In-flight Ice Accretion Prediction Code

Transcription

1 In-flight Ice Accretion Prediction Code Vladimír HORÁK*, Zdeněk CHÁRA** *Corresponding author University of Defence in Brno, Kounicova 65, Brno, Czech Republic **Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Patankou 5, Praha 6 chara@ih.cas.cz DOI: / Abstract: The phenomenon of in-flight icing may affect all types of aircraft. The paper deals with the development of the computational wing airfoil ice accretion prediction code Ice. Presented code versions enable computational rime ice and glaze ice accretion prediction on single and multi-element airfoils in acceptable time of solution. There are presented results of rime ice and glaze ice accretion predictions and compared with current ice accretion prediction codes. Various cases of predicted ice shapes are shown in dependence of air temperature. The latest Ice code version enables to solve system of several airfoils. The example of ice prediction on the wing airfoil with a slotted flap is shown for two angles of deflection. Key Words: aircraft icing, ice accretion simulation, icing code. 1. MOTIVATION The formation of ice on airplane wings occurs when the aircraft flies at a level where temperature is at, or below freezing point and hits supercooled water droplets. The in-flight icing may affect all types of aircraft. Presence of ice on an aircraft surface can lead to a number of performance degradations: changes in pressure distribution decreased maximum lift and increased drag stall occurring at lower angles of attack and increased stall speed reduced controllability. It is important to understand how the different ice shapes affect aircraft aerodynamics. It can be studied by flight tests, wind tunnel measurements, and computational simulations. Computational simulation of ice accretion is an essential tool in design, development and certification of aircraft for flight into icing conditions. Currently, there exist several approved ice accretion codes: LEWICE (LEWis ICE accretion program) is software developed by the Icing Branch at NASA Glenn Research Center CANICE code developed at the Ecole Polytechnique de Montreal ONERA (Office National d'etudes et de Recherches Aérospatiales) code in France TRAJICE code which was developed by DERA (Defence Evaluation and Research Agency) in United Kingdom CIRA code from Italian Aerospace Research Center., pp

2 Vladimír HORÁK, Zdeněk CHÁRA ICE ACCRETION PREDICTION CODE In conjunction with the project of the Czech Ministry of Industry and Trade, was developed the tool for simulating flight into icing conditions. Presented software was subsequently developed and improved. Currently, there are three main code versions: R-Ice 1.1 Rime ice accretion prediction [1] Ice 3.1 Glaze ice accretion prediction [3] Ice 4.1 Multi-element airfoils icing [4] The rime ice is formed if all the impinging water droplets freeze immediately upon impact. It tends to form at combinations of low ambient temperature, low speed (low kinetic heating) and a low value of cloud water concentration. The glaze ice creates at combinations of temperature close to freezing, high speed or high cloud liquid water content. In that case, not all of the impinging water freezes on impact, the thin layer of remainder water is flowing along the surface and freeze at other locations. The process is strongly influenced by the heat transfer. The latest code version is modified for multi-element airfoils, when the mutual flow overlap of circumfluent bodies can occur. This modification enables the solution of more complicated icing simulation cases, e.g. airfoil with slotted flap, wing slot, etc. 3. TRAJECTORIES OF WATER DROPLETS The potential flow field is calculated using 2-D panel method. The relation for any point inside the control area is in form 1 r n grad grad ln d S grad d S r n. (1) r 2 2 S S The searching solution has to respect the boundary area condition grad n v, where n v n is the normal direction velocity component on the boundary. It is possible to approximate the velocity potential, or the n value respectively, on the body surface and on the flow field potential discontinuity surfaces by a linear combination of an appropriate function class. If we choose the needed quantity of control points on the boundary in which we require to fulfill the integral equation for the gradient of potential and boundary conditions, the method leads to the set of linear equations solution for unknown coefficients of functions linear combination that approximate the solution. Potential flow field is then used to determine the trajectories of water droplets and the impingement points on the body. Droplets passing through the atmosphere are considered as spherical elements with a mass m on that the surrounding fluid forces and gravitation F act. Droplets acceleration and position vector r are given by relations d v d t p F, m d r v d t p. (2) Typical results of trajectories solution near an airfoil are presented in Fig. 1. It is perceptible that the small water droplets have trajectories similar to streamlines, vice versa the large water droplets trajectories are affected by the airfoil inherency only slightly.

