Determination of the local heat transfer coefficient using the model of the temperature boundary layer with the convective component in the rotation cavities of the LRE Turbopump

An important research task is to take into account the features of heat transfer in turbine settings of turbopump units (TPU) of liquid rocket engines (LRE). The problem of heat transfer flow, including rotational flows in the elements of turbine settings of TPU LRE, is solved using the following approaches: numerical methods, analytical joint solution of equations of motion and energy, and using of empirical equations. Heat transfer significantly affects the performance characteristics of TPU LRE. When designing the turbine settings of LRE assemblies and units, it is important to take into account the effect of heat transfer and, thus, the temperature of the working fluid flow along the length of the flow track. This is due to the fact that viscosity directly depends on temperature and determines the losses and flow pattern. Slight heating of the working fluid can lead to boiling of its components and loss of performance characteristics in supply units, especially when using cryogenic components of fuel. On the other hand, insufficient (unplanned) temperature of a component in the turbine setting leads to increased viscosity of some working fluids (for example, gel-like components), and thus to reduced efficiency of the unit. When studying the problem of rotational flows with heat transfer, it is necessary to solve the joint equations of motion and energy in the boundary conditions of LRE turbine settings, taking into account the theory of spatial boundary layer. Heat transfer processes in power plants are in many ways similar, but there are certain differences in the analysis and derivation of heat transfer equations for the LRE boundary conditions. The main differences are as follows: extremely high values of heat flows, temperatures, and pressures; high flow velocities; initial turbulent state of the flows in the core; possible gaseous and liquid state of working fluids; surface curvature effects. Using an analytical approach, we defined the equations for calculating local heat transfer coefficients in the form of Stanton criteria for the most important cases of flow in rotational cavities of TPU LRE. We obtained the local heat transfer coefficients for straight flow, rotational flows realized in the cavities between the impeller and the turbine casing and the centrifugal pump (solid state flow), in the inlet and outlet devices (free vortex). The obtained analytical expressions for the local heat transfer coefficients are consistent with the results of other author’ studies and may be applied in calculating the characteristics of an LRE turbopump track.