantities can be passed to material response solvers. Studies were performed to compare the two methods at various select locations, for both non-reacting argon flows as well reacting CO2/N2 flows. Preliminary conclusions show that, for non-reacting flows, the agreement between the two methods for surface heating is excellent (within expected uncertainties) for a freestream Knudsen number of 0.0006, and gets progressively worse as the Knudsen number increases to 0.06. Continuum breakdown analyses were performed and showed that, in general, the Gradient Length Local Knudsen number (KnGLL) from Boyd [1] and associated criteria (KnGLL > 0.05) can be accurately used to predict zones of breakdown in the flow, and associated errors for surface quantities. Furthermore, when studying reacting flow, our studies showed that while flow quantities are highly dependent on relaxation parameters and chemistry rates, it is possible to obtain a good agreement for surface heating, as long as the continuum breakdown in minimal (see Fig. 1). Finally, we studied the impact of the grid refinement on the surface quantities in DSMC.

DSMC↗

Comparison Between DSMC and CFD for Hypersonic Planetary Entry Simulations

Hypersonic planetary entry flows span a wide range of Knudsen numbers between rarefied and continuum flows. While computational fluid dynamics (CFD) techniques cannot provide an accurate solution for flows in the rarefied regime, the direct simulation Monte Carlo (DSMC) method is capable of providing accurate solutions for flows in both in the rarefied and continuum regimes but becomes prohibitively expensive as the Knudsen number decreases. For the purpose of thermal protection systems (TPS) design and post-flight reconstruction, various selected points along an entry trajectory are often solved using hypersonic solvers. The quantities of interest that are obtained from that exercise are generally surface quantities, such as pressure, heat flux and enthalpy. Then, material response solvers are used to either design the heat shield to an optimal thickness based on a choice of material, or to provide in-depth heating profiles through the material at various select locations, and compare with flight instrumentation such as the ones that flew on NASA’s two most recent Mars missions, MSL and Mars2020. While most of the heating is generally experienced during the continuum part of the entry, the heating within the rarefied regime is significant for some atmospheres, and hence the flow solutions need to be computed using the DSMC method. Ensuring consistency between hypersonic CFD and the DSMC is crucial so that reliable surface quantities can be passed to material response solvers. Studies were performed to compare the two methods at various select locations, for both non-reacting argon flows as well reacting CO2/N2 flows. Preliminary conclusions show that, for non-reacting flows, the agreement between the two methods for surface heating is excellent (within expected uncertainties) for a freestream Knudsen number of 0.0006, and gets progressively worse as the Knudsen number increases to 0.06. Continuum breakdown analyses were performed and showed that, in general, the Gradient Length Local Knudsen number (KnGLL) from Boyd and associated criterion (KnGLL > 0.05) seems conservative in predicting zones of breakdown in the flow, and associated errors for surface quantities. Updated criteria of KnGLL = 2.0 and 0.5 appear to be more appropriate for surface and flow quantities, respectively. Furthermore, when studying reacting flows, our studies showed that while flow quantities are highly dependent on relaxation parameters and chemistry rates, it is possible to obtain a good agreement for surface heating, as long as the continuum breakdown is minimal.

DSMC↗

HYPERSONIC AERODYNAMIC PROBLEMS OF THE FUTURE

Blunt shapes were of interest for the speed regime of ballistic missiles and satellite vehicles, in the main, as a result of the necessity for minimizing convective heating. But as speeds exceed escape speed, the heating due to air radiation assumes an even more important role than does the convective heating. It is shown that this change revives interest in the more slender configurations and that when the speed of a vehicle entering the atmosphere of a planet becomes sufficiently great, it may be economical to decelerate in part by retrorocket rather than entirely by aerodynamic braking. The factors discussed determine the speed limit for which retrorocket braking becomes desirable. The change in the basic characteristics of flow brought about by gas radiation at speeds well in excess of escape speed are then analyzed. It is shown that when the gas radiation energy becomes a significant part of the total energy of the flow, it is no longer possible to analyze aerodynamic flow fields with the assumption that the energy of elemental volumes remains constant, since for such cases a transfer of energy by radiation from one elemental volume to another significantly alters the flow. The increase in complexity in the analytical approaches to the problems of these hypersonic flows necessitates, more than ever, continued experimental research, even though such experiments are exceedingly difficult to perform. Extension of our experimental knowledge of these hypersonic flows is shown to be possible by study of tracked trajectories of bright meteors. Some analyses of meteor tracking data are presented which demonstrate that the tracking camera systems employed at present can provide sufficiently accurate results to yield useful aerodynamic heating information.