3 121 In-flight Ice Accretion Prediction Code Fig. 1 Influence of the water droplets diameter on their trajectories. Airfoil NACA 0018, chord is 1 m, free stream velocity is 50 ms -1 and angle of attack is 5º. 4. R-ICE 1.1 AIRFOIL RIME ICE ACCRETION PREDICTION The rime ice accretion is the simplest case of ice simulation to predict when impinging super-cooled water droplets freeze immediately upon impact. Code applies a time-stepping procedure to calculate the shape of an ice accretion [1]. The new flow field and droplet impingement recalculations are applied for every procedure step. This procedure is repeated until the desired icing time is reached. Results of the airfoil NFL0414 ice accretion prediction for the total icing duration time 1224 seconds in five time steps of solution are presented in Fig. 2. There are presented icing parameters (the R-Ice code incoming data) in the figure either. Figure also shows the final ice shape from the in-flight icing experiment [2] at the same conditions by a red color line. 0,050 y/c [1] 0,025 0,000 Chord= m; Vext=92.54 m.s -1 ; FluidP= Pa; FluidT=257.6 K; Alpha=0 o ; PartD= m; PartContent= kg.m -3, RimeIceRho=900kg.m -3 ; Steps=5; TimeStep=244.8 s; Time=1224 s. Fig. 2 Illustration of the successive rime ice accretion for the icing time 1224 sec. -0,025-0,050-0,050-0,025 0,000 0,025 0,050 x/c [1] Rime ice accretion prediction provides the comparable results like other current computational ice-accretion simulation methods [2]. It is evident from the quantitative comparison plotted in Fig. 3. Icing parameters of solutions are the same as those outlined above.

4 Vladimír HORÁK, Zdeněk CHÁRA 122 0,050 Fig. 3 Quantitative comparison of current computational iceaccretion simulation methods for the icing time 1224 sec. y/c [1] 0,025 0,000-0,025-0,050-0,050-0,025 0,000 0,025 x/c [1] 0,050 Clean Airfoil Experimental ONERA1990 Simon CANICE Paraschivoiu TRAJICE ADSE ONERA2000 Duprat NASA R-ICE 5. ICE 3.1 GLAZE ICE ACCRETION PREDICTION Generally, current ice accretion codes give satisfied results of the rime ice simulation, but glaze icing cases are the most difficult to predict. There is still room for improvement in the quality of ice-accretion-space predictions [2]. Glaze ice creates at combinations of temperature close to freezing. In that case, not all of the impinging water freezes on impact. Thin layer of water is flowing very slowly along the surface and freeze at other locations. The Ice 3.1 code uses so called a shallow water theory for the solution of the flow of thin water layer on the airfoil surface and gradual freezing. The conservative equations using for the solution of water flow in open channels are formally arranged. Conservative equations written in the general form are Q F t x S S Vectors of variables Q, flow F and sources S, S q are given by relations q. (3) A Q 2 Q Q, F Q A g I, (4) n 1 E EQ A 0 S g n I g t A dp dx A ow w oe e, (5) 2 ow w T w T oe e T e T oeq pctp oeq p owq fr owqev S q oeq pv px owq fr v owqevv. (6) o eq pctp owq fr ct L fr owqev ct Lev

5 123 In-flight Ice Accretion Prediction Code Where g represents acceleration due to gravity with components g n and g t. The quantity ρ is the liquid density, the liquid temperature is denoted by T, channel wall temperature is T w and the ambient temperature above water level is T e. Integrals I 1 and I 2 are given by the shape of the channel cross-section h h db x, I 1 h b x, d, I 2 h d. (7) d x 0 The coordinate η is measured upwards from the lowest point of channel bed level in the section x = const. and b (x, η) is the channel width. The channel geometry description is complemented by the wetted perimeter o w and the level width o e. Variable quantities: Q 1 = A represents the local flow cross-section, Q 2 = Q = A v is the flow volume and Q 3 = E = A c T expresses the thermal energy of liquid having specific heat capacity c. Quantities: F 1 is the mass flux, F 2 is the momentum flux and F 3 is the flux of energy. Vector S includes sources of mass, momentum and energy. Certain liquid volume inflows from external sources S q1 (impacting flux) with the area intensity q p [m 3 s -1 m -2 ]. Some water can freezes, the freezing fraction could be expressed from the heat balance like the area intensity q fr. Similarly, the area intensity q ev represents the quantity of evaporating water, which is determined by the vapors diffusion from the surface. Source of momentum S 2 includes: hydrostatic pressure (effect of the cross-section change da/dx), tangential component of gravity force g t (generally external volume forces), friction on the channel bed τ w and on the liquid surface τ e and the momentum component supplying from external sources with the radial velocity v px. Finally, the source of energy S 3 constitutes heat transfer on the channel wetted perimeter, heat transfer on the liquid level (coefficients α w and α e ), the heat supplied from external sources S q3 by means of liquid and the thermal influence of freezing and evaporating process, where L fr is the latent heat of fusion and L ev is the latent heat of evaporation. The formulated problem of the thin liquid layer flow solution is solved by a discontinuous Galerkin method, which could be considered as a generalized finite volumes classical method. Principles of the Galerkin method, applied to the solution of the flow of a thin water layer and gradual freezing, are closely described in [3]. Results of the glaze ice accretion prediction for the icing time 300 seconds and airfoil NACA 0012 are outlined in Fig. 4. Process of glaze ice accretion is strongly influenced by the wall temperature T w. 0 Fig. 4 Effect of wall temperature on glaze ice shapes and comparison with experiment. Input data of the solution are airfoil chord b = 0.45 m, free stream velocity v = 77.2 m s -1, angle of attack α = 0º, cloud liquid water content LWC = 0.32 g m -3, droplets median volume diameter MVD = 18 μm, ambient air temperature T e = K and wing surface temperature T w = K.

