Integer programming topology optimization for subsonic compressible flows with geometry trimming

Author(s)

Maffei, Felipe Silva ; Nogueira de Sa, Luis Fernando ; Moscatelli, Eduardo ; Picelli, Renato ; Meneghini, Julio Romano ; Nelli Silva, Emilio Carlos

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER; v. 201, p. 13-pg., 2023-02-01.

Abstract

The incompressibility hypothesis is successfully applied in a broad range of engineering problems simu-lated via computational fluid dynamics (CFD) codes. However, depending on the Mach number, the ef-fects of compressibility are no longer negligible. Recently, the first papers about topology optimization considering compressible flows were published. All of them use the continuous design variables method which has some known drawbacks. The present work proposes topology optimization considering the compressible Navier-Stokes equations and discrete variables with a step of geometry trimming. This ap-proach constrains the design variables to a binary set and solves the problem by using sequential integer linear programming, being a feasible alternative to classic density-based methods. Additionally, the solid regions are trimmed out from the physics analysis. A material model is inserted in the governing equa-tions in such a way that, it is possible to calculate the sensitivity and, at the same time, guarantee the adiabatic condition. In this work, it is observed that the minimization of entropy generation as the ob-jective function tends to converge to an undesired trivial solution. Alternatively, this work proposes the maximization of mass flow rate as the objective function to, indirectly, minimize the entropy. Further-more, it is proposed the use of a new set of inlet boundary conditions. Three optimization cases are solved: the double-pipe, the pipe-bend, and an entropy maximization problem. The optimized solutions for the pipe-bend and double-pipe problems present geometries where the constraints are satisfied with the minimum entropy generation. Using the double-pipe example, it is conducted a study to understand the impacts of TOBS-GT parameters in the solutions. The results evidenced that, in some conditions, the implementation is prone to fall in a local minimum. In the third example, entropy maximization sub-jected to volume constraint is successfully solved. Moreover, a minimization case is also solved to aid in the interpretation of the results.(c) 2022 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 21/02340-0 - Topology optimization to design labyrinth seals considering turbulent flow and fluid-structure interaction with binary variables
• Grantee: Eduardo Moscatelli de Souza
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 18/05797-8 - Addressing design challenges of offshore structures via Multiphysics topology optimization
• Grantee: Renato Picelli Sanches
• Support Opportunities: Research Grants - Young Investigators Grants
• FAPESP's process: 20/15230-5 - Research Centre for Greenhouse Gas Innovation - RCG2I
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program
• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program