Aerodynamic design optimization of three dimensional rocket nozzles using adjoint method

Date

2013-09-13

Author

Eyi, Sinan

Metadata

Show full item record

Item Usage Stats

146
views

0
downloads

A design optimization method based on three dimensional Euler equations is developed. A finite volume method is implemented to discretize the Euler equations. Newton's method is used to solve the discretized form of Euler equations. Newton's method requires the calculation of the Jacobian matrix which is the derivative of the residual vector with respect to the flux vector. Different upwind methods are used in the calculation of flux vectors. Numerical and analytical methods are utilized in the evaluation of Jacobian matrices. The efficiency and accuracy of the analytical and numerical Jacobian evaluations are compared. In order to improve the accuracy of numerical method, detailed error analyses are performed. The optimum finite difference perturbation magnitude that minimizes the error is searched. The computation time of numerical Jacobian evaluation is reduced by calculating the flux vectors with perturbed flow variables only in related cells. The performances of different sparse matrix solvers are also compared. The effects of errors in numerical Jacobians on the accuracy of sensitivities is analyzed. Results show that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. Approximately the same optimum perturbation magnitude enables the most accurate numerical flux Jacobian and sensitivity calculations.

Subject Keywords

Aerodynamic design optimization, Analytical method, Numerical methods, Euler equations

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84883647910&origin=inward
https://hdl.handle.net/11511/79927

Conference Name

21st AIAA Computational Fluid Dynamics Conference (2013)

Collections

Department of Aerospace Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Three dimensional design optimization using analytical and numerical jacobians Eyi, Sinan; Degirmenci, M.; Yumusak, M. (null; 2011-12-01) A design optimization method based on three dimensional Euler equations is developed. A finite volume method is implemented to discretize the Euler equations. Newton's method is used to solve the discretized form of Euler equations. Newton's method requires the calculation of the Jacobian matrix which is the derivative of the residual vector with respect to the flux vector. Different upwind methods are used in the calculation of flux vectors. Numerical and analytical methods are utilized in the evaluation o...
Parallel processing of two-dimensional euler equations for compressible flows Doǧru, K.; Aksel, M.h.; Tuncer, İsmail Hakkı (2008-12-01) A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for par...
Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials Ozgun, Ozlem; Kuzuoğlu, Mustafa (2011-06-23) We present numerical solution techniques for efficiently handling multi-scale electromagnetic boundary value problems having fine geometrical details or features, by utilizing spatial coordinate transformations. The principle idea is to modify the computational domain of the finite methods (such as the finite element or finite difference methods) by suitably placing anisotropic metamaterial structures whose material parameters are obtained by coordinate transformations, and hence, to devise easier and effic...
USE OF GEOMETRICAL OPTIC METHODS FOR DISADVANTAGES OF FDTD METHOD Ciydem, Mehmet; Koç, Seyit Sencer (2014-03-01) Numerical methods in space-time have long been used to solve Maxwell's partial differential equations (PDEs) accurately. Finite Difference Time Domain (FDTD), one of the most widely used method, solves Maxwell's PDEs directly in computational grid. In FDTD, grid spacings (Delta x, Delta y, Delta z) are selected to properly sample field quantities to avoid aliasing and maximum allowable time-step (Delta t) is determined to ensure numerical stability of algorithm. Due to discretization of PDEs, FDTD inherentl...
Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005) In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...

Citation Formats

S. Eyi, “Aerodynamic design optimization of three dimensional rocket nozzles using adjoint method,” San Diego, CA; United States, 2013, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84883647910&origin=inward.