PREDICTION OF ICE CRYSTAL ACCRETION WITH IN-HOUSE TOOL TAICE

Transcription

1 PREDICTION OF ICE CRYSTAL ACCRETION WITH IN-HOUSE TOOL TAICE Erdem Ayan, Serkan Özgen, Erhan Tarhan, Murat Canıbek TAI Turkish Aerospace Industries Inc. SAE 2015 International Conference on Icing of Aircraft, Engines and Structures, June 22-25, 2015, Prague, Czech Republic

2 Outline Introduction TAI ice accretion prediction in house developed tool TAICE Modifications towards ice crystal accretion prediction Ice Crystal Accretion Drag Models Heat Transfer & Phase Change Model Impingement Model Secondary Particle Behaviour Conclusions & Future Work

3 Introduction Ice crystal ingestion to aircraft engines may cause ice to accrete on internal components, leading to flameout, mechanical damage, rollback, etc. Many in-flight incidents have occurred in the last decades due to engine failures especially at high altitude convective weather conditions. Being a solid substance, ice crystals may not cause any problem for airframe components at low temperatures, since they only bounce off when they hit the airframe. However, when they face warmer flow conditions, they can change phase and pose a threat for the aircraft. These warmer flow conditions generally occur around or within the engine, on heated components (i.e. pitot and aoa probes) where local temperatures are significantly higher than the freezing temperature

4 Introduction Numerous in-flight incidents, which have occurred generally in tropical regions and at high altitudes made researchers to investigate ice accretion due to the ice crystals. In recent years, there have been important enhancements in simulating SLD. However, ice accretion due to ice crystals has not yet been studied extensively. Thus, in the framework of HAIC FP7 European Project, the physical mechanisms of ice accretion on surfaces exposed to ice-crystals and mixedphase conditions are investigated. TAI will implement models related to the ice crystal accretion calculation to the existing ice accumulation prediction program for droplets, namely TAICE. The aim of the study is to present the current status of the work performed by TAI in this field within the context of drag coefficient models, heat transfer and phase change models and impingement models

5 TAI Ice Accretion Prediction Tool TAICE Hess-Smith Panel Method for flow field computation around wings & wing sections. Lagrangian approach for particle trajectory calculations. Integral Boundary Layer Method for convective heat transfer coefficient calculations. Extended Messinger Model for computation of ice accretion rates

6 Droplet to Ice Crystal In order to use the existing ice accretion prediction tool for ice crystals, following modifications are required. Non-spherical drag model implementation, Heat-transfer and phase change models, Impact & re-emission model, Secondary particle trajectory calculations, Modifications required for solving mixed phase glaciated icing conditions

7 Ice Crystal Particle Geometric Properties The calculation of sphericity differs for an oblate (E < 1) or prolate (E > 1) particle [1]. sphericity Φ = πdp2 A crosswise sphericity d p = 3 6v p π Φ = πrp2 A A denotes the surface area of the particle, d p refers to the volume equivalent diameter and v p is the volume of the particle The orientation of the particle with respect to the flow can be taken into consideration by crosswise sphericity. A is the projected area of the particle with respect to the flow. Aspect ratio (E) and eccentricity (e) E = d 1 d 2, e = 1 min d 1 d 2, d 2 d 1 2 where d 1 and d 2 are diameters of the particle parallel and perpendicular to the revolution axis, respectively. Thus, for oblate particles Φ = 4E2/3 2+ E2 1+e ln e 1 e for prolate cases Φ = 2E 2/3 1+E arcsin(e) e Finally if the particle is assumed to be in the most stable orientation during its trajectory, crosswise sphericity can be defined as follows for oblate and prolate cases, respectively: Φ = E 2/3 Φ = E 1/

8 Drag Coefficient Models Several models exist for drag coefficient calculation in the literature. Some of these models are applicable to non-spherical particles and take orientation change into consideration [1]: Haider & Levenspiel suggest a model in terms of Φ and Re p [2]: C d = 24 Re p (1 + a(re p b ) + cre p Re p +d Re p= ρ ad p v rel μ a = exp(2.4486φ Φ ) b = (0.5565Φ ) c = exp( Φ Φ Φ ) d = exp( φ Φ Φ ) Ganser model also takes crosswise sphericity into consideration [3]: C d = 24 Re ( (Re p ) Re p p Re p Re [ log Φ ] p = [ log Φ ]

9 Drag Coefficient Models Additional drag model is suggested by Hölzer and Sommerfeld. Their model also includes the effect of orientation of the particle [4]: C d = Re p Φ Re p Φ log Φ Re p Φ3/4 Φ A study is performed to evaluate the effect of drag coefficient modeling on collection efficiency of the icing cases. Aspect ratio and diameter of the particle are varied. Following running conditions are analyzed with these drag models. Run Diameter a (μm) Aspect ratio E Equivalent diameter d (μm) Φ Φ Reynolds number E E E E E E

