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Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed...

Although receptivity plays a key role in the transition of hypersonic flows, most prior computational receptivity studies have neglected to study broadband frequency disturbance spectra. This work ...

This study investigates the influence of surface distribution of the basic flowfield on the shapes and performances of the osculating axisymmetric waveriders. First, the design method of osculating...

Shock-wave–boundary-layer interaction is one of the most important phenomena in hypersonic flights due to its ubiquitous presence and its extreme effects on the aerothermodynamic loads on the aircr...

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2018-10-01, 資料番号: PA1910019000

This paper describes a novel hypersonic facility to reproduce the high stagnation pressures and temperatures necessary for the accurate simulation of hypersonic flows in the range Mach 5–7, while p...

Analyses of dual-model scramjet engines often rely on the assumption of thermally perfect gas, for which the internal modes of molecular motion are assumed to be in thermal equilibrium. With an inc...

The presented work is a continuation of the investigation of the influence of an isolated roughness on the laminar-turbulent transition for hypersonic boundary-layer flows. The first part of the in...

Receptivity of high-speed boundary layers in calorically perfect gas is considered within the framework of fluctuating hydrodynamics introduced by Landau and Lifshitz (“Hydrodynamic Fluctuations,” ...

The hypersonic flow around a tip of a rocket-mounted Hypersonic Boundary-Layer Transition experiment has been simulated with direct numerical simulations. The numerical results reveal the local flo...

In many experimental studies of hypersonic flow in blow-down wind tunnels or shock tunnels, the flow is accelerated from rest through a conical nozzle. While a contoured nozzle is designed for a particular ratio of specific heats or a particular gas, a conical nozzle is more versatile as it can be used for any gas. Examples of such investigations are [1–3]. These were performed in the T5 piston-driven reflected shock tunnel at Caltech. It is important to understand the effect of the conicity of the free stream produced by a conical nozzle. The present work investigates how it affects the shock wave stand-off distance in axisymmetric flow over a convex blunt body. Previous work on the effect of free-stream conicity notably includes a study of its effect on pressure distribution and drag in flow over blunted slender bodies by [4], in which theoretical results based on the Newtonian approximation were compared with experiments.

E NERGY deposition has recently received significant interest as a powerful technique in a variety of high-speed flow-control applications [1–5]. To achieve energy deposition, an electromagnetic local flow/flight control (ELFC) device generates pulsed electromagnetic fields. A wide variety of ELFC devices have been developed, including, for example, laser and/or microwave discharge, electron beam, and surface dc/ac discharge [2,3,6] and the nanosecond pulse mode of dielectric barrier discharge operation [7]. The Johns Hopkins University Applied Physics Laboratory has developed a unique ELFC device denoted the SparkJet for flow and flight control [8–14]. Figure 1 illustrates schematically the three stages of energy deposition by a SparkJet device. A spark is discharged within a typical volume of several cubic centimeters (stage 1). The high-pressure gas discharges through a converging nozzle, thereby generating an impulse (stage 2). Provided there is a mechanism for recharging the gas in the cavity (stage 3), the sequence can be repeated. Research has been conducted on the SparkJet by different groups. Narayanaswamy et al. [15] have performed experiments to investigate the effect of a SparkJet discharged at different frequencies and locations upstream of a 30 deg wedge on the separation induced by a shock/boundary-layer interaction. Caruana et al. [16] have carried out numerical and experimental research on a plasma synthetic jet generated by a similar device. They have shown that this method can be applicable for separation control and noise reduction. Anderson and Knight [17] have performed analytical and numerical studies to predict the impulse from the jet and the temporal pressure and temperature inside the cavity upon discharge. They have shown that an array of SparkJets can effectively replace a flap and hence be practical in flight control. The objective of this note is the determination of the electromechanical efficiency of a particular design of a SparkJet. The electromechanical efficiency is the fraction of the electrical energy that results in the generation of the SparkJet mechanical impulse based upon a perfect gas model. The spark discharge generates a plasma with excited electronic, rotational, and vibrational states. A portion of the energy dissipated across the spark gap is channeled into heating of the gas (i.e., increasing the translational–rotational temperature), which leads to a high pressure and subsequent jet exiting through the converging nozzle, thus creating the mechanical impulse. Various definitions of the SparkJet efficiency have been published. Haack et al. [13] have experimentally found an efficiency of 35% based on the measured peak pressure inside the SparkJet. In a later study, Haack et al. [14] have experimentally shown an average efficiency of 20–30% in different operating conditions based on the measured pressure and voltage. In this paper, a novel method for determining the electromechanical efficiency is proposed based upon comparison of predictions of a theoretical model and experimental measurements.

