Effect of Super-Cooled Water Droplet Characteristics on Fan Rotor-Ice Accretion

1 ISABE-2005-1248 Effect of Super-Cooled Water Droplet Characteristics on Fan Rotor-Ice Accretion K. Das *, A. Hamed **, D. Basu * Department of Aerospace Engineering and Engineering Mechanics University of Cincinnati Cincinnati, OH 45221-0070 ABSTRACT This paper presents a methodology for numerical simulations of super-cooled three-dimensional (3-D) water droplet trajectories through aeroengine rotating machinery that includes the effect of energy exchange between the droplets and flow. The governing equations for both flow and droplets are formulated and solved within the reference frame of rotating blades. A Eulerian-Lagrangian approach is used for the continuous and discrete phases with oneway interaction models to simulate the momentum and energy exchange between the two phases. The methodology is applied to a transonic fan rotor and results are presented for the computed flow field and droplet trajectories in the rotor reference frame. Results are also presented for the computed water collection efficiency and impingement temperature distribution over the fan blade surface for different droplet sizes and initial temperatures. The droplet size affects their trajectories and collection efficiency. The results demonstrate the significant effect of energy exchange on the rotating blade impingement temperatures for the smaller droplets. While the amount of ice accretion on the fan blade is determined by the collection efficiency; its type, whether glaze or rime ice is determined by the impingement temperature. INTRODUCTION Safety concerns over aircraft icing and the high experimental cost of testing have spurred global interest in numerical simulations of the ice accretion process 1-5. Kind et al. 6 gave a literature review of computational techniques in icing simulations. Most investigations involve aerodynamic analysis of the flow around the body, prediction of droplet path and impingement location, collection rate, and, finally, a thermodynamic analysis of the freezing process. Conventionally, the flowfield and droplet trajectories **AIAA Fellow, Professor *AIAA Student Member, Graduate Student are solved separately in a Eulerian-Lagrangian approach where the interaction between phases is primarily modeled through momentum exchange. The simulations can provide droplet collection rate, droplet impingement limits and the glaze or rime ice shape 7-12. Bourgault et al. 13 used the outlined approach to conduct icing simulations on structures. Da Silveria et al. 14 compared predictions with available experimental data over a wing. Previous studies have focused on icing problems on external surfaces, including wings 7, fuselages, and helicopter blades 3. Ice accretion in aircraft engines raises additional safety and performance concerns such as mechanical damage from fan and spinner ice shedding as well as slow acceleration leading to compressor stall from ice accretion on turbofan splitters and fan and booster vanes. Numerical simulation of ice accretion in aircraft engines is highly challenging because of the complex 3-D unsteady turbomachinery flow and the effects of rotation on droplet trajectories. Solid particle dynamics in turbomachinery have been investigated to characterize associated blade surface erosion 15,16. Particle size, blade material and blade row location were found to affect the pattern and intensity of blade erosion 15-17. Erosion damage in fan and compressor blades is manifested in the pitting of leading edges and in blade chord reduction. Numerical models have been developed for simulating the associated loss of aerodynamic performance 18. However, unlike supercooled droplets, solid particles rebound after impacting blade surfaces and continue their trajectories through succeeding blade rows 19,20. Recently Hamed et al. 21 developed a methodology for the simulation of supercooled droplet trajectories through aeroengine rotating machinery. The study adopted a Eulerian-Lagrangian approach and modeled the inter-phase interaction through momentum exchange. The authors also defined a flux-based droplet collection efficiency suitable for Copyright 2005 by Hamed et. al. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission

