Hypersonic Flow Past Blunt Bodies Research Articles

Numerical Analysis of Hypersonic Flow Past Blunt Bodies with Aerospikes

Aerodynamic drag, as a result of the high surface pressure generated because of the formation of a bow shock in front of a blunt nose cone of a hypersonic vehicle, is a serious problem. An aerospike can be attached to the stagnation point of the blunt nose cone to achieve a large reduction in drag and heat load at very high speeds in supersonic or hypersonic range. Aerospike replaces the strong detached shock wave with a system of weaker oblique shock waves, and a recirculation zone is formed between the shock and the body. Aerodynamic drag reduction on supersonic and hypersonic vehicles helps in reaching the desired range or altitude, allows economizing the fuel usage, simplifies the propulsion system requirements, and maximizes the ratio of payload to takeoff gross weight. In the present study, the flow around a blunted nose cone fitted with an aerospike is numerically simulated. An analysis is performed at a high Mach number () and different length-to-diameter ratios (, 2) at different angles of attack (0, 2, 5, and 8 deg). Numerical calculations agree well with the corresponding experimental results.

Experimental modeling of three-dimensional modes of hypersonic flow past cylindrically-blunted bodies

Several sets of experimental studies of the structure of transverse hypersonic flow past blunt bodies (cylinder and truncated wedge) and heat transfer on them are performed in the UT-1M shock tube of the Central Aerohydrodynamics Institute. The purpose of the investigation was to obtain three-dimensional modes of hypersonic flow past the nose surfaces of blunt bodies in an artificially disturbed and nominally uniform flows. The controlled disturbances in the freestream were produced by thin threads pulled over the nozzle exit. In the experiment the flow was visualized using the Topler method and the heat flux distribution over the cylinder was measured using luminescent temperature transformers. The experiments show that both the flow and the heat transfer in the vicinity of the cylinder nose are very sensitive to vortex disturbances in the oncoming hypersonic flow. In a nominally uniform flow (M∞ = 8 and Re∞ = 3160–11670) a steady three-dimensional mode of flow past the nose surface of a blunt wedge could be obtained in the form of a single vortex pair.

Effects of Chemistry in Nonequilibrium Hypersonic Flow Around Blunt Bodies

In this paper, the influence of a chemical kinetic model in hypersonic flow past blunt bodies is examined. Slow and fast chemical kinetic models are investigated to identify the reliable model for applications with a wide range of Mach numbers. Solutions from the Gardiner reaction-rate set, the Moss reaction-rate set, the Park rate set of 1993, and the Dunn and Kang reaction rate are compared. High-temperature, equilibrium-constant curve fits proposed by Gupta are also examined. The new Hansen's formulation for the rate controlling temperature for the dissociation reaction is compared with Park's approach. Particular attention has been devoted to backward reaction rates, because the methods of calculation affect the flowfield structure. Sample hypersonic flowfields, typical of spacecraft reentry conditions in which reactions play an important role, are presented and compared with results from experiments and other computational fluid dynamics simulations. The differences are discussed and evaluated.

Asymptotic solution of the two-dimensional equations for a thin viscous rarefied shock layer on a cold surface

Hypersonic rarefied flow past blunt bodies is studied in the continuum-free-molecular transition regime. On the basis of an asymptotic analysis three rarefied gas flow patterns are established depending on the relation between the relevant parameters of the problem. In the first regime corresponding to a cold surface asymptotic solutions of the equations of a thin viscous shock layer are derived at low Reynolds numbers in the axisymmetric and plane cases. Simple analytical expressions for the pressure and the heat transfer and friction coefficients are obtained as functions of the freestream parameters and the body geometry. With decrease in the Reynolds number the coefficients approach the values corresponding to free-molecular flow. In this regime a similarity parameter for the hypersonic rarefied flow past bodies is determined. The asymptotic solutions are compared with numerical solutions and the results of direct statistical simulation by the Monte Carlo method.

Asymptotic Investigation of the Thin Viscous Shock Layer Equations in the Neighborhood of the Stagnation Point for Low Reynolds Numbers

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies is investigated in the neighborhood of the stagnation point. The problem of applicability of the model of a thin viscous shock layer to the regime of transition from continuum to free-molecular flow is considered. In [1], it was shown that at low Reynolds numbers three hypersonic flow regimes can be distinguished and one of those regimes was investigated. In the present study an asymptotic solution of the thin viscous shock layer equations is obtained for another flow regime. With decrease in the Reynolds number the heat transfer coefficient determined by the solution obtained approaches its free-molecular value and the friction coefficient approaches its free-molecular limit, provided that the shock layer thickness is small. The analytical solution is compared with a numerical solution and the results of calculations based on direct Monte Carlo simulation.

