Differential interferometry for studying hypersonic flows

The purpose of this article is to describe an optical technique based on differential interferometry with strongly phase-shifted beams using a white light source and a Wollaston prism. This technique is recommonded particularly for measuring very small index variations. It has been used for analyzing hypersonic flows around slender axisymmetrical bodies. The radial gas density distributions obtained in the shock layers were compared with the analytical solutions developed by Merlen and Andriamanalina (1992) and with Jones' tabulated computations (1969).List of Symbols m exponent of the obstacle's power law - R, R radii of the shock and of the obstacle, respectively - R _c radius of curvature of the spherical mirror - r radial coordinate - L obstacle length - L _m distance from model to spherical mirror - x, y cartesian coordinates with origin at obstacle nose - geometric angle of incidence - birefringence angle of the Wollaston prism, =() - wavelength - relative thickness of the obstacle - _c cone apex semi-angle - Y distance between the two partial beams at the level of the test section - n refractive index of the medium - E optical thickness - e test section width - _y light deviation along the y axis - h length of the path traveled by one of the two beams through the shock layer - gas density - _s gas density under standard conditions - freestream gas density - _min minimum detectable phase difference     

An efficient algorithm for hypersonic viscous flows

The CSCM-S algorithm proposed by Lombard et al. is a very attractive tool for solving multidimensional Euler and Navier-Stokes equations. However, it is not economical due to the use of global sweeps in the whole computational domain. In this paper we suggest a modified strategy, which combines a single-marching technique for supersonic dominated region with a multi-sweep procedure for pure subsonic and complex flowfield. The new algorithm may save significantly CPU time and is more suitable for engineering applications. The project supported by National Natural Science Foundation of China     

Viscous instability of hypersonic flow past a wedge

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 55–60, March–April, 1992.     

Simulation of supersonic and hypersonic flows

A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.     

Viscous shock layer on a plate in hypersonic flow

The results of theoretical and experimental investigations of the hypersonic flow around a plate with a shap leading edge are presented. Step-by-step verification of the numerical model of the full viscous shock layer is performed: the calculated density profiles, shock wave inclinations, and the Stanton numbers are compared with experimental data obtained using the method of electron-beam fluorescence, calorimetric gages and IR imaging system.     

Rarefied gas effect in hypersonic shear flows

Recently,as aerodynamics was applied to flying vehicles with very high speed and flying at high altitude,the numerical simulation based on the Navier-Stokes(NS)...     

Adiabatic shock capturing in perfect gas hypersonic flows

This paper considers the streamline‐upwind Petrov/Galerkin (SUPG) method applied to the compressible Euler and Navier–Stokes equations in conservation‐variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, is briefly reviewed. Of particular interest is the behavior of the shock‐capturing operator, which is required to regularize the scheme in the presence of strong, shock‐induced gradients. A standard shock‐capturing operator that has been widely used in previous studies by several authors is presented and discussed. Specific modifications are then made to this standard operator that is designed to produce a more physically consistent discretization in the presence of strong shock waves. The actual implementation of the term in a finite‐dimensional approximation is also discussed. The behavior of the standard and modified scheme is then compared for several supersonic/hypersonic flows. The modified shock‐capturing operator is found to preserve enthalpy in the inviscid portion of the flowfield substantially better than the standard operator. Published in 2009 by John Wiley & Sons, Ltd.     

Ultrasensitive glow discharge method for visualizing hypersonic flows of rarefied gases

The proposed method of visualizing hypersonic flows of a rarefied gas employs the cathode luminescence of a glow discharge. It is shown that the method possesses high sensitivity and good spatial resolving power and may be used to study flows with slip and in the transitional regime.     

Viscous heating correction for thermally developing flows in slit die viscometry

In the thermally developing region, d _yy /dx| _y=h varies along the flow direction x, where _yy denotes the component of stress normal to the y-plane; y = ±h at the die walls. A finite element method for two-dimensional Newtonian flow in a parallel slit was used to obtain an equation relating d _yy /dx/ _y=h and the wall shear stress ₀ at the inlet; isothermal slit walls were used for the calculation and the inlet liquid temperature T₀ was assumed to be equal to the wall temperature. For a temperature-viscosity relation /₀ = [1+(T–T₀]^–1, a simple expression [(hd _yy /dx/ _y=h )/ _w0] = 1–[1-F _c(Na)] [M()+P(Pr) ·Q(Gz ^–1)] was found to hold over the practical range of parameters involved, where Na, Gz, and Pr denote the Nahme-Griffith number, Graetz number, and Prandtl number; is a dimensionless variable which depends on Na and Gz. An order-of-magnitude analysis for momentum and energy equations supports the validity of this expression. The function F _c(Na) was obtained from an analytical solution for thermally developed flow; F _c(Na) = 1 for isothermal flow. M(), P(Pr), and Q(Gz) were obtained by fitting numerical results with simple equations. The wall shear rate at the inlet can be calculated from the flow rate Q using the isothermal equation.Notation x,y Cartesian coordinates (Fig. 2) - , dimensionless spatial variables [Eq. (16)] - dimensionless variable, : = Gz(x)^–1 - dimensionless variable [Eq. (28)] - t,t ^* time, dimensionless time [Eq. (16)] - , velocity vector, dimensionless velocity vector - _x , velocity in x-direction, dimensionless velocity - _y , velocity in y-direction, dimensionless velocity - V average velocity in x-direction - _yy , ^* normal stress on y-planes, dimensionless normal stress - shear stress on y-planes acting in x-direction - _w , _w ^* value of shear stress stress at the wall, dimensionless wall shear stress - _w0, _w0 ^* wall shear stress at the inlet, dimensionless variable - , ^* rate-of-strain tensor, dimensionless tensor - wall shear rate, wall shear rate at the inlet - Q flow rate - T, T ₀, temperature, temperature at the wall and at the inlet, dimensionless temperature - h, w half the die height, width of the die - l,L the distance between the inlet and the slot region, total die length - T ₂, T ₃, T ₄ pressure transducers in the High Shear Rate Viscometer (HSRV) (Fig. 1) - P, P2, P3 pressure, liquid pressures applied to T ₂ and T ₃ - , ₀, ^* viscosity, viscosity at T = T ₀, dimensionless viscosity - viscosity-temperature coefficient [Eq. (8)] - k thermal conductivity - C _p specific heat at constant pressure - Re Reynolds number - Na Nahme-Griffith number - Gz Graetz number - Pr Prandtl number     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