2 internal flow applications. Simulated results indicated that a higher proportion of the large droplets impinged the rotating blade surface. While the overall blade collection efficiency was lower for the smaller droplets, their impingement was distributed over a greater portion of the blade pressure surface. The Messinger model 22 is used in most icing simulations to analyze the freezing process and determine the ice shape. Droplet impingement temperature is a key parameter in the Messinger model, since it determines whether the ice formed will be glaze, rime or mixed. All previous studies 2-8 of ice accretion over external surfaces assumed that droplets retain their initial temperature. While this is a valid and reasonable assumption for external flows, heat transfer becomes significant in rotating turbomachinery flows where the flow temperature undergoes change in the blade passage due to the addition of energy. In the current investigation, the computational methodology developed by Hamed et al. 21 is extended to consider energy exchange between the discrete and continuous phases. Both the flow and droplets governing equations are formulated and solved in the rotating blade frame of reference. An Eulerian-Lagrangian approach is used for the continuous and discrete phases with a one-way interaction model to simulate the aerodynamic effects on the three-dimensional droplet trajectories. The temperature of supercooled droplets is calculated from the energy exchange equation based on convection heat transfer physics. The methodology is applied to the flow field and droplet trajectories in NASA rotor R-67 and results are presented showing the effect of droplet size and initial temperature on the rotor blade surface collection efficiency and impinging temperature. METHODOLOGY Both flow and particle governing equations are formulated in the rotating blade reference frame based on a Eulerian-Lagrangian approach. One-way interaction models simulate the effects of aerodynamic forces on the droplet trajectories and the energy exchange between the flow and the droplets through convection heat transfer. The numerical solution is obtained from the 3-D solution of the compressible Reynolds Averaged Navier Stokes (RANS) equations using ADPAC 23. The code utilizes a finite volume Runge-Kutta time marching scheme to solve the time-dependent form of 3-D RANS equations. The Runge-Kutta scheme has been used in many 3-D viscous flow analyses of transonic fan flow studies because of CPU economy and the ease of implementing convergence acceleration techniques 24,25,26. Convective fluxes are approximated using a second-order central difference scheme stabilized with scalar artificial dissipation. Local time stepping, implicit residual smoothing, scaled dissipation function, and a multigrid technique are employed to accelerate convergence. Several turbulence models, including the algebraic Baldwin- Lomax model, the one equation Spalart-Allmaras model, and the two-equation k-r model are available in the solver. Hamed and Vogiatzis 27 reported that the two-equation k-ε turbulence model gave better agreement with the experimentally measured surface pressure distribution in the case of shock-induced massive flow separation over 2D-CD nozzle flaps. Such severe separation is generally not encountered in high performance turbomachinery where shock waves are present in the outer region of the blade passage. This is confirmed by the results of a previous simulation of rotor R-67 flow field by Yuan et al. 28 which indicated that the predicted aerodynamic performance as well as the 3-D shock structure within the rotor passage were comparable for both the low Reynolds number k-ε and the Baldwin-Lomax algebraic turbulence models over a wide range of operating conditions. Therefore the Baldwin-Lomax algebraic turbulence model was used in the present investigation. Momentum and Energy Exchange Droplet trajectories and temperatures are determined from the numerical integration of their equations of motion and from the equation of energy exchange with the airflow in the rotating blade reference frame 15. The equation of motion in the cylindrical polar coordinates are : 2 2 d rp dθp = F 2 r + rp + ω d d τ τ (1) 2 d θp drp dθp rp = Fθ 2 + ω 2 τ dτ d dτ (2) 2 d zp = F 2 z dτ (3) In the above equations, r p, θ p and z p define the particle location in cylindrical coordinates and ω defines the blade angular velocity. The last term in

