Nomenclature Ac = accumulation parameter Cd drag coefficient Ci = lift coefficient Cm = moment coefficient Cp = pressure coefficient c = specific heat at constant pressure, J/(kg-K); airfoil chord, m D = propeller diameter, m; flexural stiffness, N-m D drag force, N d = droplet diameter, m E = total collection efficiency / = freezing fraction g = acceleration caused from gravity, m/s Hi = ice thickness, m Hp = plate thickness, m h = airfoil projected height, m hc = convective heat transfer coefficient, W/(m-K) hfg = heat of vaporization, J/kg hsi = heat of fusion, J/kg / = airfoil drag constant K = thermal conductivity, W/(m-K); inertia parameter K0 = modified inertia parameter k = roughness diameter, m LWC = liquid water content, kg/m M = local Mach number MVD = median volume droplet diameter, m m = mass, kg ra = mass flow rate, kg/s m' = mass flow rate per unit width, kg/(m-s) m" = mass flux, kg/(m-s) n = normal direction P = pressure, Pa p spatial pressure distribution, N/m <2 = heat rate, W q = normal pressure distribution, N/m

Aircraft Anti-Icing and De-Icing Techniques and Modeling

Effects of ice accretions on aircraft aerodynamics

Ice accretion on structures is discussed with an emphasis on estimating structural design iceloads and solving operational icing problems. Basic principles of modelling of icing caused by freezing precipitation, cloud droplets and wet snow, as well as simulation of icicle growth, are presented. Theoretical models of atmospheric ice accretion are critically reviewed, particularly with respect to the simulation of the relevant physical processes. The reasons for the difficulties in simulating some icing phenomena accurately are analysed and proposals for further improvements in the models are made.

Models for the growth of rime, glaze, icicles and wet snow on structures

A one-dimensional mathematical model is developed describing ice growth due to supercooled e uid impacting on a solid substrate. When rime ice forms, the ice thickness is determined by a simple mass balance. The leadingorder temperature proe le through the ice is then obtained as a function of time, the ambient conditions, and the ice thickness. When glaze ice forms, the energy equation and mass balance are combined to provide a single e rst-order nonlinear differential equation for the ice thickness, which is solved numerically. Oncethe icethickness is obtained, the water height and the temperatures in the layers may be calculated. The method for extending the one-dimensional model to two and three dimensions isdescribed. Icegrowth rates and freezing fractions predicted by the current method are compared with the Messinger model. The Messinger model is shown to be a limiting case of the present method.

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Extension to the Messinger Model for Aircraft Icing

Two-dimensional and quasi-three-dimensional in-flight ice accretion simulation codes have been increasingly used by the aerospace industry in the last two decades as an aid to the certification process. Such codes predict two-dimensional sectional ice shapes, which are then manufactured from a light material and attached as disposable profiles on test aircraft to investigate them for stability under icing encounters. Although efficient for calculating ice shapes on simple geometries, current codes encounter major difficulties or simply cannot simulate ice shapes on truly three-dimensional geometries such as nonaxisymetric nacelles, high-lift wings, engine intakes, or systems that combine external and internal flows. Modern computational fluid dynamics approaches may not encounter or engender these difficulties, and FENSAP-ICE is a combination of four modules forming a complete and generic in-flight icing simulation system, built in a way to solve successively impingement, ice accretion, heat loads, and performance degradation. The set of equations describing FENSAP-ICE's airflow solver, FENSAP, its impingement module, DROP3D, and its accretion module, ICE3D, are presented

FENSAP-ICE's Three-Dimensional In-Flight Ice Accretion Module: ICE3D

The thermal analysis of a heated surface in icing conditions has been extensively treated in the literature. Except for the work of Tribus, however, little has been done on the analysis of an unheated icing surface. This latter analysis is significant in the design of cyclic thermal deicing systems that are attractive for small high-speed aircraft for which thermal anti-icing requirements have become severe. In this paper, a complete analysis of the temperature of an unheated surface in icing conditions is presented for the several significant regimes (i.e., less than 32°F., at 32°F., and above 32°F.) as a function of air speed, altitude, ambient temperature, and liquid water content. The results are presented in graphical form and permit the rapid determination of surface temperature for a wide range of variables. Curves are presented to determine the speeds beyond which no ice accretion will occur. Curves are also presented to indicate the surface temperature and the rate of ice sublimation which takes place when an ice-covered surface emerges into clear air. One significant result of this study is the introduction of a new basic variable referred to as the "freezing-fraction," which denotes the proportion of the impinging liquid which freezes in the impingement region. The fact that some of the liquid does not freeze in the impingement region tends to explain the observed variation in ice formation shape with temperature, speed, and water catch. New test data obtained at Mt. Washington, N.H., for stagnation-point surface temperatures of an unheated plastic cylinder in natural and artificial icing conditions are included in the Appendix. These data substantiate the validity of the assumptions made in the theoretical analysis.

Bernard L. Messinger

Papers

Equilibrium Temperature of an Unheated Icing Surface as a Function of Air Speed