This paper presents an efficient procedure to reconstruct the thermodynamic properties of real fluids. An equation-of-state look-up table was constructed with adaptive triangular mesh, which not on...

An optimization routine using computational fluid dynamics is outlined and applied to axisymmetric aeroshells in hypersonic entry conditions. Two objectives are considered in the optimization: minimizing the peak heat flux at the wall and maximizing the drag coefficient. These objectives are scaled and combined into a single scalar quantity called the objective function. A weight is applied to each objective to study the tradeoff effect that the objectives have on the shape. A Pareto front is produced by varying the weight between 0 and 1 and plotting the optimal shapes. Pareto fronts are generated in three environments: laminar perfect gas air, turbulent perfect gas air, and a nine-species Mars environment. The optimal aeroshells are compared with the Mars Science Laboratory aeroshell. The optimal aeroshells generated in the two perfect gas air environments compare similarly with the Mars Science Laboratory aeroshell. The optimal aeroshells generated in the Mars atmosphere show significant deviations fro...

The ability to predict surface heating rates, as well as shear and pressure forces, is fundamental to the analysis and design of the thermal protection system for hypersonic vehicles. Approximate engineering codes that can be used to rapidly predict heating rates are extremely useful in the preliminary or conceptual design phase, whereas more detailed and expensive Navier–Stokes codes are generally used to provide more accurate heating rate predictions for final design. An earlier code has been used successfully in conjunction with inviscid flowfield codes computed on single-block structured grids. More recent inviscid codes have been developed that use unstructured grids, which greatly reduce grid generation time for complex configurations. A newer heating code had been used successfully with unstructured inviscid flowfield codes to compute laminar heating on general three-dimensional vehicles using unstructured grids and the heating rates over most of the vehicle have been shown to compare favorably wit...

It is proposed that the adverse effects from secondary diaphragm rupture in an expansion tunnel may be reduced or eliminated by orienting the tunnel vertically, matching the test gas pressure and the accelerator gas pressure, and initially separating the test gas from the accelerator gas by density stratification. This proposed configuration is termed the vertical expansion tunnel. Two benefits are 1) the removal of the diaphragm particulates in the test gas after its rupture, and 2) the elimination of the wave system that is a result of a real secondary diaphragm having a finite mass and thickness. An inviscid perfect-gas analysis and quasi-one-dimensional Euler computations are performed to find the available effective reservoir conditions (pressure and mass specific enthalpy) and useful test time in a vertical expansion tunnel for comparison to a conventional expansion tunnel and a reflected-shock tunnel. The maximum effective reservoir conditions of the vertical expansion tunnel are higher than the reflected-shock tunnel but lower than the expansion tunnel. The useful test time in the vertical expansion tunnel is slightly longer than the expansion tunnel but shorter than the reflected-shock tunnel. If some sacrifice of the effective reservoir conditions can be made, the vertical expansion tunnel could be used in hypervelocity ground testing without the problems associated with secondary diaphragm rupture.

This paper deals with aerodynamic and aerothermodynamic studies carried out to design a capsule vehicle suitable for the recovery of crewmembers from the International Space Station and/or from exploration missions to the moon or Mars. An integrated design tool called ENTRY is used to support vehicle reentry analysis and computational fluid dynamics design activities. A possible low-Earth-orbit reentry scenario, with the associated aeroheating environment, is generated and then analyzed. Several Euler and Navier–Stokes computations are performed to simulate the flowfield past the vehicle, for both perfect-gas and nonequilibrium reacting-gasmodels for the air. Numerical results and their comparison with flight data and wind-tunnel data are presented. An analysis of flowfields, obtained from numerical computations, is provided by means of flight forces and moments coefficients. Experimentally measured surface pressure distributions and aerodynamic coefficients compare rather well with numerical results.

For accurate and efficient computations of compressible gas-liquid two-phase mixture flows, the AUSMPW+ and RoeM schemes (for which the accuracy, efficiency, and robustness have been successfully demonstrated in gas dynamics) are extended to two-phase flows at all speeds. From the mixture equations of state, a new shock-discontinuity-sensing term suitably scaled for two-phase flows is derived and its performance is validated. In addition, several numerical difficulties appearing in the development of the two-phase AUSMPW+ and RoeM schemes are analyzed and successfully cured. The two-phase AUSMPW+ and RoeM schemes are then efficiently preconditioned for the simulation of all Mach number flows by employing the existing AUSM or Harten-Lax-van Leer with contact restoration types of preconditioning strategies. Various gas-liquid two-phase flows, from highly compressible to nearly incompressible flow conditions, are tested. The numerical results show the accurate and robust behavior of the proposed schemes for all speeds of two-phase flows.