3 the RHS of the first two equations represents the centrifugal force and Coriolis acceleration. The same equations can be used in stationary turbomachinery blades by setting ω=0 and using the droplet velocity in the absolute rather than the reference frame. The first term on the RHS of equations 1-3 represents the components of the aerodynamic force of interaction between the two phases. The drag due to the slip velocity relative to the flow is considered as the primary aerodynamic force on the droplets since the forces due to gravity and buoyancy are negligible compared to the aerodynamic and centrifugal forces 15,16. Forces due to inter-droplet interactions and the pressure gradient are also neglected for the small-supercooled water droplets. The aerodynamic force of interaction is expressed in terms of the drag coefficient and the droplet slip velocity as follows 15 : 3 CD F = V Vp.( V VP ) (4) 4 d p where d p is the droplet diameter and V and V P are the gas and the droplet velocity vectors. The drag coefficient C D is computed from empirical correlations involving the Reynolds number based on the relative velocity between the droplet and the gas 16. The equation for energy exchange between the droplets and the airflow is used to calculate the droplet temperatures through their trajectory. The equation is given by: dtp mpcp dt hap ( Tg Tp = ) (5) where, C p is the specific heat of the supercooled droplet and A p is the droplet surface area. The heat transfer coefficient h is evaluated using Ranz and Marshall s 29 correlation for spherical droplets. k h + d p 1/ 2 1/ 3 ( 2.0 0.6 * Re * Pr ) = (6) where d p is the droplet diameter, k is the thermal conductivity of the gas, Pr is the Prandtl number and Re is the Reynolds number based on the relative velocity between the droplets and the air flow. Combining equation (5) and equation (6) we get the following equation for the rate of change in droplet temperature dtp = dt 3 16 k 1 * * * ρ 2 pcp d p 2 3 ( 2 + 0.6* Re 1/ * Pr 1/ )* ( T T ) (7) The energy and mass exchange due to evaporation are not considered because no evaporation takes place at supercooled droplet temperatures. Equations 1-3 and 7 are solved using a four-stage Runge-Kutta time integration. At every time step the blade surfaces are scanned to determine their relative position with regard to the droplet. Once the droplet reaches a solid surface, trajectory computations are terminated, the impact location is recorded and the droplet temperature at the impact location is also noted. Similarly, if a droplet exits from the blade passage, the exit point and the droplet exit temperature are recorded. The outlined procedure was implemented in the code TURBODROP, a parallel solver based on the MPI message passing technique. In the parallelization strategy, a number of droplets are assigned to a computer node and the integration proceeds independent of other droplets. At the end of the solutions the computer nodes report the results to the master processor. By using this method for large numbers of droplets, it was found that the computational time is reduced by two orders of magnitude. Blade Surface Collection Efficiency It has been a common practice in external flows 9,12 to initiate a number of droplet trajectories which are released over incremental distance across the free stream direction until the limiting droplet trajectories define those that reach the outermost surface boundaries. The slopes of the computed trajectories relative to the free stream direction are used to define collection efficiency for ice-growth calculations. The collection efficiency is typically less than one, which is the upper limit if the droplets had not been deflected by the flow around the surface. The concept of limiting droplet trajectories in the particle frame of reference is not suitable in the case of internal turbomachinery flow through rotating blade rows where neighboring droplets can continue their trajectories in different blade passages of subsequent blade rows. Therefore the collection efficiency definition that has been used in external flows is not applicable to turbomachines. A flux-based collection efficiency was defined by Hamed et al. 21 as the ratio of the local droplet mass flux at the blade surface relative to its value at the turbomachinery inlet station. This definition is better suited for internal flow applications and is equally applicable to both rotating and stationary blades. g p

4 NUMERICS The outlined methodology was used in the numerical simulations of droplet trajectories through the NASA rotor 67, for which detailed experimental LDV measurements through the blade passages were reported by Straziser et al. 30 The total temperature and total pressure profiles were specified at inlet based on the experimental data. Adiabatic wall boundary conditions were used, with no slip at the stationary walls and prescribed rotational speeds at the rotating surfaces. The exit static pressure was specified at the tip, and the radial pressure distribution was determined from the integration of the axisymmetric radial momentum equation. Periodic boundary conditions were employed for the blade-to-blade