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NASA NTRS1993

Computational techniques for high-speed flows with viscous and chemical effects

Algorithms for solving the Euler and the Navier-Stokes equations in conjunction with chemical kinetic equations are presented. The convective flux is estimated from a quasi one dimensional interpolation procedure. Shock, contact, and expansion waves and thermochemical nonequilibrium phenomena are captured by the Lax-Friedrichs technique. Relaxation techniques were developed to enhance their effectiveness in dealing with spatial and temporal stiffness associated with the physical problems. Both explicit and implicit smoothers were implemented into the standard multigrid time stepping method. Unsteady and steady scalar problems are discussed. A perfect gas and equilibrium air shock tube problem is investigated. Numerical schemes and techniques are compared for the problems of shock and boundary layer interaction and three dimensional viscous, nonequilibrium flow encompassing an aerobrake. The results are comparable in accuracy against other high order non-oscillatory techniques. The multigrid methods are assessed using a Mach 8 flow over a complete planar body, a sphere, and a blunt delta wing at 20 deg incidence. Applying an implicit multigrid method on a nested grid of 128 by 64 nodes the reduction factor is 0.25. The central processing unit reduction factor is 2.2 after both the single and multigrid Runge-Kutta solutions converged to machine zero on a grid of 37 by 41 by 73 nodes.

Li, C. P.↗

NASA NTRS1992

Modeling of hypersonic reacting flows

The effect of nonequilibrium thermochemical processes on the aerodynamic and heat transfer characteristics of a hypersonic vehicle is illustrated with examples. It is shown that the conventional method of predicting chemical reactions always predict that the flow is closer to equilibrium than it actually is, leading to incorrect predictions of aerodynamic characteristics of a vehicle. A method is presented for predicting chemical processes using a two-temperature kinetic model, which is developed on the basis of combining conservation equations for vibrational energy and for electron electronic energy, which are also derived. The validity of the two-temperature model is proven using two types of experimental data: radiation and shock shapes.

Park, Chul↗

NASA NTRS1993

Computational flow predictions for hypersonic drag devices

The effectiveness of two types of hypersonic decelerators is examined: mechanically deployable flares and inflatable ballutes. Computational fluid dynamics (CFD) is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The results from the ideal gas solver are compared to computational results from a thermochemical nonequilibrium solver. The surface pressure coefficient, the drag, and the extend of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.

Tokarcik, Susan A.↗

NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

NASA NTRS1995

Importance of real gas effects in entry technology

Critical issues concerning real gas effects in hypervelocity flows where the thermochemical nonequilibrium effects are pronounced, are described. Emphasis is on the development and validation of benchmark analysis tools. Approaches to develop and/or enhance phenomenological models, including test techniques to acquire databases, and incorporate them into computational flow field simulation codes are described. The performance characteristics of shock tubes, ballistic ranges and arc heated wind tunnels, state of the art diagnostics are included. The following aerothermodynamic phenomena are discussed: aerodynamic parameters, viscous interactions, turbulent transition, forebody heating/heat transfer, radiative heating, Lee-Base flows and low density real gas.

Deiwert, George S.↗

NASA NTRS1994

Review of chemical-kinetic problems of future NASA missions, II: Mars entries

The present work aims to derive a set of thermomechanical relaxation rate parameters and chemical reaction rate coefficients relevant to future interplanetary missions. It also attempts to assess the impact of thermochemical nonequilibrium phenomena on radiative heating rates for the stagnation point of the Martian entry vehicle.

TRT-EXPERIMENTAL↗

NASA NTRS1995

Convective and radiative heating for vehicle return from the Moon and Mars

The aerothermal environment is examined for two vehicle forebodies near the peak heating points of lunar and martian return-to-earth trajectories at several nominal entry velocities. The first vehicle forebody is that of a 70 deg aerobrake for entry into earth orbit; the second, a capsule of Apollo configuration for direct entry into the earth's atmosphere. The configurations and trajectories are considered likely candidates for such missions. Two-temperature, thermochemical nonequilibrium models are used in the flow field analyses. In addition to Park's empirical model for dissociation under conditions of thermal nonequilibrium, the Gordiets kinetic model for the homonuclear dissociation of N2 and O2 is also considered. Temperature and emission profiles indicate nonequilibrium effects in a 2 to 5 cm post shock region. Substantial portions of the shock layer flow appear to be in equilibrium. The shock layer over an aerobrake for return from the moon exhibits the largest extent of nonequilibrium effects of all considered missions. Differences between the Gordiets and Parks kinetic model were generally very small for the lunar return aerobrake case, the greatest difference of 6.1 percent occurring in the radiative heating levels.