Asymptotic solution of the thin viscous shock layer equations at low Reynolds numbers for a cold surface

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies in the neighborhood of the stagnation line is considered. The question of the applicability of the gasdynamic thin viscous shock layer model [1] is investigated for the transition flow regime from continuum to free-molecular flow. It is shown that for a power-law temperature dependence of the viscosity coefficient μ∼Tω the quantity (Ree)1/(1+ω), where e = (γ − 1)/2γ and γ is the specific heat ratio, is an important determining parameter of the hypersonic flow at low Reynolds numbers. In the case of a cold surface approximate asymptotic solutions of the thin viscous shock layer equations are obtained for noslip conditions on the surface and generalized Rankine-Hugoniot relations on the shock wave at low Reynolds numbers. These solutions give simple analytic expressions for the thermal conductivity and friction coefficients as functions of the determining flow parameters. As the Reynolds number tends to zero, the values of the thermal conductivity and friction coefficients determined by this solution tend to their values in free-molecular flow for an accommodation coefficient equal to unity. This tending of the thermal conductivity and friction coefficients to the free-molecular limit takes place for both two-and three-dimensional flows. The asymptotic solutions are compared with numerical calculations and experimental data.

Comparison of the Calculated Results for Hypersonic Flow Past Blunt Bodies with the OREX Flight Test Data

The physico-chemical hypersonic air flow model is verified for the conditions of the experimental vehicle OREX reentry path over the altitude range H = 84 –105 km. The calculations are performed on the basis of both the viscous shock layer equations and the complete system of Navier-Stokes equations. The temperature and chemical component concentration fields calculated within the framework of the two models are in good agreement for H ≤ 100 km (Re∞ ≥ 300). The numerical results for the heat flux at the stagnation point and the electron concentration agree well with the flight test data over the entire altitude range considered.

Certain Aspects of Computer Simulation of Hypersonic Flows: Stability, Nonuniqueness, and Bifurcation of Numerical Solutions of the Navier–Stokes Equations

A number of problems associated with the nonuniqueness of numerical solutions of the Navier–Stokes equations used for simulating processes of a hypersonic real gas flow past blunt bodies are considered. The processes of evolution of a stationary pattern of flow perturbed by a single pulse at an initial time instant are considered at different values of the governing parameters of the problem. The instability of the bifurcation type resulting in transition of the nonstationary process from one branch of solution to another and the attainment of a stationary regime is investigated.

Analysis of multicomponent gas mixture flows with partial chemical equilibrium

Diffusion equations and the corresponding transfer equations with effective transfer coefficients are derived using new unknown functions (linear combinations of diffusion fluxes and of concentrations) for reactive gas mixture flows with partial chemical equilibrium. The diffusion differential equations for rapid independent reactions degenerate into algebraic equations of detailed chemical equilibrium. The component formation sources on the right-hand sides of the remaining diffusion equations contain no rapid stages. It is shown that the assumption of partial chemical equilibrium is valid for hypersonic flow past blunt bodies with a nose radius of approx. 1 m on portions of their gliding reentry paths in the Earth's and Martian atmospheres.

Vibration-dissociation coupling in nonequilibrium hypersonic viscous flows

A computational study has been performed on hypersonic high-enthalpy viscous air flow past blunt bodies. In the thermochemical processes describing this nonequilibrium flow, nonpreferential or preferential vibrationdissociation-vibration coupling and vibration-vibration energy exchanges have been taken into account. A fivespecies reactive air mixture, in which the diatomic species NI and C>2 are in thermal nonequilibrium, was considered. The set of equations was solved using a second-order implicit finite difference scheme. Several flow conditions, corresponding to a range of Mach numbers from 14 to 18, in connection with available experiments were investigated. The predicted shock standoff distance and stagnation heat flux are in agreement with the experimental data. These conditions were used by several authors to validate theirs computations. Through a code-to-code comparison, the effects of the physical modeling, on the temperatures and the species mass fractions distributions, are emphasized.

On the applicability of some approximate similitude laws in hypersonic aerodynamics

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies.

Monte Carlo simulations of hypersonic flows past blunt bodies

This paper reports on the steps taken to develop a gas-kinetic simulation of hypersonic flows past the nose region of re-entry vehicles. For the validation of both the direct simulation Monte Carlo (DSMC) and the molecular dynamics (MD) methods, the Oseen vortex decay problem was chosen to emphasize the conservation of angular momentum. Furthermore, an analytical solution of the Navier-Stokes equation exists for this problem. The results obtained with both methods correlate well with the analytical solution. The angular momentum is conserved exactly in the MD method; however, in the DSMC method, the cell sizes must be sufficiently small to conserve approximately the angular momentum because of the statistical assumptions. Both, the twoand threedimensional DSMC-codes have been verified for the hypersonic flow past a circular cylinder and a sphere, respectively. The shock stand-off distance and the pressure distribution along the body surface were compared with experimental results. In both cases, the agreement is very good. As an application to more realistic configurations, the gaskinetic flow past the nose of a typical spacecraft is discussed for different Knudsen numbers.

