The blunt-body problem in a nonuniform hypersonic viscous gas flow

The laws of heat transfer associated with the interaction of underexpanded supersonic gas jets and obstacles or blunt bodies have been investigated, for example, in [1–3]. Similar problems of nonuniform flow occur when bodies move in the wake behind other bodies; however, in this case the laws of heat transfer have so far received little attention [4–8]. It has been established that for a certain Reynolds number and flow nonuniformity parameters a zone of reverse-circulatory flow develops near the front of the blunt body. However, the conditions of transition to separated flow have not been determined. This paper presents a self-similar solution of the equations of the viscous shock layer near the stagnation line in supersonic flow past an axisymmetric blunt body located behind another body. On the basis of this solution a separationless flow criterion is proposed. The effect of the nonuniformity and the Reynolds number on the shock standoff distance, the convective heat flux and the friction drag of the blunt body is investigated. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–125, November–December, 1986. In conclusion the authors wish to thank I. G. Eremeitsev for useful suggestions and G. A. Tirskii for discussing their work.     

Thin triangular blunt-nosed plate in a viscous hypersonic flow

The effect of a small blunt nose on the hypersonic flow past a thin, high-sweep and high-aspect-ratio plate at small incidence is investigated. The analysis is made by means of numerical simulation within the framework of the parabolized Navier-Stokes equations and the Euler equations in combination with approximate methods for calculating the heat transfer. The results are compared with the data of experiments in which some nontrivial features of the heat flux distributions over the thin plate surface were revealed.     

Generalized reference enthalpy formulations and simulation of viscous effects in hypersonic flow

A generalized reference enthalpy formulation for the skin friction, heat transfer and radiation-equilibrium temperature distributions over aerodynamic surfaces in attached hypersonic / hyperenthalpic flow is proposed. The formulation, which has been extensively employed in various forms by numerous investigators in the perfect gas regime, has also been recently demonstrated to provide adequate estimates of the heat transfer distribution in thermochemically active high enthalpy flow conditions when coupled to thermochemically active Euler solutions. It is now used to reveal the relevant similitude parameters for viscous effects in hypersonic flow, and the importance of the temperature distribution across the boundary layer and of the temperature-viscosity relation. It is shown that, although reproduction of the flight total flow enthalpy as well as surface temperature is the obvious solution for full viscous simulation in (perfect gas) hypersonic flow, the hot surface testing requirement and, in a number of practical applications, also the hot flow requirement may be relaxed with reasonably small error that can be of the same order as the measurement accuracy in present-day hypersonic testing. This similitude error, however, may increase significantly in cases exhibiting strong viscous/inviscid interaction or when the laminar-turbulent transition process becomes important. In this respect, alternative full simulation solutions, which are less demanding in terms of reproduction of the high levels of flight freestream and surface temperature or even Reynolds number, are discussed. Received 6 May 1997 / Accepted 8 October 1997     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

Vortex characteristics in laminar cavity flow at very low Mach number

In the present paper, a laminar cavity is analysed at very low Mach numbers. The characteristics of core-vortices are proposed and commented. The experiments were performed in an open subsonic wind tunnel using particle image velocimetry (PIV). A rectangular cavity with a length-to-depth ratio of 4 was used (shallow and open type). Three different Reynolds numbers, based on cavity depth and free stream velocity, were examined (Re_h=4,000, 9,000 and 13,000). The upstream boundary layer was investigated using classical hot-wire anemometry and was found to be laminar. For each Reynolds number, a total of 1,000 vectors fields were acquired. The results are given in terms of conventional quantities (mean flow velocity, turbulence characteristics, Reynolds shear stress) and also in terms of vortex characteristics (such as probability density function of vortex location, vortex size and vortex circulation). Some of these vortex characteristics are then proposed in a local averaged presentation. The extraction of vortices from instantaneous flow fields has been done through the use of a home-made algorithm based on continuous wavelet analysis.     

HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

Turbulization of the wake behind a single roughness element on a blunted body at a hypersonic Mach number

The influence of a cylinder-shaped single roughness element on the laminar–turbulent transition in the presence of an entropy layer is experimentally studied. The experiments are performed on a blunted cone model at the Mach number M = 5. The roughness element is located on the blunted tip of the model. Information about the mean and fluctuating parameters of the boundary layer in the wake behind the roughness element is obtained by using hot-wire anemometry. It is shown that flow turbulization behind the roughness elements occurs at the local Reynolds number calculated on the basis of the roughness element height and equal to 400–500. It is found that the presence of the roughness element exerts a significant effect on the unsteady characteristics of the boundary layer if the roughness element height is smaller than the effective value.     

