Design and optimization of a two-element wing airfoil in a subsonic viscous flow

A numerical and analytical solution of the problem of designing a two-element wing airfoil providing maximum lift-drag ratio in a subsonic viscous flow is presented. In order to bring the theoretical results closer to the facts, viscosity and compressibility are taken into account within the framework of boundary layer theory and the Chaplygin gas model, respectively.     

Effect of the freestream turbulence scale and the leading edge shape on boundary layer laminar-turbulent transition

The effect of the leading edge shape and the turbulence scale on laminar-turbulent transition in the flat-plate boundary layer due to grid turbulence is investigated. In the experiments, the turbulence scale was changed by a factor of three and the bluntness radius of the edge by a factor of four, all other factors being fixed. It is shown that on the plate with a sharp edge the fluctuation growth rate and the laminar-turbulent transition point depend nonmonotonically on the turbulence scale. On the blunt plate transition occurs considerably earlier than on the sharp plate.     

Shape optimisation of an oscillating body in fluid flow by adjoint equation and ALE finite element methods

The purpose of this paper is to determine the shape of an oscillating body by minimising drag and lift forces, located in a transient incompressible viscous fluid flow by means of the Arbitrary Lagrangian Eulerian finite element method and an optimal control theory. A performance function is expressed by the drag and lift forces. The performance function should be minimised satisfying the state equation and the constant volume condition. Therefore, this problem can be transformed into a minimisation problem without constraint by the Lagrange multiplier method. The adjoint equation and the gradient of the performance function are used to update the shape of the body. In this study, as a minimisation technique, the weighted gradient method is applied. The final shape is obtained of which drag and lift forces are reduced by 66.2% and 92.8%, respectively. The final shape obtained by this study is compared with the final shape of the non-oscillating body. The obtained final shape of the oscillating body is significantly different from the non-oscillating body.     

Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Computation of internal high-speed separated flow with modified B–L and J–K models

The existence of shock–turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, the Baldwin–Lomax (B–L) model and the Johnson–King (J–K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier–Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J–K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J–K model is found to predict the size of the separation bubble with a higher accuracy. © 1998 John Wiley & Sons, Ltd.     

Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

An extensive investigation of the influence of the leakage flow through a labyrinth seal at supply pressure of 12 bar on the rotordynamics was performed by using numerical calculations and experimental measurements. Toward this end, an experimental rotor setup was established in Shanghai Jiao Tong University. Two labyrinth seals were chosen for comparison, e.g., an interlocking seal and a stepped one. The numerical calculations based on the bulk-flow theory and the perturbation analysis were accomplished. Simultaneous acquisitions of the fluctuating static pressure at the stator wall and the displacement of the whirling rotor were made. The influence of the aerodynamic forcing on the rotor was analyzed in terms of the axial distribution of the mean static pressure, the circumferential distribution of the fluctuating pressure, the fist critical speed and the destabilization rotating speed of the rotor. The experimental results demonstrated that the sinusoidal distribution of the fluctuating static pressure on the stator wall was closely related to the whirling motion of the rotor. The first critical speed of the rotor was reduced by the aerodynamic forcing, resulting in intensified destabilization of the rotor system. Furthermore, the numerical analyses were in good agreement to the experimental measurements.     

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.     

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

Summary The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.     

基于p型有限元法和围线积分法计算复合型应力强度因子

传统有限元法由于采用低阶插值计算应力强度因子时,需要划分的网格数较多,收敛速度较慢,得到的应力强度因子精度不足。p型有限元法在网格确定时通过增加插值多项式的阶数来提高计算精度,具有网格划分少、收敛速度快、精度高、自适应能力强等特点。本文采用基于p型有限元法的有限元计算软件StressCheck计算得到应力场和位移场,并由围线积分法导出混合型应力强度因子(SIFs)。通过几个经典算例,分析了围线的选择对计算精度的影响,计算了不同裂纹长度、不同裂纹角度和裂纹在应力集中区域不同位置时的应力强度因子。并将数值结果、理论解与文献中其他数值计算方法所得的部分结果进行了对比分析,结果表明自由度数不大于7000时,导出的应力强度因子相对误差最大不超过1.2%,数值解表现出较高的精度及数值稳定性。     

Effect of the Turbulent Energy Gradient and the Presence of a Wall on the Turbulent Process of Momentum Transport

A mathematical model of turbulent transport processes is modified to make allowance for the turbulent energy gradient and the presence of walls. The modification consists in making the variance tensor in the Gaussian probability density distribution for the initial mole velocities anisotropic for nonzero turbulent energy gradient and a ratio of the turbulence scale to the distance from the wall of the order of unity. Formulas for the variance tensor components are derived and the empirical coefficients of these formulas are determined. The expression for the dimensionless turbulent friction stress is compared with experimental data for three boundary-layer-type flows, namely, in the wake of a cylinder, in the boundary layer on a flat plate, and in a channel with parallel walls.     

Effect of the compliant interlayer on the dynamic stress intensity factor in a piecewise-homogeneous solid with a circular crack

The dynamic behavior of a circular crack in an elastic composite consisting of two dissimilar half-spaces connected by a thin compliant interlayer is studied. One half-space contains a defect aligned perpendicular to the interlayer; the defect surfaces are loaded by normal harmonic forces, which ensures the symmetry of the stress-strain state. The thin interlayer is modeled by conditions of a nonideal contact of the half-spaces. The problem is reduced to a boundary integral equation with respect to the function of dynamic opening of the defect. The numerical solution of this equation yields frequency dependences of the mode I stress intensity factor in the vicinity of the crack for different values of interlayer thickness and relations between the moduli of elasticity of the composite components. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 197–207, May–June, 2008.     

Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure

A methodology for computing three‐dimensional interaction between waves and fixed bodies is developed based on a fully non‐linear potential flow theory. The associated boundary value problem is solved using a finite element method (FEM). A recovery technique has been implemented to improve the FEM solution. The velocity is calculated by a numerical differentiation technique. The corresponding algebraic equations are solved by the conjugate gradient method with a symmetric successive overrelaxation (SSOR) preconditioner. The radiation condition at a truncated boundary is imposed based on the combination of a damping zone and the Sommerfeld condition. This paper (Part 1) focuses on the technical procedure, while Part 2 [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 2. Numerical results and validation. International Journal for Numerical Methods in Fluids 2001] gives detailed numerical results, including validation, for the cases of steep waves interacting with one or two vertical cylinders. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element simulations of fully non‐linear interaction between vertical cylinders and steep waves. Part 2: numerical results and validation

In Ma, Wu, Eatock Taylor [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure. International Journal for Numerical Methods in Fluids 2001], designated Part 1 hereafter, we have developed the methodology and solution procedure for simulating the three‐dimensional interaction between fixed bodies and steep waves based on a finite element method (FEM). This paper provides extensive numerical results and validation. The effectiveness of the radiation condition is investigated by comparing the results from short and long tanks; the accuracy of the computed data is confirmed through comparison with analytical solutions. The adopted mathematical model is also validated by comparing the obtained numerical results with experimental data. Various test cases, including non‐linear bichromatic and irregular waves and the interactions between waves and one or two cylinders, are analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of placing different obstacles in flow fields on performance of a PEM fuel cell: numerical investigation and experimental comparison

In this study a complete two-dimensional model for proton exchange membrane (PEM) fuel cells was used to investigate the effect of using different obstacles on the performances, current density and gas concentration for different aspect ratios (ARs). The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Also a series of tests are carried out to investigate and validate the numerical results of the polarization curve under the normal conditions. A PEM fuel cell with 25 cm² active area and Nafion 117 membrane with 4 mg Pt/cm² for the anode and cathode is employed as a membrane electrode assembly. The results show that the predicted polarization curves by using this model are in good agreement with the experimental results. Also the results show that the local current density reduces more obviously at a higher overpotential than at a lower overpotential because of the more obvious reflection phenomena in the downstream region. At lower operating voltage conditions, the overall cell performance decreases as the AR decreases.