# Heat transfer in a rocket engine combustion chamber while geometry changing of the channel-slot solid fuel charge

### Аuthors

Benderskyi B. Y.*, Chernova A. A.**

Kalashnikov Izhevsk State Technical University, 7, Studencheskaya str., Izhevsk, 426069, Russia

*e-mail: bib@istu.ru
**e-mail: alicaaa@gmail.com

### Abstract

Geometry changing impact of channel-slot charge while its burning on inner-chamber processes execution in flow ducts and pre-nozzle volume of the solid propellant rocket engine are being studied by mathematical modelling techniques. Setting of the conjugate problem of heat transfer in the flow ducts and pre-nozzle volume of the rocket engine combustion chamber with channel-slot solid fuel charge is presented. Numerical schemes and algorithms are being described. Mathematical modelling is being executed based on fundamental system of differential equations of viscous compressible heat-conducting gas movement. In spatial setting, solution of the problem under consideration is performed numerically using finite volumes method with account for the Rhie-Chow correction. The second-order of accuracy counter-flow scheme is employed for inviscid flows discretization, while the second-order of accuracy central scheme is applied for viscous flows. The system of difference equations is being solved by the algebraic net method, and a conjugate gradients method is applied herewith to accelerate its convergence. Various positions of burning dome are being considered while the engine operation at the static section. Profiles of longitudinal velocities components at the charge slice are being compared. The article analyses topological specifics of the combustion products flow, characteristic to various burning dome positions, and singular points are being characterized on the nozzle-cap assembly and near the charge grain-end. Thermal flow density near the structural elements of the combustion chamber is being studied. It was revealed that diameter increasing of the thermal flows channel led to maximum density decrease of thermal flows in the exceptional point and separation zones on the nozzle bottom by 2.04 and 3.6 times respectively. The article demonstrates that with the channel size increase, the decrease of velocity absolute values at the channel cut by 2.2 times is observed. As the result of the inner-channel processes analysis in the pre-nozzle volume of the solid propellant rocket engine, criteria equations for thermal flows evaluation near the exceptional points on the nozzle-cap assembly and the charge grain-end were obtained.

### Keywords:

combustion chamber, channel-slot charge, nozzle bottom, mathematical modeling, heat transfer

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