The critical nozzle has frequently been employed to measure the flow rate of various gases, but hydrogen gas, especially at high-pressure conditions, was not dealt with nearly as much using the critical nozzle due to treatment danger. According to experimental data obtained recently, it was reported that the discharge coefficient of hydrogen gas through the critical nozzle exceeds unity in a specific range of Reynolds numbers. No detailed explanation on such an unreasonable value was made, but it was vaguely inferred as real gas effects. For the purpose of the practical use of high-pressure hydrogen gas, systematic research is required to clarify the critical nozzle flow of high-pressure hydrogen gas. In the present study, a computational fluid dynamics method has been applied to predict the critical nozzle flow of high-pressure hydrogen gas. Several kinds of real gas equations that take into account the forces and volume of molecules of hydrogen gas were incorporated into the axisymmetric, compressible Navier-Stokes equations. A fully implicit finite volume scheme was used to numerically solve the governing equations. The computational results were validated with available experimental data. The results show that the discharge coefficient is mainly influenced by the compressibility factor and the specific heat ratio, which appear more remarkable as the inlet total pressure of hydrogen gas increases.

A numerical study was conducted to understand the effect of a single laser pulse on a normal shock and shock boundary layer interaction. The goal is to examine the capability of a pulsed laser energy deposition to momentarily move a normal (terminal) shock upstream in a mixed-compression inlet so as to counteract the effect of a disturbance that would move the normal shock downstream. Two numerical models were used. The perfect gas model for energy pulse was developed at Rutgers University, and the commercial software GASPex was used as the flow solver. The real gas model was developed at the University of Minnesota. The research was conducted in two phases. First, the 3-D interaction of a laser pulse with an isolated normal shock at Mach 2 was examined using the perfect gas and real gas models. A detailed comparison of the computed flowfields indicates that the principal details of the interaction are accurately predicted by the perfect gas model. Second, the perfect gas model was used to simulate the 2-D interaction of a laser pulse with a normal shock including the effects of the interaction of the shock wave with a turbulent boundary layer. Three different dimensionless energy levels (∈ = 1, 10, and 100) were considered. The interaction at ∈ = 100 demonstrated a prominent upstream movement of the normal shock and a significant though temporary increase in the length of the separation region due to interaction of the compression wave (induced by the energy spot) with the separated boundary layer.

Twomethods to infer freestream densities from in-flightmeasurements of pitot pressure and flight velocity during reentry are presented that focus on the minimization of uncertainties due to high-temperature real-gas effects and atmospheric densityfluctuation. A numerical approach leads to a curve-fit function that yields the ratio of the pitot to the dynamic pressure pt2=q1 for velocities between 0.5 and 10 km=s and altitudes up to 90 km. An analytically derived correlation is also provided. Both techniques account for equilibrium real-gas effects thus achieving very high accuracies. Independently of potential atmospheric fluctuation, remaining errors are less than 1% for almost the entire spectrum and less than 0.3% for typical lifting reentry.

A new exact solution of an oblique detonation is developed for the supersonic irrotational flow of an inviscid calorically perfect ideal gas, which undergoes a one-step, irreversible, exothermic, zero activation energy reaction as it passes through a straight shock over a curved wedge. The solution gives expressions for the velocity, pressure, density, temperature, and position as parametric functions of a variable characterizing the extent of reaction. For Chapman-Jouguet solutions, an explicit form with dependency on distance is obtained in terms of the Lambert W function. As the simple model employed is a rational limit of models used in the computational simulation of complex supersonic reactive flows, the solution can serve as a benchmark for mathematical verification of general computational algorithms. An example of such a verification is given by comparing the predictions a modern shock-capturing code to those of the full exact solution. The realized spatial convergence rate is 0.779, far less than the fifth-order accuracy that the chosen algorithm would exhibit for smooth flows, but consistent with the predictions of all shock-capturing codes, which never converge with greater than first-order accuracy for flows with embedded discontinuities.

