Certification regulations require safe flight under icing conditions, therefore, ice protection on aircraft wings and horizontal stabilizers will be necessary if critical aerodynamic performance degradation is to be avoided. The present paper developed a numerical code for prediction of heat and mass transfer in two-phase flow around aeronautical airfoils. These systems are equipped with thermal anti-ice systems that are designed to keep the surface free of ice as much as possible. The code is able to estimate the temperatures and runback water around the airfoil surface due implementation of heat transfer submodels in a baseline thermal anti-ice model: 1) it estimated the airfoil surface wetness factor by means of a runback water film and rivulets pattern flow models; 2) it evaluated the laminar and turbulent boundary layers with pressure gradient and laminar-turbulent transition over non-isothermal and permeable airfoil surfaces by performing integral and differential boundary layer analysis; and 3) it predicted the onset position and length of the laminarturbulent transition region with pressure gradient and turbulence level effects. The work followed a validation and verification process during the numerical code development. All submodels results were separately verified against experimental data. The numerical results of the thermal performance of the airfoil with the anti-ice baseline model, plus the present contributions, were validated against experimental data of an electrically heated NACA 0012 airfoil operating in the Icing Reseach Tunnel (IRT), NASA, USA.
Nomenclature
A= finite volume area exposed to flow around the airfoil, m 2 B h = heat transfer driving force B m = mass transfer driving force h = convective heat transfer coefficient,W/(m 2 · K) c p = specific heat, J/(kg · K) E = mechanical energy, J e = mechanical energy per unit of film width, J/m F = wetness factor F r = rivulets flow wetness factor F s = stream wise wetness factor G = mass flux ρ · u e , kg/(s · m 2 ) g(θ 0 ) = auxiliary function, −1/4 cos 3 θ 0 − 13/8 cos θ 0 + 15θ 0 /8 sin θ 0 − 3/2θ 0 sin θ 0 g m = mass transfer conductance, kg/(s · m 2 ) h = convection heat transfer coefficient, W/(m 2 · K) h = water film height at film break-up position, m h + = non-dimensional critical film height at film break-up position, (ρτ 2 h 3 0 )/(6µ 2 σ f g ) h 0 = critical film height at break-up position, m h r = rivulet height downstream break-up position, m h(x) = half rivulet height in function of its horizontal coordinate,R(cos θ − cosθ 0 ), m i = specific enthalpy, J/kg k = thermal conductivity, W/(m · K) m = mas flow rate, kg/s Ma = Mach number p = pressure, Pa p mixt = total mixture pressure, Pa p vap = partial vapor pressure, Pȧ q = heat flux, W/m 2 q lost = heat transfer rate lost to gaseous flow, W R = rivulets radius, m r = high speed aerodynamic recovery factor R m = mean rivulet radius within the finite volume, 1/2 · (R out + R in ), m R t = thermal resistance, K/W s = stream wise distance over airfoil surface, m St = Stanton numb...
