Experimental and Numerical Investigation of Heat Exchange between Underexpanded High-Enthalpy Air Jets and Cylindrical Models

Experiments on heat transfer in supersonic underexpanded high-enthalpy air jets are conducted on the VGU-4 induction plasmatron at the pressure in the compression chamber of 8.5 hPa. At the air flow rate of 3.6 g/s and the high-frequency generator powers of 45 kW(regime 1) and 64 kW (regime 2) the heat fluxes to the copper surface at the stagnation point of watercooled cylindrical models along the axes of dissociated air jets are measured. The models, 30 mm in diameter, could have a flat face or a hemispherical nose. In the same regimes, the stagnation pressures are measured using the Pitot tube in the shape of a cylinder, 30 mm in diameter, having either a flat face or a hemispherical bluntness with a receiving hole, 14 mm in diameter. For the experimental conditions calculations of flows in the plasmatron discharge channel and supersonic underexpanded jets issuing from the discharge channel are performed within the framework of the Navier–Stokes and Maxwell equations. The heat fluxes to the experimental models are computed and compared with the experimental data.     

HF-plasmatron experiment and numerical simulation of heat transfer in underexpanded dissociated-nitrogen jets

Experiments on heat transfer in underexpanded supersonic jets of high-enthalpy nitrogen are performed on the VGU-4 induction high-frequency plasmatron at a pressure of 10.4 GPa in a compression chamber. At gas flow rates of 2.4 and 3.6 g/s and HF generator powers of 45 and 64 kW the heat fluxes to the copper, stainless steel, MPG-7 graphite, and quartz surfaces are measured at the stagnation point of a water-cooled cylindrical, flat-ended model, 20 mm in diameter. In the same regimes the stagnation pressures are measured. The effect of the surface catalyticity with respect to nitrogen atom recombination on the heat flux is demonstrated and the qualitative catalyticity scale of the studied materials is established. In the supersonic regimes nonequilibrium nitrogen plasma flow in the discharge channel of the plasmatron and the underexpanded jet flow past the model are numerically simulated for the experimental conditions. The experimental and calculated data on the stagnation pressures and the heat fluxes to cooled surfaces of the metals, graphite, and quartz are compared.     

Effect of Gas Injection from the Surface of a Body on Its Interaction with a Temperature Inhomogeneity in a Supersonic Flow

The flow pattern in the shock layer and the aerodynamic characteristics of a hemisphere in unsteady axisymmetric interaction with a closed spherical hot-gas region embedded in the oncoming supersonic flow in the presence of intense injection of gas from the body surface into the shock layer are studied on the basis of the inviscid perfect gas model. Two cases are considered, namely, (1) when the radius of the permeable surface is greater than that of the temperature inhomogeneity and (2) when the injection is localized in the vicinity of the forward stagnation point and the permeable region is smaller the inhomogeneity.     

Solution of the equations of motion for a selectively radiating gas in a shock layer

Numerical solutions are obtained for the system of integro-differential equations describing the flow of a viscous, heat-conducting, selectively radiating gas in the region between the shock wave and a blunt body. The calculations are made for bodies of radius from 0.1 to 3 m with stagnation temperature from 6000° to 15 000° K. As a result of the calculations the convective and radiative thermal fluxes in the vicinity of the stagnation point are obtained. The effect of injection on convective and radiative heat transfer is studied.The first calculations of radiative thermal fluxes in air were made about 10 years ago in [1,2]. However, the results did not take account of the effects of emission and reabsorption, nor the interaction of the convective and radiative heating processes. These effects have been studied primarily with the use of simplified models of a radiating gas. Most often the approximation used is that of a gray gas with absorption coefficient which is independent of wavelength ([3–6] and others).The appearance in the literature of quite detailed data on the selective spectral absorption coefficients of air over a wide temperature range [7,8] has made it possible to solve the direct problem of calculating the flow field of a selectively radiating gas behind a shock wave with account for all the effects mentioned above.     

