Compressible Turbulent Boundary-Layer Heat Transfer to Rough Surfaces

Mathematical modeling of surface roughness and ablation effects on thermal protection

“…Since many experiments [2,3,[6][7][8] show that surface friction increases with growing roughness height and heat flow reaches its maximum value [6,7], the Reynolds analogy seems not to apply to rough surfaces. We can use the findings of the study [7] which presents a new approach to engineering calculations of heat flows to rough surfaces in supersonic streams:…”

“…We can use the findings of the study [7] which presents a new approach to engineering calculations of heat flows to rough surfaces in supersonic streams:…”

“…where Pr is the Prandtl number; ∞ M is the Mach number; St is the Stanton number; K Re is the Reynolds number for roughness; f C is the local friction coefficient; l is body length; h is enthalpy; T is temperature; p c , λ, α, μ are the coefficients of specific-heat capacity, thermal conductivity, heat transfer and dynamic viscosity; ρ is density; U is velocity; r is the coefficient of restitution; τ is shear stress; χ is the heat capacity ratio; η, 1 b , 2 b are constants; K is the equivalent roughness height [2,7]. Subscripts and superscripts: τ is the dynamic velocity; e is the outer edge of the boundary layer; w is the external heating surface of the streamlined body; * is the characteristic quantity (smooth surface); g is the gas phase; ∞ is parameters at infinity.…”

“…The development of aerospace technology has shown [3,[6][7][8] that roughness should be taken into account for ablative head sections of streamlined bodies and for ablative side surfaces with a relief surface structure. The relief surface structure is generated during ablation in a supersonic turbulent flow, which is confirmed in [8].…”

“…Roughness-induced growth of a heat flow in a turbulent boundary layer plays an important role in determining ablation of thermal protective material and changing the shape of an aircraft head [6][7][8].…”