Download or read book Studies of the Finite Element Technique for Transonic Flows with Shocks written by Aspi Rustom Wadia and published by . This book was released on 1978 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies of the Finite Element Technique for Transonic Flows with Shock written by Aspi Rustom Wadia and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Analysis of Subsonic Transonic and Supersonic Flows Around Missiles written by T. J. Chung and published by . This book was released on 1979 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report examines the Galerkin finite element method for solving aerodynamics problems with emphasis on transonic flows. A shock element concept was proposed and computations were carried out. In this process, a quadratic isoparametric element is divided into quadrants with each quadrant having independent trial functions. This idea allows discontinuities at the center of an element and shocks are allowed to develop freely. Rankin-Hugoniot conditions are satisfied accurately. Although this method is efficient until freesteam Mach number reaches approximately 0.95, the solution seems to deteriorate significantly for M> 0.95. Toward the end of the reporting period, the author proposed a new approach--optimal control penalty finite elements. This method is suited ideally for problems of discontinuity and shock waves as a consequence of changes in the type of partial differential equations. The resulting equations are symmetric and positive-definite, their solution being type-idependent. Numerous examples indicate that both stability and accuracy are maintained very satisfactorily for Tricomi and small perturbation equations. Detailed calculations applied to the full potential equations using this approach are beyond the scope of the present study.
Download or read book Least Squares Finite Element Simulation of Transonic Flows written by T. F. Chen and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves written by Arthur Rizzi and published by Springer-Verlag. This book was released on 2013-08-13 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Analysis of Transonic Flows in Cascades written by Akin Ecer and published by . This book was released on 1981 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method is applied for the solution of transonic potential flows through a cascade of airfoils. Convergence characteristics of the solution scheme are discussed. Accuracy of the numerical solutions is investigated for various flow regions in the transonic flow configuration. The design of an efficient finite element computational grid is discussed for improving accuracy and convergence.
Download or read book Numerical Computation of Transonic Flows by Finite element and Finite difference Methods written by United States. National Aeronautics and Space Administration. Scientific and Technical Information Office and published by . This book was released on 1978 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Least Square Finite Element Technique for Transonic Flow with Shock written by Aspi Rustom Wadia and published by . This book was released on 1977 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The governing differential equation for the one-dimensional, transonic flow in a laval nozzle in the vicinity of the throat was obtained in the non-dimensional form. A least square finite element technique was used with a linearly interpolating polynomial to reduce the governing equation to a system of non-linear algebraic equations which were solved numerically by Newton's method. The system of partial differential equations for the two dimensional flow in a laval nozzle was also obtained in the non-dimensional form. The method of integral relations was used to replace the original system of partial differential equations by a system of ordinary differential equations. Using the least square finite element technique a computer program was developed for the construction and solution of the non-linear equations for the laval nozzle problem. The results including the location of the shock in the flow are presented. (Author).
Download or read book Least Squares Finite Element Simulation of Transonic Flows written by T. F. Chen and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Analysis of Transonic Flows Over Thin Airfoils Volume II Program User s Manual written by H. C. Chen and published by . This book was released on 1976 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: A finite element program is described for computing steady and unsteady (oscillatory and transient) transonic flows over thin airfoils by solving directly the unsteady, nonlinear transonic potential equation based on small disturbance theory. The present numerical algorithm is developed using the concept of finite elements in conjunction with the least squares method of weighted residuals applied to both space and time. The basic element presently used is a product of an element in space and an element in time. The former has a cubic expansion inside each element, while the latter is a quadratic Lagrangian element. For each time step, the finite element discretization in both space and time results in a recurrence relationship in the form of a banded system of algebraic equations, which is solved by Gaussian elimination. The embedded shocks are smeared and a matching scheme for computing effectively flow over lifting airfoils is also incorporated in the program. The present computer program is composed of two parts: the first part (designated as UTRANL-I) generates, from a limited number of input cards, the necessary mesh information and, if desired, produces a CALCOMP mesh plot; the second part (UTRANL-II) carries out the analysis and displays the pressure coefficients along the chordline on printer plots. Two sample cases of flow over a NACA 64A 410 and a NACA 64A 006 airfoils are given to demonstrate the applicability and usage of the program. Te solution procedures are found to be quite efficient and accurate, permitting the aerodynamic forces to be calculated to engineering accuracy in less than ten minutes CPU time on a CDC 6600 computer for the most time consuming case among all those studied. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Elements in Fluids written by Richard H. Gallagher and published by . This book was released on 1978 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Analysis of Transonic Flows Over Thin Airfoils written by S. T. K. Chan and published by . This book was released on 1976 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: A finite element algorithm is described for computing steady and unsteady (oscillatory and transient) transonic flows over thin airfoils by solving directly the unsteady, nonlinear transonic potential equation based on small disturbance theory. The numerical algorithm is developed using the concept of finite elements in conjunction with the least squares method of weighted residuals applied to both space and time. The basic element presently used is a product of an element in space and an element in time. The former has a cubic expansion inside each element, while the latter is a quadratic Lagrange element. The embedded shocks are smeared and, in computing flow over lifting airfoils, use is made of the far field asymptotic solution to increase computational efficiency. For each time step, the finite element discretization in both space and time results in a recurrence relationship in the form of a banded system of algebraic equations, which is solved by Gaussian eliminations. Sample problems of steady flow over lifting airfoils and unsteady flow over airfoils executing harmonic motion are calculated to demonstrate the applicability and validity of the present approach. The solution procedures are found to be adequately accurate and very efficient, with unsteady solution obtainable in less than ten minutes CPU time on a CDC 6600 computer. (Author).
