Ideal gas flows with separation zones and time-dependent contact discontinuities of complicated shape

Some examples of flows with separation zones andmovable contact discontinuities obtained as a result of the numerical integration of the time-dependent equations for an ideal gas are presented. The examples concern a steady annular separation zone on the blunt nose of a body in a supersonic flow, periodic shedding of unsteady discontinuities from a cylinder in a steady uniform subsonic flow with a supercritical Mach number, and the complicated deformation of a contact (tangential) discontinuity, namely, the boundaries of a two-dimensional jet, either subsonic or supersonic, flowing into a cocurrent subsonic low-velocity flow. A multiple increase in the difference grid capacity in the numerical integration of the Euler equations indicates the absence of a noticeable scheme viscosity effect in the examples calculated. The inviscid nature of the separation flows obtained is also confirmed by their well-known counterparts constructed in the ideal incompressible fluid approximation. The time-average velocity fields of the two-dimensional jet and the intensity of its sound field are in reasonable agreement with the available data.     

Numerical Investigation of Off-Design Regimes of Flow Past Power-Law Waveriders Based on the Flows Behind Plane Shocks

The results of a numerical investigation of supersonic off-design flow past waveriders at the freestream Mach numbers M = 4 and 8 are presented. Flow regimes with M both greater and smaller than the design value M _d are analyzed. Configurations based on the flows behind plane shocks and described by power-law functions are considered. The results are obtained by the finite-volume solution of the Euler equations using higher-order TVD Runge-Kutta schemes.     

Modeling of supersonic flows near flying vehicle elements

Supersonic flows near flying vehicle elements are calculated in the approximation of the full Navier-Stokes equations for a viscous compressible heat-conducting gas with different values of free-stream. Mach and Reynolds numbers and angles of attack. The main laws of the flow near the lifting surface. and in the inlet are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 98–108, March–April, 2009.     

Euler flow in a supersonic mixed‐compression inlet

Numerical simulation of a two‐dimensional mixed compression supersonic inlet is carried out by solving unsteady compressible Euler equations via a stabilized finite element method. The geometry of the inlet is similar to the one used by Anderson and Wong for experimental investigation for Mach 3 flow. The computations are capable of simulating the start‐up problems associated with the inlet. The critical back pressure for the successful operation of the inlet is computed. The effect of inlet back pressure on the total pressure recovery and the flow distortion level is analysed. Contrary to the popular belief, it is found that in addition to the throat to inlet capture area ratio, the ramp geometry close to the throat plays an important role in the start‐up dynamics. It is demonstrated via simulations that, everything else being same, the geometries of ramp upstream of the throat that are associated with a curvature higher than a certain threshold, result in unstarting the intake. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.     

Self-sustained oscillations and bifurcations of transonic flow past simple airfoils

A turbulent flow past two symmetric airfoils, whose bow and aft portions are circular arcs, whereas midparts are flat, is studies numerically. The amplitude of lift coefficient oscillations versus the free-stream Mach number M _∞ is analyzed at zero angle of attack. Ranges of M _∞ in which there exist flow bifurcations are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 37–44, November–December, 2008     

Impact of turbulence modelling on external supersonic flow field simulations in rocket aerodynamics

This paper contains a three-dimensional study on the influence of different turbulence models for external supersonic flow field simulations, aiming at reaching the best accuracy in rocket aerodynamics. A well-studied test case -a slender body- has been used for the validation process, which involves the major turbulence models available. The SST k–ω model has been selected as the most suitable one for this kind of flows. Good agreements between numerical, theoretical and experimental results are obtained, which are used to set up some guidelines regarding the configuration of Reynolds-averaged Navier–Stokes Computational Fluid Dynamics (CFD) supersonic models for these flight regimes.     

微/纳米粒子在缩放喷管中的加速特性

冷喷涂（CGDS）过程中粒子速度是决定粒子粘附性的最重要的因素之一。本文对确定进出口压力和温度边界条件下氮气（N2）在拉阀尔喷管中的流动进行了数值分析研究,并计算了粒径在100nm到50μm之间铜和铂两种金属粒子在喷管中的加速运动过程。结果表明在喷管扩张部分的出口处有圆锥状的微弱震荡（压缩波）产生;材料密度对微米尺度的粒子的加速特性有显著影响,而对纳米尺度粒子的加速行为影响不大;在相同的入口条件下,粒子越小则其在喷管出口处的速度越大。     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

Bifurcations in the transonic flow past a symmetric airfoil

Transonic flow past an airfoil with a small curvature in its midchord region is numerically investigated. The branching of the stationary solutions of the Euler equations is established and attributed to flow instability at certain angles of attack and freestream Mach numbers. The dependence of the lift coefficient on these parameters is studied.     

