Study of Heat Transfer Correlations for Supercritical Hydrogen in Regenerative Cooling Channels

Abstract

Understanding the cooling efficiency of supercritical hydrogen is crucial to the development of high-pressure thrust chambers for regeneratively cooled liquid-oxygen/liquid-hydrogen rocket engines. Available Nusselt number correlations are compared with an extensive data set of local heat transfer coefficients to determine the domains of validity for each correlation. The data set was compiled from previous heated straight-tube experiments with supercritical hydrogen. Results indicate that particular correlations perform better than others for certain regimes of fluid properties, with the accuracy of heat transfer coefficient predictions ranging from 23 to over 100%. Correlation uncertainty due to inherent uncertainties in the equation-of-state and transport properties of supercritical hydrogen is also evaluated. The property dependent uncertainty was found to range from 2 to 10%, and therefore is not the main contributor to the larger errors in the correlation predictions. A number of published correlations for nonhydrogen supercritical fluids are shown to achieve comparable performance with hydrogen.downstream from entrance x = any property = dynamic viscosity, kg=m s = kinematic viscosity, m 2 =s = density, kg=m 3 = standard deviation Subscripts b = property evaluated at bulk temperature reference c = critical condition calc = calculated value exp = experimental value f = property evaluated at film temperature reference pc = pseudocritical ref = reference temperature type s = condition at inner-wall surface R = property evaluated by integral method IntroductionA NALYTICAL performance predictions and design analyses for regeneratively cooled liquid rocket engines use correlations to predict the heat transfer from the combusting gas to the thrust chamber wall and from the wall into the cooling fluid. Today, these correlations are used in many engineering level computational analysis tools [1] for thrust chamber cooling system design, and cycle power-balance programs [2], which are increasingly being used in the design and evaluation of complete liquid rocket engine systems. In addition, these correlations are often used to aid the design of many of the experiments aimed at obtaining benchmark computational fluid dynamics data [3]. They are also used as validity checks of computational results. These semi-empirical heat transfer correlations are highly dependent on the fluid transport properties and the conditions at which the fluid is flowing [4-6]. Although a number of coolant-side correlations have been proposed for hydrogen [7][8][9][10][11][12][13][14][15], their ability to accurately predict heat transfer over a wide range of operating conditions has typically been limited.Improved thrust chamber design requires accurate correlations for different geometries, such as high aspect ratio rectangular channels and curvature, as well as asymmetric heating and varying heat flux. For correction factors and new correlations to have any merit, it is important to understand the limitations of current correlations for ...

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