Properties of hypersonic separated flows at moderate reynolds numbers

The hypersonic rarefied flow past a flat plate with a transverse barrier and past a plate with a bend in the generator (a compression angle) is studied at Reynolds numbers Re≤10⁴. Direct statistical modeling (Monte Carlo method) is used to investigate the characteristics of the separated flow formed on the plate as a function of the Reynolds number, the surface temperature, the barrier dimensions, and the internal degrees of freedom of the molecules. The results obtained are compared with those for analogous high-Re flows. The possibility of using the similarity criteria derived for the continuum flow regime is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 134–144, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00577) and the Program of State Support for Leading Scientific Schools (grant No. 96-15-9606).     

On lubrication models for vertical rivulet flows

Meccanica - Rivulet flows are ubiquitous both in nature and industrial applications. Because of the typical length scales involved, most analyses of these flows rely on the so-called lubrication...     

VITA measurements of transition in transitional hypersonic boundary layer flows

The variable interval time-averaging (VITA) technique is applied to the hot-wire measurements made in three axisymmetric, transitional hypersonic boundary layers. The average duration of conditionally sampled events is used to detect the transition region. It is found that the stability Reynolds number at the peak in the average duration of conditionally sampled events correlates well with the stability Reynolds number that is intermediate to the onset of transition and peak heating. This VITA-identified location of transition moves upstream under the effects of both an adverse pressure gradient and wall cooling; this agrees with previous experimental and computational studies. The VITA technique, therefore, offers an alternative method to obtain details of the location of transition in hypersonic stability experiments, in which hot-wire measurements of the transitioning boundary layers are made.     

Effective property models for homogeneous two-phase flows

Using an analogy between thermal conductivity of porous media and viscosity in two-phase flow, new definitions for two-phase viscosity are proposed. These new definitions satisfy the following two conditions: namely (i) the two-phase viscosity is equal to the liquid viscosity at the mass quality = 0% and (ii) the two-phase viscosity is equal to the gas viscosity at the mass quality = 100%. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. These new models are assessed using published experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels in the form of Fanning friction factor (f_m) versus Reynolds number (Re_m). The published data include different working fluids such as R-12, R-22, argon (R740), R717, R134a, R410A and propane (R290) at different diameters and different saturation temperatures. Models are assessed on the basis minimizing the root mean square error (eRMS). It is shown that these new definitions of two-phase viscosity can be used to analyze the experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels using simple friction models.     

Development of some hypersonic benchmark flows using CFD and experiment

Abstract. This paper presents a set of test cases in high speed aerodynamics that describe our perceived relationship between experiment and computation. Computational fluid dynamics, with sensible interpretation, can guide experimental design, so that wind tunnel studies can focus better on fundamental ‘benchmark’ studies. Likewise experimental data may be used as feed back to evaluate codes and to improve their physical modelling. Here we present several test cases, developed in our laboratory, that we regard as basic ‘building blocks’ for high speed aerodynamics. These include: design for boundary-layer/pressure-gradient interaction; cavity flows; shock-wave/boundary-layer interactions; techniques for a graduated and controlled study of three-dimensional separated flows. Received 10 October 2001/ Accepted 19 November 2002 Published online 4 February 2003 Correspondence to: R. Hillier (r.hillier@ic.ac.uk) An abridged version of this paper was presented at the 23rd Int. Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001     

Calculation of stagnation streamline quantities in hypersonic blunt body flows

An approximate method for the efficient calculation of stagnation-streamline quantities in hypersonic flows about spheres or cylinders is suggested. Based on the local similarity of the flow field the two-dimensional Navier-Stokes equations are simplified to a one-dimensional approximation for the stagnation streamline. These equations are solved with an implicit finite-volume scheme. Comparisons with fully two–dimensional Euler and Navier–Stokes calculations for flows about spheres are presented, that include perfect gas flows and flows in chemical non-equilibrium. Comparisons with a number of experiments conclude this report. Received 8 May 1996 / Accepted 31 October 1996     

Numerical investigation of hypersonic nozzle flows at high reynolds numbers

The direct problem of viscous gas flow in a hypersonic nozzle of given geometry is solved on the basis of simplified Navier-Stokes equations. At a stagnation pressure of the order of several thousands of atmospheres, a compressibility factor is introduced into the equation of state. The gasdynamic parameter profiles and the Mach number distribution along the nozzle axis are obtained. The results of earlier calculations of profiled nozzles are revised. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–164, January–February, 1999.     

Correction to: Rarefied gas effect in hypersonic shear flows

Acta Mechanica Sinica - In the original publication two mistakes caused by typesetting emerged during the Springer internal production