Heating enhancement caused by a transverse control jet in hypersonic flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition. Received 28 August 1996 / Accepted 6 June 1997     

激波冲击SF6重气泡引发射流的数值模拟

为深入研究重气泡内激波聚焦和射流生成的机理,采用高精度计算格式和高网格分辨率对马赫数为1.23的平面入射激波与SF₆重气泡的作用过程进行数值模拟,计算结果与文献中实验吻合较好。结果显示:入射激波在重气泡内首先在流向上汇聚形成上、下对称的高压区,随后,这对高压区在SF₆重气泡中心对称轴处再次碰撞,完成激波聚焦过程,并在气泡下游界面附近形成远大于初始压力和密度的局部高压高密度区,体现出SF₆重气泡极强的聚能效应;激波聚焦还引起气泡下游界面附近的涡量变化,涡对的旋转能够加速射流形成与发展。因此,SF₆重气泡下游界面附近的高压区和涡量分布对形成射流结构均有促进作用。     

Vorticity and its rate of change just downstream of a curved shock

A theory is developed for the vorticity and its substantial derivative just downstream of a curved shock wave, the resulting formulas are exact, algebraic, and explicit. Analysis is for a cylinder-wedge or sphere-cone body, at zero incidence, whose downstream half-angle is θ_b. Derived formulas directly depend only on the ratio of specific heats, γ, the freestream Mach number, M ₁, the local slope and curvature of the shock, and the dimensionality parameter, σ, which is zero for a two-dimensional shock and unity for an axisymmetric shock. In turn, the slope and curvature depend on γ, M ₁, and θ_b. Numerical results are provided for a bow shock in which θ_b is 5°, 10°, or 15°, M ₁ is 2, 4, or 6, and γ = 1.4. There is little dependence on the half angle but a strong dependence on the freestream Mach number and on dimensionality. For vorticity and its substantial derivative, the dimensionality dependence gradually decreases with increasing Mach number. In comparison to the two-dimensional case, an axisymmetric shock generates considerable vorticity in a region relatively close to the symmetry axis. Moreover, the magnitude of the vorticity, in this region, is further enhanced in the flow downstream of the shock. This dimensionality difference in vorticity and its substantial derivative is attributed to the three-dimensional relief effect in an axisymmetric flow.

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Wall pressure fluctuations in the reattachment region of a supersonic free shear layer

A study was made of the wall pressure fluctuations in the reattachment region of a supersonic free shear layer. The free shear layer was formed by the separation of a Mach 2.9 turbulent boundary layer from a backward facing step. Reattachment occurred on a 20° ramp. By adjusting the position of the ramp, the base pressure at the step was set equal to the freestream pressure, and the free shear layer formed in the absence of any turning. An array of flush-mounted, miniature, high-frequency pressure transducers was used in the vicinity of the reattachment region to make multichannel measurements of the fluctuating wall pressure. Contrary to previous observations of this flow, the reattachment region was found to be highly unsteady, and the pressure fluctuations were found to be large. The overall behavior of the wall pressure loading is similar in scale and magnitude to the unsteadiness of the wall pressure field in compression ramp flows at the same Mach number. Rayleigh scattering was used to visualize the instantaneous shock structure in the streamwise and spanwise direction. Spanwise wrinkles on the order of half the boundary layer thickness were observed on the shock sheet.     

Density field of supersonic separated flow past an afterbody nozzle using tomographic reconstruction of BOS data

The background oriented Schlieren (BOS) technique has been applied to determine the density field in an oblique shock-separated turbulent boundary flow. Measurements were made for two cases, namely, with/without jet flow from the afterbody which is a nozzle. In addition, oil flow and Schlieren visualizations were carried out—the results show certain upstream features of interest including shock excursions. The mean density field from BOS is discussed along with results from conventional Schlieren flow visualization. The data extracted from the mean density field obtained through BOS have been compared for the jet-off and jet-on cases. The data obtained also show the mean density in the base region (jet-off case) to be about 50% of the freestream density and match the isentropic values for the underexpanded jet at the exit. The study involving shock–boundary interaction, movement of freestream shock over the afterbody in the presence of a jet plume provides understanding of flow physics in a flow regime where whole field velocity measurements are extremely difficult.     

Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function

Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Shock structure in separated nozzle flows

In the case of high overexpansion, the exhaust jet of the supersonic nozzle of rocket engines separates from nozzle wall because of the large adverse pressure gradient. Correspondingly, to match the pressure of the separated flow region, an oblique shock is generated which evolves through the supersonic jet starting approximately at the separation point. This shock reflects on the nozzle axis with a Mach reflection. Thus, a peculiar Mach reflection takes place whose features depend on the upstream flow conditions, which are usually not uniform. The expected features of Mach reflection may become much difficult to predict, depending on the nozzle shape and the position of the separation point along the divergent section of the nozzle.      

