Tianjin Key Laboratory of Indoor Air Environmental Quality Control, School of Environmental Science and Engineering, Tianjin University, Tianjin, China.
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana.
Indoor Air. 2019 Mar;29(2):320-330. doi: 10.1111/ina.12530. Epub 2019 Jan 30.
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-ε 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-ε 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-ε 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.
伴随法可以根据最优设计目标（例如，热舒适度的最小预测平均投票值 PMV）来确定室内环境的设计变量。该方法计算目标函数相对于设计变量的梯度，以便使用优化算法沿最快方向最小化目标函数。由于在优化过程中，目标函数受雷诺平均纳维-斯托克斯 (RANS) 方程和 RNG k-ε 模型控制，因此应求解所有相应的伴随方程，而不是之前研究中使用的“冻结湍流”假设。本研究为 RNG k-ε 湍流模型开发了伴随方程，并将其应用于二维通风腔和三维两人办公室。对于这两种情况，使用伴随 RNG k-ε 湍流模型的设计过程导致设计函数接近零，而使用“冻结湍流”假设的设计过程则没有。本研究成功地使用新方法设计了一个两人办公室，以在两个使用者周围达到最佳的热舒适度水平。
