Morphing of Flying Configuration Using Spanwise Movable Leading Edge Flaps,in Supersonic Flow

The computation of the flow over flattened wing-fuselage flying configuration (FC) with movable leading edge flaps in spanwise direction is here considered. Hyperbolical potential solutions are given in closed form and are used for the determination of hybrid solutions for the Navier-Stokes layer, over this FC with the flaps in retracted and in open position. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolutionary Iterative Optimum-Optimorum Theory with Aerospace Applications

In this paper, the author tries to improve the accuracy of the start solutions for the aerodynamical global optimization of the FC shapes by replacing the three-dimensional, analytical hyperbolical potential solutions with new own developed hybrid numerical solutions for the Navier-Stokes layer (NSL). These solutions have also analytical properties and are split. It follows a more rapid convergence and, consequently, a speed up of the computation time. The evolutionary iterative optimum-optimorum theory uses these hybrid solutions after the first step of iteration and easy allows the weak interactions with the structure, via new and/or modified initial constraints, requested for the structure point of view. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

From Inviscid to Viscous Aerodynamical Global Optimal Shape's Design

The refinement of the global aerodynamical optimal design (OD) of the shape of a flying configuration (FC) can be performed by improving of the start solutions for the optimization and/or of the optimization strategy itself. The proposed strategy is the own developed iterative optimum–optimorum theory. The study is here focused on the further improvement of her new, original, reinforced, zonal, spectral solutions for the partial–differential equations (PDEs) of the three–dimensional compressible Navier–Stokes layer (NSL), which govern the flow over the FCs, in subsonic and supersonic flow. These NSL's solutions, which are good suited for the computation and, especially, for the global optimal design, use the analytical potential solutions of the flow over the same FC twice: firstly as outer flow, at the NSL's edge (instead of the parallel flow used by Prandtl in his boundary layer theory) and, secondly, the velocity's components are products between the corresponding potential velocities and polynomial expansions with arbitrary coefficients, which are used to satisfy the NSL's PDEs. The use of analytical elliptical potential solutions leads to subsonic and the use of hyperbolical potential solutions leads to supersonic stabilized and rapid convergent NSL's solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hybrid Solutions for Stationary and Instationary Three-Dimensional Compressible Navier-Stokes Layer

New, original hybrid solutions for the three-dimensional instationary compressible full Navier-Stokes layer are here proposed. These numerical solutions have also important analytical properties, due to the analytical hybridization and are split, due to the use of the logarithmic density function (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New Zonal,Spectral Solutions for the Navier‐Stokes Layer and Their Applications

New zonal, spectral forms for the axial, lateral and vertical velocity's components, density function and absolute temperature inside of compressible three‐dimensional Navier‐Stokes layer (NSL) over flattened, flying configurations (FC), are here proposed. The inviscid flow over the FC, obtained after the solidification of the NSL, is here used as outer flow. If the spectral forms of the velocity's components are introduced in the partial differential equations of the NSL and the collocation method is used, the spectral coefficients are obtained by the iterative solving of an equivalent quadratical algebraic system with slightly variable coefficients.     

Multipoint Aerodynamical Shape Optimization of Flying Configurations with Spanwise Movable Leading Edge Flaps,in Supersonic Flow

The multipoint aerodynamical shape optimization of a flying configuration (FC) is realized by morphing. Spanwise movable leading edge flaps are used. It leads to two enlarged variational problems, with free boundaries. The own developed iterative optimum-optimorum theory, which searches the global optimized shape inside an elitary class of flying configurations (FCs) and new hybrid solutions for the compressible full Navier-Stokes PDEs, are used. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical solutions of the boundary layer flow of power-law fluid over a power-law stretching surface

This article discusses analytical solutions for a nonlinear problem arising in the boundary layer flow of power-law fluid over a power-law stretching surface. Using perturbation method analytical solution is presented for linear stretching surface. This solution covers large range of shear thinning and shear thickening fluids and matches excellently with the numerical solution. Furthermore, some new exact solutions are found for particular combination of m (power-law stretching index) and n (power-law fluid index). This leads to generalize the case of linear stretching to nonlinear stretching surface. The effects of fluid index n on the boundary layer thickness and the skin friction for nonlinear stretching surface is analyzed and discussed. It is observed that the boundary layer thickness and the skin friction coefficient increase as non-linear parameter n decreases. This study gives a new dimension to obtain analytical solutions asymptotically for highly nonlinear problems which to the best of our knowledge has not been examined so far.     

