Subsonic Compressible Flow Past a Body with Developed Cavitation

The essence of the Prandtl rule consists in the fact that in a flow at a Mach number M < 1 the transverse dimensions of a sharp-ended slender body must be reduced by a factor of 1/(1 - M²)^1/2 to conserve the same pressure distribution over the body surface as in a flow with the same velocity at M=0.Following Prandtl [1], the derivation is repeated with reference to axisymmetric flow with developed cavitation.     

Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle

This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813–847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813–847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli’s function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli’s function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813–847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.     

Existence of Stationary Supersonic Flows Past a Pointed Body

In this paper we study the mathematical aspects of the stationary supersonic flow past a non-axisymmetric curved pointed body. The flow is described by a steady potential flow equation, which is a quasilinear hyperbolic equation of second order. We prove the local existence of the solution to this problem with a pointed shock attached at the tip of the pointed body, provided the pointed body is a perturbation of a circular cone, and the vertex angle of the approximate cone of the pointed body is less than a critical value. The solution is smooth in between the shock and the surface of the body. Consequently, such a structure of flow near the tip of the pointed body and its stability is verified mathematically. Accepted October 13, 2000?Published online January 22, 2001     

Subsonic Flows in a Multi-Dimensional Nozzle

In this paper, we study the global subsonic irrotational flows in a multi-dimensional (n ≥ 2) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. First, we prove the existence of the global uniformly subsonic flow in a general infinitely long nozzle for arbitrary dimension with sufficiently small incoming mass flux and obtain the uniqueness of the global uniformly subsonic flow. Then we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely, provided that the incoming mass flux is less than the critical value. This gives a positive answer to the problem of Bers on global subsonic irrotational flows in infinitely long nozzles for arbitrary dimension (Bers in Surveys in applied mathematics, vol 3, Wiley, New York, 1958). Finally, under suitable asymptotic assumptions of the nozzle, we obtain the asymptotic behavior of the subsonic flow in far fields by means of a blow-up argument. The main ingredients of our analysis are methods of calculus of variations, the Moser iteration techniques for the potential equation and a blow-up argument for infinitely long nozzles.     

Existence and Stability of Supersonic Euler Flows Past Lipschitz Wedges

It is well known that, when the vertex angle of a straight wedge is less than the critical angle, there exists a shock-front emanating from the wedge vertex so that the constant states on both sides of the shock-front are supersonic. Since the shock-front at the vertex is usually strong, especially when the vertex angle of the wedge is large, then a global flow is physically required to be governed by the isentropic or adiabatic Euler equations. In this paper, we systematically study two-dimensional steady supersonic Euler (i.e. nonpotential) flows past Lipschitz wedges and establish the existence and stability of supersonic Euler flows when the total variation of the tangent angle functions along the wedge boundaries is suitably small. We develop a modified Glimm difference scheme and identify a Glimm-type functional, by naturally incorporating the Lipschitz wedge boundary and the strong shock-front and by tracing the interaction not only between the boundary and weak waves, but also between the strong shock-front and weak waves, to obtain the required BV estimates. These estimates are then employed to establish the convergence of both approximate solutions to a global entropy solution and corresponding approximate strong shock-fronts emanating from the vertex to the strong shock-front of the entropy solution. The regularity of strong shock-fronts emanating from the wedge vertex and the asymptotic stability of entropy solutions in the flow direction are also established.     

含中心裂纹压电体的二维精确解

解析地研究了含中心裂纹的压电体，它在无穷远处承受机电载荷，并在裂面上满足由Parton和Kudryavtsev以及Hao和Shen提出的绝对电边界条件。在平面应变假设下，给出其二维精确解，并提供了机械应变能释放率和裂尖能量释放率等数值结果。考虑工业应用范围之内常用的远场载荷时，由绝对电边界条件得出的能量释放率表现出明显的非线性特征及载荷相关性，而不是完全与电场无关，这一结论与Xu和Rajapakse在较小载荷下得到的规律不同。     

On the Asymptotic Limit of Flows Past a Ribbed Boundary

We consider a stationary Navier–Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional to a small parameter ε, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system of the Navier–Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is allowed without any constraint. The work of Š. N. supported by Grant IAA100190505 of GA ASCR in the framework of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.     

