Circular Airfoil Research Articles

Использование метода декомпозиции области для распараллеливания моделирования течения вязкой несжимаемой среды методом LS-STAG и дополнительного предобуславливания

As a rule, the main part of the computational costs in the numerical solution of problems in continuum mechanics consists in the solving of large sparse systems of linear algebraic equations. For this reason, efficient parallelization of this particular procedure can significantly speed up the simulation. To solve this problem, two main approaches can be used. The simplest approach consists in parallelizing of matrix-vector operations in a usual iterative solver. It requires several synchronization points and exchanges of coefficients at each iteration of the solver, which does not significantly speed up the simulation process as a whole. Therefore, domain decomposition methods are preferable. These methods involve dividing the computational domain into subdomains, constructing and solving separate problems in them, as well as some procedure to coordinate the solution between subdomains to ensure global convergence. Subdomains can overlap, as in the Schwartz method used in OpenFOAM, or they can be separated by interface sections, on which their own interface task is built, as in the Schur complement method. The latter method is used in this research to construct a parallel algorithm for viscous incompressible flow simulation by using the immersed boundary method LS-STAG with cut-cells and level-set functions. The resulting matrix of the interface system has a block tridiagonal structure. To speed up prototyping, OpenMP parallel programming technology is used in the software implementation of the developed algorithm, so computational experiments are carried out only on systems with shared memory, in particular on individual nodes of the educational and experimental cluster of the Applied Mathematics Department, Bauman Moscow State Technical University. To verify and evaluate the effectiveness of the developed parallel algorithm, a well-studied test problem about simulation of two-dimensional flow around a stationary circular airfoil is considered. Computations on a sequence of meshes with different numbers of subdomains show that the parallel algorithm allows one to obtain the same numerical solution as the original algorithm of the LS-STAG method, and the computed values of the Strouhal number and drag coefficient are in good agreement with the experimental and computational data known in the literature. Experiments demonstrate that the developed algorithm with domain decomposition allows to accelerate simulation even in sequential mode by reducing the number of solver iterations, i.e. the domain decomposition method acts as an additional preconditioner. Due to this property, the acceleration is superlinear when simulating in parallel mode with developed algorithm. This effect persists up to a certain number of subdomains, which depends on the size of the problem.

Damage analysis of wind turbine blade with different stacking parameters

Considering the damage and failure of wind turbine blades under gravity, centrifugal force and aerodynamic load, the influence of blade laminating parameters to the damage characteristics of wind turbine blades is studied. Different stacking schemes were designed by changing the stacking angle, stacking sequence and the ratio of ±Xn in the material. The maximum stress position of the blade was analyzed. At the same time, the failure factor of Tsai_Wu was used as the failure criterion to analyze the possibility of blade failure. The results show that the maximum stress of the blade appears at the junction of the leading edge web and the airfoil near circular airfoil and DU_35A17 airfoil; in the range of 40° ∼ 50°, as the layup angle increases, the blade Tsai_Wu failure factor shows a downward trend. On both sides of about 45°, the change trend of the Tsai_Wu failure factor is different with the increase of ±Xn thickness ratio; the Tsai_Wu failure factor of the blade material is greatly affected by the stacking angle and the thickness ratio of ±Xn.

Simulation of viscoelastic flow past circular airfoil by using the modified LS-STAG immersed boundary method

The LS-STAG immersed boundary cut-cell method modification for viscoelastic flow computations is presented. Rate type viscoelastic flow models (linear and quasilinear) are considered. Rate type viscoelastic flow models (linear and quasilinear) are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software allows to simulate viscous incompressible flows by using the LS-STAG method and it modifications. The LS-STAG-discretization of extra-stress equations for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson Segalman fluids was developed. Formulae for differential types of convected time derivatives (Oldroyd, Cotter — Rivlin, Jaumann — Zaremba — Noll derivatives) the LS-STAG discretization was obtained. Normal non-newtonian stresses are computed at the centers of base LS-STAG mesh cells and shear non-newtonian stresses are computed at the cell corners. Time-stepping algorithm is based on the first order predictor-corrector scheme. To validate developed numerical method the test problem about viscoelastic Oldroyd-B flow past a circular airfoil was used. Computational experiments were carried out at Weissenberg number in the range from 0 to 4. The computed values of the drag coefficients and the wake length are in good agreement with the experimental data.