Structure of supersonic turbulent flows in the vicinity of inclined backward-facing steps

Supersonic (M_∞ = 2−5) turbulent flows in the vicinity of a two-dimensional backward-facing step with an inclined leeward side are considered by methods of mathematical modeling. The wave structure of the flow with a varied angle of inclination of the leeward side of the step and a varied free-stream Mach number is considered. __________ Translated From Prikladnaya Mekhanika I Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 48–58, November–December, 2006.     

Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.     

Numerical simulation of gap effect in supersonic flows

The gap effect is a key factor in the design of the heat sealing in supersonic vehicles subjected to an aerodynamic heat load. Built on S-A turbulence model and Roe discrete format, the aerodynamic environment around a gap on the surface of a supersonic aircraft was simulated by the finite volume method. As the presented results indicate, the gap effect depends not only on the attack angle, but also on the Mach number.     

无网格法在三维复杂超音速流场模拟中的应用研究

对最小二乘无网格方法在含复杂外形三维超音速流场中的应用进行了研究.选用分解法求解采用最小二乘法得到的对称方程组,针对最小二乘无网格方法的计算特点生成近似正交均匀分布的离散点,对B1AC2R常规导弹超音速流场采用最小二乘无网格方法进行了无粘数值模拟,计算了B1AC2R常规导弹在不同攻角下的轴向力、法向力及俯仰力矩系数,并将数值结果与实验结果进行了比较.结果表明,最小二乘无网格方法在求解含复杂外形超音速流场时具有较高的准确度,将其应用于三维含复杂外形超音速流场的模拟是完全可行的.     

Numerical calculations of supersonic underexpanded jets in a cocurrent flow with the use of parabolized Navier-Stokes equations

Results of a numerical study of three-dimensional supersonic jets propagating in a cocurrent flow are described. Averaged parabolized Navier-Stokes equations are solved numerically on the basis of a developed scheme, which allows calculations in supersonic and subsonic flow regions to be performed in a single manner. A jet flow with a cocurrent flow Mach number 0.05 ⩽ M_∞ ⩽ 7.00 is studied, and its effect on the structure of the mixing layer is demonstrated. The calculated results are compared with available experimental and numerical data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 54–63, May–June, 2008.     

Numerical modeling of the stabilization of a supersonic flat-plate boundary layer by a porous coating

On the basis of a numerical solution of the two-dimensional Navier-Stokes equations, the stability and the receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate with a passive porous coating partially absorbing flow disturbances is studied. The results of direct numerical simulation are in good agreement with the data of the linear stability theory. The studies confirm the possibility of effectively stabilizing the second mode of the supersonic boundary layer using porous coatings.     

NUMERICAL INVESTIGATION OF EVOLUTION OF DISTURBANCES IN SUPERSONIC SHARP CONE BOUNDARY LAYERS

The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory (LST) which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.     

Effects of dimensional wall temperature on Reynolds stress budgets in a supersonic turbulent channel flow with thermally perfect gas

ABSTRACT

Direct numerical simulations of temporally evolving supersonic turbulent channel flow of thermally perfect gas are conducted at Mach number 3.0 and Reynolds number 4800, combined with constant dimensional wall temperatures from 149.075 to 1788.90?K to study the influence of dimensional wall temperature on the characteristics of Reynolds stress budgets. It is found that, as the dimensional wall temperature increases, the production, diffusion, pressure–velocity gradient correlation and dissipation terms increase, whereas the compressibility-related term decreases. This is mainly due to variations in mean flow properties. The mechanism of inter-component transfer (ICT) is insensitive to the dimensional wall temperature. The ICT relating to the pressure–velocity gradient correlation term can be divided into inner and outer regions, and the critical position separating these regions is at the semi-local scaling of approximately 16 irrespective of the different dimensional wall temperature.     

二维时-空守恒格式及其在激波传播计算中的应用

将改进后的一维时－空守恒格式推广到了二维情形,得到了一个新的一般形式的二维Ｅｕｌｅｒ方程时－空守恒格式,并用该格式对几个具有复杂波系的流场进行了数值模拟。结果表明,该格式保留了一维格式通用性好、结构简单的优点,其计算结果精度高,对激波等间断具有很强的分辨率。