Experimental and Numerical Study of Cooling Gas Injection in Laminar Supersonic Flow

Abstract

In this study, we investigate film cooling on an inclined flat plate in a laminar supersonic flow. The influence of the most relevant parameters, the Mach and Reynolds numbers of the freestream, the blowing ratio, and the blowing geometry, is examined using numerical simulations and in experiments. Importantly, a correlation factor that describes the effect of the most important parameters for a large range of flow conditions has been developed from a simple heat balance model. Unlike the results for turbulent conditions that are typical for cooling turbine blades, interestingly, we have found that considerably less cooling gas mass flows are needed to cool the surface over a large area. In laminar boundary layers no turbulence appears, so that neither the cooling gas strongly mixes with the main stream nor does the blowing momentum influence the cooling effectiveness, provided that a boundary-layer transition is not induced by the cooling gas injection. Our results, presented here, agree with the results of previous investigations of laminar supersonic flow conditions. Nomenclature C = Chapman-Rubesin factor c p = specific thermal capacity F = blowing ratio FU = flux vector in the x direction GU = flux vector in the y direction HU = vector of the viscosity terms h = enthalpy k = thermal conductivity M = momentum ratio Ma = Mach number _ m c = cooling gas mass flow _ m 0 e = mass flow entering the mixing layer from the main flow Pr = Prandtl number _ q = wall heat flux Re e = unit Reynolds number behind the front shock Re x 0 = Reynolds number based on x 0 s = slot width in the streamwise direction T = mean temperature in the mixing layer T aw;c = adiabatic wall temperature for the case with cooling T r = recovery temperature T 0;c = total temperature of the cooling gas t = slot width in the spanwise direction U = state vector u = velocity in the x direction v = velocity in the y direction x = distance from the leading edge, parallel to the model surface x ref = empirical reference length x s = distance from the leading edge to the center of the blowing opening x 0 = distance from the center of the blowing opening y = distance normal to the model surface = boundary-layer thickness = cooling effectiveness = heat transfer coefficient = dynamic viscosity = correlation factor = density = Mach angle = blowing angle Subscripts c = with cooling nc = no cooling e = boundary-layer edge 1 = freestream 0 = stagnation conditions Superscript * = values determined at the reference temperature

An experimental study on the efficiency of transpiration cooling in laminar and turbulent hypersonic flows

“…2). Similar experiments were performed by Heufer and Olivier (2008) in a shock tunnel with a high enthalpy flow field. Despite some additional information with respect to the influence of the ratio of surface temperature to total temperature on the cooling efficiency, their experiments provided similar behavior concerning the Reynolds number effects.…”

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

“…In addition, a comparison with the experimental results by Heufer and Olivier [3] is performed. For the exact setup and flow conditions, we refer to [6] and [3], respectively. Moreover, we compile these comparisons of experiments with numerical simulations now in terms of the correlation factor ξ described later.…”

“…The first procedure is simply known as film cooling. Here, the coolant is injected through a single spanwise slit or row of holes, either by blowing in the (inclined) wall-normal direction (see, e.g., [2][3][4][5][6]) or by wall-parallel blowing through a backward-facing step (see, e.g., [7][8][9][10][11]). When blowing through multiple, uniformly distributed, discrete holes or slits, this is labeled effusion cooling; see, e.g., [12][13][14].…”

Numerical Simulation of Coolant Variation in Laminar Supersonic Film Cooling

“…Both effects lead to a significant reduction of the resulting wall heat flux and skin friction. 4 The cooling efficiency might be intensified by using coolants with favorable properties, such as a low viscosity, a low thermal conductivity and a high specific heat capacity. A low molar mass, i.e., a low density of the coolant, will result in a thicker protective layer and lead to smaller gradients at the wall.…”

“…The approximation ( ) is frequently used for experiments in super-and hypersonic test facilities. 1,2,4,5 It is assumed, that the reservoir temperature is equal to the wall temperature and that the heat flux throughout the whole boundary layer is predominantly influenced by the gas properties of the main flow. The cooling efficiency η depends on various flow quantities, which were correlated by Heufer et al 4 to an empirically justified non-dimensional factor ξ.…”