An Embedding Method for Bluff Body Flows: Interactions of Two Side-by-Side Cylinder Wakes

We introduce a simple method for the numerical simulation of bluff body flows where the solid object is represented by a distributed body force in the Navier–Stokes equations. The body force density is found at every time step to reduce the velocity within the computational cells occupied by the rigid body to a prescribed value. The method combines certain ideas from the immersed boundary method which was developed to treat biofluid mechanical flows and the volume-of-fluid method for simulating flows with fluid–fluid interfaces. The main advantage of this embedding method is that the computations can be effected on a regular Cartesian grid, without the need to fit the grid to the bluff body surfaces. Thus, flow past several complex bodies can be treated as easily as flow past a single body. The method is validated by reproducing well-established results for vortex shedding from a stationary cylinder. The flow past two side-by-side cylinders is then investigated. When the distance between the cylinders is small, they are seen to shed vortices in-phase, whereas for larger distances, the shedding occurs in anti-phase. For intermediate distances, various shedding patterns are observed, including quasi-periodic, asymmetric and chaotic regimes. Mean values and phase portraits associated with the cylinder lift and drag coefficients, as well as spectral analysis of the same data, are used to describe the flow. A transition diagram that can be compared with experiments or models outlines the various dynamical regimes as a function of the distance between the cylinders and the Reynolds number.     

Heat Transfer of a Cylindrical Body with Catalytic Surface in Subsonic Nonequilibrium Air Plasma Flow

Fluid Dynamics - Steady-state subsonic flows of nonequilibrium air plasma past a cylindrical body with plane face and heat transfer are investigated under the conditions characteristic of testing...     

TVD格式在超音速喷管三维粘性流动求解中的应用

详细给出了任意三维曲线坐标系中Ｎｏｖｉｅｒ－Ｓｔｏｋｅｓ方程的对流项ＴＶＤ格式的构造过程，建立了数值求解三维粘性流动的计算方法，应用该方法对三维超音速喷管中有激波及无激波情况下的两种工况的层流流场进行了数值求解，并与实验做了对比。结果表明本文建立的计算方法具有较高的精度，同时也证明ＴＶＤ格式具有分辩率高，稳定收敛等优点，为进一步开展叶栅流场及紊流的研究打下了基础。     

Existence and Uniqueness of Time-Periodic Physically Reasonable Navier-Stokes Flow Past a Body

Let be a three-dimensional exterior domain of class C^2,, 0<<1. Assume that a Navier-Stokes liquid is moving in under the action of a body force F that is time-periodic of period T, and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x| as |x|^–1 and its spatial gradient decays as |x|^–2, both uniformly in time. In addition, the pressure p decays like |x|^–2 and its gradient like |x|^–3, for almost all t[0,T]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finns physically reasonable solutions [4]. Moreover, we show that our time-periodic solutions are unique in a very large class, namely, the class of time-periodic weak solutions satisfying the energy inequality and with corresponding pressure fields verifying mild summability conditions in ×[0,T].     

Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Thermal Instability in a Horizontal Porous Channel with Horizontal Through Flow and Symmetric Wall Heat Fluxes

The linear thermoconvective instability of the basic parallel flow in a plane and horizontal porous channel is investigated. The boundary walls are assumed to be impermeable and subject to symmetric and uniform heat fluxes. The wall heat fluxes produce either a net heating or a net cooling of the fluid saturated porous medium. A horizontal mass flow rate is externally impressed leading to a stationary basic state with a temperature gradient inclined to the vertical. A region of possibly unstable thermal stratification exists either in the lower half-channel (boundary heating), or in the upper half-channel (boundary cooling). The convective instability of the basic flow is governed by the Rayleigh number and by the Péclet number. In the case of boundary heating, the thermal instability arises when the Rayleigh number exceeds its critical value, that depends on the Péclet number. The change of the critical Rayleigh number as a function of the Péclet number is determined numerically for arbitrary normal modes oblique to the basic flow direction. The most dangerous modes are the longitudinal rolls, with a wave vector perpendicular to the basic velocity. There exists a minimum value of the Péclet number, 19.1971, below which no linear instability is detected.     

