Influence of Cooling-Gas Properties on Film-Cooling Effectiveness in Supersonic Flow

Abstract

Film cooling is considered a prerequisite for the safe operation of future high-performance rocket engines. Wallnormal or inclined cooling-gas injection into a laminar boundary-layer airflow at Mach 2.6 through a single infinite spanwise slit with various cooling gases using direct numerical simulations and experiments are investigated. Among the investigated gases, helium and hydrogen perform best with respect to cooling effectiveness and skin friction decrease. An arbitrary variation of various cooling-gas parameters shows that the diffusion coefficient has virtually no influence on the cooling effectiveness, whereas low cooling-gas viscosity, low thermal conductivity, high heat capacity, low molar mass, and low density are highly beneficial. In light of this large number of parameters, an extension of the single-species cooling-effectiveness correlation to binary gas-mixture flows is challenging, if possible at all. Nomenclature C = Chapman-Rubesin factor c = mass fraction c f = skin friction coefficient c p = heat capacity at constant pressure c v = heat capacity at constant volume D = ordinary diffusion coefficient D T = thermal diffusion coefficient e = internal energy F = blowing rate I = identity matrix j = diffusion mass-flux vector k = Boltzmann constant L = characteristic length M = molar mass Ma = Mach number Pr = Prandtl number p = pressure q = heat-flux vector R = gas constant Re u = unit Reynolds number Re ∞ = global Reynolds number Sc = Schmidt number T = temperature t = time v = velocity vector X = mole fraction x s = slit position x, y, z = streamwise, spanwise, and wall-normal directions α = blowing angle or thermal diffusion rate η = cooling effectiveness ϑ = thermal conductivity κ = specific heat ratio μ = dynamic viscosity ξ = correlation parameter ϵ = second Lennard-Jones parameter ρ = density σ = first Lennard-Jones parameter Ω = transport collision integral Subscripts c = cooling-gas values (species 2) i = species i is = isothermal uc = uncooled w = values at wall ∞ = freestream values (species 1) Superscripts = Eckert values ⋆ = dimensional values

Numerical Simulation of Film Cooling in Supersonic Flow

“…This section is intended to give a brief overview of the simulation setup, extensive details can be found in the referenced literature. For the DNS we use our in-house code NS3D, which has been used successfully for the calculation of film and effusion cooling in laminar and turbulent supersonic boundary-layer flow [7,9,11,14]. The governing equations for a flow of two mixing, non-reacting calorically perfect gases are the continuity equation, the three momentum equations, the energy equation, and the equation of state, all for the mixture values.…”

“…Simple blowing modelling by fixing the blowing distribution at the wall in fast CFD tools has implications: For narrow placed orifices a standard modelling with no knowledge of the actual blowing distribution resulting from included channels and a plenum chamber is inappropriate and indicates a false, too high critical blowing ratio for inducing turbulence tripping by the blowing [9]. Various cooling gases have been considered for binary-gas flow, and the comparison with the results of analogous experiments at RWTH Aachen showed somewhat lower experimental values, most probably caused by disturbances coming from the blowing device, rendering the flow no more laminar [11]. Employing simulations with deliberately manufactured cooling gases, cooling-gas properties beneficial for a high cooling effectiveness could be clearly identified: The diffusion coefficient shows virtually no influence on the effectiveness, whereas low coolinggas viscosity, low thermal conductivity, high heat capacity, low molar mass and low density turned out to be highly beneficial.…”

Thermal Protection System and Thermal Management for Combined-Cycle Engine: Review and Prospects

“…Coolant temperature has a relatively complicated impact on the air film cooling effect, but in general, if the coolant temperature rises, the air film cooling effect will be weakened. In a study by Keller [44], the effects cooling gas properties on air film cooling in supersonic flow environments was explored, and research findings about numerical simulation of supersonic boundary laminar flow were proposed. As for the effect of the cooling gas properties on the gas film, the gaseous-diffusion coefficient was found to have no effect on the cooling performance, yet the cooling effect can be improved by low thermal conductivity, low viscosity, high Prandtl number, low molar mass, and low density of the cooling gas.…”

Numerical simulation of supersonic film cooling in a rearward-facing slot

“…Although the semi-models made a distinction before and after the turning point, structural changes in the flowfield were not inspected because of the limitation associated with the one dimension nature of the models. The detailed structures of flowfield at this turning point can be obtained using computational fluid dynamic (CFD) method, but so far, there is rare CFD work concentrating on the flowfield changes at this point, including the Reynolds-averaged Navier-Stokes (RANS) based works of O'Connor and Haji-Sheikh, 19 Maqbool et al, 20 Peng et al, 21 large eddy simulation (LES) by Konopka et al, [22][23][24] and direct numerical simulation (DNS) by Keller et al 25 and Keller and Kloker. 26 O'Connor and Haji-Sheikh 19 and Maqbool et al 20 modeled film cooling in supersonic nozzle to develop an experimentally validated tool.…”

“…Konopka et al 22 investigated film cooling with favorable and adverse pressure gradients, analyzed the effects of shock wave on film cooling 23 and later they extended their work to consider the conditions of film coolant using helium and hydrogen. 24 Keller et al 25 and This study aims to analyze changes in flowfield structures at the turning point in supersonic film cooling using CFD method. O'Connor and Haji-Sheikh 19 reported that the normal film injection to the mainstream resulted in about 50% reduction in cooling effectiveness, so the tangential injection of film gas is considered in this article.…”