极高超声速稀薄气体原子辐射效应的p-DSMC方法

极高超声速流动激波层内的高温导致内能模态的激发并伴随热辐射发生, 过高的温度使得空气分子完全解离, 原子组分对辐射热的贡献将达到80%以上. 本文基于优化的原子辐射模型, 提出追踪光子?直接模拟蒙特卡罗(p-DSMC)方法, 研究了稀薄流区不同马赫数下的高超声速二维圆柱绕流的壁面辐射加热, 获得了有无激发辐射效应的壁面压力和热流以及沿驻点线变化的平动、振动和转动温度. 在不考虑激发辐射效应的情况下, 得到的壁面压力和热流与已有的模拟结果符合的非常好, 误差均在5%以内, 尤其是在驻点位置, 误差在1%以内; 获得的平动、振动以及转动温度均与文献结果符合的很好. 在相同的来流条件下, 考虑辐射效应后发现, 来流速度低于10 km/s时, 辐射加热不明显, 在驻点区域, 辐射加热占对流加热比重在7%左右; 来流速度大于10 km/s时, 在驻点区域, 辐射加热占对流加热比重将超过30%. 考虑辐射效应后, 对非平衡区的平动、转动和振动温度的最大值影响不大. 此外, 另一个重要结论是, 流场中原子的浓度是影响壁面辐射热流大小的一个重要因素.      

Experimental simulation of heat transfer in an HF-plasmatron with lengthened segmented discharge channel

Subsonic and supersonic air induction plasma flows in a VGU-4 100 kW plasmatron with segmented water-cooled cylindrical nozzle with the outlet cross-section 40 mm in diameter are investigated experimentally. The enthalpy on the axis of flow is measured in subsonic air jets. The heat fluxes are measured at the stagnation flow point on a cylindrical water-cooled model 50 mm in diameter located in subsonic air and nitrogen jets. The effect of the generator power, nozzle length, and pressure in the plasmatron pressure chamber on the distributions of the heat flux and the pressure at the stagnation point on the surface of cylindrical models 20 mm in diameter with a plane and hemispheric nose is investigated along the axis of underexpanded dissociated air jets.     

Laminar heat transfer near an asymmetric stagnation point

This paper considers the laminar boundary layer at an obstacle near the stagnation point of a three-dimensional incompressible potential flow, asymmetric with respect to this point (e.g., for a jet incident at an angle on an obstacle). The effect of compressibility is investigated in the example of a plane subsonic flow. The solution in the close vicinity of the stagnation point is obtained by expanding in series with respect to the longitudinal coordinate, and for the more distant vicinity, the problem is solved by the method of local similarity. It is shown that in this case (in contrast with a symmetric flow [1, 2]) the maximum heat flux does not coincide with the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–145, November–December, 1976.The author thanks V. V. Lunev for stating the problem and for scientific guidance.     

Experiments on dynamic behavior of near-field region in variable property jet with swirling flow

The dynamic behavior of the near-field region in a coaxial variable property jet has been experimentally investigated under a swirling flow produced by rotating cylindrical inner and outer tubes, focusing on how the swirl of the outer jet affects the formation of a stagnation point in the swirling inner jet. The inner and outer jets rotate in the same direction. Air, CO₂, or He is issued from the inner tube as a variable property jet, and air is issued from the outer tube in this work. In the case of a CO₂ jet (a high-density, low-viscosity gas jet), a stagnation point flow is more easily formed than in the case of an air jet, and the stagnation point location is significantly lower than in that of the air jet. When the swirl of the outer jet is introduced, a stagnation point flow is more easily formed than in the case of a nonswirling outer jet, and the stagnation point location is much lower than in the case of a nonswirling outer jet. In the case of a He jet (a low-density and high-viscosity gas jet), the inner jet does not have a stagnation point flow, and its overall behavior remains nearly unchanged even under high swirl numbers of the inner and outer jets. These results clearly show that the density and viscosity differences between the inner and outer jets have a significant impact on the dynamic behavior of the near-field region in the coaxial swirling jet. The significant lowering of the stagnation point location can be physically explained by considering the theoretical equation obtained in this work.     

