Continuum Sensitivity Analysis using Boundary Velocity Formulation for Shape Derivatives
| dc.contributor.author | Kulkarni, Mandar D. | en |
| dc.contributor.committeechair | Canfield, Robert A. | en |
| dc.contributor.committeechair | Patil, Mayuresh J. | en |
| dc.contributor.committeemember | Alyanak, Edward J. | en |
| dc.contributor.committeemember | Choi, Seongim Sarah | en |
| dc.contributor.committeemember | Kapania, Rakesh K. | en |
| dc.contributor.department | Aerospace and Ocean Engineering | en |
| dc.date.accessioned | 2016-09-29T08:00:42Z | en |
| dc.date.available | 2016-09-29T08:00:42Z | en |
| dc.date.issued | 2016-09-28 | en |
| dc.description.abstract | The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. | en |
| dc.description.abstractgeneral | Many natural and man-made systems exhibit behavior which is a combination of the structural elastic response, such as bending or twisting, and aerodynamic or fluid response, such as pressure; for example, flow of blood in arteries, flapping of a bird’s wings, fluttering of a flag, and flight of a hot-air balloon. Such a coupled fluid-structure response is defined as aeroelastic response. Flight of an aircraft through turbulent weather is another example of an aeroelastic response. In this work, a novel method is proposed for calculating the sensitivity of an aircraft’s aeroelastic response to changes in the shape of the aircraft. These sensitivities are numbers that indicate how sensitive the aircraft’s responses are to changes in the shape of the aircraft. Such sensitivities are essential for aircraft design. The method presented in this work is called Continuum Sensitivity Analysis (CSA). The main goal is to accurately and efficiently calculate the sensitivities which are used by optimization tools to compute the best aircraft shape that suits the customers needs. The key advantages of CSA, as compared to the other methods, are that it is more efficient and it can be used effectively with commercially available (nonintrusive) tools. A unique contribution is that the proposed method can be used to calculate sensitivities with respect to a few or many shape design variables, without much effort. Integration of structural and fluid sensitivities is carried out first by applying CSA individually for structural and fluid systems, followed by connecting these together to obtain the coupled aeroelastic sensitivity. We present the first application of local formulation of CSA for nonintrusive implementation of high-fidelity aeroelastic sensitivities. The following challenging tasks are tackled in this research: (a) deriving the sensitivity equations and boundary conditions, (b) developing and linking computer codes written in different languages (C++, MATLAB, FORTRAN) for solving these equations, and (c) implementing CSA using commercially available tools such as NASTRAN, FLUENT, and SU2. CSA can improve the design process of complex aircraft and spacecraft. Owing to its modularity, CSA is also applicable to multidisciplinary areas such as biomedical, automotive, ocean engineering, space science, etc. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:8689 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/73057 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | continuum sensitivity | en |
| dc.subject | shape derivatives | en |
| dc.subject | shape optimization | en |
| dc.subject | aeroelasticity | en |
| dc.subject | fluid-structure interaction | en |
| dc.title | Continuum Sensitivity Analysis using Boundary Velocity Formulation for Shape Derivatives | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Aerospace Engineering | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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