Download or read book A Contribution to the Finite Element Analysis of High Speed Compressible Flows and Aerodynamics Shape Optimization written by Mohammad Kouhi and published by . This book was released on 2014 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers a contribution to two most interesting research elds in aerodynamics, the fi nite element analysis of high-speed compressible flows (Part I) and aerodynamic shape optimization (Part II). The fi rst part of this study aims at the development of a new stabilization formulation based on the Finite Increment Calculus (FIC) scheme for the Euler and Navier-Stokes equations in the context of the Galerkin nite element method (FEM). The FIC method is based on expressing the balance of fluxes in a spacetime domain of nite size. It is tried to prevent the creation of instabilities normally presented in the numerical solutions due to the high convective term and sharp gradients. In order to overcome the typical instabilities happening in the numerical solution of the high-speed compressible flows, two stabilization terms, called streamline term and transverse term, are added through the FIC formulation in space-time domain to the original conservative equations of mass, momentum and energy. Generally, the streamline term holding the direction of the velocity is responsible for stabilizing the spurious solutions produced from the convective term while the transverse term smooths the solution in the high gradient zones. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. In order to investigate the capability of the proposed formulation, some numerical test examples corresponding to subsonic, transonic and supersonic regimes for inviscid and viscous flows are presented. The behavior of the proposed stabilization technique in providing appropriate solutions has been studied especially near the zones where the solution has some complexities such as shock waves, boundary layer, stagnation point, etc. Although the derived methodology delivers precise results with a nearly coarse mesh, the mesh refinement technique is coupled in the solution to create a suitable mesh particularly in the high gradient zones. The comparison of the numerical results obtained from the FIC formulation with the reference ones demonstrates the robustness of the proposed method for stabilization of the Euler and Navier-Stokes equations. It is observed that the usual oscillations occur in the Galerkin FEM, especially near the high gradient zones, are cured by implementing the proposed stabilization terms. Furthermore, allowing the adaptation framework to modify the mesh, the quality of the results improves signi cantly. The second part of this thesis proposes a procedure for aerodynamic shape optimization combining Genetic Algorithm (GA) and mesh re nement technique. In particular, it is investigated the e ect of mesh re nement on the computational cost and solution accuracy during the process of aerodynamic shape optimization. Therefore, an adaptive remeshing technique is joined to the CFD solver for the analysis of each design candidate to guarantee the production of more realistic solutions during the optimum design process in the presence of shock waves. In this study, some practical transonic airfoil design problems using adap- tive mesh techniques coupled to Multi-Objective Genetic Algorithms (MOGAs) and Euler flow analyzer are addressed. The methodology is implemented to solve three practical design problems; the fi rst test case considers a reconstruction design optimization that minimizes the pressure error between a prede ned pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coe cient (Cl). The solutions obtained with and without adaptive mesh re nement are compared in terms of solution accuracy and computational cost. These design problems under transonic speeds need to be solved with a ne mesh, particularly near the object, to capture the shock waves that will cost high computational time and require solution accuracy. By comparison of the the numerical results obtained with both optimization problems, the obtainment of direct bene ts in the reduction of the total computational cost through a better convergence to the final solution is evaluated. Indeed, the improvement of the solution quality when an adaptive remeshing technique is coupled with the optimum design strategy can be judged.
Download or read book Finite Element Method for Transonic Cascade Flows written by W. G. Habashi and published by . This book was released on 1981 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transonic Flow Computations in Cascades Using Finite Element Method written by H. U. Akay and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods in Fluid Dynamics written by North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development and published by . This book was released on 1972 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: ;Contents: On the numerical approximation of some equations arising in hydrodynamics; Approximation of Navier-Stokes equations; Sur l'approximation des equations de Navier-Stokes des fluides visqueux incompressibles; Numerical solution of steady state Navier-Stokes equations; Numerical solution of the Navier-Stokes equations at high reynolds numbers and the problem of discretization of convective derivatives; Numerical analysis of viscous one-dimensional flows; A critical analysis of numerical techniques: the piston-driven inviscid flow; Transient and asymptotically steady flow of an inviscid compressible gas past a circular cylinder; The blunt body problem for a viscous rarefied gas; The choice of a time-dependent technique in gas dynamics; Application of finite elements methods in fluid dynamics; Computational methods for inviscid transonic flows with inbedded shock waves; Numerical treatment of time-dependent three-dimensional flows; Un example de modele mathematique complexe en mecanique des fluides.