Calculation of supersonic viscid flow near stagnation line of a blunt body

A numerical study is made of supersonic flow of a viscous gas in the vicinity of the stagnation line of plane and axisymmetric blunt bodies (cylinder, sphere). As in [1–5], which consider the compressed layer of a viscous gas in the vicinity of the stagnation point, use is made of the locally self-similar approximation, which is used to transform the Navier-Stokes equations into a system of ordinary differential equations. In the present paper the solution is sought with the simplifications of [5] and with more general conditions, which makes it possible to study a broad class of flows. The proposed numerical algorithm permits obtaining the structure of the compressed layer near the stagnation line, including the shock wave and the boundary layer. The calculations made on a computer for different flow conditions are illustrated by graphs.The author wishes to thank G. I. Petrov, G. F. Telenin, and L. A., Chudov for their interest in the study and for their helpful discussions. discussions.     

Self-entrainment of air on stepped spillways

The pseudo-bottom-inception point related to air entrainment is located further upstream on stepped spillways than on smooth spillways, for otherwise identical conditions. Its position is relevant concerning cavitation aspects, flow losses and flow depths. This Paper presents and discusses visual observations made with a high-speed camera and air concentration measurements in the vicinity of the pseudo-bottom air inception point on a stepped model spillway. Insight into the bottom aeration processes is provided, pointing at the effects of dynamic and turbulent air-phase surface troughs instantaneously protruding to the pseudo-bottom. In addition, the measured data were analyzed with regard to the extensions of these surface troughs. The trough bases were found to reach approximately 70–80% of the mixture flow depth upstream of the inception point, to 60–70% at the inception point and to 40–50% at the equilibrium flow region downstream of the inception point. The highly-turbulent character of developed flow is described and the general air transport process specified on the basis of air concentrations and related parameters.     

Enhancement of turbulent heat transfer during interaction of an impinging axisymmetric mist jet with a target

The flow structure and heat transfer of a mist jet with a low mass concentration of droplets (within 1%) impinging onto a flat surface aligned normal to the jet are studied numerically. The mathematical model is based on solving a system of Reynolds-averaged Navier-Stokes equations for a two-phase flow with the kinetic equation of the probability density function for coordinates, velocity, and temperature of particles. Addition of droplets is demonstrated to enhance heat transfer substantially, as compared with an impinging single-phase air jet in the region directly adjacent to the stagnation point of the jet.     

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion, induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.     

Effect of radiation on flow near stagnation point

We consider the problem of hypersonic flow about a blunt body with account for radiative energy transport. In the absence of absorption of radiation in the compressed layer, even for small optical thickness of the gas, as is known [1], physically incorrect solutions are obtained, since the gas enthalpy at the stagnation point on the body becomes zero. This takes place because the gas element on the zero streamline irradiates its energy completely. Naturally, the contradiction which arises in the absence of absorption must be resolved within the radiation scheme itself and is not removed, generally speaking, with the introduction of additional physical limitations.The flow of a radiating gas in the vicinity of the stagnation point is considered in [2, 3] using the simplest one-dimensional model. Under definite assumptions this flow is described by a single integrodifferential equation. However, account for gas absorption by expanding the integrand in a Taylor series in the vicinity of its local value, which is used in these studies, does not yield the possibility of obtaining a physically correct solution at the body. An analysis of this equation is made in the present paper.     

尖锐前缘气动加热机理与激波脱体距离研究

针对尖锐前缘所处的气动环境,分析了由于前缘尖化所带来的稀薄效应影响。应用理论方法推导了尖锐前缘驻点气动热的计算方法和计算公式,并结合CFD方法、DSMC方法和Fay-Riddel工程方法对其前缘钝头的流场、驻点热流进行了计算和对比分析。计算结果表明,由于前缘的尖化使得稀薄气体效应提前出现,从而影响到前缘的激波厚度、激波形状和激波脱体距离等流动现象,导致激波结构复杂化,可能会对进气道唇口的斜激波带来不利的影响。另外稀薄效应的影响降低了驻点热流,缓解了尖化前缘的气动热环境。     