SATELLITE↗

Performance trade-offs and research problems for hypersonic transports

The purpose of this paper is to examine the mission capability of hydrogen-fueled hypersonic transports and to discuss some of the major technical approaches that may be used with such vehicles . It is the intention of this paper to indicate only the technical feasibility and capabilities of hypersonic transports. The equally important problems involving economic feasibility and operational problems have not been considered, since the study of these problems is thought to be premature until technical feasibility has been established.

Hypersonic aircraft↗

Hypersonic flight simulation- aerodynamics

In this lecture an attempt is made to partially assess the current status and direction of laboratory simulation of the aerodynamics of full-scale, hypersonic flight. Problems of simulation related to establishing satisfactory flow fields and the determination of the basic aerodynamic quantities consisting of pressures, forces, and moments, on scale models in these laboratory environments are discussed. In addition, some questions arising in extending scale-model data to full-scale are noted. Other important hypersonic simulation problems are the subjects of later lecturers.

Flight Simulation↗

Vi. Hypersonic Cruise Vehicles

Interest has been recently expressed in the military use of hypersonic cruise vehicles as bombers, transports, reconnaissance aircraft, and perhaps recoverable boosters. The purpose of this paper is to give a very brief summary of the state of the art in aerodynamics, aerodynamic heating, propulsion, and to indicate the performance possibilities of such an aircraft based on this state of the art. A great deal of research applicable over broad regions of the hypersonic speed range is in progress (refs. 1 and 2, for example) but for the present purpose, discussion will be confined to cruising vehicles which are boosted to cruise speed and altitude. For this purpose a Mach number of 6 has been chosen as the design point, which is considered to be about the limiting Mach number for the use of hydrocarbon fuel and is also considered to be a logical starting point for the use of liquid hydrogen fuel.

Aerodynamic heating↗

An Analysis of the Applicability of the Hypersonic Similarity Law to the Study of Flow About Bodies of Revolution at Zero Angle of Attack

The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits.

PRESSURE DISTRIBUTION - BODIES OF REVOLUTION↗

On Parametric Sensitivity of Reynolds-Averaged Navier-Stokes SST Turbulence Model: 2D Hypersonic Shock-Wave Boundary Layer Interactions

Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.

Hypersonic↗

Hypersonic Flight and the Re-Entry Problem: The Twenty-First Wright Brothers Lecture