directions. The solution domain for both -D flow and droplet trajectory simulations extended 80% chord upstream and 45% chord downstream of the rotor blade row. RESULTS AND DISCUSSIONS Rotor 67 is the first stage rotor of a two-stage fan with a design pressure ratio of 1.63 and a mass flow rate of 33.25 kg/sec 30. The tip radius varies from 25.7 cm at the leading edge to 24.25 cm at the trailing edge, and the hub/tip ratio varies from 0.375 to 0.478. It has 22 blades with 1.56 aspect ratio. A design speed of 16043 RPM corresponds to a rotor tip speed of 429 m/sec and a relative inflow Mach number of 1.38 at the tip. The total temperature and pressure at the rotor entrance is 518 0 R and 2116 lbf/ft 2 respectively at this design condition. A gridindependent study was conducted for the turbomachinery flow solution using three levels of grid refinements. The coarse grid consisted of 81 65 49 grid points in the stream-wise, blade-to-blade and the hub-to-tip directions. The medium grid consisted of 145 81 65 grid points and the fine grid consisted of 161 97 81 grid points. All three grids were clustered near the walls using a hyperbolic tangent function. The minimum grid spacing in the wall normal direction for all the three levels of grid was 1.0 10-4 times the chord with 15 grid points within the boundary layer for all three mesh levels. Figure 1 shows the meridional view of test fan rotor with the aerodynamic survey locations where the experimental measurements were taken. The computational domain with the medium grid is shown in Figure 2. Figure 3 presents the computed relative Mach number contours for the fine grid at 70%, 50% and 30% span from the tip. In general, one can observe a significant span-wise variation in the rotor flow field with subsonic flow near the hub and supersonic flow regime in the tip region. At 70% span, no shock structure is visible, but a small transonic bubble is predicted near the leading edge of the suction surface consistent with experimental observation 30. At 50% span, a shock is formed at the suction side but it does not extend across the blade passage to the pressure side, whereas at the 30% span location one can see a complex shock structure with a bow wave ahead of the blade and a normal shock inside the blade passage. Figure 4 presents the computed profiles of the flow angle, the static pressure ratio and the stagnation temperature at the rotor exit for all threegrid levels. The measured experimental data at aerodynamic survey location 2 are also presented in Figure 4. One can see that the experimental results are very close to the predicted radial variation of the exit static pressure ratio and the exit flow angle for both medium and fine grids. The agreement between the predicted total temperature ratio profile and the experimental data is less satisfactory. In a previous computational study, Chima 24 reported significant agreement with the experimental results for the total temperature ratio and the static pressure ratio at the exit but deviation from the flow angle experimental results. Jennions et al. 25 and Yeuan et al. 28 reported better agreement with the experimental results near both peak efficiency and near stall. Based on the grid independence study for the turbomachinery flow solution, the droplet simulations were performed in the turbomachinery flow field obtained from the medium grid. The simulations were conducted for 50,000 droplets injected with zero velocity and distributed for uniform influx at the computational upstream boundary. Figure 5 shows a representative 3-D view of droplet trajectories for 30- micron droplets in the rotor frame of reference. It is apparent that the droplets enter the blade passage with a positive incidence angle in the rotor reference frame as a result of their lower absolute velocities compared to the flow. Consequently, the droplets subsequently impinge on the rotor pressure surface. Figure 6 shows the radial variation of the of the droplet exit mass flow rate at exit station 2 for three different droplet sizes. It can be seen that a higher percentage of ingested 15-micron droplets exits the rotor blade passage without impinging the blade surface. The percentage decreases with increased droplet sizes. The rotor blade surface collection efficiency contours are compared in Figure 7 for all three-droplet sizes. As expected, the collection efficiency is greater for the larger droplets since a higher percentage of them impinge on the rotating