Greendyke, Robert B.↗

NASA NTRS1996

User's Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)

This user's manual provides detailed instructions for the installation and the application of version 4.1 of the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). Also provides simulation of flow field in thermochemical nonequilibrium around vehicles traveling at hypersonic velocities through the atmosphere. Earlier versions of LAURA were predominantly research codes, and they had minimal (or no) documentation. This manual describes UNIX-based utilities for customizing the code for special applications that also minimize system resource requirements. The algorithm is reviewed, and the various program options are related to specific equations and variables in the theoretical development.

Gnoffo, Peter A.↗

NASA NTRS1996

Experimental and Computational Aerothermodynamics of a Mars Entry Vehicle

An aerothermodynamic database has been generated through both experimental testing and computational fluid dynamics simulations for a 70 deg sphere-cone configuration based on the NASA Mars Pathfinder entry vehicle. The aerothermodynamics of several related parametric configurations were also investigated. Experimental heat-transfer data were obtained at hypersonic test conditions in both a perfect gas air wind tunnel and in a hypervelocity, high-enthalpy expansion tube in which both air and carbon dioxide were employed as test gases. In these facilities, measurements were made with thin-film temperature-resistance gages on both the entry vehicle models and on the support stings of the models. Computational results for freestream conditions equivalent to those of the test facilities were generated using an axisymmetric/2D laminar Navier-Stokes solver with both perfect-gas and nonequilibrium thermochemical models. Forebody computational and experimental heating distributions agreed to within the experimental uncertainty for both the perfect-gas and high-enthalpy test conditions. In the wake, quantitative differences between experimental and computational heating distributions for the perfect-gas conditions indicated transition of the free shear layer near the reattachment point on the sting. For the high enthalpy cases, agreement to within, or slightly greater than, the experimental uncertainty was achieved in the wake except within the recirculation region, where further grid resolution appeared to be required. Comparisons between the perfect-gas and high-enthalpy results indicated that the wake remained laminar at the high-enthalpy test conditions, for which the Reynolds number was significantly lower than that of the perfect-gas conditions.

Hollis, Brian R.↗

NASA NTRS1998

Real-Gas Aerothermodynamics Test Facilities

This chapter provides an overview of the current ground-based aerothermodynamic testing capabilities in Western Europe and the United States. The focus is on facilities capable of producing real-gas effects (dissociation, ionization, and thermochemical nonequilibrium) pertinent to the study of atmospheric flight in the Mach number range of 5 < M < 50. Perceived mission needs of interest to the Americans and Western Europeans are described where such real-gas flows are important. The role of Computational Fluid Dynamics (CFD) in modern ground testing is discussed, and the capabilities of selected American and European real-gas facilities are described. An update on the current instrumentation in aerothermodynamic testing is also outlined. Comments are made regarding the use of new facilities which have been brought on line during the past 3-5 years. Finally, future needs for aerothermodynamic testing, including instrumentation, are discussed and recommendations for implementation are reported.

James 0. Arnold↗

NASA NTRS1995

Capsule Aerothermodynamics. CFD Prediction Methodology; Database for CFD Validation; Capsule Flight Programs: AFE and Apollo Lessons Learned

Features of chemically reacting separated hypersonic flows are identified and issues concerning their analysis and simulation are discussed. Emphasis is placed on flows of high temperature dissociating and ionizing air and current methods for studying and characterizing these flows, including separation, are reviewed. The aeroassist orbital transfer vehicle and its flight trajectory are used for illustration. Thermochemical nonequilibrium phenomena are emphasized and extension of continuum analysis to the high altitude slip-flow regime is considered.

Deiwert, George S.↗

NASA NTRS1995

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

NASA NTRS1995

Vibrational and Electronic Energy Transfer and Dissociation of Diatomic Molecules by Electron Collisions

At high altitudes and velocities equal to or greater than the geosynchronous return velocity (10 kilometers per second), the shock layer of a hypersonic flight will be in thermochemical nonequilibrium and partially ionized. The amount of ionization is determined by the velocity. For a trans atmospheric flight of 10 kilometers per second and at an altitude of 80 kilometers, a maximum of 1% ionization is expected. At a velocity of 12 - 17 kilometer per second, such as a Mars return mission, up to 30% of the atoms and molecules in the flow field will be ionized. Under those circumstances, electrons play an important role in determining the internal states of atoms and molecules in the flow field and hence the amount of radiative heat load and the distance it takes for the flow field to re-establish equilibrium. Electron collisions provide an effective means of transferring energy even when the electron number density is as low as 1%. Because the mass of an electron is 12,760 times smaller than the reduced mass of N2, its average speed, and hence its average collision frequency, is more than 100 times larger. Even in the slightly ionized regime with only 1% electrons, the frequency of electron-molecule collisions is equal to or larger than that of molecule-molecule collisions, an important consideration in the low density part of the atmosphere. Three electron-molecule collision processes relevant to hypersonic flows will be considered: (1) vibrational excitation/de-excitation of a diatomic molecule by electron impact, (2) electronic excitation/de-excitation, and (3) dissociative recombination in electron-diatomic ion collisions. A review of available data, both theory and experiment, will be given. Particular attention will be paid to tailoring the molecular physics to the condition of hypersonic flows. For example, the high rotational temperatures in a hypersonic flow field means that most experimental data carried out under room temperatures are not applicable. Also, the average electron temperature is expected to be between 10,000 and 20,000 K. Thus only data for low energy electrons are relevant to the model.