Introduction D ENSE gas dynamics studies the dynamic behavior of gases in the dense regime, i.e., at temperatures and pressures close to the thermodynamic critical point. In such conditions, complex gasdynamic phenomena can appear in the transonic and supersonic regimes.1 In spite of the additional complexity of the fluid response in the dense regime, the use of dense gases is not only necessary but, in some applications, advantageous. For instance, dense gas effects play a critical role in the performance of turbomachinery and heat-transfer equipment of organic Rankine cycles (ORCs).2 This motivates the interest in developing numerical tools for the analysis and design of advanced ORC turbomachinery components. In the past, several methods for so-called “real gas flows” have been derived. Such methods were in general tailored to deal with hypersonic reacting flows, for which the use of robust upwind numerical solvers was mandatory. Unfortunately, upwind schemes require characteristic decompositions, making their realization for complex multidimensional systems quite involved. On the other hand, for nonreacting flows of gases close to saturation conditions, governed by complex equations of state, and characterized by “exotic” but quite weak waves, the use of sophisticated characteristic decompositions is not essential. For these flows, it could be more convenient to use central schemes, which, in spite of higher numerical diffusivity, have the advantage of conceptional simplicity and low computational cost. In the present work, a centered numerical solver for the computation of inviscid and viscous dense gas flows is developed. A thirdorder-accurate centered method for perfect gas flows3 is extended to the computation of dense gases. The proposed scheme is systematically compared to a well-known second-order flux-difference splitting scheme4 implemented within the same code. The computations are performed using either the van der Waals or the realistic Martin–Hou5 equation of state. The scheme is then extended to the computation of viscous dense gas flows. The fluid viscosity and thermal conductivity are evaluated using thermophysical models appropriate for gases close to saturation conditions. The proposed method is validated for several inviscid and viscous flow problems involving dense gas phenomena.

The gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme is extended to hypersonic flow simulations and thus shows that the compressible inviscid flow solutions of the simulations are efficiently and accurately obtained from the BGK scheme without the disastrous shock instability phenomenon that occurs in most hypersonic flow simulations involving strong shock waves. For this particular study, the effect of chemistry in hypersonic flows has not been taken into account. Hence, the assumption of calorically perfect gas is imposed in all simulations. The high-order resolution of the scheme is achieved by utilizing monotone upstream-centered schemes for conservation laws-type initial reconstruction. While, an implicit-type time-integration method known as the approximate factorization– alternating direction implicit is adopted for computing both steady and unsteady calculations. The gas-kinetic scheme is tested meticulously in four two-dimensional numerical examples, namely, the blunt-body problem, the double Mach reflection problem, the axisymmetric blunt-body problem, and the flow over a 15-deg ramp. The numerical results of the BGK scheme when compared with the other schemes and experimental data show that this numerical technique is robust, accurate, and stable for hypersonic flow.

Dense gasdynamics studies the flow of gases in the thermodynamic region above the upper saturation curve, close to the liquid-vapor critical point. In recent years, great attention has been paid to certain substances, known as the Bethe‐Zel’dovich‐Thompson (BZT) fluids, which exhibit negative values of the fundamental derivative of gasdynamics for a whole range of temperatures and pressures in the vapor phase. This can lead to nonclassical gasdynamic behaviors, such as rarefaction shock waves, mixed shock/fan waves, and shock splitting. The uncommon properties of BZT fluids can find practical applications, for example, in the reduction of losses as a result of wave drag and shock/boundary-layer interaction in organic Rankine cycle turbines. The present work provides a detailed numerical study of transonic BZT fluid flows past a simplified configuration, represented by an isolated NACA0012 airfoil. The objective is to investigate the influence of BZT effects on the airfoil performance (specifically on the lift-to-drag ratio).

A numerical method for the simulation of hot gas nozzle flows is explained. This method solves the Reynolds-averaged Navier-Stokes equations in a finite volume context. Numerical simulations of the Vulcain and Vulcain 2 separated nozzle flows are presented. For these simulations, three different gas models were used: The gas was assumed to be either a) a perfect gas, b) in chemical equilibrium, or c) in chemical nonequilibrium. Comparisons with experimental data are provided. Free-shock separation, restricted-shock separation and cap-shock patterns are discussed. Postcombustion in the shear layer where the hydrogen-rich nozzle gas mixes with the ambient air is investigated.