Numerical investigation of the structure of nonequilibrium three-dimensional hypersonic flow past blunt bodies

Three-dimensional dissociating air flow past blunt bodies is investigated within the framework of the parabolized Navier-Stokes equations in the thin layer approximation. Multicomponent diffusion, barodiffusion and homogeneous chemical reactions, including dissociation-recombination and exchange reactions, are taken into account. The boundary conditions are assigned in the free stream and at the surface of the body with allowance for heterogeneous catalytic reactions and slip effects. The problem of flow at zero angle of attack past blunt bodies possessing two planes of symmetry is investigated numerically for flow patterns varying from smeared layer structure to almost ideal flow (Re∞=50-105). The flow conditions corresponded to the motion of a body with lift along a re-entry trajectory [1]. The contribution of the chemical reactions in the shock wave as compared to the diffusion flux at the edge of the shock wave was estimated. The edge of the shock wave is assumed to correspond to the point at which the density profile has the greatest slope. The influence of slip effects and barodiffusion on the flow characteristics is demonstrated. The results of the calculations are compared with calculations based on the thin viscous shock layer model [2].

Hypersonic three-dimensional viscous shock layer in a nonuniform gas flow in the neighborhood of the stagnation point

Three-dimensional hypersonic viscous gas flow past smooth blunt bodies in the presence of injection or suction is considered. The effect of the nonuniformity of the approach stream on the shock-wave standoff, the flow structure and the friction and heat transfer coefficients is investigated with reference to the examples of flow from a supersonic spherical source and flow of the far wake type. It is shown that this effect depends importantly on the Reynolds number, the nature of the nonuniformity and the shape of the body.

Investigation of hypersonic three-dimensional flow past blunt bodies within the framework of the parabolized Navier-Stokes equations

The flow of a homogeneous gas in a three-dimensional hypersonic viscous shock layer, which includes the shock wave structure, is examined within the framework of the parabolic approximation of the Navier-Stokes equations. The Navier-Stokes equations are simplified on the basis of the asymptotic analysis carried out in [1], are written in variables of the Dorodnitsyn type [2] and are solved by the method proposed in [3, 4] extended to the case of three-dimensional flows. The flow at zero angle of attack past elliptic paraboloids, two-sheeted hyperboloids and triaxial ellipsoids is calculated. Some results of investigating the flow past such bodies are presented. Flow past a sphere in the analogous approximation was considered in [5], where a comparison was also made with the solution of the complete Navier-Stokes equations [6, 7].

Study of the effect of a strong blast of a gas from the surface on a hypersonic flow past blunt bodies

Study of the effect of a strong blast of a gas from the surface on a hypersonic flow past blunt bodies

Effect of nose shape on hypersonic flow past slender blunt bodies at an angle of attack

We examine some characteristics of hypersonic flow past slender blunt bodies of revolution at a small angle of attack α≲τ≪1, where τ is the relative body thickness. It is shown that, within the framework of hypersonic theory, for a correct-consideration of the effect of the conditions in the transitional section between the nose and the lateral surface it is necessary, in the general case, to specify the circumferential distribution of the force effect for the nose and the mass of the gas. For small α, the effect of the nose, just as in two-dimensional flows [1–4], shows up only through its drag coefficient cx, for α=0. On this basis, the similarity law [1–4] for flow past such bodies, with arbitrary form of the lateral surface and differing in the shape of the nose blunting, which is valid over the entire disturbed region, with the exception of a small vicinity of the nose, is extended to the case in question.

Hypersonic flow past ducted blunt bodies of revolution

Chernyi [1, 2] has examined the problem of hypersonic flow past a ducted cone with sharp leading edge. In the following we present an analysis of the characteristic features of this problem in the case of a blunt leading edge.

Calculation of three-dimensional unsteady hypersonic gas flow past slender blunt bodies

Calculation of three-dimensional unsteady hypersonic gas flow past slender blunt bodies

Theory of the high-entropy layer in hypersonic flows

WE consider the inverse problem of hypersonic flow with an infinitely great Mach number of the oncoming flow at a condensation jump differing little from the jump obtained by using the explosive analogy. By joining the external and internal asymptotic expansions it has been possible to construct the body and study the flow immediately adjacent to the body, namely the flow in the entropy layer. The very concept of the theory of the high-entropy layer formed when a hypersonic flow flows past blunt bodies, is due to the papers of Cheng [1], V. V. Sychev [2–4] and Yakyra [5]. Comprehensive reviews of the advances of this theory were made first by Mirels [6], and later by Guiraud, Vallee and Zolver [7], to whom are also due a whole series of original results. A thorough approach to the investigation of the flow in the entropy layer was made by Freeman [8]. It was developed in greater detail from the mathematical point of view in the paper by Hornung [9], who also compared the theoretical and experimental data [10]. An analysis recently undertaken by the authors [11, 12] led to simple qualitative results on the structure of the velocity field in the inverse problem where the form of the shock wave is defined by a power function of the coordinates. The questions discussed below are closely connected with those studied in papers [8–12]. Their solution is based on the assumption that the front shock differs little from the jump obtained by the use of the explosive analogy [13–17] to calculate the hypersonic flows. However, precisely this small difference makes it possible to construct streamlined bodies the contours of which deviate from the particle trajectories in the problem of a strong explosion [18–20] the more strongly, the further the points chosen for the comparison are situated from the nose. Both the equation of the contour of the streamlined body and also the equation of the particle trajectory in the explosion are expressed asymptotically in terms of power functions, but the exponents of these functions differ by a finite quantity.