ice shape prediction for turbofan rotating blades

AIAA-2006-020944th AIAA Aerospace Sciences Meeting & Exhibit

January 9-12, 2006Reno, NV

Ice Shape Prediction For Turbofan Rotating Blades

K. Das**, A. Hamed*, D. Basu**

Department of Aerospace Engineering and Engineering MechanicsUniversity of Cincinnati

Cincinnati, OH 45221-0070

ABSTRACT

This paper presents a parametric study of ice accretion on a high bypass turbofan engine booster rotor. Both flow and droplets’ governing equations are formulated and solved in the reference frame of the rotating blades. A Eulerian-Lagrangian approach is used for the continuous and discrete phases with one-way interaction model to simulate momentum and energy exchange on the droplets and their effects on the three-dimensional droplet trajectories. The flux-based collection efficiency is calculated for the rotor blade at 60%, 70%, 80%, 90% and 100% engine design speed. A quasi-3D analysis of the ice accretion over the rotor blade is conducted based on the computed flow characteristics using the code LEWICE. Results are presented for the ice shape variation along the span, inlet temperature and rotor speeds. The highest accumulation was predicted on the blade pressure side leading edge near the hub and increased with reduced rotor speed and flow 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 process1-7. The numerical simulations involve aero-thermodynamic analysis of the external flow field, tracking the droplet trajectories and the impingement locations, and the thermodynamic analysis of the freezing process. _________

*AIAA Fellow, Professor**AIAA Student Member, Graduate Student

Most simulations have been carried out for external low speed flows over wings and fuselage8-13 and in some cases for helicopter blades14. Kind et al.15 conducted a literature review of computational techniques in icing simulations. The most common approach is to solve the flowfield and droplet governing equations separately. The panel method is widely used to simulate the flowfield, sometimes coupled with a boundary layer analysis. The Lagrangian approach is used in the droplet trajectory simulations. Simulated results usually include the droplet collection efficiencies, impingement limits and ice shape. Da Silveria et al.16 compared the predictions of various collection efficiency methods with available experimental data over a wing and a fuselage

Ice accretion in aircraft engines raises safety and performance concerns such as mechanical damage from fan and spinner ice shedding and slow acceleration leading to compressor stall from ice accretion on turbofan splitters and fan and booster vanes. The compressible 3-D unsteady turbomachinery flow and the effects of rotation on droplet trajectories present additional challenges in the simulation of ice accretion in aircraft engines. However extensive research has been conducted to simulate solid particle dynamics in turbomachinery and characterize associated blade surface erosion17,18. The pattern and intensity of blade erosion were found to be affected by particle size, blade material and blade row location17-19. Numerical models have been developed for simulating the associated loss and aerodynamic performance20. The blade collection efficiency of supercooled droplets requires tracking their trajectories until their first blade surface encounter. Unlike solid particle, they do not rebound and continue their trajectories through succeeding blade rows21-23.

1Copyright © by Das et. al. Published by American Institute of Aeronautics and Astronautics Inc., with permission

Hamed et al.24 developed a methodology for the simulation of supercooled droplet trajectories through aeroengine rotating machinery. It is based on a Eulerian-Lagrangian approach and one way modeling of the inter-phase interactions. The methodology was tested on rotor-67, which is a high-speed research fan with highly twisted blades. Simulated results in rotor-67 at design speed indicated that the overall blade collection efficiency was higher near the leading and a greater proportion of large droplets encountered the rotating blade surface. Unlike the external flow over wings, the flow temperature rise through the fan rotor can affect droplet temperature as they travel through the blade passage. The effect of energy exchange between the discrete and continuous phases was subsequently taken into consideration by Das et al.25. It did not affect the droplet trajectories and blade collection efficiencies but caused the droplet temperature to rise through the rotor and the effect was greater for smaller droplets.

Experience with engine icing tests indicates that maximum ice accretion takes place at part-load conditions during engine idling. Das et al26

conducted a preliminary investigation on supercooled droplet trajectories through the rotor passage at part load conditions. The results indicated that the rotational speed has a significant effect on droplet impingement locations, and the peak collection efficiencies at the blade pressure surface leading edge increased with rotor speed reduction.

The present study deals with the icing simulation of turbofan engine booster rotor at part load conditions. Simulations are carried out for the GE-NASA energy efficient engine (E3) 27,28

booster stage rotor to characterize the ice shape at 60%, 70%, 80%, 90% and 100% design speed. Computational results are presented at the design and off-design speeds for the droplet collection efficiency distribution over the blade surface and the calculated ice shapes at different radial locations.

