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

The 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 objective function is controlled by the Reynolds-averaged Navier-Stokes (RANS) equations with the RNG k-epsilon model during the optimization process, all the corresponding adjoint equations should be solved, rather than the frozen turbulence assumption used in previous studies. This investigation developed adjoint equations for the RNG k-epsilon turbulence model and applied it to a two-dimensional ventilated cavity and a three-dimensional, two-person office. Design processes with the adjoint RNG k-epsilon turbulence model led to a near-zero design function for the two cases, while those with the frozen turbulence assumption did not. This investigation has successfully used the new method to design a two-person office with optimal thermal comfort level around the two occupants.