Hypersonic Flow Past the Spherical Nose of a Body in the Presence of a Magnetic Field

The hypersonic flow past the nose of a spherical body containing current sources generating a magnetic field is investigated theoretically and numerically. The magnetohydrodynamic (MHD) flow is analyzed on the basis of the complete system of Navier-Stokes equations containing the force and thermal MHD terms and the electrodynamic equations. Local and integral thermal and aerodynamic characteristics of the body are found. It is shown that the presence of a magnetic field makes it possible to reduce the heat flow to the body in the neighborhood of the stagnation point by several times. However, in this case the total body drag increases.     

Plane Problem of Three-Dimensional Stability for a Hinged Plate with Two Symmetric End Cracks

The plane stability problem for a rectangular plate with two symmetric end cracks is solved in three-dimensional formulation. The three-dimensional linearized theory of stability and the finite-difference method are used. The effect of the crack parameter on the critical load is examined__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 47–52, April 2005.     

一种特殊梯度分布的功能梯度圆柱壳的二维分析

功能梯度材料是一种新型材料,其结构分析已成为当今力学研究的热点。本文对一种特殊梯度分布的功能梯度材料圆柱壳进行了二维精确分析。从弹性力学平面应变问题的基本方程出发,引入应力函数,导出功能梯度材料圆柱壳受静载作用下的控制微分方程。假设材料的杨氏模量沿半径方向呈幂函数分布,泊松比为常数,利用分离变量法,导出了简支边界情况下功能梯度圆柱壳的精确解。通过算例分析了不同梯度变化时,功能梯度圆柱壳内的应力和位移变化规律。计算结果表明不同梯度分布的圆柱壳结构中的应力、位移沿厚度方向的变化规律是不同的,有时甚至差别很大。因此对于材料性质梯度变化的功能梯度材料圆柱壳,必须针对其自身特点,建立相应的理论分析模型。     

Note on the Heat Transfer of Flows over a Stretching Wall in Porous Media: Exact Solutions

In this note, heat transfer over a stretching sheet with mass transfer in a porous medium is revisited. Analytical solutions are presented for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions are expressed by the Kummer’s function. Closed-form solutions are found and presented for some special parameters. The solutions might offer more insights of the heat transfer characteristics compared with the numerical solutions.     

Existence of Minimizers for a Variational Problem in Two‐Dimensional Nonlinear Magnetoelasticity

We prove the existence of energy‐minimizing configurations for a two‐dimensional, variational model of magnetoelastic materials capable of large deformations. The model is based on an energy functional which is the sum of the nonlocal self‐energy (the energy stored in the magnetic field generated by the body, and permeating the whole ambient space) and of the local anisotropy energy, which is not weakly lower semicontinuous. A further feature of the model is the presence of a non‐convex constraint on one of the unknowns, the magnetization, which is a unit vector field. (Accepted November 20, 1997)     

Exponential Decay of the Vorticity in the Steady-State Flow of a Viscous Liquid Past a Rotating Body

We construct a Sobolev homeomorphism in dimension \({n \geqq 4,\,f \in W^{1,1}((0, 1)^n,\mathbb{R}^n)}\) such that \({J_f = {\rm det} Df > 0}\) on a set of positive measure and J _f  < 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f _k such that \({f_k\to f}\) in \({W^{1,1}_{\rm loc}}\).