Kinematic problem of an ideal incompressible fluid flow around an arbitrarily moving airfoil

An unsteady kinematic problem for arbitrary two-dimensional motion of an airfoil in an ideal incompressible fluid with formation of one and two vortex wakes is solved. The problem is solved by the method of conformal mapping of the flow domain onto a circle exterior; solution singularities in the vicinity of a sharp edge are analyzed, and the initial asymptotics of the solution is taken into account. The calculated results are found to be in good agreement with available experimental data on visualization of the flow pattern. The necessity of correct modeling of the initial stage of vortex-wake formation is demonstrated. A regular flow pattern is found to form after three and more periods of oscillations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 120–128, March-April, 2009.     

Estimation of the losses in hydrodynamic cascades due to periodic flow unsteadiness

The losses in hydrodynamic cascades caused by periodic flow unsteadiness are theoretically estimated on the assumption that the losses are due to energy expenditure to the formation of unsteady trailing vortices shed from the profiles of the cascades. The trailing vortex intensity is determined within the framework of the inviscid fluid model, by solving the corresponding problems in the linear formulation. The work done on the trailing vortex formation is determined by the increment of the kinetic energy of the flow induced by the corresponding vortices. Examples of calculations are presented for the case of periodic unsteadiness of the flow due to the hydrodynamic interaction of the cascades. The calculated results are compared with the experimental data.     

Numerical modeling of ideal incompressible fluid flow over a step

Results of calculations of fluid flow over a step located on a channel bottom are given. Numerical modeling is performed for the model of free-boundary potential flows of an ideal incompressible fluid using a finite-difference method with dynamically adaptive grids. The behavior of the free surface in the neighborhood of the step is studied as a function of the incident-flow velocity. The results are compared with experimental data. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 17–22, November–December, 2006.     

Oblique entry of a wedge into an ideal incompressible fluid

A new approach to the solution of the self-similar problem of the entry of a wedge into an ideal fluid at an arbitrary angle to the free surface is proposed. The method is based on the construction of the expressions for the complex velocity and the derivative of the complex potential in a parametric variable domain. An integral and an integro-differential equation are obtained for determining the absolute magnitude and the angle of the velocity vector at the free boundary. The calculated results for the free surface shape, the angles of contact between the free surface and the wedge, and the coefficients of the hydrodynamic forces are presented.     

Supersonic two-phase flow around a wedge

Supersonic two-phase flow around bodies is encountered in calculating the flow around the last stages of blades of condensing turbines, in studying the motion of airplanes under cloudy conditions, etc. In the latter case, there is, along with erosion of the forward edges of the wing profiles, a change in the wave structure and interference situation in the flow about the airplane, leading to off-design regimes of motion. Supersonic flow of a two-phase mixture around a wedge, without taking account of the influence of the particles on the flow, was investigated in [1–3]. In [4], also in this kind of simplified setting, a study was made of the interaction of particles with the surface of a wedge in which reflection of the particles from the wall was taken into account. Morganthaler [5] made an experimental study of the flow of a mixture of air and aluminum oxide particles around a wedge. In [6] a theoretical study was made of a supersonic two-phase flow around thin flat axially-symmetric bodies. In particular, for the flow around a wedge, closed form solutions were obtained for the form of the shock wave, the gas streamlines and particle paths, and the distribution of all the parameters along the surface of the wedge. On the basis of the equations given in [7] and the method of characteristics, which were developed for flows consisting of a mixture of a gas and heterogeneous particles in nozzles [8,9], we present below a study of a supersonic two-phase flow around a wedge.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–88, March–April, 1972.     

Slip and no-slip squeezing flow of liquid food in a wedge

Squeezing flow in a wedge simulates a number of practical processes, e.g. lubrication, coating and the sensory evaluation of liquid foods. This paper reports analytical approximate solutions for both slip (or lubricated) and no-slip squeezing flow of liquid food in a wedge, in which the power law fluid model was used. The solutions do not seem to be more complex than that for squeezing flow between two parallel disks and may be used as a variation of the psycho-physical models of in-mouth viscosity and food spreadability. Alternatively, a rheometer for testing liquid foods may be developed according to the equations described in this paper.     

Criteria for the Separation of Unsteady Ideal Fluid Flow past a Smooth Airfoil

Criteria for the separation of unsteady flow past a closed smooth airfoil are studied using the ideal fluid model and the Brillouin-Villat criterion. The necessary separation conditions are formulated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 74–81, January– February, 2006.     

