Effect of sound-absorbing materials on intensity of disturbances in the shock layer on a flat plate aligned at an angle of attack

Results of a numerical and experimental study of characteristics of disturbances in a hypersonic shock layer on a flat plate covered by a sound-absorbing coating and aligned at an angle of attack are presented. Experiments and computations are performed for the free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 6 · 10⁴. A possibility of suppressing pressure fluctuations in the shock layer at frequencies of 20–40 kHz with the use of tubular and porous materials incorporated into the plate surface is demonstrated. Results of numerical simulations are found to be in good agreement with experimental data.     

An investigation of electromagnetic wave propagation in plasma by shock tube

This paper presents the electromagnetic wave propagation characteristics in plasma and the attenuation coefficients of the microwave in terms of the parameters he, v, w, L, wb. The φ800 mm high temperature shock tube has been used to produce a uniform plasma. In order to get the attenuation of the electromagnetic wave through the plasma behind a shock wave, the microwave transmission has been used to measure the relative change of the wave power. The working frequency is f = (2-35)GHz (ω=2πf, wave length A =15cm-8mm). The electron density in the plasma is ne = (3×10^10-1×10^14) cm^-3. The collision frequency v = (1×10^8-6×10^10) Hz. The thickness of the plasma layer L = (2-80)cm. The electron circular frequency ωb=eBo/me, magnetic flux density B0 = (0-0.84)T. The experimental results show that when the plasma layer is thick (such as L/λ≥10), the correlation between the attenuation coefficients of the electromagnetic waves and the parameters ne,v,ω, L determined from the measurements are in good agreement with the theoretical predictions of electromagnetic wave propagations in the uniform infinite plasma. When the plasma layer is thin (such as when both L and A are of the same order), the theoretical results are only in a qualitative agreement with the experimental observations in the present parameter range, but the formula of the electromagnetic wave propagation theory in an uniform infinite plasma can not be used for quantitative computations of the correlation between the attenuation coefficients and the parameters ne,v,ω, L. In fact, if ω<ωp, v^2<<ω^2, the power attenuations K of the electromagnetic waves obtained from the measurements in the thin-layer plasma are much smaller than those of the theoretical predictions. On the other hand, if ω>ωp, v^2<<ω^2 (just v≈f), the measurements are much larger than the theoretical results. Also, we have measured the electromagnetic wave power attenuation value under the magnetic field and without a magnetic field. The result indicates that the value measured under the magnetic field shows a distinct improvement.     

Experimental and numerical analysis of the structure of pseudo-shock systems in laval nozzles with parallel side walls

Detailed numerical and experimental investigations of pseudo-shock systems in a Laval nozzle with parallel side walls are carried out. The location of the pseudo-shock system is defined in this system of two choked Laval nozzles by the ratio of the critical cross sections A₂^*/A₁^*{{A}_{2}^*/{A}_{1}^*} , the stagnation pressure loss across the shock system and viscous losses. The wall pressure distributions and high-speed schlieren videos recorded in the experiments are compared to the results of a steady and an unsteady numerical simulation. For the steady case, good agreement is found between the calculated and measured shock structure and pressure distribution along the primary nozzle wall, except for a remaining slight deviation in the shock position. For the unsteady case, in which asymmetric shock configurations are observed, deviations of the results with respect to the stochastic wall attachment of the shock system are given which indicate the necessity of further investigations on that topic.     

Wave processes in the shock layer on a flat plate at an angle of attack

A numerical and experimental study of receptivity of the viscous shock layer on a flat plate aligned at an angle of attack to external acoustic perturbations is performed. Density and pressure fluctuations are measured in experiments at the free-stream Mach number M _∞ = 21 and Reynolds number Re ₁ = 6·10 ⁵ m ⁻¹ . Direct numerical simulations of receptivity of the viscous shock layer to external acoustic perturbations in wide ranges of the governing parameters are performed by solving the Navier-Stokes equations with the use of high-order shock-capturing schemes. The calculated intensities of density and pressure fluctuations are found to be in good agreement with experimental data. Results of the study show that entropy-vortex disturbances dominate in the shock layer at small angles of attack, whereas acoustic perturbations prevail at angles of attack above 20°.     