Huo, Winifred M.↗

NASA NTRS1997

Aerodynamics of Stardust Sample Return Capsule

Successful return of interstellar dust and cometary material by the Stardust Sample Return Capsule requires an accurate description of the Earth entry vehicle's aerodynamics. This description must span the hypersonic-rarefied, hypersonic-continuum, supersonic, transonic, and subsonic flow regimes. Data from numerous sources are compiled to accomplish this objective. These include Direct Simulation Monte Carlo analyses, thermochemical nonequilibrium computational fluid dynamics, transonic computational fluid dynamics, existing wind tunnel data, and new wind tunnel data. Four observations are highlighted: 1) a static instability is revealed in the free-molecular and early transitional-flow regime due to aft location of the vehicle s center-of-gravity, 2) the aerodynamics across the hypersonic regime are compared with the Newtonian flow approximation and a correlation between the accuracy of the Newtonian flow assumption and the sonic line position is noted, 3) the primary effect of shape change due to ablation is shown to be a reduction in drag, and 4) a subsonic dynamic instability is revealed which will necessitate either a change in the vehicle s center-of-gravity location or the use of a stabilizing drogue parachute.

Mitcheltree, R. A.↗

NASA NTRS2004

Computational Aerothermodynamic Design Issues for Hypersonic Vehicles

A brief review of the evolutionary progress in computational aerothermodynamics is presented. The current status of computational aerothermodynamics is then discussed, with emphasis on its capabilities and limitations for contributions to the design process of hypersonic vehicles. Some topics to be highlighted include: (1) aerodynamic coefficient predictions with emphasis on high temperature gas effects; (2) surface heating and temperature predictions for thermal protection system (TPS) design in a high temperature, thermochemical nonequilibrium environment; (3) methods for extracting and extending computational fluid dynamic (CFD) solutions for efficient utilization by all members of a multidisciplinary design team; (4) physical models; (5) validation process and error estimation; and (6) gridding and solution generation strategies. Recent experiences in the design of X-33 will be featured. Computational aerothermodynamic contributions to Mars Pathfinder, METEOR, and Stardust (Comet Sample return) will also provide context for this discussion. Some of the barriers that currently limit computational aerothermodynamics to a predominantly reactive mode in the design process will also be discussed, with the goal of providing focus for future research.

Olynick, David R.↗

NASA NTRS1997

Aerodynamics of the Mars Microprobe Entry Vehicles

The selection of the unique aeroshell shape for the Mars Microprobes is discussed. A description of its aerodynamics in hypersonic rarefied, hypersonic continuum, supersonic and transonic flow regimes is then presented. This description is based on Direct Simulation Monte Carlo analyses in the rarefied-flow regime, thermochemical nonequilibrium Computational Fluid Dynamics in the hypersonic regime, existing wind tunnel data in the supersonic and transonic regime, additional computational work in the transonic regime, and finally, ballistic range data. The aeroshell is shown to possess the correct combination of aerodynamic stability and drag to convert the probe's initial tumbling attitude and high velocity at atmospheric-interface into the desired surface-impact orientation and velocity.

Mitcheltree, R. A.↗

NASA NTRS2005

Computational Aerothermodynamic Design Issues for Hypersonic Vehicles

A brief review of the evolutionary progress in computational aerothermodynamics is presented. The current status of computational aerothermodynamics is then discussed, with emphasis on its capabilities and limitations for contributions to the design process of hypersonic vehicles. Some topics to be highlighted include: (1) aerodynamic coefficient predictions with emphasis on high temperature gas effects; (2) surface heating and temperature predictions for thermal protection system (TPS) design in a high temperature, thermochemical nonequilibrium environment; (3) methods for extracting and extending computational fluid dynamic (CFD) solutions for efficient utilization by all members of a multidisciplinary design team; (4) physical models; (5) validation process and error estimation; and (6) gridding and solution generation strategies. Recent experiences in the design of X-33 will be featured. Computational aerothermodynamic contributions to Mars Path finder, METEOR, and Stardust (Comet Sample return) will also provide context for this discussion. Some of the barriers that currently limit computational aerothermodynamics to a predominantly reactive mode in the design process will also be discussed, with the goal of providing focus for future research.

Gnoffo, Peter A.↗

NASA NTRS1997

Computational Aerothermodynamic Design Issues for Hypersonic Vehicles

Gnoffo, Peter A.↗