不可压缩机翼绕流的有限谱法计算

结合有限谱QUICK格式求解不可压缩粘性流问题。这一格式用于模拟不同攻角下的NACA1200机翼绕流问题。利用体积力,提出了将流场速度从0加速到来流速度的方法。区别于传统的压力梯度为零的边界条件,推导出一个更精确的压力边界条件。为使速度散度保持为零,在泊松方程中给速度散度一个特殊的处理。这一成果说明了有限谱法不但具有很高的精度,而且能灵活地和其他格式一起构造出新的格式,从而成功地应用到复杂流场不可压缩流动的数值计算中。     

An incompressible rubber wedge under the tension of a line load at its tip

An analysis is made of the stress distribution and the deformation pattern near the apex of an incompressible rubber wedge under the tension of a concentrated force. The asymptotic method for the tip stress field is developed. The problem is treated as a plane strain case. Finally, the FEM numerical results agree with the theoretical ones.     

Non-Isothermal Lava Flows over a Conical Surface

Using the equations of a non-isothermal thin layer of viscous fluid with an exponential dependence of the viscosity on temperature, a family of hydrodynamic models of a cooling lava flow over a conical surface in the presence of mass supply is constructed. These models correspond to asymptotically different rates of heat exchange with the ambient medium. The evolution of the free-surface shape and the temperature fields is investigated numerically for a stationary mass supply. Using the matched asymptotic expansions method, solutions valid both near and very far from the mass supply region are constructed. The solutions obtained are compared with known analytical solutions for isothermal flow.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 62–75.Original Russian Text Copyright © 2005 by Osiptsov.     

Nonstationary ideal incompressible fluid flows: Conditions of existence and uniqueness of solutions

The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical interpretation of these results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 130–145, July–August, 2008.     

Symmetry breaking and preliminary results about a Hopf bifurcation for incompressible viscous flow in an expansion channel

This computational study shows, for the first time, a clear transition to two-dimensional Hopf bifurcation for laminar incompressible flows in symmetric plane expansion channels. Due to the well-known extreme sensitivity of this study on computational mesh, the critical Reynolds numbers for both the known symmetry-breaking (pitchfork) bifurcation and Hopf bifurcation were investigated for several layers of mesh refinement. It is found that under-refined meshes lead to an overestimation of the critical Reynolds number for the symmetry breaking and an underestimation of the critical Reynolds number for the Hopf bifurcation.     

Low-velocity viscous incompressible fluid flow around a hollow porous sphere

The problem of a viscous incompressible fluid flow around a hollow porous sphere in the Stokes approximation, in which the filtration flow through the sphere shell obeys the Darcy law, is solved. The force acting on the sphere from the fluid is calculated. The limiting cases are considered. The stream function is constructed.     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

On the continuous squeezing flow in a wedge

The paper is concerned with the continuous squeezing flow of Oldroyd-type fluids in a two-dimensional wedge. The flow mimics the lubrication action in a squeezing flow and is important in that there exists a similarity solution for any simple fluid. We are only concerned with Oldroyd-type fluids, however. It is shown by using a parameter continuation method that the Oldroyd-B model has a limiting Weissenberg number. The Phan Thien/Tanner model does not have this limiting Weissenberg number.     

Numerical solution of a viscous incompressible flow problem through an orifice

A steady flow problem of a viscous, incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers. A problem of such type has been solved by applying LAD method given by Roache [1]. The resulting system of linear equations is solved by Hockney's method [2].     

High-order LES modeling of turbulent incompressible flow

This article presents the high-order algorithms that we have developed for large-eddy simulation of incompressible flows, and the results that have been obtained for the 3D turbulent wake of a cylinder at a Reynolds number of $\mathit{Re}=3900$. To cite this article: R. Pasquetti, C. R. Mecanique 333 (2005).     

Non-radial flow of an incompressible fluid of second grade in a contracting channel

The steady non-radial flow of an incompressible fluid of second grade in a contracting channel is studied. The dependence of the flow on the material parameters of the fluid and on the channel angle is investigated. A similarity transformation is introduced for the streamfunction which reduces the P.D.E. to a sequence of O.D.E.s. A series solution is employed to solve the problem.

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Sommario Si studia il flusso stazionario non radiale di un fluido di secondo grado incomprimibile in un canale convergente, esaminandone la dipendenza dai parametri materiali del fluido e dall'angolo di apertura del canale. Si introduce una trasformazione di similitudine per la funzione di corrente che riduce l'equazione di moto ad una serie di equazioni differenziali ordinarie, risolte numericamente.