10 Run # 1 Run # 2 Run # 3 When sphericity differs from 1, models predictions start to deviate from each other. When Φ < 0.6 this difference is much bigger. However, sphericity is not the only parameter that effects the drag coefficient. Generally, the higher the Stokes number, the lower the difference between the models. Run Diameter a (μm) Aspect ratio E Equivalent diameter d (μm) Φ Φ Reynolds number Stokes Number % Difference in Max. β Value E E E E E E

11 Run # 4 Run # 5 Run # 6 For lower sphericity values, Haider & Levenspiel model collection efficiency prediction is generally higher than the predictions of other drag models. Collection efficiency curves of the Ganser and Hölzer & Sommerfeld drag models behave similar to each other in the run conditions which are considered. Run Diameter a (μm) Aspect ratio E Equivalent diameter d (μm) Φ Φ Reynolds number Stokes Number % Difference in Max. β Value E E E E E E

12 Heat Transfer and Phase Change Models The general form of the heat equation is: m p c p dt p,m dt = πd p Nu Φ k a(t a T p,s ) For non-spherical particles, Nusselt number can be defined in terms of Re, Pr, Φ and Φ using the Richter correlation: 7.2 Nu = ΦRe 1/2 Pr 1/3 Φ Re 2/3 Pr 1/3 Φ Theoretically, this expression can be applied to all particles. However, for oblate particles and when aspect ratio is lower than 0.8, this relation yields unrealistic results. As it is suggested by Villedieu et al [1], Frössling correlation [5] for non-spherical particles can be extended by using the relationship between C d and Nu. Thus, the final equation is as follows: Nu = 2 Φ Pr 1/3 Φ 1/4 Re p 1/2 One obtains the Frössling correlation by setting Φ = 1: Nu = Pr 1/3 Re p 1/2 Φ

13 Heat Transfer and Phase Change Models According to the Mason s study, for ice crystal melting and evaporation, following assumptions can be made [6]: The ice core temperature is uniform and the particle begins to melt when its temperature has reached the melting temperature, T f. The ice core temperature remains constant and equal to T f during all the melting phase. The ice core and the surrounding liquid film are spherical and concentric. The heat transfer between the liquid film and the ice core is purely conductive. The ice particles do not shed their liquid water film during the melting phase. In this study, the specified model is used which is the extended version of Mason s model The model consists of three steps: In the first step when T p < T f, pure ice particle temperature increases up to melting temperature and mass exchange may occur at the particle surface by sublimation. Total mass and the final heat transfer equation is as follows: dm p Sh = m dt sub = πd p ρ Φ ad v,a y v,s y v,a dt p m p c i dt = πd Nu p Φ k a T a T p m sub L f + L v Sh = 2 Φ Sc 1/3 Φ 1/4 1/2 Re p ; Sherwood number, Sc = ν D; Schmidt number

14 Heat Transfer and Phase Change Models In the second step T p = T f, particle starts to melt and is surrounded by a concentric water layer. Mass exchange may occur at the particle surface by evaporation. This step continues until ice particle is completely melted. At the end of this step, particle becomes spherical. Evaporation rate m ev can be calculated with the following equation dm p dt = m Sh ev = πd p Φ ρ ad v,a (y v,s y v,a ) Then the final heat transfer equation is as follows: Nu πd p Φ k a T a T f = m ev L v + m f L f In the third step, when T p > T f droplet temperature increases from melting temperature and mass exchange may occur by evaporation. dt p m p c w dt = πd pnuk a T a T p m ev L v In all these steps, temperature inside the particle is supposed to be uniform

15 Case # Flow Velocity m/s, RH % Sphericity Particle init. diam. (μm) Flow Temp., o C Initial Temp., o C 1, , , 6, , 0.70, , 551, , , , , Implemented heat transfer and phase change model is validated with the Hauk s experiments which were performed within the HAIC project [7]. The maximum difference is around 15%. Experimental melting time for irregular shaped particles are smaller than the calculated melting time due to their higher surface area. Final liquid droplet diameters also seem compatible with each other. Maximum difference between the experimental and calculated droplet diameter is around 4%. The success of the models seems similar for both spherical and irregular shapes

16 Impingement Model Ice crystal impact on a surface may result in three scenarios depending on particle and surface properties [1]: Sticking regime: the particle totally adheres to the wall. Bouncing regime: the particle bounces off the wall upon impact. In this case the size and shape of the particle does not change but its velocity is altered. Shattering regime: The particle breaks down into smaller fragments. Depending on the presence of a liquid film on the wall or water inside the impinging particle, some fragments may be re-emitted into the flow, while others may adhere to the surface. The threshold between bouncing and shattering regimes depends on the particle kinetic energy before impact. A dimensionless number L, which is the ratio of the normal kinetic energy to the surface energy is defined: L = πρpd p 3 v pn 2 12 πe σ T p d p 2 = 1 12 ρ p d p v2 pn where v pn is the component of the impact velocity vector perpendicular to the wall and e σ is the surface energy per unit area. e σ T p