Turbulent, mixing of a scalar quantity in a 2-d mixing layer using matched asymptotic expansions

In this note analytical solutions for the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow are developed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, linearized using Göertler’s [ZAMM 22 (1942) 244] perturbation argument and examined. Though successful for the mean velocity field, the regular expansion yields inconsistent solutions for the transport of a scalar. Sources of the non-uniformity are identified and a consistent result is obtained using matched asymptotic expansions. This result explains the success of semi-empirical convective velocity closures used by several researchers for a turbulence length scale equation.     

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract

In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.     

柔性圆柱形微管道内的电动流动及传热研究

研究了在纯压力驱动下,流体通过壁面带有某种电荷的聚电解质层（PEL）的微管道，即柔性微管道的电动流动和热传输特性.基于先前得到的电势和速度的解析解以及流向势的数值解,在热充分发展的情况下, 假设壁面热流恒定,利用有限差分法求解了包括黏性耗散和Joule(焦耳)热影响下的能量方程，获得了无量纲温度数值解.通过数值计算，给出了相关的无量纲参数对速度、温度以及Nusselt(努赛尔)数的影响.研究表明,当其他参数固定时,无量纲速度和温度随着无量纲聚电解质层厚度d的增大而减小,随着聚电解质层中等效双电层厚度与双电层厚度之比K_λ的增大而增大；Nusselt数随着Joule热系数S的增大而减小,随无量纲聚电解质层厚度d的增大而减小,随着K_λ的增大而增大.     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

A comparative analysis of approaches for investigating hypersonic flow over blunt bodies in a transitional regime

Hypersonic flows of a viscous perfect rarefied gas over blunt bodies in a transitional flow regime from continuum to free molecular, characteristic when spacecraft re-enter Earth's atmosphere at altitudes above 90-100 km, are considered. The two-dimensional problem of hypersonic flow is investigated over a wide range of free stream Knudsen numbers using both continuum and kinetic approaches: by numerical and analytical solutions of the continuum equations, by numerical solution of the Boltzmann kinetic equation with a model collision integral in the form of the S-model, and also by the direct simulation Monte Carlo method. The continuum approach is based on the use of asymptotically correct models of a thin viscous shock layer and a viscous shock layer. A refinement of the condition for a temperature jump on the body surface is proposed for the viscous shock layer model. The continuum and kinetic solutions, and also the solutions obtained by the Monte Carlo method are compared. The effectiveness, range of application, advantages and disadvantages of the different approaches are estimated.     

HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet

In the present study, we have described the stagnation point flow of a viscous fluid towards a stretching sheet. The complete analytical solution of the boundary layer equation has been obtained by homotopy analysis method (HAM). The solutions are compared with the available numerical results obtained by Nazar et al. [Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int J Eng Sci 2004;42:1241–53] and a good agreement is found. The convergence region is also computed which shows the validity of the HAM solution.     

Fully–coupled model for electrokinetic flow and transport in microchannels

We investigate the electrokinetic flow and mass transport in microchannels. Therefore, mathematical models of the electrical, fluid-mechanical and chemical processes are established. Within the electrical double layer (EDL), approximative analytical solutions can be found and matched asymptotically to the numerical (FEM) solution of the channel core. The results of the simulations show a strong coupling between the processes. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

浅水回流的混合有限分析解

混合有限分析法是一种在局部矩形单元上进行离散的数值格式,为了适应非规则边界,建立了Sigma坐标系的浅水回流数学模型。采用1)风引起的回流,2)密度驱动的回流,3)假潮,来检验数学模型和数值方法。计算结果和相应的分析解的比较表明模型和方法是可行的有效的。该技术可用于近海水域的水流和水质的数值模拟。     

Analyzing the longitudinal effect of hypersonic flow past a conical cone via the perturbation method

To analyze the hypersonic flow past a conical cone, the variations of gasdynamic properties subjected to the longitudinal curvature effect by using the perturbation method. An outer perturbation expansion has been carried out by recent researchers, but a problem occurred, the outer expansion solutions are not uniformly valid in the shock layer, however, the outcome near the conical body surface called vortical layer remains deflective. This study intends to discover uniformly valid analytical solutions in the shock layer by applying the inner perturbation expansions matching with the out expansions to analyze the characteristics in the whole region including shock layer and vortical layer. Starting from the zero-order approximate solutions for hypersonic conical flow is then applied as the basic solutions for the outer perturbation expansions of a flow field. The governing equations and boundary conditions are also expanded via outer perturbations. Using an approximate analytical scheme in the derivation process, first-order perturbation equations can be simplified and the approximate closed-form solutions are obtained; furthermore, the various flow field quantities, including the normal force coefficient on the cone surface, have been calculated. According to the variations of gasdynamic properties, the longitudinal curvature effect for the hypersonic flow past a conical cone can be determined. Thicknesses of shock layer and vortical layer can be predicted as well. The physical phenomena inside both layers can be investigated carefully, the conditions for an elliptic cone with longitudinal curvature, m = 1 and n = 2 and other conditions of parameters; the perturbation parameter, ε_m2 = 0.1, semi-vertex angle of the unperturbed cone, δ = 10°, and hypersonic similarity parameter, K_δ = M_∞δ = 1.0, the thickness of vortical layer, η_VL, can be calculated at the position angle of conical cone body, ? = 30° was demonstrated here. Results show how very thin the vortical layer is approximately only 10% of the shock layer close to the body, the pressure in the whole shock layer is verified to be uniformly valid which agrees with previous studies. Large gradient changes in entropy and density are found when the flow approaches the cone surface, the most important is, this method provides a benchmark solution to the hypersonic flow past a conical cone and to assist the grids and numerics for numerical computation should be fashioned to accommodate the whole flow field region including the vortical layer of rapid adjustment, and let the analysis become more effective and low cost.     

Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface

In the present analysis, we study the steady mixed convection boundary layer flow of an incompressible Maxwell fluid near the two-dimensional stagnation-point flow over a vertical stretching surface. It is assumed that the stretching velocity and the surface temperature vary linearly with the distance from the stagnation-point. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. Analytical and numerical solutions of the derived system of equations are developed. The homotopy analysis method (HAM) and finite difference scheme are employed in constructing the analytical and numerical solutions, respectively. Comparison between the analytical and numerical solutions is given and found to be in excellent agreement. Both cases of assisting and opposing flows are considered. The influence of the various interesting parameters on the flow and heat transfer is analyzed and discussed through graphs in detail. The values of the local Nusselt number for different physical parameters are also tabulated. Comparison of the present results with known numerical results of viscous fluid is shown and a good agreement is observed.     

DTM-BF方法和可渗透收缩壁面上带滑移速度的非稳态磁流体力学流动

研究了运动的粘性导电流体中可渗透收缩壁面上非稳态磁流体边界层流动,利用解析和数值方法对问题进行了研究,并考虑了壁面速度滑移的影响．提出了一个新的解析方法（DTM-BF）,并将其应用于求解带有无穷远边界条件的非线性控制方程的近似解析解．对所有的解析结果和数值结果进行了对比,结果显示两者非常吻合,从而证明了DTM-BF方法的有效性．另外,对不同的参数,得到了控制方程双解和单解的存在范围．最后,分别讨论了滑移参数、非稳态参数、磁场参数、抽吸/喷注参数和速度比例参数对壁面摩擦、唯一解速度分布和双解速度分布的影响．     

Viscosimetric flow of an incompressible elastoviscoplastic material under the presence of a lubricant on the boundary surfaces

Generalizing the model of large deformations by accounting for the viscous properties of materials, we obtain the analytical solutions of some quasistatic boundary value problems concerning the viscosimetric flows of an elastoviscoplastic material in the gap between the rigid coaxial cylindrical surfaces when, in the neighborhood of one of the rigid cylinders (either internal or external), there is a layer of an elastic non-Newtonian lubricant, and the rigid adhesion conditions are satisfied on boundary surfaces. The conditions are studied of origination of a flow in the lubricant layer and in the basic material. The values of the maximum velocity are specified under which the flow does not tresspass the lubricant layer.     

Numerical simulation of the turbulent boundary layer equations via a Runge-Kutta algorithm

This paper addresses a hybrid computational procedure for the step-by-step calculation of momentum transfer in turbulent boundary layer flows along flat plates. The proposed procedure relies on a modified method of lines wherein transversal discretizations are carried out by a “control volume” being infinitesimal in the streamwise direction and finite in the transversal direction of the fluid flow. Using mixing length theory and coarse intervals in the transversal direction, the resulting system of ordinary differential equations of first order may be readily integrated on a personal computer utilizing a fourth-order Runge-Kutta algorithm. In general, a maximum number of sixteen lines is necessary at the trailing edge of the flat plate for a typical calculation. As a consequence, computing time and storage for each run were very small when compared to other finite-difference methods. Furthermore, to validate the hybrid procedure involving the method of lines and control volumes (MOLCV), comparisons with experimental data have been done in terms of both velocity distributions and local skin friction coefficients. For all cases tested, the proposed methodology predicts the growth of the boundary layer of gases correctly.