Inverse Design of Enclosed Environment by CFD-based Adjoint Method

Wei Liu, Purdue University


This study is to develop the inverse design method. This investigation firstly reviewed the inverse design method that has been used or has great potential for the inverse design of an enclosed environment and demonstrated the application of these methods through several examples. The current backward methods can only handle an inverse design in known flow context. Forward methods are promising for inverse design of enclosed environments. The CFD-based adjoint method may only identify the local optima of the design objective, but the computing effort remains the same regardless of the number of the design variables. The CFD-based genetic algorithm method can find the global optima of the design objective, however the computing effort is significantly large. The proper orthogonal decomposition (POD) method can reduce the computing effort, although the resulting accuracy can be poor. By considering both the efficiency and accuracy, the CFD-based adjoint method shows great potential for the inverse design of enclosed environment. This study then developed the CFD-based adjoint method that can be used for inverse identification of air supply location, size, and parameters. The design objective could be local air distribution. The developed method could compute the derivative of the design objective over the design variables using the local contributions of the derivative of the Navier-Stokes equations over the node positions by finite element method (FEM). The developed CFD-based adjoint method was implemented in OpenFOAM, which is a CFD toolbox and can be used to simulate a broad range of physical problems. In the third part of this investigation, the developed method was used to identify the optimal air supply location, size, or parameters for validation. By using the measured air velocity and temperature in several locations in a ventilated cavity, the CFD-based adjoint method can identify the air supply location, size, and parameters that can lead to the same air velocity and temperature in those locations. However, the results show that different air supply location, size, and parameters could result in the same air velocity and temperature in those locations. This implies that multiple solutions exist and can be identified by the method. The computing costs did not vary with the number of design variables. This study then used the CFD-based adjoint method to find the optimal design variables of air supply locations, size, and parameters for a single-aisle airliner cabin to design a desirable thermal environment. By setting the occupant region as the design domain with a minimal predicted mean vote for thermal comfort, this study aimed to determine the corresponding air supply conditions for mixing and displacement ventilation systems under summer and winter conditions. The results show that it is possible to find the optimal air supply conditions in fewer than 10 design cycles if the initial conditions for design variables are provided within a reasonable range. This design method has a high computing efficiency. In addition, the results show that a displacement ventilation system provides a better thermal comfort level than a mixing ventilation system. To speed up the inverse design process, this study then evaluated four fast fluid dynamics (FFD) models in terms of solving the Navier-Stokes equations, integration with turbulence models, and solving the adjoint equations. This study developed the FFD solvers in OpenFOAM and validated them for predicting steady-state and transient flow in indoor environments. The effect of the time step size was also investigated. This study then validated the FFD solvers for solving the adjoint equations and the FFD-based adjoint method for inverse identification problems and inverse designs in indoor environments. The results showed that FFD was 20 times faster than CFD in predicting transient indoor airflow, and similar computational accuracy could be maintained; the FFD-based adjoint method was 4–16 times faster than the CFD-based adjoint method in the inverse design process. In the sixth part of this investigation, this study developed two adaptive coarse grid generation methods by analyzing the grid related truncation errors in solving the Navier-Stokes equations by FFD. Method 1 is to generate a grid coarser than that for grid independent solution but can still provide accurate FFD predictions. Method 2 is to generate a very coarse grid that provides acceptable FFD predictions. This study assessed the performance of the two coarse grid generation methods by using them to simulate three typical indoor airflows: forced convection flow, natural convection flow, and mixed convection flow. The assessment showed that the coarse grid generated by Method 1 could accelerate the FFD simulation by at least 2 to 5 times and the similar computational accuracy could be maintained. The coarse grid generated by Method 2 was able to realize faster-than-real-time FFD simulation for the cases tested in this study. (Abstract shortened by ProQuest.)




Chen, Purdue University.

Subject Area

Civil engineering|Mechanical engineering

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