Coupled Inverse And Forward Modeling For Temperature-Heat Flux And Application Of Underfloor Heating In An Aircraft Cabin

Thermal boundary conditions in commercial airliner cabins are crucial for creating a comfortable cabin environment. Cabin temperature distributions depend on the thermo-fluid boundary conditions of the boundary walls and the air supply. The design targets are to create an average temperature of 24? around the upper human body and 26? near the ankle level. For precision design, designers may turn to inverse modeling, i.e., finding the required underfloor heating rate and air-supply temperature based on the targeted thermal comfort demand. However, when designing an indoor environment, the thermal boundary conditions are not directly determined based on the demanding temperature distribution indoors but are primarily based on assumptions. A lengthy iterative guess-and-correction procedure is required to obtain the thermal boundary conditions that are finally used. To remedy this problem, researchers propose inverse modeling, i.e., finding the unknown causal information, such as thermal boundary conditions, based on the expected consequences, such as target temperature distribution indoors.The contribution ratio of indoor climate (CRI) is applied to describe the cause-effect relation between the wall convective heat fluxes and the resulted discrete temperatures at certain points, which can be cast into a matrix. This study proposes an inverse method based on Tikhonov regularisation and least-squares optimisation using computational fluid dynamics (CFD) to determine the wall boundary convective heat fluxes. The wall convective boundary heat fluxes can then be solved by inverse matrix operations with discrete target temperatures at distinct points. The only prerequisites to implement the proposed inverse method are a fixed flow field and the given target temperatures at certain points in space. Then, the wall boundary surface temperatures are solved according to Newton's cooling law if the convective heat transfer coefficient is known. The third step is to run a radiation computation for the wall boundary radiative heat release to the space. This investigation demonstrates how such a combined inverse-forward three-step model can determine the underfloor heating rates and air-supply temperature in an aircraft cabin. However, the current target temperature specification is determined by intuition or experience rather than by systematic derivation. This investigation proposes to evaluate the specification of target temperature points using the eigenvalue decomposition to the governing matrix. A connection was established between the eigenvalues and the condition number of the matrix that describes the posedness of the problem. The condition number of matrix can be expressed as a function of eigenvalues (the ratio of the maximum eigenvalue to the minimum eigenvalue). This study focuses on the optimal determination of the number and locations of target temperature points when inversely designing thermal boundary conditions in an indoor environment.To validate the aforementioned inverse-forward modeling strategy, this study conducted an experimental test in a simplified cabin-like enclosure and MD-82 cabin. The effects of the number and locations of the target temperature points on the inverse solution were analyzed based on a two-dimensional ventilation enclosure. The inverse-forward three-step model was used to determine the total underfloor heating rates and air-supply temperature in a single-aisle aircraft cabin. The design targets are to create an average temperature of 248? near the upper human body and 26? at the ankle level. The effects of the number and locations of the target temperature points on the inverse solution were also analyzed based on a single-aisle aircraft cabin.The excellent performance of the proposed inverse-forward model was also verified by the measurement data in the cabin-like enclosure during model validation.The effects of the number and locations of the target temperature points on the inverse solution were analyzed based on a two-dimensional ventilation enclosure. The results showed that the proposed inverse model provides accurate solutions with appropriately specified target temperature points. Locating the target temperature points downstream of the flows that sweep boundary walls can help reduce the posedness of the governing matrix and thus can improve solving precision. There is no need to adopt more target temperature points than the number of unknown thermal boundaries. In some circumstances, if more target temperature points than the number of unknown boundaries are provided, it is recommended to select the points that correspond to eigenvalues of the matrix far from zero. The results show the proposed methodology is able to provide total underfloor heating power rates and air-supply temperature that comply with the measurement data and the forward-simulation boundary conditions.The excellent performance of the combined inverse-forward model was also justified by the measurement data in the cabin like enclosure.