Diffusion and kinetic effects in the spherical expanding e ows of argon‐ helium mixtures have been studied using the direct simulation Monte Carlo technique at the Knudsen numbers from 0.0015 to 0.03 and pressure ratios from 100 to 10,000. Similarity analysis was used to analyze the e ow structure in supersonic e ow region, spherical shock wave, and subsonic area behind it. Both kinetic and diffusion effects ine uence the shock-wave thickness, parallel and transverse species temperatures, diffusion velocities, the effectiveness of species separation, and ambient gas penetration. In the supersonic region the effect of “ freezing” the parallel temperature has been found in all considered cases. The temperature freezing comes e rst for heavier molecules of argon. The transverse temperature for both species follows the temperature in the isentropic expansion. Accumulation of the hot light (helium) component occurs in the leading front of the spherical shock wave. The multitemperature regime of the e ow inside the shock wave is found and studied using the similarity factor, which is based on theratio of stagnation pressures calculated at critical-source-e ow and background conditions. Nomenclature C = constant; Eq. (5) F = transformed mole-fraction function; Eq. (15) f = mole fraction of heavier component H = transformed temperature function; Eq. (15) Kna = Knudsen number based on the length scale parameter at ine nity L Kn¤ = Knudsen number based on the critical radius of a spherical source r¤ K2 = similarity parameter, Re¤.pa=p0¤/ 1=2

Analysis of boundary-layer transition data from supersonic quiet tunnels, as well as flight experiments has indicated that, in the absence of surface roughness and high levels of freestream disturbances, linear stability theory can be used as a guide for estimation of the onset of transition. Transition data from two different hypersonic flight experiments are analyzed using parabolized stability equations, including chemistry effects associated with high-temperature boundary layers. The results suggest that transition in both of these cases is caused by the amplification of second mode disturbances. The analysis shows that, consistent with previous findings for supersonic flows where first mode disturbances induce laminar-turbulent transition, N factors of about 9.5 and 11.2 correlate the transition onset locations from these two high-Mach-number experiments. Therefore, the e N method can be used for smooth body transition prediction in hypersonic vehicle design. The effect of chemistry on boundary-layer stability is also studied and is shown to be destabilizing.

A technique is presented for carrying out relatively low-cost numerical simulations of the interaction between three-dimensional microelectromechanical systems (MEMS)- and mesoscale actuators and a laminar boundary layer. The jet-type actuators take the form of a diaphragmlocated at the bottom of a cavity. When the diaphragm is driven by piezoceramic, for example, it de� ects, reduces the cavity volume, and drives air out of an ori� ce as a jet into the boundary layer. In an attempt to avoid an in� ow phase into the cavity, we study the effects of a “puff-like” jet produced when the diaphragmis driven by a short-duration constant force, or the cavity pressure is suddenly increased by providing air from a microvalve. The theoretical model for the actuator is based on classic thin-plate theory for the diaphragmdynamics andmodi� ed unsteady pipe-� owtheory for the � uid dynamics in the ori� ce/nozzle leading to the boundary layer. The cavity � uid dynamics is not modeled in detail; the compressible � owinit is neglected, and the instantaneouspressure there is determined viathe perfect gas law.A velocity–vorticity method is used to compute the perturbation � ow� eld created in the boundary layer. This method is capable of full direct numerical simulations, but for the present results the governing equations were linearized. The cavity and boundary-layer � ow� elds are linked by requiring continuity of velocity and pressure at the ori� ce exit. The computational methods are used to investigate such questions as the need for fully interactive computations and the differences between meso- and MEMS-scale actuators.

A new parabolized Navier ‐Stokes (PNS) algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects. Innovative techniques are used to automatically detect and measure the extent of the embedded regions. Within the embedded regions, the PNS equations are globally iterated to duplicate the results that would be obtained with the complete Navier ‐Stokes (NS) equations. Once an embedded region is computed, the algorithm returns to the standard space-marching PNS mode until the next embedded region is encountered. This procedure has been successfully incorporated into NASA’ s upwind PNS code and it has been validated by its application to several two-dimensional test cases. All of these test cases include embedded regions that produce signie cant upstream effects. The present numerical results arein excellent agreement with previous NS computations and experimental data. In addition, these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach.

The focus of this study is on cavitation in the wake of a high-velocity underwater projectile. A physical model based on the Euler equations is presented in terms of two-phase mixture properties. Mathematical closure is achieved by providing equations of state for the possible thermodynamic states: compressible liquid, compressible two-phasemixture,andcompressiblepurevapor.Fortheoperatingconditionsstudiedhere,allstatesaresubcritical. Theproposedmodelissolvedusingahybridcomputationalschemedevelopedtoaccuratelyresolvepropertyproe les across discontinuities. The model is validated with several one-dimensional test cases that have known analytic solutions. For modeling the hypervelocity underwater projectile, the model is shown to compute unsteady shockwave development as well as the projectile-wake cavitation zone. The model is then used to conduct a parametric study on the affect of e ow and projectile properties on cavitation.

