Jet Flow Past a Plate with a Spoiler in the Presence of a Stagnation Zone

An exact analytical solution of the problem of the jet flow past a flat plate with a spoiler is obtained for the case in which there is a stagnation zone near the spoiler. The Chaplygin method of singular points and the theory of elliptic theta-functions are used to construct the solution. The pressure in the stagnation zone is determined from the Brillouin-Villat condition of smooth separation. It is found that the lift and drag coefficients, considered as functions of the stagnation zone length, have extrema at points corresponding to the smooth separation condition.     

Comments on On an Exact Analytical Solution of the Boussinesq Equation,Transport in Porous Media 39, 339–345, 2000

Transport in Porous Media -     

Almost analytic solutions and their tests of the horizontal diffusion equation for the movement of water in unsaturated soil

Itisalwaysdifficulttofindthesolutionsoftheequationforthemovementofwaterinunsaturatedsoi1.Theprimar}'reasonisthatthehydraulicconductivityK(T)orthediffusivityofsoiIwaterD(o)isfunctionofwaterpotential(W)orwatercontent'(o)'Atpresent,thegeneralwaystofindthesol…     

Advances in modeling of water in the unsaturated zone

This paper reviews recent advances in analytical and numerical solution of problems of water flow through rigid soils in the unsaturated zone. The Richards model remains the most widely accepted and fertile framework for water flow analyses. More general formulations are reserved for the analysis of problems involving macroporosity, thermal effects, and air pressure effects. Many exact and approximate solutions have been derived for particular boundary value problems of homogeneous soils using methods such as quasi-linear analysis, Green-Ampt analysis, perturbation, and the kinematic wave approximation. Numerical simulators have become bigger and more accurate due to improvements in the areas of nonlinear solution procedures, mass conservation, computational efficiency, and computer hardware. Problems of natural heterogeneity have been addressed primarily through application of various stochastic methods to the Richards model. The stochastic formulations generally refute the concept of simple equivalent homogeneous properties, but do themselves offer a certain limited potential for a predictive capability.     

On solving the problem of an ideal incompressible fluid flow around large-aspect-ratio axisymmetric bodies

Based on Babenko’s fundamental mathematical ideas, principally new (unsaturated) algorithms are developed for the numerical solution of problems of a potential axisymmetric ideal fluid flow around bodies of revolution, in particular, an ellipsoid of revolution with an aspect ratio equal to 1000. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 56–67, September–October, 2006.     

On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique

The problem of magneto‐hydrodynamic fluid flow past a nonlinear stretching sheet in the presence of a transverse magnetic field is analyzed. The governing equations are transformed into a nonlinear ordinary differential equation that is solved using a novel spectral homotopy analysis method and the Matlab in‐built numerical solverttbvp4c. The new technique removes some known limitations of the homotopy analysis method and offers a more systematic way of selecting initial approximations and the optimal auxiliary parameter ?. A comparison with the numerical solution confirms the robustness, the computational efficiency, and the accuracy of the technique. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Displacement of NAPL Lenses and Plumes in a Phreatic Aquifer

The movement of an LNAPL lens above a sloping or horizontal water table, and a DNAPL lens above an impermeable surface is discussed. The governing equations are derived, using the vertical equilibrium approach and assuming the water mobility to be much greater than that of the NAPL. Analytical solutions are obtained for onedimensional movement of a lens along a sloping water table. They describe the lens movement with the formation of a jump at the leading front (large-scale approximation), and the distribution of NAPL in the transition zone near the jump (smallscale approximation). A model,describing the movement of a lens, taking into account NAPL retention,is proposed. Approximate onedimensional solutions for the movement of a NAPL lens along sloping or horizontal surfaces under such conditions are presented for this model. Some approximate analytical solutions for twodimensional lens (plume) formation and movement are obtained for the case of a point source at a sloping surface.     

Effect of residual oil saturation on the flow through a porous medium in the neighborhood of an injection well

Models of the residual oil saturation and models of its effect on the flow in injection wells are proposed. The threshold nature of the dependence of the residual oil saturation on the capillary number determines a change in the flow regimes in the neighborhood of the injection well. The cases of pure, contaminated, and compressible reservoirs are considered. The dependences of the basic problem parameters on the displacement conditions and the state of the reservoir are obtained, together with formulas for the pressure distribution and well injectivity. The topicality of such a simulation for field calculations is demonstrated.     

On the derivation of an admissibility condition for phase boundary propagation in an SMA bar based on a 3-D formulation

There is some considerable difficulty in determining the solution uniquely for a propagating phase boundary in shape memory alloy (SMA) bar. In this paper, we establish an admissibility condition starting from a three-dimensional (3-D) internal-variable formulation to resolve this issue. We adopt a 3-D formulation in literature which is based on a constitutive model with specific forms of the Helmholtz free energy and dissipation rate. Then the 3-D dynamical equations are reduced to the 1-D rod equations for three phase regions (coupled with the radial effect and surface condition) by using two small parameters. Connection conditions at the phase interfaces are determined. By considering the traveling-wave solution for the rod system, we eventually derive three conditions across a sharp phase boundary corresponding to the 1-D sharp-interface model, including the two usual jump conditions and an additional condition. The third condition is then used to supplement the 1-D sharp-interface model to study an impact problem. The unique solution is constructed analytically for all possible impact velocity, including three kinds of wave patterns according to different levels of the impact velocity. The results are compared with those obtained by the maximal dissipation rate criterion.     

弹道枪不同水深下全淹没式发射膛口流场的数值分析

为了解弹道枪水下全淹没发射时,水深对膛口流场演化特性的影响,建立了二维轴对称非稳态膛口流场模型。采用流体体积函数多相流模型、标准k-ε湍流模型和Schnerr-Sauer空化模型,结合动网格及用户自定义函数技术,对水下全淹没发射膛口流场演变全过程进行了数值模拟。搭建了弹道枪水下可视化射击实验平台,对12.7 mm口径弹道枪在水中全淹没式发射时膛口流场演化过程进行了观测,并验证了数值模型的合理性。在此基础上,对比了不同水深下（h=1～100 m）膛口流场的演化特性。通过对比发现：在不同水深条件下,在膛口流场影响范围内,弹丸膛外行程随时间的变化均满足指数函数规律;水越深,膛口流场典型波系结构形成所需时间越长,且燃气在膛口轴向马赫盘处的温度和压力峰值越低,压力振荡幅度也越小,更快趋于平稳,但在径向上,水越深,压力振荡持续时间越长。