Conservation laws for laminar axisymmetric jet flows with weak swirl

The conservation laws for laminar axisymmetric jet flows with weak swirl are studied here. The multiplier approach is used to derive the conservation laws for the system of three boundary layer equations for the velocity components governing flow in laminar axisymmetric jet flows with weak swirl. Conservation laws for the system of two partial differential equations for the stream function are also derived.     

A remark on the Lipschitz estimates of solutions to Navier–Stokes equations

In this paper, we establish a constant‐type growth estimate in the Lipschitz norm of solutions to the 2D Navier–Stokes equations with fractional diffusion and a polynomial‐type growth estimate of solutions to the 3D axisymmetric Navier–Stokes equations. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical solutions of laminar swirl decay in a straight pipe

In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.     

Remarks on axisymmetric solutions of the incompressible euler system

Considering the incompressible Euler system with 3-D axisymmetric data, we give several global existence results corresponding to several classes of smooth or singular data.     

Asymptotic analysis of the Stokes flow in a thin cylindrical elastic tube

The purpose of this article is to perform an asymptotic analysis for an interaction problem between a viscous fluid and an elastic structure when the flow domain is a three-dimensional cylindrical tube. We consider a periodic, non-steady, axisymmetric, creeping flow of a viscous incompressible fluid through a long and narrow cylindrical elastic tube. The creeping flow is described by the Stokes equations and for the wall displacement we consider the Koiter's equation. The well posedness of the problem is proved by means of its variational formulation. We construct an asymptotic approximation of the problem for two different cases. In the first case, the stress term in Koiter's equation contains a great parameter as a coefficient and dominates with respect to the inertial term while in the second case both the terms are of the same order and contain the great parameter. An asymptotic analysis is developed with respect to two small parameters. Analysing the leading terms obtained in the second case, we note that the wave phenomena takes place. The small error between the exact solution and the asymptotic one justifies the below constructed asymptotic expansions.     

Numerical simulation of axisymmetric afterbody flows with jet exhaust

A fifth-order accurate compact difference scheme was used to compute the flow over an axisymmetric afterbody with jet exhaust. The solution was based on the mass-averaged Navier-Stokes equations combined with a two-parameter differential model of turbulence. The computations were performed on a specially generated mesh such that the flow in the exterior and interior of the nozzle could be described simultaneously. Numerical results are presented for various external flow conditions and various chamber pressures.     

Self-similar point vortices and confinement of vorticity

This papers deals with the large time behavior of solutions of the incompressible Euler equations in dimension 2. We consider a self-similar configuration of point vortices which grows like the square root of the time. We study the confinement properties of a blob of vorticity initially located around the first point vortex and moving in the velocity field produced by itself and by the other point vortices. We find a su?cient condition on the point vortices such that the vorticity stays confined around the first point vortex at a rate better than the square root of the time. The relevance to the large time behavior of the Euler equations is discussed.     

Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet

This paper deals with the unsteady axisymmetric flow and heat transfer of a viscous fluid over a radially stretching sheet. The heat is prescribed at the surface. The modelled non-linear partial differential equations are solved using an analytic approach namely the homotopy analysis method. Unlike perturbation technique, this approach gives accurate analytic approximation uniformly valid for all dimensionless time. The explicit expressions for velocity, temperature and skin friction coefficient are developed. The influence of time on the velocity, temperature and skin friction coefficient is discussed.     

Error analysis of the L2 least‐squares finite element method for incompressible inviscid rotational flows

In this article we analyze the L² least‐squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity‐vorticity‐pressure formulation. The least‐squares functional is defined in terms of the sum of the squared L² norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first‐order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H¹ norm for velocity and pressure and a suboptimal rate of convergence in the L² norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Combined method for solving an inverse boundary value problem of aerohydrodynamics for an axisymmetric body

A method was designed for determining the shape of an axisymmetric body from a given velocity distribution in its meridional cross section. The method is based on an iterative process involving the solution to an inverse problem in the plane case and the solution to a direct problem for the body. The iterative process has been implemented in a software program. Numerical computations are presented that illustrate the efficiency of the method.     

Viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow with diffusion

We establish viscosity vanishing limit of the nonlinear pipe magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed diffusion. The convergence is verified under various Sobolev norms, including the L^∞(H¹) norm.     

Convergence of gauge method for incompressible flow

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field and a gauge variable , , was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and verifies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretization. However, the boundary conditions for the auxiliary field are implemented explicitly (vertical extrapolation). The resulting momentum equation is decoupled from the kinematic equation, and the computational cost is reduced to solving a standard heat and Poisson equation. Moreover, such explicit boundary conditions for the auxiliary field will be shown to be unconditionally stable for Stokes equations. For the full nonlinear Navier-Stokes equations the time stepping constraint is reduced to the standard CFL constraint . We also prove first order convergence of the gauge method when we use MAC grids as our spatial discretization. The optimal error estimate for the velocity field is also obtained.

     

Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points

In this article, we consider the entropy-expansiveness of geodesic flows on closed Riemannian manifolds without conjugate points. We prove that, if the manifold has no focal points, or if the manifold is bounded asymptote, then the geodesic flow is entropy-expansive. Moreover, for the compact oriented surfaces without conjugate points, we prove that the geodesic flows are entropy-expansive. We also give an estimation of distance between two positively asymptotic geodesics of an uniform visibility manifold.     

Heat transfer in unsteady axisymmetric second grade fluid

This work looks at the heat transfer effects on the flow of a second grade fluid over a radially stretching sheet. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. Mathematical analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). The modelled non-linear partial differential equations in two dependent variables are reduced into a partial differential equation with one dependent variable. The resulting non-linear partial differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence is properly discussed. The series solutions and graphs of velocity and temperature are constructed. Particular attention is given to the variations of emerging parameters such as second grade parameter, Prandtl and Eckert numbers.     

Scattering of vortices in the Abelian Higgs model

We study the scattering of vortices in the Abelian (2+1)-dimensional Higgs model. We show that in the case of the symmetric head-on collision of N vortices, their trajectories are rotated by the angle π/N after the collision. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 77–91, July, 2008.     

Non-Uniqueness of Almost Unidirectional Inviscid Compressible Flow

Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with the Mach number equal to one (sonic states). Analytical quasi-one-dimensional results are supplemented by quasi-one-dimensional and axisymmetric three-dimensional finite volume computations. Good agreement between quasi-one-dimensional and axisymmetric results, including the presence of multiple stationary solutions, is presented for axisymmetric nozzles with reasonably small slopes of the radius.     

Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom

We consider the Cauchy problem of a mathematical model for an incompressible, homogeneous, Newtonian fluid taking into account internal degrees of freedom. We first show that there exists a unique global strong solution when the given initial data are small in some sense. Then, we deduce the optimal decay rates for velocity vector in L² ? norm and L^p ? norm for p > n. These decay estimates depend only on the spatial dimension and the decay properties of the heat solution with the same data. Copyright © 2013 John Wiley & Sons, Ltd.     

可允许度量下有限能量辛涡旋的渐近行为献给钱敏教授90华诞

假设(X,ω)是一个具有紧致单连通Lie群G Hamilton作用的紧致光滑辛流形.本文证明只要Riemann面的柱形端口具有一个比标准柱形度量增长速度快的线性度量,那么任何一个有限能量辛涡旋将以指数衰减的速度收敛到辛流形X在正则值辛约化的扭曲分支或非扭曲分支上.本文结果无需假设群G在正则水平集上的作用是自由的.因此,它直接推广了Ziltener在群作用自由的假设下得出的相关结果.本文结果在作者关于量子化Kirwan同态的系列工作中有重要应用.     

Semi-elliptic computation of an axi-symmetric transonic nozzle flow

A newly developed, semi-elliptic computational algorithm is employed to predict the transonic flow inside an axisymmetric, convergent-divergent nozzle featuring small wall radius of curvature at the throat. The predictions obtained are compared against flow measurements for this nozzle, which have been reported elsewhere. Good agreement between the corresponding measurements and predictions is revealed, thus validating the computational algorithm and demonstrating its value as a design tool.