17 Impingement Model The current model takes three possible scenarios into account. Accordingly [1]: Case L 0.5 : quasi-elastic bouncing with no fracturing, Case 0.5 L 90 : inelastic bouncing with particle fragmentation and loss of kinetic energy. Case L 90 : highly inelastic impact with high particle fragmentation and high loss of kinetic energy. The most important effect of the presence of liquid water layer on the wall or within the particle is the probability of particle adhering partially or completely to the wall. Water layer thickness within the particle h p, can be calculated using the particle liquid water content: 2h p = d p d p,i = 6 π m p m p,i ρ w + m p,i ρ p,i The model is based on the following expression for P D : P D = 1 P B π m p,i ρ p,i 1 3 with P B = min 1, K B ξ n δ p + δ w The dimensionless film thicknesses δ p and δ w are δ p = h p d p and δ w = h w d p

18 Impingement Model K B is an adjustable parameter and ξ n is the normal restitution coefficient defined as: ξ n = ξ n B = 1 L 0.5 ξ n B = 0.5 L F ξ nn = 0.5 L L 90 L 90 In the Lagrangian approach, the model is implemented as follows: For each particle impact, P D is calculated. If P D = 1, the particle is assumed to totally adhere to the wall and there is no reemission of secondary particles. If P D < 1, a fraction of the impinging mass flow rate equal to P D is assumed to adhere to the wall and the remaining part equal to 1 P D is re-emitted to the air flow

19 Secondary Particle Behaviour If L 90, the impinging particle either bounces of the wall with a probability P B = 1 P D or adhere to the wall with a probability P D. If P B = 0, the particle is assumed to totally adhere to the wall. If P B > 0, the particle partially adheres to the wall and a secondary particle is re-emitted. If L 90, the impinging particle partially adheres to the wall or fragments into smaller particles, where P D is the ratio of the deposited mass to the incident mass. If P D = 1, the particle is assumed to totally adhere to the wall. If P D < 1, the particle partially adheres to the wall and a secondary particle is re-emitted to the air. Following secondary particle properties are evaluated depending on the calculated threshold value. o o o o o o Mass flow rate, Particle diameter, Solid and liquid mass fractions, Ice core density, Sphericity, Particle velocity

20 Diameter a (μm) Aspect ratio E Equivalent diameter d (μm) Φ Φ Reynolds number Stokes Number Mach Number E E Circular X-Section The model is based on the following expression for P D : P D = 1 P B with P B = min 1, K B ξ n δ p + δ w NACA 0012 K B strongly affects the collection efficiency curves. When the number of K B increases, the collection efficiency decreases. The effect of K B on collection efficiency curves differs depending on the test case even if all other flow parameters are same

21 Run Diameter a (μm) Aspect ratio E Eq. Dia. d (μm) Run Reynolds Number Stokes Number E E E E E E E E-01 For the analyzed cases, with increasing Reynolds Number, sphericity and crosswise sphericity particles spreads in a larger area. All of the drag models give similar results. However, Heider&Levenspiel results differs more from others. Φ Φ

22 Conclusion Ganser, Haider & Levenspiel, Hölzer & Sommerfeld Drag coefficient models, Heat Transfer & Phase Change and Impingement models, secondary particle trajectory calculations were successfully implemented to TAICE. Currently used models will be enhanced when the results of HAIC experiments become available. Collection efficiency curves which are obtained with different drag models for the particles having various diameter and aspect ratio are compared. Implemented heat transfer and phase change model results are compared with Hauk s experimental results. Melting time and final liquid diameter values are similar both for calculated and experimental results. Influence of the adjustment variable K B in impingement model is discussed. Thus, further calibration of K B is required for accurate ice accretion determination for each icing test case

23 References 1. Villedieu P., Trontin P., Chauvin R., Glaciated and mixed phase ice accretion modeling using ONERA 2D icing suite, 6 th AIAA Atmospheric and Space Environments Conference, Atlanta, AIAA , Haider A., Levenspiel O., Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technology, Vol. 58, pp , Ganser, G.H., A rational approach to drag prediction of spherical and nonspherical particles, Powder Technology, Vol. 77, pp , Hölzer A., Sommerfeld M., New simple correlation formula for the drag coefficient of non-spherical particles, Powder Technology, Vol. 184, pp R-M, Frössling, N., The evaporation of falling drops (in German), Gerlands Beiträge zur Geophysik, Vol. 52, pp , Mason, B.J., On the melting of hailstones, Quart. J. Roy. Meteor. Soc., Vol. 82, pp , Hauk P., Roisman I., Tropea C., Investigation of the Melting Behaviour of Ice particles in an Acoustic Levitator, 6 th AIAA Atmospheric and Space Environments Conference, AIAA, Reston, VA,