Regenerative Cooling Analysis

Overview

The motivation for this code was to explore the cooling performance of using regenerative cooing channels. Regenerative cooling is a very effective cooling method and is used in a majority of launch vehicle engines. This code calculates the axial temperature profile along the channels at varying aspect ratios to determine the optimal value with the given constraints.

Methodology

The main tool used in this analysis is NASA CEA (Chemical Equilibrium with Applications). CEA is a FORTRAN code developed by NASA Lewis Research Center (now known as NASA Glenn). The program calculates the chemical equilibrium product concentrations and thermodynamic and transport properties for given reactants. With specified reactants along with their respective temperatures and the chamber pressure, CEA aims to minimize Gibbs Free Energy to determine the equilibrium constants of the products. A CEA wrapper for MATLAB was used to perform calculations for this analysis.

Additionally, CoolProp was used to find the thermophysical properties of the cooling fluid, which in this case was liquid methane. CoolProp is a free and open-source tool that aims to offer similar functionality to that of REFPROP.

The case considered for this analysis was a liquid methane and liquid oxygen rocket. The following chamber values and nozzle geometry were inputted into CEA to determine the thermodynamic properties along the nozzle.

The methane enters from the bottom of the nozzle and travels towards the injector. The channels consisted of a simple rectangular cross-section with varying aspect ratios and a varying number of channels. The following table lists the channel properties used to perform the cooling analysis.

This analysis assumes steady flow along with neglecting backside heat transfer (convective and radiative heat transfer from the outer chamber wall and the atmosphere).

A thermal circuit can be set up to model the system. The gas-side convective heat transfer coefficient can be found using Bartz Equation. Iterate on the gas-side wall temperature until the value converges.

Results

The code results in a surface plot to visualize the maximum temperature along the nozzle (at the throat) with respect to the number of channels and various ratios. Additionally, the code produces plots to demonstrate how the cooling fluid properties change through the channels (i.e. pressure drop, temperature rise, and velocity).

Contour Plot of Wall Temperature, Number of Channels, and Channel Aspect Ratio

Temperature of Methane Through Channel

Future Developments

This code is being written in Python. Future iterations of the code will feature a GUI so that the user can specify the propellants and minimum channel dimensions to optimize the number of channels and aspect ratio. Additionally, an axially variable cross-sectional area will be added rather than the current constant cross-sectional area.

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