Planar laser-induced fluorescence (PLIF) images of nitric oxide in hypersonic flow over a wedge and a hemisphere are compared with a theoretical PLIF model. The theoretical PLIF images are based on computational fluid dynamics (CFD) models including a perfect-gas model and a nonequilibrium chemistry model. Two-dimensional maps of the flow parameters generated by the CFD are used to predict the theoretical PLIF images, including the effects of collisional quenching. We find good agreement between the model and the experimental measurements. We explain how this method of computational flow imaging can be useful for designing experiments.

Two-dimensional shock wave reflection and refraction phenomena for dense gases in the high pressure and density region near the thermodynamic critical point are compared and contrasted to shock phenomena over well-known configurations for dilute, perfect gases. Both transient and steady wave fields are simulated using a time-accurate, predictor-corrector total variation diminishingscheme that solves the Euler equations incorporating the van der Waals thermodynamic model. Detailed displays of wave field structure for both perfect gas and dense gas flowfields are shown. Nonclassical wave phenomena, such as disintegrating shocks, expansion shocks, and shock-fan composite waves for wedges, ramps, circular arcs, and other geometries, demonstrate significant differences in dense gas flowfields from those of perfect gases

The method of characteristics (MOC) is employed computationally in the simulation of planar or axisymmetric, steady, supersonic flows in highly underexpanded freejets. The gas is assumed to be inviscid and nonreacting but may be vibrationally frozen, relaxing, or equilibrated. The ordinary-differential equations obtained by the MOC are integrated along the characteristics by a combined second-order, explicit-first-order, implicit method in regions of the flow with relatively rapid vibrational energy transfer (VET) and by a fully second-order, explicit method in regions with either slow or very rapid VET. Results from MOC simulations of flows with constant specific-heat ratios are verified by comparison with results obtained in previous MOC computations of expansion-fan flows and with empirically based correlations giving the size of the barrel-shock structure as a function of stagnationto-ambient-pressure ratio. Comparisons are also made between MOC results for a vibrationally relaxing gas and results for vibrationally frozen and equilibrated gases, to verify the computational methods used to simulate flows with VET. The demonstrated capability for simulating underexpanded freejet flowfields represents a useful tool for predicting the results of experiments conducted in a small-scale shock-tunnel facility.

The extension of time-marching computations to fluids with arbitrary equations of state is demonstrated by means of stability analyses, simplified problems, and practical applications. Most of the examples use the properties of supercritical hydrogen for which the density varies by more than an order of magnitude for small changes in pressure and temperature, but representative computations for incompressible fluids and perfect gases are also given to demonstrate the generality of the procedure. Because representative flow velocities in typical supercritical fluids applications are much lower than the speed of sound, convergence enhancement through eigenvalue control is often necessary. This is accomplished through a generalization of earlier preconditioning methods that enables efficient computation of arbitrary equation of state fluids, perfect gases, and incompressible fluids by a single procedure. The present approach thus provides a single method that is uniformly applicable to all equations of state

A description of the method for the e owe eld in the noise suppressing nozzle calculation is presented. The method is formulated for the Favre-averaged Navier ‐ Stokes equations. It is based on an explicit monotone second-order approximation, Godunov-type numerical scheme. The e rst set of calculations is made without turbulent and molecular viscosity being taken into account and shows that the Euler approach allows the main features of the complicated e ow in the mixer ‐ ejector nozzle to be described. Special experiments cone rm this idea and make the exactness of computational e uid dynamics results more clear.

Results of numerical simulations of plug-nozzles are presented, and a phenomenological insight into the e owe eld development at different ambient pressures is given. Therefore, a e nite volume program using unstructured grids was adapted to the special boundary conditions of plug nozzles. Calculations were performed solving the Euler and Navier ‐ Stokes equations under ideal, perfect gas assumptions. Turbulence is taken into account with a k-e turbulence model. Numerical simulations are compared with experimental results of hot-run tests of a toroidal subscale model plug engine. Principal physical processes like expansion waves, compression shocks, and the recirculating base e ow region are in good agreement with available experimental data, and can therefore be predicted well. The simulations of a full-size plug nozzle, dee ned for a post Ariane 5 launcher, reveal a e owe eld behavior similar to the one observed with the toroidal subscale plug engine. Nomenclature I = impulse Mmix = molar mass p = pressure rO/F = mass ratio oxidizer/fuel mixture T = temperature a = angle « = nozzle area ratio k = isentropic coefe cient

