Viscous Shock Layer Research Articles

Kinetic Viscous Shock Layer near the Leading Edge of a Thin Rotating Disk

Kinetic Viscous Shock Layer near the Leading Edge of a Thin Rotating Disk

Hypersonic Nonequilibrium Flow around Sharp Edge

A regularized problem has been formulated to describe the flow of a molecular gas in a hypersonic macrokinetic nonequilibrium thin viscous shock layer (kinetic TVSL) near a sharp edge. It is shown that the solution of the regularized kinetic TVSL problem on the sharp edge, the description of friction and heat transfer coincides with the solution of the Navier–Stokes analogue of this TVSL problem. It is shown that in the kinetic TVSL the friction stress and the normal heat flow on the wall in the vicinity of the sharp edge are identical with the corresponding values in the Navier–Stokes TVSL. The similarity of currents near the sharp edge in the kinetic and Navier–Stokes versions of the TVSL is indicated. A method for constructing a solution to the kinetic TVSL problem for the vicinity of a sharp edge based on the Navier–Stokes TVSL solution is indicated. A formula is obtained for calculating the pressure on the surface in the kinetic TVSL flow near the sharp edge through the components of the solution (on the wall) of the Navier–Stokes TVSL flow problem.

Coupled heat transfer between a viscous shock gasdynamic layer and a transversely streamlined anisotropic half-space

The purpose of the article is to analytically solve the conjugate problem of heat transfer in a viscous shock layer on a blunt object and thermal conductivity in an anisotropic half-space. A feature of the flow around such bodies near the critical point is that in this case, the boundary layer equations are not satisfied and it is necessary to solve the Navier-Stokes equations together with the equations of continuity, state, and energy, however, in a stationary formulation of an incompressible flow. The problem of coupled heat transfer between a viscous shock gasdynamic layer and anisotropic half-space with the assumption of incompressibility of the gasdynamic flow behind the normal part of the shock wave is posed. An analytical solution to this problem is obtained with a boundary condition at the gas-solid object interface in the form of a parameter – temperature, as well as an analytical solution to the thermal conductivity problem in an anisotropic half-space with the same boundary condition.

Stagnation-point heating of Fire II with a non-Boltzmann radiation model

The present work analyzes the stagnation-point radiative heating in the Fire II flight experiment by devising a collisional-radiative model with non-local absorption. In the stagnation-line flow-field calculations, a viscous shock layer method with a thermochemical nonequilibrium model is utilized. In the radiation calculations, a line-by-line method with the non-Boltzmann electronic populations is employed by adopting the quasi-steady state approach of the electronic master equation calculations. In constructing the electronic master equation, the best set of the electron and heavy-particle impact excitation rates is proposed to achieve better agreement with the measured radiative heating flight data. In the flow-radiation coupling procedure, the effect of the non-local absorption is modeled by devising an iterative process between the quasi-steady state electronic master equation and the radiative transfer equation calculations. Escape factors of the strongest atomic lines and the diatomic nitrogen vacuum ultraviolet systems with the non-local absorption effect are also proposed to more efficiently consider the non-local nature of the radiative transition. When compared with the experimental data from the Fire II trajectories, it is found that the present collisional-radiative model with the non-local absorption improves the ability to predict non-Boltzmann radiative heating.

Similarity of Polyatomic Gas Flows in the Kinetic Shock Layer

The two-dimensional problem of high-speed nonequilibrium homogeneous polyatomic gas flow past a surface formulated on the basis of macrokinetic 13-moment equations with the use of the two-layer thin viscous shock layer (TVSL) approximation in the neighborhood of non-slender bodies is considered. A class of similarity variables which make it possible to reduce the complex kinetic problem considered to the well-known Navier—Stokes problem of thin viscous shock layer is suggested.

Calculation of Nonequilibrium Radiation of Shock Waves in the Air Using Two Models

The results of the numerical modeling of the spectral radiating capacity of shock-wave-heated air are presented. Two models of nonequilibrium radiation emitted from the relaxation zone behind the strong shock wave front are used. The first model is based on Euler equations and formulated for the one-dimensional problem of kinetic processes behind the shock front. The second model is based on the two-dimensional Navier-Stokes equations for a viscous shock layer on the nose surface of a blunt body in a hypersonic flow. The problem of the interpretation of the Fire-II flight experiment are discussed using the above-mentioned models.