5 blade surface. The collection efficiency is lower for the smaller droplets; however, their impingement is distributed over a larger area of the overall blade pressure surface. Figure(s) 8 and 9 present the droplet temperature rise (T p - T pi ) along the trajectory normalized by the difference between flow and droplet temperatures at inlet (T gi T pi ). One can see the energy exchange can lead to significant droplet temperature rise through the rotor flow field that exceeds 50% of the initial temperature difference in the case of 15µm droplets. The strong influence of droplet size can be seen from the results of Figure 8 for the three different mean diameters (15µm, 30µm and 45µm). The rate of droplet temperature rise is much faster for the smaller droplets, since it is inversely proportional to the square of their diameter according to equation 7. Figure 9 indicates that the proper definition of dimensionless droplet temperatures rise enables the designer to use correlations independent of the initial droplet temperature. Figure 10 presents the radial variation in the normalized droplet temperature rise at the rotor exit for three different droplet sizes. The exit temperature is seen to decrease with increased droplet size, which is consistent with the results of Figure 8 for the droplet temperature variation along the trajectory. Figure 11 presents the impingement temperature distribution on the blade pressure surface for different droplet sizes. One can see at the same initial temperature the impingement temperatures are higher for smaller droplets. In addition, smaller droplets exhibit greater variation in impingement temperature along the blade chord. This is very important since higher impingement temperatures may result in glaze ice or no ice formation at all, whereas lower impingement temperatures can produce rime or mixed ice. The formation of glaze ice is therefore more probable with smaller droplets while rime ice is more probable with larger droplets. SUMMARY Numerical simulations are carried out to predict supercooled droplet trajectories through aeroengine rotating machinery. Both the momentum and the energy exchange between the droplets and the gas phase are modeled in the simulation. Computational results are presented for NASA transonic rotor 67 at peak efficiency. The computed 3-D turbomachinery flow field is presented for three different levels of grid refinement and compared with existing experimental data. Both the medium and fine grids showed nearly identical predictions that were in agreement with the experimental data. The relative Mach number contours show complex 3-D shock structure in the fan rotor. The results indicate that droplet size has a significant effect on both droplet trajectory and temperature as droplets travel through the rotor flowfield. In general, the blade surface collection efficiency is higher for larger droplets and the impingement temperature is higher for smaller droplets. The energy exchange does not alter the droplet trajectories or blade surface collection efficiency but strongly affects the impingement temperature and hence the type of ice formed on the blade. ACKNOWLEDGEMENTS This research was sponsored by Ohio Aerospace Institute grant CCRP 2003-05. The authors would like to thank Dr. Kattalaicheri Venkataramani of GE Aircraft Engines, Cincinnati for many useful discussions and Mr. Robert Ogden of UC for his technical support. REFERENCES 1. Gent, R.W. TRAJICE2-A combined water droplet and ice accretion prediction code for airfoils, Royal Aerospace Establishment TR 90054, 1990. 2. Brahimi, N.T., Tran, P., and Paraschivoiu, I., Numerical Simulation and Thermodynamic Analysis of Ice Accretion on Aircraft Wings, Center de Development Technologique de Ecole Polytechnique de Montreal, Final report C.D.T Project C159, 1994. 3. Gent, R. W., Markiewicz, R. H., Cansdale, J. T., Further Studies of Helicopter Rotor Ice Accretion and Protection, 1987, Vertica, Vol. 11, No. 3, pp. 473-492. 4. Caruso, S.C. NEARICE-An Unstructured Mesh Navier-Stokes Based Ice Accretion Prediction Method, AIAA Paper no 94-0606, 1994. 5. Guffond D., et Bruent L., Validation du Programme Bidimensional de Captition, ONERA RT no. 20/5146 SY, 1985. 6. Kind, R.J., Potapczuk, M.G., Feo, A, Golia, C. and Shah, A.D. Experimental and Computational Simulation of in-flight Icing Phenomena, Progress in Aerospace Sciences vol. 34. 1998. pp 257-345. 7. Ruff, G.A., and Berkowitz, B.M., User s Manual for the NASA Lewis Ice Accretion Prediction Code (LEWICE), NASA-CR- 185129, May 1990.

