Application of semiempirical correlations for multidimensional heat transfer in rocket engine cooling channels

Heat transfer in cooling channels of liquid rocket engine thrust chambers is an intrinsically multidimensional problem due to the geometry of the channels, often rectangular in section, and the asymmetric distribution of heat input from the hot combustion gas. In this study, the possibility of addressing this problem with semiempirical correlations for the coolant heat transfer and multidimensional numerical simulations for the heat conduction in the wall is investigated. Using experimental data from a test campaign of a cooling channel representative of liquid rocket engine conditions, semiempirical correlations are derived. Both cases of constant and variable heat transfer coefficient along the perimeter of the channel section are considered. The resulting correlations are then used to evaluate their reliability in reproducing the experimental wall temperature data from the same test campaign. For comparison, a correlation taken from the open literature and obtained with experimental data of circular heated tubes is also considered. The results demonstrate that correlations based on a constant heat transfer coefficient fail to reproduce with sufficient accuracy the test cases characterized by higher wall temperatures, while correlations based on a variable heat transfer coefficient overestimate the wall temperature in the initial sections of the channel.