6 Vladimír HORÁK, Zdeněk CHÁRA 124 It could be noted that the results outlined above qualitatively correspond to the experimental observations of glaze ice shapes. Comparison in Fig. 5 acknowledges that the presented solution could 0,06 be considered at least as y/b a fully comparable with 0,04 the current ice accretion prediction codes. 0,02 Clean Airfoil Experimental Fig. 5 Quantitative comparison of current computational ice accretion simulation methods from [2]. 0,00-0,02-0,04-0,06-0,02 0,00 0,02 0,04 0,06 0,08 x/b 0,10 Paraschivoiu CANICE ADSE TRAJICE Duprat ONERA NASA LEWICE 6. INFLUENCE OF AIR TEMPERATURE ON ICE SHAPES The glaze ice accretion process is strongly dependent on temperature, besides other icing parameters like air liquid water content (LWC) and median droplets diameter (MVD). Influence of air temperature T on iced airfoil shapes predicted by the Ice code, version 3.1, is shown in Fig. 6, where we can see various cases of glaze ice shapes: stream-wise shape (b), (c), double-horn shape (d), (e), and span-wise ridge shape (f). (a) Rime ice (b) Glaze ice: T = K (c) Glaze ice: T = K (d) Glaze ice: T = K (e) Glaze ice: T = K (f) Glaze ice: T = K Fig. 6 Ice code simulation of air temperature influence on iced airfoil shapes for T = T w. Airfoil NFL0414, chord 0.45 m, angle of attack α = 0 o, free stream velocity v = 77.2 m s -1, MVD = 18 μm, LWC = 0.32 g m -3, atmospheric pressure 100 kpa, icing time 900 seconds.

7 125 In-flight Ice Accretion Prediction Code 7. ICE 4.1 MULTI-ELEMENT AIRFOILS ICING The latest Ice code version [4] enables to solve system of several airfoils, by default, up to eight separate parts. Model algorithms have been extended to involve mutual flow overlap of multi-element airfoils (e.g. overlap between the airfoil and flap). The typical results of air streamlines of droplet trajectories around an airfoil with a slotted flap are presented in Fig. 7. There are seen droplet trajectories and impact locations near the airfoil leading edge. Trajectories of droplets impacting an airfoil surface are depicted by a black square. The impact locations where droplet trajectories intersect an airfoil surface may be divided into several separated subsections. It can be seen for the case of airfoil with the slotted flap in landing position. The flap is not fully overlapped in this case. Then black squares of impinging droplets trajectories are divided on one impacting the airfoil and another one impacting the flap surface. Fig. 7 Droplet trajectories near an airfoil with a slotted flap and for flap in landing position The ability of the Ice code 4.1 version to predict ice accretion of flapped airfoils is presented on the case of the wing airfoil with a slotted flap. Example of the ice prediction on the wing airfoil with the slotted flap for angles of flap deflection 20 and 38 is shown in Fig. 8 Fig. 8 Example of ice prediction on the wing airfoil with a slotted flap for angles of deflection 20 and 38 Mentioned ice accretion on the flap causes the reduction of the gap size between main element and flap. Consequently, it can have a large impact on the performance degradation of iced multi-element airfoils. Lastly, there is a potential mechanical problem in the elevator mechanism itself.

8 Vladimír HORÁK, Zdeněk CHÁRA CLOSING REMARKS The Ice code enables computational rime ice and glaze ice accretion prediction on single and multi-element airfoils in acceptable time of solution. Mathematical model has been modified for variable wall temperature along the airfoil surface. The code was also subsequently improved for the better approximation of transition boundary layer location. The code is designed for the icing simulation as an aid to the certification process of small transport aircraft for flight in icing conditions according to international aircraft standards, where maximum and intermittent maximum icing conditions are specified. Presented code could be considered at least as a fully comparable with the current ice accretion prediction codes. ACKNOWLEDGEMENT The work presented in this paper has been supported by the Czech Science Foundation project No. P101/10/0257, by the Czech Ministry of Industry and Trade project FT-TA/044 InICE, and by the Ministry of Defense project No. FVT REFERENCES [1] V. Horák and B. Hoření. Wing Airfoil Rime Ice Accretion Prediction. In Engineering Mechanics Svratka, May [2] R. J. Kind. Ice Accretion Simulation Evaluation Test. RTO Technical Report 38, November [3] B. Hoření and V. Horák. Wing Airfoil Glaze Ice Accretion Prediction: Thin Freezing Water Layer. In Sixth International conference on Mathematical Problems in Engineering and Aerospace Sciences ICNPAA Cambridge Scientific Publishers, [4] B. Hoření, V. Horák, and Z. Chára. Improved Ice Accretion Prediction Code. Advances in Military Technology, Vol. 3, No. 1, p , September 2008.