Plasma mitigation of shock wave: experiments and theory

Two types of plasma spikes, generated by on-board 60 Hz periodic and pulsed dc electric discharges in front of two slightly different wind tunnel models, were used to demonstrate the non-thermal plasma techniques for shock wave mitigation. The experiments were conducted in a Mach 2.5 wind tunnel. (1) In the periodic discharge case, the results show a transformation of the shock from a well-defined attached shock into a highly curved shock structure, which has increased shock angle and also appears in diffused form. As shown in a sequence with increasing discharge intensity, the shock in front of the model moves upstream to become detached with increasing standoff distance from the model and is eliminated near the peak of the discharge. The power measurements exclude the heating effect as a possible cause of the observed shock wave modification. A theory using a cone model as the shock wave generator is presented to explain the observed plasma effect on shock wave. The analysis shows that the plasma generated in front of the model can effectively deflect the incoming flow; such a flow deflection modifies the structure of the shock wave generated by the cone model, as shown by the numerical results, from a conic shape to a curved one. The shock front moves upstream with a larger shock angle, matching well with that observed in the experiment. (2) In the pulsed dc discharge case, hollow cone-shaped plasma that envelops the physical spike of a truncated cone model is produced in the discharge; consequently, the original bow shock is modified to a conical shock, equivalent to reinstating the model into a perfect cone and to increase the body aspect ratio by 70%. A significant wave drag reduction in each discharge is inferred from the pressure measurements; at the discharge maximum, the pressure on the frontal surface of the body decreases by more than 30%, the pressure on the cone surface increases by about 5%, whereas the pressure on the cylinder surface remains unchanged. The energy saving from drag reduction is estimated to make up two-thirds of the energy consumed in the electric discharge for the plasma generation. The measurements also show that the plasma effect on the shock structure lasts much longer than the discharge period.

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具损伤压电智能层合板的动力分析

基于应变能等效原理、高阶剪切变形理论和Hamilton变分原理,考虑复合材料铺设层内的损伤效应,建立了具损伤压电智能层合板的运动控制方程,并运用Galerkin方法进行求解.数值算例中,讨论了损伤效应、厚跨比及压电层厚度与层合板总厚度之比对四边简支压电智能层合板自由振动频率的影响和外部控制电压对其动力响应的影响.     

多层电磁弹性圆柱壳内波的轴向传播

对多层电磁弹性圆柱壳内波的轴向传播进行了分析。根据柱坐标系下电磁弹性多层结构的几何方程、平衡方程和本构方程,推导出了两个层间变量所满足的状态方程。通过状态方程的解和层间变量连续性条件,得到了多层圆柱体内外表面层间变量的传递关系。最后利用边界条件,导出了波在传播时所满足的频散方程,并求得该结构的模态参数。以一个三层的压电/压磁材料组成的柱壳结构作为数值算例,计算出波在其中轴向传播时的频散关系和模态参数,并对计算结果进行了分析。     

Bending of Composite Plates under Static and Dynamic Loading

The stationary bending of a two-dimensional elastic system of joined rectangular plates with different mechanical properties and boundary conditions is studied. A technique for solving the corresponding problem is proposed. It is based on approximate approaches in combination with a generalization of the force method. It is established that the static strain state of the system is essentially dependent on the difference between the elastic moduli of the constituent plates. It is also shown that with certain boundary conditions, the dependence of the first resonant frequency on the relative position of plates along the contact line is nonmonotonic__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 77–84, January 2005.     

Attenuation of shock waves propagating over arrayed baffle plates

The paper reports results of shock tube experiments of the attenuation of shock waves propagating over arrayed baffle plates, which is motivated to simulate shock wave attenuation created accidentally at the acoustic delay line in synchrotron radiation factory upon the rupture of a metal membrane separating the acceleration ring at high vacuum and atmospheric test chambers. Experiments were carried out, by using double exposure holographic interferometry with double path arrangement, in a 100 mm×180 mm shock tube equipped with a test section of 180 mm×1100 mm view field. Two baffle plate arrangements were tested: Oblique and staggered baffle plates; and vertical symmetric ones. Pressures were measured along the shock tube sidewall at individual compartments for shock Mach numbers ranging from 1.2 to 3.0 in air. The results were compared with a numerical simulation. The rate of shock attenuation over these baffle plates was compared for vertical and oblique baffle plates. Shock wave attenuation is more pronounced in the oblique baffle plate arrangements than in the vertical ones. PACS 47.40.Nm; 42.40.Kw Communicated by C. Needham     

Interaction of a Streamwise Vortex with an Oblique Shock Wave

Interaction of a supersonic streamwise vortex with an oblique shock wave is considered. A mathematical model of the streamwise vortex is constructed. Three interaction regimes (weak, moderate, and strong) are found. It is shown numerically that vortex breakdown is possible in the case of strong interaction. The influence of the governing parameters on the interaction type is studied. It is shown that the main effect on the interaction type is exerted by the streamwise velocity and angle of the wedge forming the shock wave. The effect of splitting of the primary vortex on the shock wave in the case of moderate and strong interaction regimes is found.     

Asymptotic Solution of the Problem of Heat Transfer between Two Plates and a Uniform Fluid Flow

For low Peclet numbers, analytic expressions are obtained for three highest terms of the asymptotic expansion of the solution of the convective heat-transfer problem for a system consisting of two parallel plates with identical lengths identical and constant surface temperatures and an infinite uniform fluid flow with a low Prandtl number.     

Numerical study of spherical blast-wave propagation and reflection

The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate. Received 27 July 2000 / Accepted 25 January 2002 – Published online 17 June 2002     

On Boundary Damping for a Weakly Nonlinear Wave Equation

In this paper an initial-boundary value problem for a weakly nonlinear string(or wave) equation with non-classical boundary conditions is considered. Oneend of the string is assumed to be fixed and the other end of the string isattached to a spring-mass-dashpot system, where the damping generated by thedashpot is assumed to be small. This problem can be regarded as a rather simple model describing oscillationsof flexible structures such as suspension bridges or overhead transmission lines in a windfield. A multiple-timescales perturbation method will be usedto construct formal asymptotic approximations of the solution. It will also beshown that all solutions tend to zero for a sufficiently large value of thedamping parameter. For smaller values of the damping parameter it will be shownhow the string-system eventually will oscillate.     

Reisner板的哈密尔顿体系及其辛正交解析法

基于Ｒｅｉｓｎｅｒ板理论，通过对混合能变分原理的修正，建立了更一般的哈密尔顿型广义变分原理，并给出了Ｒｅｉｓｎｅｒ板问题的哈密尔顿正则方程及其共轭辛正交解析法