On the high-accuracy approach to flow simulation aroundthe airfoils by using vortex method

Some problems connected to vortex methods development for 2D incompressible flow simulation around airfoils are discussed. In the numerical schemes and algorithms which are normally used in the vortex methods, the airfoil is approximated by a polygon consists of rectilinear panels, and the the vortex sheet intensity, which is placed on the airfoil surface line and simulates the airfoil’s influence the flow, is assumed to be piecewise-constant or piecewise-linear function. The most accurate mathematical models and numerical algorithms, based on such approaches, provide the estimation for the order of the error between O(h) and O(h2) for the average vortex sheet intensity over the panels (h is the maximal panel length). In the present research a new approach is developed, where the vortex sheet intensity is assumed to be discontinuous piecewise-linear or piecewise-quadratic function and the curvature of the panels is taken into account. In order to compute the coefficients of the main system of the algebraic equations, the least squares method is used instead of commonly used no-through or no-slip conditions at separate control points or over the panels in the average. It is shown, that the developed approach is much more accurate in comparison with previously known ones: for some test problems (flows around a circular airfoil, an elliptical airfoil and Zhukovsky airfoil) it permits to obtain numerical solution which has error of order O(h4).

Numerical simulation of the flow around two circular airfoils positioned across the stream using the LS-STAG method

The flow around two circular airfoils positioned side by side (across the stream) at different distances between the airfoils is considered. The LS-STAG method, which belongs to the class of immersed boundary method is used for numerical simulation that makes it possible to calculate using rather coarse meshes. Stationary and trigger flow regimes have been simulated, as well as the patterns of flow with synchronization of two vortex trails in-phase and in anti-phase. For each regime, the typical dependences of coefficients of drag force and lift force on the time are presented. The obtained results are in good agreement with the known experimental and computational data.

Numerical simulation of the flow around two fixed circular airfoils positioned in tandem using the LS-STAG method

In recent years the popularity of immersed boundary methods has been increasing in computational hydrodynamics. One of the most effective methods of this class is the LS-STAG method developed in 2010, which allows computations on sufficiently coarse grids. A software package was developed to solve a number of hydrodynamics and hydroelasticity problems by the LS-STAG method. We present the results of the testing the developed software package by simulating a flow around two fixed circular airfoils positioned in tandem at different distances between the airfoils. We simulate the flow modes for which two symmetric vortices, two asymmetrical vortices, and a vortex wake form behind the front airfoil. For each mode, the typical time dependences of the drag force and lift coefficients are presented. The results agree well with the experimental data in the literature and numerical results of other authors.

Design and numerical investigation of swirl recovery vanes for the Fokker 29 propeller

Swirl recovery vanes (SRVs) are a set of stationary vanes located downstream from a propeller, which may recover some of the residual swirl from the propeller, hoping for an improvement in both thrust and efficiency. The SRV concept design for a scaled version representing the Fokker 29 propeller is performed in this paper, which may give rise to a promotion in propulsive performance of this traditional propeller. Firstly the numerical strategy is validated from two aspects of global quantities and the local flow field of the propeller compared with experimental data, and then the exit flow together with the development of propeller wake is analyzed in detail. Three kinds of SRV are designed with multiple circular airfoils. The numerical results show that the swirl behind the propeller is recovered significantly with Model V3, which is characterized by the highest solidity along spanwise, for various working conditions, and the combination of rotor and vane produced 5.76% extra thrust at the design point. However, a lower efficiency is observed asking for a better vane design and the choice of a working point. The vane position is studied which shows that there is an optimum range for higher thrust and efficiency.