Short-duration wind tunnel with combined heating and stabilization of parameters

A high-enthalpy short-duration wind tunnel (hotshot wind tunnel) is designed for different operation modes ensured by combining various methods of test gas heating [by an electric arc, chemical energy, adiabatic compression, and heating in an external source of heat (with respect to the settling chamber)]. The wind tunnel is designed for the following ranges of parameters: stagnation pressure p ₀ = 1–200 MPa, stagnation temperature T ₀ = 600–4000 K, Mach number M = 4–20, and test time t < 1 s. The wind tunnel can operate both in the regime of the classical hotshot facility with decreasing parameters of the test gas and in the regime with stabilization of parameters owing to synchronized motion of the opposite pistons of the pressure multiplier toward each other.     

Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL SHOCK-SHOCK INTERACTIONS ON A BLUNT BODY

A numerical study is conducted to simulate the effects of extraneous shock impingement on a blunt body in viscous hypersonic flow. The interaction of extraneous shock with the leading-edge shock results in a very complex flow field that contains local regions of high pressure and intense heating. The heating and pressure can be orders of magnitude higher than the peak values in the absence of shock impingement. The flow field is calculated by solving thin-layer Navier-Stokes equations with a finite-volume flux splitting technique developed by van Leer. For a zero or small sweep of the body, a type IV interaction occurs, which produces a lambda shock structure with a supersonic jet embedded in the otherwise subsonic flow; for a moderate sweep of about 25^°, a type V interaction occurs in which a subsonic shear layer sandwiched in supersonic flow is produced with a transmitted shock. In the present study, both type IV and type V interactions are investigated. Results of the present numerical investigation are compared with available experimental results. For the present conditions, the peak pressure is 2.2 times the unimpinged stagnation point pressure and the peak heating is 3 times the unimpinged stagnation point heating. The flow for a type IV interaction is found to be unsteady.     

Film boiling on a hot body moving in a fluid

We investigate the transient film boiling in the vicinity of a stagnation point on the frontal surface of a very hot blunt body which moves with a constant velocity in an incompressible viscous fluid in the presence of a vapor layer near the body surface. Within the unsteady two-phase boundary layer approximation, the equations of motion of the liquid and vapor phases are formulatedwith account of the conservation of mass, momentum, and energy on the a priori unknown phase interface. In the vicinity of the stagnation point on the body surface, the solution of the boundary layer equations is sought in the form of series in the longitudinal coordinate. For the leading terms of the series, a parabolic system of partial differential equations is obtained, which is solved numerically. The similarity parameters controlling the film boiling process are determined. On the basis of parametric numerical calculations, the dynamics of the vapor layer are investigated for the case of a plane hot body moving in water with the room pressure and temperature. In the space of governing parameters, the limits of the existence of steady and unsteady film boiling regimes are found.     

Rarefied gas flow near the forward stagnation point of a blunt body at hypersonic speeds

With reduction of the density in a hypersonic stream the transition of the flow from continuum to free molecule takes place gradually. The transition region may be divided into several regimes, in each of which a definite physical phenomenon is most significant. For the case of the flow in the vicinity of the forward stagnation point of a blunt body these phenomena include increase of the thickness of the detached shock wave and of the boundary layer, the presence of viscous flow in the entire disturbed layer ahead of the blunt body, reduction of the number of collisions between molecules and the associated relaxation effects, the increasing role of the interaction of the stream molecules with the surface, and the phenomena of slip and temperature jump.     

The impingement of sonic and sub-sonic jets onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using particle image velocimetry (PIV). The results indicate that as a free jet impinges on a flat surface at an inclined angle the jet is turned by and spread laterally onto the impingement surface. The impingement angle of the jet is the dominant parameter in determining the rate of turning/spreading for the jet. The stagnation point is located using the PIV data and is found upstream of the geometric impingement point and upstream of the location of maximum pressure. The location of the stagnation point is a strong function of impingement angle and a weak function of impingement distance and pressure ratio. The location of the stagnation point is compared with the location of maximum pressure and compared to a curve fit for the location of maximum pressure based an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow.