The conical deformation of a delta wing with sonic leading edges

The optimal conical deformation of a delta wing with sonic leading edges is determined in a linear formulation of the problem. The drag of the wing caused by the creation of the lifting force is taken as the objective function. It is established that a superelliptical distribution of the local angle of attack over the wing span corresponds to the minimum drag. A representation in the form of a hypergeometric function is found for the directrix of the wing in a cross section. The results obtained are compared with the results of a numerical investigation within the Euler model.     

Contribution to the propeller aerodynamic interference

Propeller wake can significantly change the flowfield at the downstream lifting surfaces and therefore influence its aerodynamic coefficients. The numerical model of the propeller presented here is using discrete vortices to form vortex sheet that is leaving each blade. Model is also applicable for combination of lifting surface and propeller using undeveloped propeller vortex sheet in determination of aerodynamic interference of the propeller on the downstream lifting surface, wing or tail for small angle of attack. This low computational cost numerical model is suitable for implementation in component build–up method used in preliminary estimation of aerodynamic coefficients for different propeller aircraft configurations.     

Optimal apogee burn time for low thrust spinning satellite in low altitude

In this study, the optimal burn time for low-thrust impulsive propulsion systems is investigated to raise the perigee altitude of a low-Earth orbit. The maneuver is done using spin-stabilized attitude control and impulsive thrusting system for a time interval centered about apogee point. On the one hand, the low value of the thrust level causes more burn time needed to accomplish the transfer. This, in turn, will cause more thrust loss due to the deviation between the thrust axis (spin axis) and the velocity vector of the satellite. On the other hand, for small thrust duration, the transfer needs more revolutions around the Earth and more travel in lower altitudes with dense atmosphere and more drag loss. To transfer the satellite with minimum propellant mass, a compromise between velocity losses due to both drag and thrust deviation angle should be made. An analytical approximate correlation between average thruster burn time and total required propellant mass is formulated in this study and an analytical optimal solution for burn time is found. Nonlinear programming is used to find optimal burn time history. Comparing the analytical and numerical results shows a very good match.     

3‐D Inviscid Transonic Condensing Flow around a Swept Wing

Transonic condensing flow is an interesting phenomena because of the large change in temperature over a small area. This drop in temperature allows the moist air to condense. It is the purpose of this paper to examine the effect of sweep on condensing flow. The geometry of the wing model starts with NACA‐0014 at the wall and reduces to a NACA‐0010 at the tip. The span of the wing is 2.5 times the maximum chord length. The effect of sweep is examined by comparing a model wing with a sweep angle of 11.3 with a straight trailing edge that has no thickness and then a straight leading edge with a 11.3 trailing edge sweep. The free stream Mach number is 0.8 and angle of attack is 0. A 2‐D calculation shows that the NACA‐0014 and NACA‐0010 have a region of supersonic flow but due to the effect of sweep the sonic line does not extend to the tip. This change of the supersonic region influences the area of condensation on the wing. The swept wing has a lower total drag coefficient for the adiabatic and all condensation cases compared to the straight leading edge wing and second for the each wing the trend of increasing drag with humidity is shown.     

The optimal conical twist of a delta wing

The problem of reducing the drag of a wing at a specified lift in a supersonic flow is investigated. A solution for a delta wing is obtained in a simplified formulation of the optimization problem and a theoretical analysis. It is shown that the optimal conical wing is formed by elements of elliptical cones and planes. Numerical modelling of the flow of a non-viscous non-heat-conducting gas past the wing is performed, and the results of the theoretical analysis and direct optimization are compared. ©2012     

三角翼大迎角流场结构和气动力特性的计算分析研究

采用数值计算方法对亚音速三角翼纵向及带有小侧滑和横侧小扰动情况下的流场结构进行了计算,利用数值计算所得到的大迎角流动流场数据,结合相关的实验研究结果,建立了对大迎角旋涡流场结构进行定量分析的方法．给出了三角翼大迎角情况下相应的气动力、力矩系数,以及机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律,并对带有小侧滑和横侧小扰动情况下对横侧力矩的影响进行了计算与分析．计算结果表明,在前缘分离涡破裂前的上游旋涡区内,前缘分离涡轴线基本保持为直线,且随着迎角增加,前缘分离涡轴线位置愈靠近翼根,并远离翼面;在前缘分离涡破裂的初始阶段,于旋涡轴线处,压力系数会迅速增加,沿涡轴线方向速度迅速减小,在垂直于流向的截面内,愈靠近涡轴线处,沿涡轴线方向速度愈小,甚至出现负值,说明沿涡轴线方向出现回流．当绕机翼上表面前缘分离涡破裂后,将会导致横侧运动不稳定,如果受到小扰动,将产生横侧力矩发散．     

High performance computation for DNS/LES

The paper is focused on high-order compact schemes for direct numerical simulation (DNS) and large eddy simulation (LES) for flow separation, transition, tip vortex, and flow control. A discussion is given for several fundamental issues such as high quality grid generation, high-order schemes for curvilinear coordinates, the CFL condition for complex geometry, and high-order weighted compact schemes for shock capturing and shock–vortex interaction. The computation examples include DNS for K-type and H-type transition, DNS for flow separation and transition around an airfoil with attack angle, control of flow separation by using pulsed jets, and LES simulation for a tip vortex behind the juncture of a wing and flat plate. The computation also shows an almost linear growth in efficiency obtained by using multiple processors.     

Die Begriffe Auftrieb,Widerstand und Zirkulation bei Schaufeln von Strömungsgittern

Summary The force on a wing of a cascade can be divided in the two components lift and drag like the force on a single wing. The magnitude and direction of the lift component are calculated. The change of the flow direction is caused not only by the lift but also by the drag. Approximately the flow can be calculated as the field of vortices with a circulation corresponding to cascade wings without drag.      

Flow over a Wing with an Attached Free Vortex

Exact solutions are constructed for two-dimensional inviscid potential flow over a wing with a free line vortex standing over the wing. The loci of positions of the free vortex are found, and the lift is calculated. It is found that the lift on the wing can be significantly increased by the free vortex.     

Optimal design of a minimum weight thermal diffuser with constraint on the output thermal power flux

The object of this paper is the development of efficient mathematical and numerical tools to find the optimal shape of a minimum-weight thermal diffuser with a priori specifications on the inward thermal power flux (TPF) and a bound on the outward TPF. The present problem arises in connection with the use of high-power solid state devices in future communications satellites. In a space application the thermal power must ultimately be dissipated to the environment by using heatpipes and correspondingly large radiating areas. However, heatpipes can accept only a limited TPF from a source. Hence we have the requirement of a minimum-weight thermal diffuser with a uniform bound on the outward TPF. Shape optimal design and finite elements methods are used. Complete numerical results are provided.This research was supported by the Natural Sciences and Engineering Research Council of Canada, Strategic Grants G-0573 and G-0654 (Communications) and Operating Grant A-8730.     

开敞式索膜结构的气动失稳临界风速

考虑几何非线性的影响,利用无限薄的旋涡薄层模拟气流在结构表面形成的扰动,由非稳态Bernoulli方程和环量定理将空气压力表示成旋涡密度的函数;然后由涡格法结合耦合边界条件求出旋涡密度,根据系统的稳定性判据得到结构发散失稳临界风速的解析表达式．通过三维开敞式膜结构的计算分析,发现空间膜结构的曲率是影响结构气动失稳临界风速的主要因素．     

An Improved Vortex Lattice Method for Nonstationary Problems

The vortex lattice method is improved for modeling nonlinear highly nonstationary processes appearing in an interaction of bodies that undergo an irregular motion in a proximity of solid boundaries with large-scale vortex structures. We show that keeping the condition of freezing the vortex buildups in the medium leads, in the vortex lattice method, to eliminating the arbitrariness in the calculated time step, singularity radius, and the buffer-zone radius.For the ensemble of discrete vortices that model the surface of tangential discontinuity of the velocity, we propose an economical method for solving the Cauchy problem. The method decreases the discretization error related to the replacement of this surface with a system of discrete vortices.A test for the improved vortex lattice method has been conducted for a nonstationary nonlinear problem on nonharmonic angular oscillations of a wing in a stationary medium near a solid surface in the case where there is no gap between the wing and the surface.By using the improved vortex lattice method, one succeeded, for the first time, in obtaining a solution of a problem of this type that converges from the numerical point of view. A comparison of the obtained results with known experimental data shows a good agreement.     

Finite-time Euler singularities: A Lagrangian perspective

We address the question of whether a singularity in a three-dimensional incompressible inviscid fluid flow can occur in finite time. Analytical considerations and numerical simulations suggest high-symmetry flows as promising candidates for finite-time blowup. Utilizing Lagrangian and geometric non-blowup criteria, we present numerical evidence against the formation of a finite-time singularity for the high-symmetry vortex dodecapole initial condition. We use data obtained from high-resolution adaptively refined numerical simulations and inject Lagrangian tracer particles to monitor geometric properties of vortex line segments. We then verify the assumptions made in the analytical non-blowup criteria introduced by Deng et al. [Commun. PDE 31 (2006)] connecting vortex line geometry (curvature, spreading) to velocity increase, to rule out singular behavior.     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

Asymptotics of eigenvalues of the nonlinear eigenvalue problem arising from the near mixed-mode crack-tip stress-strain field problems

In the present paper, approximate analytical and numerical solutions to nonlinear eigenvalue problems arising in nonlinear fracture mechanics in studying stress-strain fields near a crack tip under mixed-mode loading are presented. Asymptotic solutions are obtained by the perturbation method (the artificial small parameter method). The artificial small parameter is the difference between the eigenvalue corresponding to the nonlinear eigenvalue problem and the eigenvalue related to the linear “undisturbed” problem. It is shown that the perturbation technique is an effective method of solving nonlinear eigenvalue problems in nonlinear fracture mechanics. A comparison of numerical and asymptotic results for different values of the mixity parameter and hardening exponent shows good agreement. Thus, the perturbation theory technique for studying nonlinear eigenvalue problems is offered and applied to eigenvalue problems arising in fracture mechanics analysis in the case of mixed-mode loading.     

Wind-Power Transforming Systems

In this article, we give a brief account of theoretical and experimental investigations, as well as engineering designs, of different types of rotors (propeller-type rotors and Darrieus-type rotors). In numerical studies, we used the vortex lattice method. We obtained instant and averaged-in-time values of the coefficients of the centrifugal, drag, side, and head forces, as well as the value of the relative torque, the wind-power use coefficient, the configuration of the vortex trace, and the velocity field and contour lines. The results of numerical studies agree well with experimental data.     

Exact solution for an optimal impermeable parachute problem

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle—the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.     

Optimization of the double sided spiral groove thrust bearing: A comparison to approximate analytical solutions

Reliable high performance bearings are essential in rotordynamics. As speeds and loads are continuously increased the demands on bearing technology grow simultaneously. Optimization of bearing characteristics becomes more important under these circumstances. For hydrodynamic thrust bearings, recently a special design has been presented, which is supposed to enhance the load carrying capacity by 60% compared to the best known thrust bearing type. The bearing consists of two spiral grooved surfaces and is therefore called a double sided spiral groove bearing. Early calculations of the bearing performance base on approximate analytical methods. In order to verify those results, a detailed numerical model of the bearing is presented by the authors. With the help of a particle swarm optimization method, optimal bearing parameters are determined and a comparison is drawn to other thrust bearing designs. It is shown that previously published results overestimate the performance of the double sided spiral groove bearing severly. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)