METHODOLOGY

Both flow and particle governing equations are formulated in the rotating blade frame. A Eulerian-Lagrangian approach is employed for the flow field and droplet trajectories and one-way interaction model was used to simulate the

effects of momentum and energy exchange on the droplet trajectories.

The droplet trajectories are determined from the numerical integration of the equations of motion in the blade rotating reference frame24-26:

(1)

(2)

(3)

In the above equations, rp, p and zp define the particle location in cylindrical coordinates, and the blade angular velocity. The last term in the RHS of the first two equations represent the centrifugal force and Coriolis acceleration. 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 relative velocity 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. Forces due to inter-droplet interactions and pressure gradient are also negligible 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 follows15:

(4)

Where dp is the particle diameter and and are the gas and the droplet velocity vectors. The drag coefficient CD is computed from empirical correlations involving the Reynolds number based on the relative velocity between the droplet and the gas18-20.

The change in droplet temperatures along their trajectory is determined from the energy exchange rate between the droplets and the airflow. Only the heat transfer by convection is taken into consideration since no phase change takes place at supercooled droplet temperatures.


(6)

where, Cp is the specific heat of the supercooled droplet and p is the droplet density. The heat transfer coefficient h is evaluated using Ranz and Marshall’s34 correlation for spherical droplets:

(7)

Where k is the thermal conductivity of the gas, Pr is the Prandtl number.

Computational Details

The numerical solution for the three-dimensional compressible Reynolds Averaged Navier Stokes (RANS) equations in the rotating frame is obtained using ADPAC29. The code utilizes finite volume, Runge-Kutta time marching scheme to solve the time dependent form of 3-D RANS equations. 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 convergence30-32. Several turbulence models including the algebraic Baldwin-Lomax model, one equation Spalart-Allmaras model and two-equation k-R model are available in the solver. Rotor-67 flowfield simulations by Yuan et al.33

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.

The total temperature, total pressure and absolute flow angles were specified at the booster inlet. Adiabatic wall and no slip boundary conditions were prescribed on the stationery and rotating surfaces. The exit static pressure was specified at the hub, and the radial pressure distribution from the integration of the axisymmetric radial momentum equation. Periodic boundary conditions were applied across the solution domain that extended 10% chord upstream and 15% chord downstream of the rotor blade row.

The computational grid selection was based on prior experience24 with the Rotor-6736

simulations, in which three different grid resolutions were used in a grid independence study. The selected grid consists of 95 81 65 points in the stream-wise, blade-to-blade and the hub-to-tip directions. Grids were clustered near the walls using a hyperbolic tangent function. The minimum grid spacing in the wall normal direction was 1.0 10-4 times the chord with 15 grid points within the boundary layer.

Equations 1-3 and 6 are solved using a four-stage Runge-Kutta time integration starting from the droplet inlet conditions upstream of the blades. The droplet distance from the blade passage is monitored throughout the droplet trajectory until impingement on a surfaces or exit from the blade passage. 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 each 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. Distributed computing was found to reduce the computational time by two orders of magnitude for the 50,000 droplet trajectories considered at each operating point in the current investigation.

The trajectory simulations were carried out for 30 m droplets that were assumed to be spherical with uniform loading across the inlet. The relative humidity was considered to be 100 % with liquid water content of 0.01.

Collection Efficiency

The limiting droplet trajectories have been commonly used for the definition of collection efficiency for external flows9-12 by initiating a number of droplet trajectories that are released over incremental distance across the free stream direction until they reach the surface outermost boundaries. The slopes of the limiting 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 had the droplets not been deflected by the flow around the surface. The concept of limiting droplet trajectories in the particle frame of reference is not suitable for turbomachinery flow


due to blade rotation and because neighboring droplets could continue their trajectories in different blade passages of subsequent blade rows. Therefore, a flux based collection efficiency was defined by Hamed et al.24 as the ratio of the local droplet mass flux at the blade surface to its value at the turbomachinery inlet station. This definition, which is equally applicable to stationary and rotating blades, is utilized in the present investigation.

Ice Shape Calculation

Utilizing LEWICE icing physics, a quasi-3D approach was adopted using the computed collection efficiency at a number of radial blade sections. In this approach the 2D potential flow, droplet trajectory modules, and heat transfer calculation procedures of LEWICE version 3.035

The convective heat transfer coefficients, pressure coefficients and the droplet collection efficiency distributions at a number of rotating blade sections are extracted to use as input for the ice accretion prediction. A pitchwise averaged flow meridional inlet velocity and droplet inlet temperatures were extracted from the 3D flowfield and droplet trajectory data at each radial location for use in the 2D LEWICE code.