6 8. Potapczuk, M.G., and Bidwell, C.S, Numerical Simulation of Ice Growth on a MS-317 Swept wing Geometry NASA-TM-103705, 1991. 9. Chung, J. and Addy, Jr, H.E. A Numerical Simulation of Icing Effects on a Natural Laminar Flow Airfoil, 2000, NASA TM-2000-209775. 10. Bidwell C.S and Mohler S.R. Collection Efficiency and Ice Accretion Calculations for a Sphere, a Swept MS(1)-317 Wind, a Swept NACA 0012 Wing Tip, an Axisymmetric Inlet and a Boeing 737-200 Inlet NASA TM-106821, 1995. 11. Flemming, R.J., and Lednicer, D.A., High Speed Ice Accretion on Rotorcraft Airfoils, NASA CR-3910, Aug. 1985. 12. Flemming, R. J.; Shaw, R. J.; Lee, J. D., The performance characteristics of simulated ice on rotorcraft airfoils, NASA CR-0101, Aug. 1985. 13. Bourgault, Y., Habashi W.G., Dompierre J., Boutanios Z, Di Bartolomeo W., An Eulerian Approach to Supercooled Droplets Impingement Calculations, AIAA Paper-97-0176, 1997 14. Da Silveira, R.A., Maliska, C.R., Estivam, D.A., Mendes, R., Evaluation of Collection Efficiency Methods for Icing Analysis, Proceedings of 17th International Congress of Mechanical Engineering, November 10-14, 2003, Sao Paulo. 15. Hamed, A. and Tabakoff, W., Experimental and Numerical Simulations of the Effects of Ingested articles in Gas Turbine Engines, AGARD CP 558, Erosion, Corrosion and Foreign Object Damage in Gas Turbines, November, 1994. 16. Tabakoff, W., Hamed, A., & Wenglarz, R., "Particulate Flows, Turbomachinery Erosion and Performance Deterioration," Von Karman Lecture Series 1988-89, May 24-27, 1988, Brussels, Belgium. 17. Hamed, A., Jun, Y. D., and Yeuan, J, J., Particle Dynamics Simulations in Inlet Separator with an Experimentally Based Bounce Model, 1993, AIAA-1993-2156. 18. Hamed, A., Tabakoff, W., and Singh, D., Modelling of Compressor Performance Deterioration Due to Erosion, International Journal of Rotating Machinery, Vol. 4, November 1998, pp. 243-248. 19. Tabakoff, W., Hamed, A. & Metwally, M., "Effect of Particle Size Distribution on Particle Dynamics and Blade Erosion in Axial Flow Turbines," Journal of Gas Turbine and Power, Vol. 113, October 1991, pp. 607-615. 20. Hamed, A. & Kuhn, T.P., Effects of Variational Particle Restitution Characteristics on Turbomachinery Erosion, Journal of Engineering for Gas Turbines and Power, July 1995, Vol. 117, pp. 432-440. 21. Hamed, A., Das, K., and Basu, D., Numerical simulations of ice droplet trajectories and collection efficiency on aero-engine rotating machinery, AIAA-2005-1248 22. Messinger, B.L. Equillibrium Temperature of an Unheated Icing Surface as a Function of Air Speed, Journal of Aerospace Sciences Vol. 20. 1953, pp. 29-42. 23. Hall, E.J., Lynn, S.R., Heidegger, N.J. and Delaney, R.A., ADPAC v1.0-user s Manual, NASA-CR-1999-206600. 24. Chima, R.V., Viscous Three-Dimensional Calculations of Transonic Fan Performance, 1992, in CFD Techniques for Propulsion Applications, AGARD Conference Proceedings No. CP-510, AGARD, Neuilly-Sur-Seine, France, pp. 21-1 to 21-19. 25. Jennions, I. K., and Turner, M. G., Three- Dimensional Navier-Stokes Computations of Transonic Fan Flow Using an Explicit Flow Solver and an Implicit k-ε solver, Journal of Turbomachinery, 1993, Vol. 115, pp. 261-272. 26. Arnone, A., Viscous Analysis of Three- Dimensional Rotor Flows Using a Multigrid Method, 1993, ASME Paper No. 93-GT-19. 27. Hamed, A., and Vogiaztis, C., Assessment of Turbulence Models in Overexpanded 2D-CD Nozzle flow Simulations, 1995, AIAA-1995-2615. 28. Yeuan, J, J, Liang, T., and Hamed, A., Viscous Simulations In a Transonic Fan Using k-ε and algebraic turbulence models, 1998, AIAA-98-0932. 29. Ranz, W. E., and Marshall, W. R. Jr., Evaporation from Drops, Part II, Chem. Eng. Prog., Vol. 48, No. 4, pp. 173-180, April 1952. 30. Strazisar A. J., Wood, J. R., Hathaway, M. D., and Suder, K. L., Laser Anemometer Measurements in a Transonic Axial Flow Fan Rotor, 1989, NASA Technical paper 2879.

7 Fig. 1 Computational Grid Fig. 2 Aerodynamic survey locations 70 % span from shroud 50 % span from shroud 30 % span from shroud Figure 3. Relative Mach number contours for radial locations

8 Figure 3. Comparison of computed results for different grid dimensions with experimental data Figure 5. Droplet trajectory in the rotor relative frame Figure 6. Effect of size on droplet mass flow at the rotor exit

9 a. Droplet diameter = 15 micron b. Droplet diameter = 30 micron c. Droplet diameter = 45 micron Figure 7. Effect of droplet size on blade surface collection efficiency

10 Figure 8. Effect of size on droplet temperature (Droplet initial temp=233k) Figure 9. Effect of droplet initial temperature on subsequent droplet temperature rise (Droplet dia= 30 micron) Figure 10. Effect of droplet size on exit temperature 15-micron 30-micron 45-micron Figure 11. Effect of droplet size on blade pressure surface impingement temperature (Droplet initial temp=233k)