Transmission characteristics of EM wave in a finite thickness plasma

One of the key factors for solving the problems of re-entry communication interruption is electromagnetic(EM) wave transmission characteristics in a plasma.Theoretical and experimental studies were carried out on specific transmission characteristics for different plasma sheath characteristic under thin sheath condition in re-entry state.The paper presents systematic studies on the variations of wave attenuation characteristics versus plasma sheath thickness L,collision frequency ν,electron density n e and wave working frequency f in a φ 800 mm high temperature shock tube.In experiments,L is set to 4 cm and 38 cm.ν is 2 GHz and 15 GHz.n e is from 1×10 10 cm(-3) to 1×10 13 cm(-3),and f is set to 2,5,10,14.6 GHz,respectively.Meanwhile,Wentzel-Kramers-Brillouin(WKB) and finite-difference time-domain(FDTD) methods are adopted to carry out theoretical simulation for comparison with experimental results.It is found that when L is much larger than EM wavelength λ(thick sheath) and ν is large,the theoretical result is in good agreement with experimental one,when sheath thickness L is much larger than λ,while ν is relatively small,two theoretical results are obviously different from the experimental ones.It means that the existing theoretical model can not fully describe the contribution of ν.Furthermore,when L and λ are of the same order of magnitude(thin sheath),the experimental result is much smaller than the theoretical values,which indicates that the current model can not properly describe the thin sheath effect on EM attenuation characteristics.     

Experimental study of plasma flow in a disk MHD channel under conditions of spontaneous formation of a current layer

The results of an experimental study of the plasma flow in a disk channel under conditions of strong hydromagnetic interaction are presented. It is shown that if the condition Re_mH ₀ ² /80.2 is satisfied for the magnetic Reynolds number at some point of the stream, then a current layer develops at that point characterized by a high electric-current density and high conductivity and temperature. The formation of the current layer leads to strong local retardation of the stream, the appearance of a shock wave, and a number of other nonlinear hydromagnetic phenomena. The experimental results are in agreement with theoretical studies conducted earlier.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 31–37, May–June, 1974.     

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.     

Correlation of the separation region length in shock wave/channel boundary layer interaction

 Results of an experimental investigation of the characteristics of a separation region induced by the interaction of an externally generated oblique shock with the turbulent boundary layer formed in a rectangular half channel are discussed. The experiments were carried out in the supersonic wind tunnel of the Institute of Theoretical and Applied Mechanics SB RAS at a free-stream Mach number M _∞=3.01 over a range of Reynolds numbers Re ₁=(9.7–47.5)×10⁶ m^-1 and at zero incidence and zero yaw of the model. Particular attention is paid to the size of the zone of the upstream propagation of disturbances (upstream influence region) under different experimental conditions: with varied values of the shock wave strength, half channel width, and Reynolds number. It is shown, in particular, that the normalized upstream influence region length as a function of inclination angle of the shock generator in a rectangular half channel is readily approximated by a simple exponential function. In support of the known reference data obtained for supersonic numbers M _∞ and moderate Re in other configurations, it is also shown that the upstream influence region length decreases with increasing Reynolds number. Generalization of experimental data on the length of the upstream influence region formed in similar geometric configurations is possible using an additional reference linear scale which is the distance from the leading edge of the shock generator to the exposed surface. A substantial dependence of the reference dimensions of separation region on the half channel width is also established. Received: 20 January 1997/Accepted: 30 June 1997     

Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Curing effects on the acoustical properties of epoxy polymers

This paper presents an experimental method for measuring the attenuation and the velocity of longitudinal ultrasonic waves propagating through flat epoxy polymer samples. The study takes place in the first phase of epoxy polymer's polymerization, where these materials pass slowly from liquid state to the solid state. For this purpose an experimental setup was introduced, suitable for the accurate evaluation of the acoustic properties Δα andc _ℓ ^e , when the epoxy polymers are in their first phase of polymerization, while they are cured for 24 hours at room temperature (20°C). The ultrasonic method used is the pulse echo-through transmission technique. From the variation ofc _ℓ ^e and Δα during the first phase of epoxy polymers curing, the three characteristic states: liquid, semi-solid and solid, are clearly determined. It is also observed that plasticizer reduces the testability and the semi-solid state shows greater attenuation than either the liquid or the solid state.     

