Wave processes in a viscous shock layer and control of fluctuations

In high-velocity high-altitude flight, the thick boundary layer on the surface of a flying vehicle merges with the bow shock wave so that, even at a large distance from a leading edge, they may form the so-called viscous shock layer (VSL). Like the boundary layer, the laminar VSL is unstable, and flow disturbances arising and developing in this layer induce its transition to the turbulent flow regime. However, the mechanisms governing their emergence and development in the hypersonic VSL may differ substantially from those investigated in supersonic flows with lower Mach numbers [1, 2]. A better understanding of the receptivity and instability mechanisms is a necessary condition for the development of efficient methods for controlling the laminar-turbulent transition in a hypersonic flow around flying vehicles.

In the framework of the approximation of local similarity to the Navier-Stokes equations, an investigation is made of the axisymmetric flow of homogeneous gas in a hypersonic shock layer, this including the region of transition through the shock wave. Boundary conditions, which take into account blowing of gas, are specified on the surface of the body and in the undisturbed flow. A numerical solution to the problem is obtained in a wide range of variation of the Reynolds number and the blowing parameter. Expressions are found for the dependences on the blowing parameter usually employed in boundary layer theory of the coefficients of friction and heat transfer on the surface of the body, which are divided by their values obtained for blowing parameter equal to zero. It is shown that these dependences are universal and the same as the dependences obtained from the solution of the equations of a hypersonic viscous shock layer with modified Rankin-Hugoniot relations across the shock wave and from the solution of the boundary layer equations.

A hypersonic viscous shock layer over a flat plate at the free-stream Mach number M∞ = 21 is investigated both numerically and experimentally. The shock layer is excited by either external acoustic field or blowing/suction on the plate surface. The interaction of disturbances with the leading edge shock wave and their development in the boundary layer are simulated by solving the Navier-Stokes equations with a high-order shock-capturing scheme. Data of numerical simulations are compared very favorably with measurements conducted in a hypersonic nitrogen wind tunnel using the electron-beam fluorescence techniques. Numerical simulations show that the interference between natural and artificially excited disturbances can be used for active control of the instability development. This conclusion is confirmed experimentally.

The streamlining of bodies with catalytic surfaces is investigated within the framework of a model of a hypersonic three-dimensional viscous shock layer.

Effects of controlled heat addition into the high temperature, chemically reacting shock layer of a large angle (60°) blunt cone with a spherical nose have been experimentally investigated. The exothermic oxidation of ablated chromium from the surface of the cone at hypersonic Mach numbers triggers the heat release process. A conical skirt with a base diameter of 70 mm and a semi-apex angle of 30°, culminating into a nose of radius 30 mm, has been used as the test model. An in-house hypersonic free-piston driven shock tunnel facility, HST3, was used for the experiments at a stagnation enthalpy of 6.31 MJ/kg and a freestream Mach number of 9.84. The temperature distribution in the shock layer was experimentally measured by the two-color ratio pyrometry technique, using a Digital Single Lens Reflex (DSLR) camera as a pyrometer. The temperature field was corrected for discrete radiative line emissions obtained through emission spectroscopy. Surface heat flux measurements were taken using carefully calibrated thin film platinum heat transfer gauges mounted on an insulating Macor substrate. Shock stand-off distances were measured through Schlieren imaging of the flow using a high-speed camera at 20 000 frames per second, and also by a new intensity-scan based method using the processed color image from the DSLR camera. Calculations showed a 173 K rise in the temperature of the gas layer in the stagnation region due to chromium oxidation. The net surface heat flux on the blunt cone was also found to increase by about 31 W/cm2. The shock stand-off distance, as ascertained from Schlieren images, increased from about 3.82 mm (±1.4%) to 4.45 mm (±1.5%), a 17% rise. Analytical calculations, taking chromium oxidation reaction kinetics into consideration, to relate the total exothermic heat release to its distribution into various processes demonstrated that chromium oxidation releases about 78 W/cm2 energy in the stagnation region of the shock layer. 1.9% of this energy increases the temperature of the gas layer, 40% is convected back into the airframe, 0.4% is lost from the rear of the Macor substrate by conduction, and about 8% is radiated into the model. The remaining 50% of the heat was used up in pushing the shock layer away from the body by raising its density, thereby increasing shock stand-off distance.

Introduction A TOMS and molecules in the hot shock layer formed in front of a hypersonic vehicle often release some of their internal energy by spontaneous emission of electromagnetic radiation. The isotropically emitted radiative energy propagates through the shock layer, sometimes undergoing absorption, until a portion of the remaining energy eventually reaches the body surface and heats the vehicle. In cases of high-speed entries of large vehicles, the radiative heating can be larger than the convective heating from the hot gas. It is therefore crucial to the design of the protective heat shield that this radiative-transport process be modeled accurately. In practice radiative transport is typically reduced to a onedimensional line-of-sight problem by assuming small body curvature and small tangential flow gradients. This approach is known as the tangent slab model. In this Note, we present a three-dimensional transport model based on geometric view factors between the emitting volumes and surface elements, which significantly improves the accuracy of radiative heat-flux estimates for an optically thin shock layer. This method can also be applied to absorbing gases, but the cost can be significantly more than the tangent slab model if fine spectral resolution is required.

