Differential Boundary-Layer Analysis and Runback Water Flow Model Applied to Flow Around Airfoils with Thermal Anti-ice

Abstract

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...

Numerical simulation of an airfoil electrothermal anti-icing system

“…The runback water distributions predicted in this article for case 22A, 67A, and 67B (Figures 8(b), 9(b) and 10(b)) are close to those of ANTICE and Silva et al For convenience, Table 4 presents the limits of impingement, runback water, heated zone, runback icing predicted in this article, and the deviation between present results and Silva et al 30 For case 22A, the runback water is predicted to vanish near the impingement limits, for case 67A, almost all of the runback water evaporates in the region just upstream of the heaters, while regarding case 67B, the runback water flows downstream the heated zone and freezes. Therefore, case 22A is fully evaporative anti-icing, case 67A is evaporative anti-icing, and case 67B is running-wet anti-icing.…”

“…In case 67B, anti-icing system uses less power but results in runback icing which would lead to aerodynamic penalties. The runback icing region which is not predicted by Silva et al 30 is estimated for case 67B about 2.8% and 2.5% of s/c downstream the start location of freeze on the lower and upper surface individually.…”

“…The numerical code is now used to compute the local water collection efficiency, and then the equilibrium surface temperature and the mass flux of the runback water. The cases are chosen from the paper published by Al-Khalil et al 29 The results are compared with both experimental and numerical results of Al-Khalil et al 29 for NACA 0012 (1.828 m span by 0.914 m chord, with seven heater blocks, Figure 6), and with numerical results of Silva et al 30 for the same cases. Each heater block has several layers, including silicone foam (3.43 mm), fiberglass (0.89 mm), heater (0.03 mm), elastomer (0.26 mm), and erosion shield (0.2 mm).…”

“…12,18,30 Al-Khalil et al 29 conducted anti-icing experiments at the NASA Glenn Research Center to validate ANTICE for steady-state hot air and electrothermal anti-icing simulations. Silva et al 30 performed numerical studies of anti-icing systems using both integral and differential boundary layer methods and compared their results with the experimental results of Al-Khalil. The icing conditions used in the reference cases are presented in Table 1 and the detailed locations of the heaters as well as power densities are presented in Table 2.…”

“…A turbulence level of Tu in equation ( 18) is assumed as the same with Silva's 30 work in 2009 for the prediction of the start location of transition. The freestream Tu value is 0.7% and can increase up to 6% near the test body according to Silva et al 30 Therefore, Tu values were adjusted by the authors 30 to get appropriate values of the locations of the transition for cases 22A, 67A, and 67B. In order to make the same input data, Tu values assumed in this article is according to Silva's work, which are presented in Table 3.…”