Shock compressibility of polystyrene of variable initial density

The dynamic compressibility of polystyrene [C₆H₅-CH-CH₂]_n with initial densities of 1.0, 0.7, 0.5, and 0.3 g/cm³ has been investigated at pressures of 200–400 kbars. The D–₀ (wave velocity-initial density) relations are presented for specimens of normal and reduced density tested under identical conditions. Wave velocity-particle velocity relations are given for polystyrene of normal and reduced density together with the shock Hugoniots. The simplest equation of state satisfactorily describing the entire set of experimental data is selected.     

Influence of the initial boundary layer on base pressure

The base pressure p_b, for an initial turbulent boundary layer, is determined for supersonic nonisothermal flow about a two-dimensional backward-facing step. This problem has been considered previously. In solving it in [1, 2], use was made of the Korst condition [3], which assumes equality of the total pressure p_j ^* on the line of constant mass to the pressure behind the closing oblique shock. However the pressure at the reattachment section p_* is lower than that behind the closing shock by 30–40% [4], and consequently the Korst condition is inaccurate. Therefore in the references cited only qualitative agreement with experiment was obtained. In contrast with [1, 3], Nash [5] introduces p_*; however, it is defined by an empirical coefficient. In the present study, to find p_b we make use of the condition of conservation of mass in the base region, written in the form of the equality p_j ^*=p_*, where p_* is defined from the assumption of minimum thickness of the dissipative layer at the reattachment section.Satisfactory agreement with the available experimental data is obtained without the use of correction factors. In the simplest case, when the thickness of the oncoming boundary layer ₁=0, the proposed method is no more complex than that of Korst. The determination of the base pressure with ₁=0 is considered in §1, and the determination with ₁>0 is considered in §2.     

单模大扰动的Richtmyer-Meshkov不稳定性

采用高精度的多介质Ghost-Fluid方法,对马赫数为1.15的激波分别作用于单模大扰动Air-CO2、Air-SF6、Air-N2和Air-He界面后的Richtmyer-Meshkov不稳定现象进行了数值研究,得到了不同时刻扰动界面的演化图像,给出了流场的密度等值线和密度纹影图,同实验结果吻合较好。给出了界面的扰动增长随时间变化的情况,并同理论模型进行了对比。对激波从轻气体进入重气体的情况,扰动增长可采用Sadot模型描述线性阶段和早期非线性阶段;对于弱激波同密度接近的气体界面的相互作用,线性阶段时间较长,可用线性模型描述。     

One-dimensional shock wave interaction with rubber and low-porosity foam

One-dimensional interaction between a planar shock wave and a rubber or low-porosity foam is investigated experimentally and numerically. The considered polyurethane foam is of high density (ρ _c=290 kg/m³) and lowporosity (ϕ=0.76), and this corresponds to an intermediate condition between rubber and high-porosity foam. Stress-strain relations for the low-porosity foam are investigated by machine tests, which show larger deformation against compressive force and higher non-linearity in stress-strain curve as compared with rubber. Also the low-porosity foam shows a hysteresis cycle. Experiments on shock wave-foam interactions are conducted by using a shock tube. Experimental time history of the surface stress of the foam at the end of the shock tube does not show shock type stress increase, but continuous excessive stress rise can be seen, and then dumping vibration approaching to gas dynamic pressure of the reflected shock wave is followed, and the highest stress amounts about 3∼4 times of the pressure after the reflected gas dynamic shock wave. Interactive motions of gas and the low-porosity foam are analyzed using the Lagrangean coordinates system. An elastic model for a low-porosity foam is assumed to be a single elastic material with the measured stress-strain relation. Results of numerical simulations are compared with the shock tube experiments, which show essentially same stress variations with experimental results.     