Up to this point the discussion of the problems of rocket vehicles has been confined to the effects of phenomena which have in the past been important ones for lower speed aircraft and will continue to be important for aircraft of all speeds. Now with considerable extension of both speed and altitude, other phenomena also become important. The nature of some problems will be altered, as a result, and new problems, of course, will be encountered. First, it is well to note that our interest in bluff bodies for ballistic vehicles in particular, and in rounded-nosed bodies generally, has changed our emphasis in aerodynamics. The detached bow waves which occur with such bodies at high supersonic speeds complicate the calculations of the flow-field characteristics. In the present period, much attention is being given to such studies. In addition, at the very high altitudes attained by most of the rocket-craft, the mean free path of air molecules can be of the same order, or long, compared to the dimensions of the vehicles. Thus, slip-flow and free-molecule-flow studies are of interest, particularly for satellite vehicles." The aerodynatnicist must deal with air having unfamiliar states and properties. Second, at hypersonic speeds where, for example, air is greatly decelerated, it may undergo considerable change in composition, the degree of change depending upon many factors. Dissociation of oxygen and nitrogen molecules can occur and, in addition, thermal ionization of many of the constituents. It is naturally to be expected that the convective heat transfer will, as a result, be altered from what it was for the "perfect" gas, and this has been the subject of much recent research effort. Moreover, the decelerated gas becomes capable of radiating energy and the radiative heat transfer must generally be considered for hypersonic vehicles, particularly for long-range ballistic rockets. It is not only the aerodynamic heating problems that are affected. The fact that at very high air temperature the gas becomes electrically conductive introduces new problems in radio wave transmission and reception. In addition, a conducting gas flow can, of course, be influenced by a magnetic field. The study of such flows, which has been termed "magneto gas dynamics," is still in too primitive a state to indicate how important a role it can play, but many interesting possibilities suggest themselves. Third, our experience with airplanes powered by air-breathing engines has naturally been restricted to the stratosphere, or lower. Our ignorance increases with altitude. For rockets, literally, "the sky's the limit," and it is not surprising that a great emphasis has now been placed on obtaining a more thorough understanding of the whole atmosphere. These studies are not aimed at an understanding of the chemical and physical characteristics alone, but also of the occurrence of high-energy particles, from meteors to cosmic rays, and the nature of the problems they will promote.

Wright Brother↗

NASA Hypersonics Overview

This briefing is an overview of NASA's hypersonic portfolio and core capabilities. The scope of work is fundamental research spanning technology readiness and system complexity levels; critical technologies enabling re-usable hypersonic systems; system-level research, design, analysis, validation; and, engage, invigorate and train the next generation of engineers. This briefing was requested by the Aeronautics Subcommittee of the NASA Advisory Council.

Aeronautics Hypersonic↗

Nosetip Bluntness Effects on Transition at Hypersonic Speeds: Experimental and Numerical Analysis Under NATO STO AVT-240

The existing database of transition measurements in hypersonic ground facilities has established that the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream as the nosetip bluntness is increased with respect to a sharp cone. However, this trend is reversed at sufficiently large values of the nosetip Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nosetip bluntness. This transition reversal phenomenon, which cannot be explained on the basis of linear stability theory, was the focus of a collaborative investigation under the NATO STO group AVT-240 on Hypersonic Boundary-Layer Transition Prediction. The current paper provides an overview of that effort, which included wind tunnel measurements in three different facilities and theoretical analysis related to modal and nonmodal amplification of boundary layer disturbances. Because neither first and second-mode waves nor entropy-layer instabilities are found to be substantially amplified to initiate transition at large bluntness values, transient (i.e., nonmodal) disturbance growth has been investigated as the potential basis for a physics-based model for the transition reversal phenomenon. Results of the transient growth analysis indicate that disturbances that are initiated within the nosetip or in the vicinity of the juncture between the nosetip and the frustum can undergo relatively significant nonmodal amplification and that the maximum energy gain increases nonlinearly with the nose radius of the cone. This finding does not provide a definitive link between transient growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition during the reversal regime was highly sensitive to wall roughness, and furthermore, was dominated by disturbances that originated near the nosetip.

Numerical analysis↗

Nosetip Bluntness Effects on Transition at Hypersonic Speeds: Experimental and Numerical Analysis

The existing database of transition measurements in hypersonic ground facilities has established that the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream as the nosetip bluntness is increased with respect to a sharp cone. However, this trend is reversed at sufficiently large values of the nosetip Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nosetip bluntness. This transition reversal phenomenon, which cannot be explained on the basis of linear stability theory, was the focus of a collaborative investigation under the NATO STO group AVT-240 on Hypersonic Boundary-Layer Transition Prediction. The current paper provides an overview of that effort, which included wind tunnel measurements in three different facilities and theoretical analysis related to modal and nonmodal amplification of boundary layer disturbances. Because neither first and second-mode waves nor entropy-layer instabilities are found to be substantially amplified to initiate transition at large bluntness values, transient (i.e., nonmodal) disturbance growth has been investigated as the potential basis for a physics based model for the transition reversal phenomenon. Results of the transient growth analysis indicate that stationary disturbances that are initiated within the nosetip or in the vicinity of the juncture between the nosetip and the frustum can undergo relatively significant nonmodal amplification and that the maximum energy gain increases nonlinearly with the nose radius of the cone. This finding does not provide a definitive link between transient growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition during the reversal regime was highly sensitive to wall roughness, and furthermore, was dominated by disturbances that originated near the nosetip. Furthermore, the present analysis shows significant nonmodal growth of traveling disturbances that peak within the entropy layer and could also play a role in the transition reversal phenomenon.