Numerical model for circulation-control flows

Current computational models for circulation-control flows have been applied, in most cases, to elliptical airfoils having only one blowing slot. We describe a two-dimensional Navier-Stokes solver that has been developed for modeling the flowfields of a circular airfoil with two jets. In its original form, the Baldwin-Lomax algebraic turbulence model is shown to be inadequate for describing compound boundary layers such as those produced by the wall jet. A new turbulence model is therefore proposed. To account for the nonequilibrium production of turbulence at the slot exits and for its suppression due to wall curvature, two corrections to the turbulence model were implemented

Implicit solution of the incompressible Navier-Stokes equations on a non-staggered grid

This paper presents an implicit procedure for the solution of the incompressible Navier-Stokes equations in primitive variables. The time dependent momentum equations are solved implicitly for the velocity field using the approximate factorization technique. The continuity equation is satisfied at each time step through the solution of a Poisson type equation for the static pressure. A consistent finite-difference scheme which satisfies the compatibility condition using a non-staggered grid is used in the finite difference approximation of the static pressure Poisson equation. The results of the numerical computations in a driven cavity, which are presented for the history of the residues, at several Reynolds numbers using different computational parameters, demonstrate the excellent convergence characteristics of the solution procedure. A stability analysis is conducted for the non-iterative phase and numerical results are presented for a given set of compational parameters. Numerical results obtained for the steady state static pressure in the driven cavity are presented for the first time at Re =1000 using a non-staggered grid, and the steady state velocity, vorticity, and pressure contours at Re = 100, 400, and 1000, are compared with the computational results of other investigators. Additional results using a curvilinear grid are also presented for the flow in a cascade of circular airfoils at Re = 1000.

On sound generated when a vortex is chopped by a circular airfoil

An analysis is made of the sound produced when a rectilinear vortex is cut by a circular airfoil translating at zero angle of attack. The flow Mach number is sufficiently small that the airfoil is acoustically compact, and detailed predictions are given for a vortex whose axis is nearly normal to the plane of the airfoil. The two principal components of the radiation are associated with axial and azimuthal distributions of vorticity, the latter being non-zero when there exists a finite axial velocity defect in the core of the vortex. Comparison is made with similar predictions for a two-dimensional airfoil of infinite span, and the general effects of arbitrary, finite span are briefly discussed.

COMPARISON OF BOUNDARY-FITTED COORDINATES WITH FINITE-ELEMENT APPROACH FOR SOLUTION OF CONDUCTION PROBLEMS

This paper compares the boundary-filled coordinates/finite-difference scheme with a finite-element method for solving transient conduction problems in complex geometries. Various boundary conditions are considered on two-dimensional bodies with square and completely circular cross sections and a circular airfoil cross section. Wherever possible, the temperature distribution obtained numerically using both methods is compared with the analytic solution. For an identical mesh system, the boundary-fitted coordinates approach is found to be more accurate and economical in terms of both computational time and storage requirement than the finite-element method. A parametric study of the conduction problem for various heat generation rates and Biot numbers has been performed.

Theoretical research on Voith·Schneider·Propeller

Assuming the two dimensional flow and the uniform longitudinal induced velocity on the propeller stream, the Voith·Schneider·Propeller is solved approximately. Thrust, torque, lateral force, position of thrust line, maximum attack angle of the blade element and its peripheral position are expressed by the simple functional relations. By these relations of the fundamental quantities of the Voith. Schneider. Propeller, the characteristic curves are calculated, and also the applicable region of the formula are found. Calculated example of the characteristic curves coincide closely to Hans Kreitner's experiments. Comparing with more strict solutions of the Voith. Schneider. Propeller by elliptec integrals, these approximate simple functional relations would be serviceable to explaine the complicated acting conditions of the travers or lateral circular airfoil gitter type propeller.