Results of a numerical and experimental study of characteristics of disturbances in a hypersonic shock layer on a flat plate covered by a sound-absorbing coating and aligned at an angle of attack are presented. Experiments and computations are performed for the free-stream Mach number M ∞ = 21 and Reynolds number Re L = 6 · 104. A possibility of suppressing pressure fluctuations in the shock layer at frequencies of 20–40 kHz with the use of tubular and porous materials incorporated into the plate surface is demonstrated. Results of numerical simulations are found to be in good agreement with experimental data.

An analysis technique applicable to the problem of leeward vortex-induced heat transfer on a sharp cone at high angles of incidence under hypersonic laminar flow conditions is presented. The analysis, a three-dimensional hypersonic viscous shock layer approach in conjunction with a numerical solution procedure, is shown to be both applicable and accurate based on comparisons of heat-transfer distributions, surface pressure distributions, and leeward meridian flow-field profile measurements taken in a hypersonic wind tunnel. Detailed calculations of the embedded vortex flow field on the leeward side of the cone are presented in such a manner as to clearly portray exactly how embedded vortex flow influences local heating rates.

A numerical investigation is carried out within the framework of the multicomponent total viscous shock layer model [6, 7], according to which when Re∞ ≳ 100 the flow near a blunt body can be divided into a shock wave zone and a viscous shock layer. At the inner edge of the shock wave the generalized Rankine-Hugoniot relations are imposed, and in the shock layer the complete system of viscous shock layer equations is solved with allowance for vibrational relaxation and nonequilibrium dissociation and ionization reactions.

The model of a perfect gas is used in a numerical simulation of unsteady effects in a viscous shock layer near the stagnation streamline near the front part of a rotating blunt body in an inhomogeneous external flow with pressure difference ΔPt8, temperature difference ΔTt8, and vorticity difference ΔΩ. The evolution of nonlinear disturbances due to the passage of a heated region and a change of the injection regime is followed. A divergence finite-difference scheme of second order of approximation across the shock layer, realized by vector sweeps with allowance for the boundary conditions on the surface of the body and behind the separated bow shock wave, is used.

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].

Active control of disturbances in a hypersonic shock layer

Shock layer temperature profiles are obtained through analysis of radiation from shock layers produced by a blunt body inserted in arc jet flow. Spectral measurements have been made in a nitrogen flow of 54.4 gm/s at an enthalpy of 8.72 MJ/kg. Vibrational temperatures for N2+ are obtained by matching spectral regions from arc jet spectra with spectra generated using the NEQAIR code. Temperature profiles obtained from the radiation layers show a vibrational temperature higher than the rotational temperature near the front of the shock and both temperatures decrease as the flow approaches the body. The spectral measurements are made and analysis completed for four distances, from the surface of the blunt body. The corresponding shock layer thickness is approximately 3.6 cm. Although the shock layer appears to be in thermal nonequilibrium, the measured rotational temperature approaches the single temperature results of viscous shock layer calculations at this test condition.

Results are presented in this article of numerical calculations of a viscous shock layer with the associated heat exchange in the vicinity of the critical point of a spherical blunt body taken into account in the presence of nonequilibrium chemical processes in the shock layer and on the surface of the body about which the flow takes place. A number of papers [1–4], in which specification of the surface temperature of the obstacle was utilized, have been devoted to the numerical investigation of a nonequilibrium viscous shock layer. At the same time the surface temperature of a body varies in actual flight due to heating, and together with this there is catalytic activity of the material, which appreciably complicates the problem and necessitates the simultaneous treatment of the course of processes in the gaseous and solid phases. The use of a separate formulation is difficult in this case, since the formulas for the thermal flux from the gaseous phase are of an estimative nature [5] when a volume nonequilibrium chemical reaction is present for a surface having an arbitrary catalytic activity. Taking account of the associated heat exchange has been done before for a number of problems of boundary-layer theory [6, 7], and in this case it has permitted determining the characteristics which are most important from the practical standpoint under conditions of flight along a specified trajectory, as well as under specified time-independent conditions of flight at altitudes at which the approximation of a viscous shock layer is valid. The effect of catalytic activity is discussed for a number of surface materials, and it is shown that the use of the formulas of boundary layer theory can appreciably distort the behavior of the surface temperature as a function of time for a certain altitude range.

An unsteady viscous shock layer near a stagnation point is studied. The Navier-Stokes equations are analyzed in the limit γ → 1, Re0 → ∞, df/dt = αn-mF(t/αm). The Reynolds number Re0 is defined in the paper by Eq. (1.3) (df/dt is the velocity of the body with respect to an inertial frame of reference moving with the original steady velocity −V't8, α2 = (γ − 1)/(γ + 1)). Various flow regimes in the case α ≪ 1, ɛ ≪ l, n ≥ max(2m, m + 1), m ≥ 0, where ɛ2 = 1/Re0 are analyzed. Equations are derived that generalize the asymptotic analysis to the case of a viscous unsteady flow of gas in a thin three-dimensional shock layer. The problem of a thin unsteady viscous shock layer near the stagnation point of a body with two curvatures is formulated. Examples of numerical solution are given for different ratios of the principal curvatures of the body, the wall temperature, the parameters of the original steady flow, and the acceleration and deceleration regimes.