Aero-heating modelling on the ablative noses during flight trajectory

PurposeThe purpose of this paper is to present the more accurate estimation of aero-heating for the ablative 3-D noses by using the viscous shock layers and similarity of viscous boundary layer methods.Design/methodology/approachThe combination of viscous shock layer, similarity of viscous boundary layer (SVBL) methods, Park ablation and Baldwin–Lomax turbulent models is presented in this paper. The proposed method reduces computational memory and run time as compared to the time marching algorithms during flight trajectory. Therefore, the space marching algorithm and finite difference method is used, and the governing equations are transferred into curvature coordinate by using the mapping terms.FindingsThe solving for an ogive nose during flight trajectory shows that the convergence of this technique is fast as compared to the user defined function based on the fluent solvers, program to axisymmetric regular geometry code and other research. The results of this research are validated by the mentioned research studies. The relative error for the aero-heating, species concentration of the shock layer gas mixture because of dissociation/ionization of air and surface ablation results is less than 6, 5 and 11 per cent, respectively.Research limitations/implicationsThe required time for an aerodynamic design of hypersonic noses reduces as the induced aero-heating is one of the principal design parameters in standpoint aerodynamic, structural and other terms. The magnitude of this parameter, surface temperature and surface recess because of ablation should be corrected during flight trajectory.Social implicationsThe results of this research are applicable for aerospace industries.Originality/valueThe originality of this paper is 90 per cent.

Modeling Flow in a Shock Viscous Layer

This paper considers the two-dimensional problem of the theory of viscous hypersonic flows formulated for the high-velocity translational-nonequilibrium flow of a monatomic gas past a surface based on macrokinetic 13-moment Grad equations using the model of a two-layer thin viscous shock layer (TVSL) near non-thin bodies. A class of similarity variables is proposed that allows the kinetic problem of the TVSL to be reduced to the well-studied Navier–Stokes problem of the TVSL.

Approximate analytical solutions for heat fluxes in three-dimensional hypersonic flow over blunt bodies

Analytical expressions for the heat flux divided by its value at the stagnation point which depend on the geometric parameters invariant with respect to the choice of the coordinate system, as well as expressions depending on the geometry and the pressure on the surface which have a wider applicability range are obtained in the problem of three-dimensional hypersonic flow over blunt bodies at large and moderate Reynolds numbers. These formulas are derived by solving the thin viscous shock layer equations for a perfect gas using the integral method of successive approximations developed by the author. The accuracy and the range of applicability of the analytical solutions are estimated by comparing them with numerical solutions. On the basis of comparisons with numerical solutions for multicomponent chemically nonequilibrium air at altitudes from 90 to 50 km of the spacecraft reentry trajectory in the Earth’s atmosphere it is shown that the formulas obtained can be used for calculations of the heat flux on an ideal catalytic surface of bodies in hypersonic chemically reacting gas flow.

Numerical Investigation Of The Evolution Of Disturbances On A Flat Plate In A Hypersonic Flow Of A Mixture Of Vibrationally Excited Gases

The problem of the evolution of disturbances in a hypersonic viscous shock layer on a plate in the flow of a mixture of vibrationally excited carbon dioxide and nitrogen is considered by solving of the Navier – Stokes equations. Two channels of vibrational relaxation of CO2 molecules in collisions with CO2 and in collisions with N2 were taken into account by using a two-temperature model of relaxation flows in modeling the thermal nonequilibrium. The data on the dynamics of the evolution of disturbances on f flat plate in a wide range of determining parameters (attack angle α = 5÷20°, concentration of CO2 in mixture, braking temperature T0 = 2000÷4000 K) are presented in this paper.

Viscous Shock Layer Around Slender Bodies with Nonequilibrium Air Chemistry

A method has been developed which can reliably compute nonequilibrium viscous shock layer over blunt-nosed bodies. This method considerably improves computational efficiency, especially for long slender bodies. The shock shape is generated as a part of the solution in this method, and in the nose region, the shock shape is calculated from an algebraic relation and corrected by global passes through that region. The current algorithm yields a considerable decrease of more than 60% in CPU time relative to other VSL methods. In the present study, both seven and eleven species air models were tested. The seven species analysis includes N, O, N2, O2, NO, NO+ and e−. The eleven species analysis includes the same species plus N+, O+, $$\text{N}_{2}^{ + }$$ , $$\text{O}_{2}^{ + }$$ . The chemical reaction models for seven and eleven species are taken from Blottner and Gupta, respectively. The governing equations are solved with a spatial-marching, implicit, finite-difference method. The solution is obtained by solving a couple of normal momentum and continuity equations. The results of the present technique show good agreement compared to the STS_2 flight data and other numerical solutions.