Heat transfer at the surface of a triangular body in a hypersonic viscous gas flow

The boundary layer on a semi-infinite triangular body of power-law shape is calculated for viscous interaction with an external hypersonic flow. The results of calculating the characteristics of the three-dimensional boundary layer are presented. The formation of secondary return flows and zones of intensified heat transfer on the surface of the body in the neighborhood of lines of flow divergence is noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 77–82, January–February, 1988.     

Stability of low Reynolds number flow with viscous heating

Summary The stability of fully developed plane Couette flow and pipe flow with viscous heating is studied at low Reynolds number for a Newtonian liquid with a temperature-dependent viscosity. The solution is obtained by a direct integration method of the eigenfunction equations, with eigenvalues located in the complex plane by means of the argument principle of complex variable theory. An instability will occur in plane Couette flow, but outside the parameter range which will be encountered in practice. There is no comparable instability in pipe flow. It can be concluded that a thermal mechanism does not cause the low Reynolds number instabilities observed in polymer processing operations.

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Zusammenfassung Für eine newtonsche Flüssigkeit mit temperaturabhängiger Viskosität wird die Stabilität der voll entwickelten ebenen Couette-Strömung und Rohrströmung bei niedrigen Reynolds-Zahlen untersucht. Die Lösung wird durch direkte Integration der Eigenwert-Gleichungen gewonnen, wobei das Argument-Prinzip der Funktionentheorie auf die in der komplexen Ebene gelegenen Eigenwerte angewandt wird. In der ebenen Couette-Strömung wird eine Instabilität gefunden, jedoch außerhalb des in der Praxis realisierten Parameter-Bereichs. In der Rohrströmung gibt es dagegen keine vergleichbare Instabilität. Man kommt zu dem Schluß, daß thermische Mechanismen nicht für die in Polymer-Verarbeitungsprozessen beobachteten bei niedrigen Reynolds-Zahlen auftretenden Instabilitäten verantwortlich gemacht werden können.

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With 6 figures and 1 table     

非结构混合网格化学非平衡粘性绕流数值模拟

在非结构混合网格上对化学非平衡粘性绕流进行了数值模拟。控制方程为考虑了化学非平衡效应的二维Navier-Stokes方程,化学动力学模型为7组元、7反应模型。控制方程中的对流项采用VanLeer逆风分裂格式处理,并应用MUSCL方法及Minmod限制器扩展到二阶精度,粘性项用中心差分格式处理。时间推进采用显式5步龙格-库塔方法。为了适应高超声速流场计算,对VanLeer通量分裂方法进行了改进,并引入了化学反应时间步长。对RAMC-II模型的飞行试验流场进行了数值模拟,计算结果与试验测量数据符合较好,并与参考文献中的数值模拟结果吻合。     

Influence of intense surface cooling on hypersonic viscous flow past a delta wing

The influence of intense surface cooling on the parameters of a laminar boundary layer flow on a thin delta wing in a hypersonic viscous perfect-gas stream is studied for the strong viscous-inviscid interaction regime. The effect of the power-law shape of the wing cross-section and the wing thickness to boundary-layer displacement thickness ratio on the local and total aerodynamic characteristics is numerically investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–64, July–August, 1998.     

Free-piston driver optimisation for simulation of high Mach number scramjet flow conditions

The University of Queensland (UQ) is currently developing high Mach number, high total pressure scramjet flow conditions in its X2 and X3 expansion tube facilities. These conditions involve shock-processing a high-density air test gas followed by its unsteady expansion into a low-pressure acceleration tube. This relatively slow shock-processing requires the driver to supply high pressure gas for a significantly greater duration than normally required for superorbital flow conditions. One technique to extend the duration is to operate a tuned free-piston driver. For X2, this involves the use of a very light piston at high speeds so that, following diaphragm rupture, the piston displacement substitutes for vented driver gas, thus maintaining driver pressure much longer. However, this presents challenges in terms of higher piston loading and also safely stopping the piston. This article discusses the tuned driver concept, the design of a very lightweight but highly stressed piston, and details the successful development of a new set of tuned free-piston driver conditions for X2.     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.