Freestream Mach Number↗

TO36 Hypersonic Study

Commercial Hypersonic Transportation Market Study. At the request of NASA, Deloitte conducted an independent market study to provide an independent assessment on the economic viability of hypersonic and supersonic air transportation to inform ongoing strategic planning of research areas within the government and industry and to focus on the areas for technology development and vehicle design requirements. The Study was organized into three primary areas of investigation: Defining the Market appetite for high speed air transport, Defining the business cases; and Assessing Barriers in the environment. The market demand was assessed across a range of Mach numbers from Mach 2 to Mach 6 and ticket price elasticity was determined by surveying potential customers, literature reviews and stakeholder and expert interviews for passenger aircraft, private aircraft and cargo markets. The business case analyses assessed potential business cases across a three-dimensional trade space: flight speed (Mach 2-6), passenger capacity (20-200 passengers) and design range (2500-7500 nmi.). By using the SpaceWorks Rosetta model, we were able to assess each combination in the trade space and to determine the steady state Internal Rate of Return (IRR or profit) was our primary figure of merit and allowed us to rank order the business cases to understand the trends and draw conclusions from the complex trade space. Lastly, we assessed other potential barriers to high speed flight. These were determined through literature review and stakeholder/expert interviews. Once these were compiled, we developed an objective scoring system to allow us to determine overall significance and challenge to aspiring market entrants. The majority of the research was conducted between July and December of 2020 and the results compiled and communicated to NASA in the first quarter of calendar year 2021. This report, along with the companion briefing deck, document the summation of our research and serve as a data repository for use by future researchers in government and industry.

hypersonic aircraft↗

A Comparison of NO Laser-Induced Fluorescence Models at Conditions Relevant to Supersonic and Hypersonic Flows

Planar laser-induced fluorescence (PLIF) of the nitric oxide (NO) molecule has been widely used in wind tunnel facilities for flow visualization, velocity, and temperature measurements. The experimental PLIF measurements are often compared with synthetic PLIF images using computationally derived temperatures, pressures, velocities, and species mole fractions. This approach is commonly referred to as computational flow imaging (CFI). In the present work, we compare signal intensity from PLIF models with experimental PLIF measurements obtained within a low pressure gas cell system at pressures and NO mole fractions relevant to supersonic and hypersonic flowfields. Experimental measurements were compared to several different laser induced-fluorescence models reported in the literature including LIFBASE, LINUS, and a NASA two-level model. The experimental measurements agreed well with all of the models at lower pressures and lower NO mole fractions; the fluorescence there is linear with both of these parameters. However, at higher pressures and mole fractions, the signal becomes nonlinear with respect to these parameters as self-quenching limits the signal and absorption further limits the signal. In fact, for the experimental path length of the experiment, the combination of high pressure and high NO mole fraction causes the experimental results to deviate significantly from the predicted results that neglect absorption of the incident laser sheet. The LINUS model, which allows absorption to be calculated, provided results that agreed better with the experimental measurements. Since supersonic and hypersonic flowfields may contain a region of the flow with high pressures and measurements in large-scale facilities often include a long path length, neglecting absorption may have a significantly negative effect on the CFI comparison to experimental PLIF images. As a result, PLIF models that account for absorption should be included in computational flow imaging approaches for laser induced fluorescence.

laser-induced fluorescence↗