Effect of the mode composition disturbances in a high-enthalpy wind tunnel on wave processes in the hypersonic viscous shock layer

A numerical and experimental study of the spectral distribution of disturbances hotshot wind tunnel was performed. It was found that disturbances are the superposition of fast acoustic waves propagating along axial direction and oblique slow acoustic waves which have less amplitude. Numerical simulation of disturbances evolution in the nozzle of the wind tunnel was carried out by solving 2D Navier-Stokes equations using the ANSYS Fluent program package. Experiments were carried out in the IT-302M high-enthalpy hotshot wind tunnel ITAM SB RAS.

Asymptotic investigation of heat transfer and skin friction in three-dimensional hypersonic rarefied gas flows

The three-dimensional hypersonic rarefied gas flow over blunt bodies is investigated in a transitional (from the free molecule to the continuum) flow regime. The problem is solved within the framework of the asymptotically correct thin viscous shock layer model by an asymptotic method developed for low Reynolds numbers. Simple analytical expressions are obtained for the Stanton number and the coefficients of skin friction and pressure on the windward surface of the body as a function of its geometrical characteristics and the free stream parameters. These solutions are represented in an invariant form that is independent of the choice of the system of coordinates. The limits of applicability of the asimptotic solution are estimated. It is shown that, when the Reynolds number tends to zero, the solutions for the Stanton number and the coefficients of skin friction and pressure approach to the values in the free molecule flow regime at unit accommodation coefficient.

Influence of vibrational relaxation on perturbations in a shock layer on a plate

The influence of excitation of molecular vibrational degrees of freedom on the mean flow and perturbation development in a hypersonic (M = 6–14) viscous shock layer is studied. The layer originates on a plate placed in a flow of air, carbon dioxide, or their mixture at high stagnation temperatures (2000–3000 K). The mean flow and pressure pulsation on the surface of the plate are measured in an IT-302M pulsed wind tunnel (Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences). Numerical simulation is carried out in terms of a model of a thermally perfect gas using the ANSYS Fluent program package based on solving nonstationary two-dimensional Navier-Stokes equations. External flow perturbations are introduced into the computational domain in the form of plane monochromatic acoustic waves using UDF modules built in the computational code. It is shown that the excitation of vibrational degrees of freedom in carbon dioxide molecules considerably influences the position of the head wave and intensifies perturbations in contrast to air in which the fraction of vibrationally excited molecules is low at the same parameters of the oncoming low. The influence of the excitation of vibrational degrees of freedom is studied both for equilibrium gas and for a vibrationally nonequilibrium gas. Nonequilibrium vibrational degrees of freedom are simulated using a two-temperature model of relaxation flows in which the time variation of the vibrational energy is described by the Landau-Teller equation with regard to a finite time of energy exchange between vibrational and translational-rotational degrees of freedom of molecules. It is found that the vibrational nonequilibrium has a damping effect on perturbations.

Experimental investigation of flow past simple model bodies in hypersonic wind tunnels at similar values of the Mach and Reynolds numbers but at different physical flow velocities

The pressure distributions over the surfaces of simple model bodies, such as hemisphere, wedge, and cone, and the bow shock stand-off distances from these bodies are investigated in hypersonic wind tunnels with similar-in-value Mach and Reynolds numbers but considerably different flow velocities (u = 790 to 5950 m/s). These are the tunnels with an ohmic heater and electric-arc and MHD gas flow accelerators. Flow pattern visualization followed by photometering measurements are used for determining the bow shock stand-off distance. At low gas densities the method of anomalous dispersion of the sounding radiation is employed for visualizing the flow. The pressure distributions over the body surfaces and the bow shock stand-off distances are calculated from the Navier-Stokes equations and thin viscous shock layer (TVSL) theory. The measured parameter values are in agreement with those calculated from Navier-Stokes equations. For the cone and the wedge the discrepancy is within 10%.