Shock wave diffraction in the presence of a supersonic co-flow jet

The interaction between a diffracting shock wave and a uniform jet is a case that so far has only been partially investigated. This interaction is extremely important for the control of noise generation and improvement of combustor performance. To fill this knowledge gap, three geometries of the diffracting corner, namely a straight ramp, a serrated ramp, and a rounded corner, have been tested experimentally to study the interaction of shock diffraction with a supersonic co-flow jet at incident Mach numbers of 1.31 and 1.59, with Reynolds numbers of \(1.08\times 10^{6}\) and \(1.68\times 10^{6}\), respectively. Schlieren photography was employed to analyse the evolution of the flow phenomena. The aim is to provide a qualitative understanding of the interaction between the diffracting shock wave and the uniform jet relevant to future high-speed transport. The results show that the flow field evolves more rapidly and develops stronger structures for a higher shock Mach number. The diffraction around a rounded splitter develops a periodical vortical structure which continues after the disturbance introduced by the passage of the shock wave is removed.     

Secondary loss generation by gas turbine support struts

Short cylindrical struts are commonly employed to carry services across the annular flow passages of gas turbines and to provide mechanical support. Velocity variations along the span of the strut will be large and secondary flow becomes important. For bluff bodies, boundary layer separation tends to be fixed close to the maximum thickness of the strut, or any sharp edges, so that secondary flow effects have only a minor influence on wake formation. In the case of more streamlined shapes, the effect of Reynolds number and freestream turbulence level on boundary layer growth are much more significant. Moreover, the secondary flows generated by the interaction between the strut cross-section and the end-wall boundary layers may influence the position of separation, thus changing the distributions of pressure on the strut surface and in the wake. These modifications lead to large variations in the total drag force experienced by the strut. A recent wind tunnel investigation is described in which wake pressure measurements have been used to determine the additional losses produced by the secondary flow generation. Experiments have been performed on isolated struts for both circular and streamlined cross-section over a range of Reynolds number, aspect ratio and thickness-to-chord ratio. A principal finding is that the results for the streamlined struts may be reduced to a correlation which embraces the effects of cross-sectional geometry as well as the end-wall boundary layer thickness, the Reynolds and the Mach numbers.     

Unsteadiness of the shock wave structure in attached and separated compression ramp flows

Wall pressure fluctuations have been measured upstream of the corner-line in several two dimensional, adiabatic, compression ramp flows. The nominal freestream Mach number was 3 and the Reynolds number, based on boundary layer thickness, was 1.4 million. The measurements show that the shockwave structure is unsteady in both separated and attached flows, resulting in a region in which the wall pressure signal is intermittent. Statistical properties of this intermittent region, and of the separated flow, are presented and correlated with results from other studies.     

Mach number effects on shock-bubble interaction

An investigation of Mach number effects on the interaction of a shock wave with a cylindrical bubble, is presented. We have conducted simulations with the Euler equations for various incident shock Mach numbers () in the range of , using high-resolution Godunov-type methods and an implicit solver. Our results are found in a very good agreement with previous investigations and further reveal additional gasdynamic features with increasing the Mach number. At higher Mach numbers larger deformations of the bubble occur and a secondary-reflected shock wave arises upstream of the bubble. Negative vorticity forms at all Mach numbers, but the “c-shaped” vortical structure appeared at gives its place to a circular-shaped structure at higher Mach numbers. The computations reveal that the (instantaneous) displacements of the upstream, downstream and jet interfaces are not significantly affected by the incident Mach number for values (approximately) greater than . With increasing the incident Mach number, the speed of the jet (arising from the centre of the bubble during the interaction) also increases. Received 21 December 2000 / Accepted 23 April 2001     

自然超空泡与尾喷流相互作用的数值模拟

认识带尾喷流和自然超空泡的水下高速航行体流体动力特性并发展其预报与控制方法仍是水动力学领域极具挑战性的课题．本研究采用CFD方法对尾喷流和自然超空泡之间的相互作用进行了数值研究．针对发动机欠膨胀超音速喷流,采用现有实验结果验证了基于两方程湍流模型的二维轴对称流动数值模型的可靠性．尾喷流在空气和蒸汽环境中流动的数值计算结果表明,由于蒸汽环境中背压较低,欠膨胀尾喷流无法及时形成压缩波,使得蒸汽环境中尾喷流的过膨胀区和气相扩散区的体积比空气中大;尾喷流很难形成规则的激波格栅,波系结构相对简单．针对携尾喷流的平头航行体超空泡流状态的数值模拟结果表明,尾喷流注入超空泡后迅速充满航行体周围的空腔区域;尾喷流与超空泡尾迹区域形成的回射流相互作用最终导致超空泡断裂,断裂过程中伴随着燃气泡的下泄现象;受空泡壁面约束,尾喷流难以在狭窄的超空泡空腔内完全膨胀,尾喷流的激波波系结构有显著的变化：在喷嘴附近受到压缩,在远离喷嘴区域受到超空泡水汽掺混的破坏;空泡内压强基本维持在饱和蒸汽压附近,没有显著增加．     

