Geometry Optimization in Three-Dimensional Unsteady Flow Problems using the Discrete Adjoint

An efficient approach to the geometry optimization problem of a non-axisymmetric flow channel is discussed. The method combines geometrical transformation with a computational fluid dynamics solver, a multi-objective genetic algorithm, and a response surface. This approach, through geometrical modifications and simplifications allows transforming a non-axisymmetric problem into the axisymmetric one in some specific devices i.e., a scroll distributor or a volute. It results in a significant decrease in the problem size, as only the flow in a quasi-2D section of the channel is solved. A significantly broader design space is covered in a much shorter time than in the standard method, and the optimization of large flow problems is feasible with desktop-class computers. One computational point is obtained approximately eight times faster than in full geometry computations. The method was applied to a scroll distributor. For the case under analysis, it was possible to increase flow uniformity, eradicate separation zones, and increase the overall efficiency, which was followed by energy savings of 16% for the scroll. The results indicate that this method can be successfully applied for the optimization of similar problems.

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Unsteady Discrete Adjoint Formulation for Two-Dimensional Flow Problems with Deforming Meshes

AIAA Journal ◽

10.2514/1.29924 ◽

2008 ◽

Vol 46 (6) ◽

pp. 1351-1364 ◽

Cited By ~ 62

Author(s):

Karthik Mani ◽

Dimitri J. Mavriplis

Keyword(s):

Two Dimensional ◽

Flow Problems ◽

Dimensional Flow ◽

Discrete Adjoint ◽

Adjoint Formulation ◽

Two Dimensional Flow

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Assessment of Unsteady Flows in Turbines

Journal of Turbomachinery ◽

10.1115/1.2928001 ◽

1992 ◽

Vol 114 (1) ◽

pp. 79-90 ◽

Cited By ~ 57

Author(s):

O. P. Sharma ◽

G. F. Pickett ◽

R. H. Ni

Keyword(s):

Unsteady Flow ◽

Three Dimensional ◽

Flow Simulation ◽

Experimental Investigations ◽

Flow Parameters ◽

Research Activities ◽

Flow Features ◽

Computational Fluid Dynamics Cfd ◽

Turbine Design ◽

The Impact

The impacts of unsteady flow research activities on flow simulation methods used in the turbine design process are assessed. Results from experimental investigations that identify the impact of periodic unsteadiness on the time-averaged flows in turbines and results from numerical simulations obtained by using three-dimensional unsteady Computational Fluid Dynamics (CFD) codes indicate that some of the unsteady flow features can be fairly accurately predicted. Flow parameters that can be modeled with existing steady CFD codes are distinguished from those that require unsteady codes.

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Asymmetric three-dimensional Stokes flows about two fused equal spheres

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2007.1872 ◽

2007 ◽

Vol 463 (2085) ◽

pp. 2329-2350 ◽

Cited By ~ 15

Author(s):

Michael Zabarankin

Keyword(s):

Meromorphic Functions ◽

Three Dimensional ◽

The Body ◽

Fredholm Integral Equations ◽

Rigid Spheres ◽

Riemann Boundary ◽

Fredholm Equations ◽

Flow Problems ◽

Toroidal Coordinates ◽

Class Of Functions

Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler–Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.

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