RESULTS AND DISCUSSIONS

Numerical simulations were conducted for the flow field and droplet trajectories through the GE-NASA energy efficient engine (E3) booster stage. The detail design data for the engine, whose cross section is shown in Fig. 1, were reported by Sullivan et al.27. The booster has 56 blades, a hub-tip ratio of 0.782 and an aspect ratio of 2.12 at inlet. The design total temperature and pressure ratio across the rotor are 1.1776 and 1.683 respectively at the corrected RPM of 3727 and mass flow rate of 143.74 kg/sec. The off-design operating conditions for the booster rotor were obtained from the performance maps for the core and bypass stream of the low-pressure compression system28.

Figure 2 presents the computed relative Mach number contours on representative blade-to-blade surfaces at design speed. One can see an oblique shock at the leading edge that does not reach the pressure side. Similar shock structure is visible for all the three cross sections indicating

little spanwise variation compared to rotor-6724. This is consistent with the design conditions as documented by Sullivan et al27. Figure 3 compares the radial profiles of the design flow variables to the circumferential average of the rotor exit computational results at 100% rotor speed. It can be observed that the computed total temperature ratio and absolute flow exit angle are in reasonable agreement with the design data. The total temperature ratio shows slight disagreement near the hub whereas the absolute exit angle deviates from the design data near the tip.

Figure 4 shows of the computed relative Mach number at different part speed conditions. One can see that the flow is mainly subsonic at 70% rotor speed but has significant supersonic regions that end with a shock wave at the blade suction side at 90% speed. A small transonic bubble is seen near the suction surface leading edge at the intermediate 80% rotor speed.

Figure 5 shows the computed droplet collection efficiency at four different off-design speeds. The results indicate that the highest collection efficiency is predicted at the lowest rotor speed. In general, the peak collection efficiency is near the tip at the pressure surface leading edge. The suction surface collection efficiency is not shown because it is limited to a very small region near the leading edge. Prior predictions in Rotor - 67 by Hamed et al24-16 also indicated peak collection efficiency at the pressure surface leading edge, but the spanwise variation was different for the highly twisted research rotor.

Figure 6 and 7 show the computed ice shapes at four blade sections located at 10%, 40%, 70% and 90% span from the hub. The ice forms mostly on the blade pressure surface with little accumulation on the suction surface leading edge. Thicker ice shapes are predicted at the lower rotor speeds, and the mass of accreted ice tends to decrease as one moves from hub to tip. Comparing figures 6 and 7 one can see significant reduction in ice accretion with increased rotor speed. The higher flow velocities and surface temperatures contribute to this trend, in addition to the reduced blade collection efficiency.

Figure 8 compares the ice accretion shapes for different rotor speeds near the hub and tip. The greatest accumulation is at 60% design speed ice accretes at the leading edge of the pressure


surface. With increased rotor speed the ice disappears from the leading edge suction side the pressure surface area covered with ice decreases and finally disappears at 80% and 90% rotor design speed. Similar trends are observed near the tip. Figure 11 shows the effect of freestream temperature on ice accretion. One can see that a modest temperature rise can lead to significant change in the ice shape. As expected, the highest ice accumulation occurs at the lowest temperature and diminishes with increased inlet temperature.

CONCLUSIONS

A numerical study was conducted to investigate ice accretion on a turbofan booster stage. The inter-phase coupling between the air and droplet are modeled through both momentum and energy exchange equations The simulations are carried out in the GE-NASA energy efficient engine (E3) booster rotor at 60%, 70%, 80%, 90% and 100% design speed and 266.5K, 267K, 267.5K, 268K, 268.5K and 269K droplet inlet temperatures.

Results are presented for the radial variation in ice shapes at various rotational speed and air temperatures. The results indicate thicker ice shapes at the leading edge of the blade and more pressure surface coverage towards the hub. Ice formation increases with engine speed reduction and is very sensitive to inlet temperature changes.

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.

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Figure 1. Cross section of E3 engine

10 % span from hub

10 % span from tip

Mid-span

Booster stage rotor


Figure 2. Mach contours at different span

Figure 3. Comparison with design data

70% Design Speed

80% Design Speed 90% Design Speed


Figure 4. Mach number at mid-span



Figure 5. Collection efficiency on blade pressure surface


10% from hub

40% from hub

70% from hub

90% from hub

Figure 6. Ice shape variation at 60% design speed

Figure 7. Ice shape variation at 70% design speed


60% Design 70% Design 80% Design 90% Design

Figure 8. Effect of rotor speed on ice shape (at 10% span from hub)

60% Design 70% Design 80% Design 90% Design

Figure 9. Effect of rotor speed on ice shape at (90% span from hub)


266K 266.5K 267.5K

268K 268.5K 269K

Figure 10. Ice shape variation with flow temperature (60% design speed)

ice shape prediction for turbofan rotating blades

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