A pressure-based Mach-uniform method for viscous fluid flows

A pressure-based, Mach-uniform method is developed by combining the SLAU2 numerical scheme and the higher temporal order pressure-based algorithm. This hybrid combination compensates the limitation of the SLAU2 numerical scheme in the low-Mach number regime and deficiencies of the pressure-based method in the high-Mach number regime. A momentum interpolation method is proposed to replace the Rhie-Chow interpolation for accurate shock-capturing and to alleviate the carbuncle phenomena. The momentum interpolation method is consistent in addition to preserving pressure–velocity coupling in the incompressible limit . The postulated pressure equation allows the algorithm to compute the subsonic flows without empirical scaling of numerical dissipation at low-Mach number computation. Several test cases involving a broad range of Mach number regimes are presented. The numerical results demonstrate that the present algorithm is remarkable for the calculation of viscous fluid flows at arbitrary Mach number including shock wave/laminar boundary layer interaction and aerodynamics heating problem.     

Shock wave configurations and flow structures in non-axisymmetric underexpanded sonic jets

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.     

Calculation of hysteresis and flow-rate oscillations of base pressure in supersonic annular nozzles

The interaction of the turbulent axisymmetric near wake behind the face of the central body of an annular nozzle with the supersonic annular jet discharging from this nozzle is analyzed. The flow in the monoparametric near wake is calculated by the integral method [1] while the flow in the nonviscous jet is calculated by the method of through calculation using a monotonic explicit difference system of the first order of accuracy [2]. The interaction between the nonviscous and turbulent streams is determined by the displacement thickness of the wake. The initial conditions of the wake are determined from the integral conditions of attachment with the mixing flow in the isobaric base region. The interaction flow is described by the particular solution of the equations which passes through the singular saddle point — the throat of the wake. The near wake and base pressure in different modes of discharge from an annular nozzle at the exit cross section of which the ratio of outer and inner radii is y₂/y₁ = 1.3 and the Mach number is M = 2.54 are calculated as an example. The region of hysteresis of the base pressure, connected with the ambiguity of the interaction flow owing to the formation of the throat of the wake within the first or second barrel of the jet, and the parameters of the low-frequency flow-rate oscillations of base pressure in this region are determined. The results of the calculations are in satisfactory agreement with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–130, January–February, 1977.     

Baroclinic vortex sheet production by shocks and expansion waves

Vortex sheet production by shocks and expansion waves refracting at a density discontinuity was examined and compared using an analytical solution and numerical simulations. The analytical solution showed that with a small exception, vortex sheet strength is generally stronger in fast/slow shock refractions. In contrast, expansion waves generated a stronger vortex sheet in slow/fast refractions. This difference results in larger vorticity deposited by shocks in fast/slow refractions and by expansion waves in slow/fast refractions. Shock refractions become irregular and the analytical solution fails when either incident, transmitted or reflected shock, exceeded the angle limit for an attached shock. To investigate vortex sheet production outside the range of analytical solutions and to verify the applicability of the planar-interface analytical solution to a curved interface, shock refraction through a sinusoidal interface was numerically simulated in the shock frame of reference. It is found that variation in the local incidence angle along the curved interface creates pressure waves that affect the level of deposited vorticity. This contributes to the difference between predictions from local analysis and numerical computation. Furthermore, an interesting behavior of the shock and expansion wave-deposited vorticity in supersonic ramp flow was discovered. When the high- and low-density streams were swapped, while keeping the incident flow Mach numbers constant, a vortex sheet of equal magnitude but of opposite sign was generated.     

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

Comparison of velocity and temperature measurements with simulations in a hypersonic wake flow

A hypersonic shock-tunnel flow around an axisymmetric model of a planetary entry probe is analyzed. Planar laser-induced fluorescence is applied to measure both the velocity and the rotational temperature everywhere in the central plane of the flow field. The experimental test case is compared to simulations using the direct simulation Monte Carlo (DSMC) method. While the Mach 9.7 flow at a freestream Reynolds number based on the model diameter of 35,000 is chemically frozen, effects of thermal non-equilibrium and localized rarefaction cannot be neglected. DSMC and measurements agree well within the outer wake, but disagree close to the centerline, where in particular the measured velocity is higher than values predicted by the simulations. The experimental results indicated a shorter recirculation region and increased local fluctuations in the free shear layer upstream of the wake recompression shock when compared to the simulation. These effects are attributed to incipient transition, which is not observed in the simulations, as the simulations did not model the effects of freestream fluctuations. Furthermore, measured and simulated vorticities are compared with theoretical predictions.     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).