In many hypersonicows, the excited states of some chemical species are the dominant radiators. Often, those electronically excited particles are present in small concentrations and the chemical kinetics mechanisms for their formation are very complicated and costly to implement in a fully coupled computationaluid dynamics method. An ef® cient computational method is presented for the calculation of chemical species present in trace amounts, including excited state species. The usefulness of this overlay method is demonstrated with several examples: OH(A) formation from water vaporin a hypersonicshocklayer, state-speci® cCO vibrational relaxation and CO( a) formation in a rocket motor nozzle, and CO( a) kinetics in an expandingow. The overlay calculations allow a careful sensitivity analysis of the kinetics modeling and permit comparison with radiance data obtained inight. HEREhas been a general interest within the hypersonics com- munity to study optical emissions from chemically reacting ¯ ows in nonequilibrium. Such radiation can be measured in both ground-based andight experiments with well-established instru- mentation techniques. These measurements provide data to validate the modeling of species concentrations and temperatures in hyper- sonicows. The approach commonly used today to model thespectral radiant intensity for differentow conditions is to ® rst obtain a solution to the conservation equations for species concentrations and tempera- tures as a function of their location in theow. An important aspect of theow modeling is that the chemical kinetics model applies to the ground-state species only. Then a separate radiation model uses theowsolutiontocomputethespectralradianceateachpointinthe ¯ ow. The radiation model generally consists of two parts: computa- tion of the excited state species concentrations and the line-by-line spectral distribution of the radiation. Usually, the ® rst part of the model has the greater degree of uncertainty. To calculate the excited state populations, one typically assumes a master set of rate equations for populating the excited state levels. For the calculation of radiation in the ultraviolet to visible spectral region, these equations represent the distribution of excited states in the atomic or molecular vibrational, rotational, and electronic lev- els. When the collision rate is suf® ciently high, it is also assumed thattheexcitedstatepopulationdistributionisthequasi-steady-state (QSS) solution of the master set of equations. This condition occurs if two criteria are met. First, the time constants for the population excitation equations must be fast compared with the average gas ¯ ow residence time. Second, the production and destruction rates are closely balanced. 1 The QSS condition has been found to hold for the population of the electronic states of NO for stagnation re- gionows for 10-cm-radius spheres at a speed of 5 km/s and up to altitudes of 80 km (Ref. 2). However, there are other situations where it is expected to fail. The second assumption usually made in the solution of the mas- ter equations for the excited state populations is that the primary creation mechanism is by electron or neutral collisions with the ground-state species. As theow density decreases, collisions be- tween two ground-state species that directly produce the excited state species become important. These chemiluminescent reactions are known to be potentially important for the two cases that we present here. The addition of excited state mechanisms to the reaction set in- creases the computational cost of theow solution. In rare® ed con- ditions, many reaction paths are possible and must be included. Often the rate constants and branching ratios are not well known. Forthese reasons,multiplecomputationsareoften required toquan- tify the sensitivityof theinclusionorexclusion ofspeci® cprocesses and the uncertainty in the rate constants. Hence, an ef® cient computational method is required to calculate the electronically excited states in both compressed and expanding ¯ ows. A method is presented, based on the key assumption that the excited electronic state species concentrations are suf® ciently small such that they are trace species compared with the bulkow. Then, anexamplecalculationoftheconcentrationofelectronicallyexcited hydroxylradicals, OH( A),in a stagnation regionowisconsidered. This calculation can be compared directly with the conventional, uncoupled approach. This comparison provides the validation of the method. The second example corresponds to the calculation of the excited stateCO(a)populationinanexpandingowfromasolidrocketmo- tor.Thisproblemcannotbesolvedintheuncoupledmannerbecause the long lifetime of the CO( a) state and the low collision frequency in the expandingowmake the use ofthe QSSapproximation ques- tionable. The large number of reactions and processes that need to beconsideredwillillustratethe ef® ciency and usefulnessof thepro

The feasibility of experimentally evaluating the high-temperature real-gas effects on the e uid ‐ mechanical behavior of hypersonic e ows in shock tunnels and hot-shot tunnels is examined. Considering the intrinsic limitations of those facilities, the real-gas effects on aerodynamic characteristics, separated e ows, and shock-boundary-layer interactions, turbulent transitions, and leeward/base e ow are considered to be the possible subjects of simulation in those facilities. A new empirical reaction rate model is proposed to numerically reproduce the existing experimental data on species concentrations. Based on this model, the average density ratios expected across a normal shock wave formed over a model placed in an impulse tunnel are calculated. By comparing these density ratios with the e ight values, it is pointed out that the best simulation is achievable at an enthalpy of 8 MJ/kg, and that two-thirds of the real-gas effects could be simulated at that enthalpy. It is proposed that the real-gas effects measurements in an impulse tunnel be validated by comparing the e ow patterns over simple shapes obtained in a tunnel with those obtained in a ballistic range.