Experimental investigation of the interaction between weak shock waves and granular layers

 The paper describes new experimental results regarding the pressure fields in front of and inside granular layers of different materials during their collision with weak shock waves. A variety of waves result from the shock wave-granular layer interaction. The pressure behind the reflected wave from the material interface approaches the equilibrium value, P ₅, which would have been reached had the shock wave reflected from a solid end-wall. The wave succession inside the layer depends solely on two processes: the complex interaction of the compaction wave with the granular material and the gas filtration, which affects the particles by the drag forces between the two phases. Inside a material with a permeability coefficient f>0.001 mm² the transmitted wave moves with a constant velocity which is largely governed by the gas filtration. For low permeability materials ( f<0.0003 mm²) the transmitted wave trajectory strongly depends on the compaction wave propagation. In such cases the compaction wave was found to be unsteady and its acceleration was higher in material having low material densities. The maximum compressive stress values, P _c , reached at the shock tube end-wall, covered by the materials under investigation, manifested as an unsteady pressure peak twice as large as the gas pressure P ₅, measured ahead of the layer. Comparing the present data with those available in the literature showed that the amplitude of the unsteady pressure peak was higher in materials having low effective densities, γ, and small permeability coefficients f. Contrary to flexible foams where the available experimental data indicated that the compressive stress in the post peak period converges to P ₅=P _g , the results obtained in the present study indicated that during the test time the compressive stress, P _s , was well preserved in the material and for most of the sample length its value was within the range P _s >P ₅>P _g . Received: 4 March 1996 / Accepted:26 September 1996     

Precursor ionization ahead of strong shock waves in argon

The mechanism of precursor ionization ahead of strong shock waves has been studied in a low density shock tube. The experimental results are illustrated with Arrhenius plots with kink points dividing them into two parts with apparent activation energy ratio 1:2, namely with the values 7.7 eV and 15.3 eV, and varying with first and third power of the density respectively. A model is proposed to interpret the facts where the process taking place in the precursor region, is a two step photo ionization accompanied with the drift flow effect of the gas relative to the shock wave or the ionization recombination effect according to whether the shock speed and initial density are low enough. The product of the A-A collision excitation cross section coefficientS ^* multiplied by the radiation cross sectionQ ^* of ArgonS ^*×Q ^*=1×10⁻³⁶ (cm⁴eV⁻¹) and the three body recombination coefficient of Argon at room temperaturek _ra =1×10⁻²⁴ (cm⁻⁶s⁻¹). The project supported by the National Natural Science Foundation of China     

Reynolds‐stress modelling of M = 2.25 shock‐wave/turbulent boundary‐layer interaction

M = 2.25 shock‐wave/turbulent‐boundary‐layer interactions over a compression ramp for several angles (8, 13 and 18°) at Reynolds‐number Re=7 × 10³ were simulated with three low‐Reynolds second‐moment closures and a linear low‐Reynolds standard k–ε model. A detailed assessment of the turbulence closures by comparison with both mean‐flow and turbulent experimental quantities is presented. The Reynolds‐stress model which is wall‐topology free and which uses an optimized redistribution closure, is in good agreement with experimental data both for wall‐pressure and mean‐velocity profiles. Detailed analysis of three components of the Reynolds‐stress tensor (comparison with measurements and transport‐equation budgets) provides a critical evaluation of full Reynolds‐stress models for the separated supersonic compression ramp. The discrepancy observed in the shock‐wave foot region, between computations and measurements for the Reynolds‐stresses profiles, could be explained by considering the experimental shock‐wave oscillation and directions for future modelling work are indicated. Copyright © 2007 John Wiley & Sons, Ltd.     

Achieving an optimal shock-wave mitigation inside open channels with cavities for weak shock waves: A computational study

This paper deals with a numerical study of weak shock-waves propagation and their attenuation in channel flow having different heights and exhibiting a hollow circular cavities with different depths and diffraction angles inside. The effect of initial diffraction angle and cavity depth on the shock mitigation is investigated. A better shock attenuation is achieved with diffraction angle θ_w = 90° by a factor of approximately 17% in terms of shock-Mach number and 38% in terms of total energy. The obtained results show also, in addition to the initial diffraction angle and cavity depth, the importance of reducing the channel heights as well as the position of the reduced section in achieving an optimal shock-wave attenuation. The presence of a cavity inside the channel helps to attenuate faster the shock wave. The underlying physics relies on the shock diffraction phenomenon that generates large amount of vortical structures capable of dissipating part of the shock energy by inducing a pressure loss behind it. A subtle arrangement of channel position/height and a cavity location leads to an efficient pressure attenuation by approximately a factor of 57% for M_s = 1.6 and 16% for M_s = 1.1.