Burnett hypersonic thin shock layer near the windward side of a flat plate

A one-layer model of a Burnett thin shock layer is simplified to fit the problem of a rarefied gas hypersonic flow along the windward side of a flat plate placed at a large angle of attack with an incident flow; here, the mathematical apparatus of the theory of a two-layer hypersonic thin viscous shock layer near nonthin bodies is used. This theory suggests that in the structure of a flow, between the followed body’s surface and the incident undisturbed flow, we have two typical regions-sublayers (a smeared pressure shock plus the shock layer proper). It is shown that the considered Burnett thin shock layer problem in the two-layer approximation completely reduces to the corresponding Navier-Stokes problem.

Vibrational-Chemical Kinetics in Mars Entry Problems

The paper deals with kinetic theory methods modelling of reacting gas flows near spacecrafts entering the Mars atmosphere. For mixtures containing CO2 molecules, the complete kinetic scheme including all vibrational energy transitions, dissociation, recombination and exchange chemical reactions is proposed. For the prediction of gas dynamic parameters and heat transfer to the surface of a spacecraft, a detailed approach taking into account state-to-state CO2 vibrational and chemical kinetics as well as multi-temperature approaches based on quasi-stationary vibrational distributions are used. A more accurate but complicated and time consuming state-to-state model is applied for the numerical simulation of a one-dimensional flow in a boundary layer near the entering body surface. More simple quasi- stationary three-temperature, two-temperature and one-temperature approaches are used for the numerical study of a 2-D viscous shock layer under entry conditions. The vibrational distributions near the surface are far from the local vibrational and chemical equilibrium and a noticeable difference is found between the values of CO2 vibrational-specific energies at the surface obtained by means of the state-to-state and quasi-stationary approaches. At the same time, for all considered approaches, the kinetic model for vibrational distributions and chemical reactions has a weak influence on the heat transfer to the non-catalytic vehicle surface.

Asymptotic Burnett model of the gas flow in a thin shock layer near a cylinder

Using the two-layer ideology of the theory of a viscous shock layer assuming the presence in the structure of the flow between the streamlined surface and the overrunning unperturbed stream of two (each with its own specific) characteristic areas-layers (smeared-out shock + shock layer itself), the complete Burnett equations are simplified in accordance with the problem of the cross-sectional flow-around of a round cylinder by the hypersound flow of rarified gas. The unitary asymptotic composite system of equations is formulated describing the flow in the entire thin shock layer including both of its above-mentioned structural areas (of the sublayer). Unlike the full Burnett equations, the obtained equation of the Burnett thin shock layer has an order not exceeding the order of the corresponding Navier-Stokes problem of the hypersonic thin shock layer, for which the research tool is sufficiently well developed.

A comparative analysis of approaches for investigating hypersonic flow over blunt bodies in a transitional regime

Hypersonic flows of a viscous perfect rarefied gas over blunt bodies in a transitional flow regime from continuum to free molecular, characteristic when spacecraft re-enter Earth's atmosphere at altitudes above 90-100km, are considered. The two-dimensional problem of hypersonic flow is investigated over a wide range of free stream Knudsen numbers using both continuum and kinetic approaches: by numerical and analytical solutions of the continuum equations, by numerical solution of the Boltzmann kinetic equation with a model collision integral in the form of the S-model, and also by the direct simulation Monte Carlo method. The continuum approach is based on the use of asymptotically correct models of a thin viscous shock layer and a viscous shock layer. A refinement of the condition for a temperature jump on the body surface is proposed for the viscous shock layer model. The continuum and kinetic solutions, and also the solutions obtained by the Monte Carlo method are compared. The effectiveness, range of application, advantages and disadvantages of the different approaches are estimated.

Control of disturbances of a hypersonic viscous shock layer on a flat plate

Receptivity of a viscous shock layer on a flat plate aligned at an angle of attack to external multiwave acoustic perturbations is studied. It is shown that external acoustic waves and periodic controlled perturbations introduced from the surface of the plate mounted at an angle of attack smaller than 20° generate entropy-vortex disturbances with a similar spatial distribution in the viscous shock layer. This result allows numerical implementation of the interference method of controlling disturbances generated in the viscous shock layer on the plate by external acoustic waves at one frequency and at a spectrum of frequencies by introducing blowing-suction perturbations on the plate surface with appropriate amplitudes and phases.