An experimental study of the combined effects of leading-edge bluntness and real gas behavior on shock wave/boundary-layer interaction has been performed. Pressure and heat transfer distributions have been measured over a compression corner for a range of corner angles, including the datum case of flat plate flow. On the flat plate and upstream of the corner, the pressure and heat transfer for the blunt leading-edge configuration were found to lie above the corresponding sharp leading values. On the ramp, there was a considerable reduction in the pressure and heat transfer when the leading edge was blunt. Also, the extent of the interaction was seen to be smaller with the blunt leading edge. These results are similar to those from perfect gas studies. The differences between the sharp and blunt leading-edge data appear to be less pronounced at the higher enthalpy. This is thought likely to be because of the reduced shock standoff, which occurs as a result of dissociation. A comparison between the heat transfer data on the ramp face and predictions from the generalized reference enthalpy theory was seen to be reasonable. The upstream influence and plateau pressure were found to be in fair agreement with data from low enthalpy experiments. A C CD c d h hr L lu M n Pr p qw Rex

Using a finite volume computational technique, we have investigated the chemically reacting inviscid flow of pure nitrogen over a blunt cone (half angle 13.5 deg) at an incidence of 30 deg. Although the effects of viscosity have been disregarded, the flow is three dimensional and contains a complex shock-vortical structure on the leeward surface of the blunt cone. We selected constant freestream conditions to correspond to those typical of the test section of ground based experimental facilities capable of producing strong dissociation effects. A range of cone sizes has been studied to produce flows ranging across the non-equilibrium regime as well as the limiting cases of chemically frozen (perfect gas) flow and flow that is in chemical equilibrium throughout. We found that the pitching moment coefficient on the body is a strong function of the degree of bluntness and that there are small but significant chemical effects superimposed on the bluntness effects. The effect of chemistry is most complicated for the bluntest body. There are strong chemical effects on the leeward flow.

A study of transpiration cooling of blunt bodies such as a hemicylinder is made by solving Navier-Stokes equations. An upwind, implicit time-marching code is developed for this purpose. The study is conducted for both perfect-gas and real-gas (chemical equilibrium) flows. Investigations are carried out for a special wall condition that is referred to as no heat flow into the wall condition. The effects of air injection on wall temperature are analyzed. Analyses are carried out for Mach numbers ranging between 6-10 and Reynolds numbers ranging between 10(6)-10(7). Studies are made for spatially constant as well as spatially varying mass injection rate distributions, White cold air injection reduces the wall temperature substantially, transpiration cooling is relatively less effective when the gas is in chemical equilibrium.

Two important characteristics of separated flow, namely, the scale of interaction and the peak heat transfer, have been examined under high-enthalpy, hypersonic conditions. Experimental data have been obtained in a free-piston shock tunnel using a compression corner model. The data are examined in terms of established perfect gas theories, and are seen to be in reasonable agreement with these theories and also with data from perfect gas experiments. This indicates that, for the present conditions, the real gas effects on separation and reattachment are small.

The hypersonic aerodynamic characteristics of a winged body concept representing a candidate single- stage-to-orbit vehicle which features wing tip fin controllers and elevon/body flap control surfa'Fs are predicted at points along a nominal trajectory for Mach numbers from 5 to 27 and angles of attack from 19 to 32 degrees. Predictions are derived from surface properties based on flow solvers for inviscid and viscous, laminar flows acting as a perfect gas, as a gas in chemical equilibrium and as a gas in chemical non- equilibrium. At a Mach number of 22, the lateral aerodynamic characteristics of the vehicle are determined based on an inviscid analysis at side slip angles of 2 and 4 degrees and 32 degrees angle of attack; a viscous analysis was carried out to determine the effect of gas chemistry model on surface pressure and to determine the incremental aerodynamics for control surface deflections. The results show that the longitudinal pitch characteristics of the baseline configuration, i.e., zero control surface deflections, are significantly altered by real gas chemistry at angles of attack greater than 30 degrees and Mach numbers greater than 9; and, that aerodynamics derived from inviscid solutions are of sufficient accuracy for preliminary analysis. Also, it is shown that a Mach number of 22, the choice of gas chemistry model has a large impact on surface pressure levels at highly localized regions on the vehicle and that the vehicle can be trimmed at control surface deflections less than 11 degrees.