Optimal design of an indoor environment using an adjoint RNG k-ε turbulence model

¹ Tianjin Key Laboratory of Indoor Air Environmental Quality Control, School of Environmental Science and Engineering, Tianjin University, Tianjin, 300072, China
² School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA

^* Corresponding author: yanchen@purdue.edu

Abstract

The computational fluid dynamics (CFD)-based adjoint method can determine design variables of an indoor environment according to the optimal design objective, such as minimal predicted mean vote (PMV) for thermal comfort. The method calculates the gradient of the objective function over the design variables so that the objective function can be minimized along the fastest direction using an optimization algorithm. Since the RNG k-ε model is the most popular model used in CFD, the corresponding adjoint equations of the turbulence model should be solved during the design process, rather than the “frozen turbulence” assumption used in the existing approach. This investigation developed adjoint equations for the RNG k-ε turbulence model and applied it to a two-dimensional ventilated cavity. Design processes with the adjoint RNG k-ε turbulence model led to a near-zero design function for the cavity case, while that one with the RNG k-ε turbulence model did not.