### Numerical Correlation of Heat Transfer From an Array of Hot-Air Jets Impinging on 3D Concave Surface

Mathieu Fregeau, F Saeed, I Paraschivoiu
unpublished
The paper presents numerical heat-transfer correlations established from numerical CFD study of a 3D hot-air jet array impinging on curved (circular) surface. The results are in the form of numerical correlations for the average and maximum Nusselt number for different nozzle-to-nozzle spacing, nozzle-to-surface height and hot-air jet mach numbers typical of those in an hot-air anti-icing system employed on aircraft wings. The paper presents a validation case and show that the results obtained
more » ... rom the CFD study are in good agreement with experimental data found in literature. The paper presents an interpolation technique, the dual Kriging method, that make use of the numerical database for anti-icing simulation on aircraft wings. The benefit of using the dual Kriging method is that it preserves the non-linear nature of the heat-transfer distribution from a hot-air jet impinging on a curved surface. NOMENCLATURE a i = derivative function coefficient c 1 ... c 8 = correlation coefficient C p = specific heat at constant pressure d = piccolo hole (jet) diameter G = mass-flow rate of air per unit area, ˙ m S H = nozzle-to-surface distance h c = heat transfer coefficient h ave = average heat transfer coefficient h = eucledian's distance I = identity Matrix k = thermal conductivity K = generalized covariance term N u = Nusselt number based on jet dia., hcd k Re = Reynolds number, ˙ m = mass-flow rate of air, ρ jet A noz V jet M = Mach number n = number of samples per variable N = number of variables P r = Prandlt number, Cpµ k ˙ q = heat flux S = reference surface area s = coordinate along surface with origin at center of jet axis, y = 0 plane T = temperature, K U = general function V jet = mean jet velocity at exit of piccolo tube W = nozzle-to-nozzle distance X = multi-variable sampling x = one variable sampling x, y, z = coordinate system with origin at center of jet exit Γ = Kriging matrixˆΓ matrixˆ matrixˆΓ = weighted Kriging matrix µ = dynamic viscosity ν = kinematic viscosity, µ/ρ ρ = fluid density σ = weight value Φ = derivative function Ψ = covariance function Superscripts: (˜) = interpolated function or variables from which we interpolate Subscripts: (anti) = from the anti-icing system (ave) = averaged (jet) = at the exit of piccolo tube (jet condition) (max) = at the maximum point of the indexed variable (s) = at the surface