Transient Behavior in Axial Compressors in Event of Ice ... - CiteSeerX

Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition GT2015 June 15 – 19, 2015, Montréal, Canada

GT2015-42413

TRANSIENT BEHAVIOR IN AXIAL COMPRESSORS IN EVENT OF ICE SHED

Swati Saxena Rajkeshar Singh GE Global Research Center One Research Cirle, Niskayuna, NY 12309, USA

Andrew Breeze-Stringfellow Tsuguji Nakano GE Aviation 1 Neumann Way, Evandale, OH 45215, USA

Particle cross-sectional area, m2 Aerodynamic Drag coefficient acting on spherical ice particle Cp Specific heat at constant pressure, J/kg −o C Dp Particle diameter, m E Total energy, J e Internal energy, J f Body force per unit volume, N/m3 FD Aerodynamic drag acting on an ice particle N fD Aerodynamic drag acting on N particles, N h Heat transfer coefficient hm Mass transfer coefficient H Total enthalpy, J Lc Compressor length, m Lv Latent heat of vaporization for water, J Lf Latent heat of fusion for ice, J m˙ Mass flow rate, kg/s mp Particle mass, kg N Number of particles Nc Corrected HPC speed N Number of particles p Static pressure, Pa Psat Air saturation pressure at a given temperature, Pa Q˙ Heat exchange between continuous and discrete phase J/s r Radius, m rm Mean pitch-line radius, m RH Relative humidity s Discrete phase source term SH,q Specific humidity

ABSTRACT Incidents of partial or total thrust loss due to engine icing at cruise have been recorded over past several years. These events increase the demand for better understanding of compressor dynamics under such conditions. In the present study, physics based compressor blade row model (BRM) is used to evaluate the effect of booster ice-shed on axial high pressure compressor (HPC) at flight and approach idling conditions (65% - 82% Nc). A representative aviation high-bypass turbofan engine HPC is used in this study. Transient behavior of compressor with varying ice ingestion conditions is compared and inter-stage dynamics is analyzed. Stage re-matching occurs due to heat exchange between air and ice which dictates the stall inception stage in the compressor. It is found that although T3 drop is closely related to compressor stall inception, the transient mechanism of iceshed also plays an important role. Comparisons are made with steady energy balance equation to determine total water content (TWC) at HPC inlet to emphasize the importance of compressor transients. The ice amount, its ingestion duration and rate affect the onset of stall. HPC might sustain through a slower ice-shed while a faster ice-shed can lead to compressor stall with little or no chances of recovery. Understanding this transient behavior and inter-stage dynamics due to ice-shed will help in designing and implementing passive or active stall control mechanisms.

Ap CD

NOMENCLATURE A Cross-sectional area at a given axial location along the compressor, m2

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Discrete phase energy source term Discrete phase momentum source term Discrete phase mass source term Time, s Static temperature, K Axial component of flow velocity, m/s Mean pitch-line HPC speed, m/s Circumferential velocity, m/s shaft work, J/s Compressor inlet Compressor exit Axial flow coefficient Density, kg/m3 Particle (ice crystal) density, kg/m3 Pressure rise coefficient across blade Specific heat ratio for air Core speed , rad/s

SE SM SV t T u U vθ w˙ s 25 3 φ ρ ρp Ψ γ ω

aircraft flies through clouds containing SCL, water can come in contact with airframe and freeze instantly or run-back and freeze resulting in ice accretion. The ice accretion can occur on all parts that are below freezing such as fan blades, low pressure compressor blades and vanes and frame struts. Eventually, the accreted ice sheds from the surfaces upstream of compressor and causes ice ingestion into compressor. Such incidents have reported power-loss events including engine stall and surge, flameout, momentary power loss and compressor damage due to iceshed [1, 2]. Ice chunks impinging on front stage rotor blades can cause severe mechanical damage. There have been efforts to model ice-accretion in fan and low pressure compressor and predict system performance . Jorgenson et al. [3] utilized engine system modeling and mean-line compressor flow analysis code to identify potential ice accretion regions in fan and LPC, thus improving predictive capability to forecast the onset of compressor icing events. Mazzawy [4] presented a numerical model to predict mixed phase ice-accretion and shedding in turbo-fan engines in presence of ice-crystals. High-fidelity studies have also been performed to simulate iceaccretion in cascade. Veillard et al. [5] demonstrated droplet impingement using a quasi-steady mixing-plane model on NASA compressor stage 35 which gives further insight on ice-accretion locations. May et al. [6] concluded that a better ice detection mechanism will improve the engine control response in case of icing events. The compressor maps including ice-blockage were used in the control algorithm. These efforts can provide better understanding of the ice behavior at HPC inlet. Studies have been performed to understand aero-mechanical effects of water/rain ingestion in HPC. Day et al. [7] reported reduction in compressor delivery pressure in presence of water on a low speed axial compressor operating at part speed in a descent configuration. In this study, the thermodynamic effects were neglected which would be important in HPC and would result in more complicated stage-matching. Since thermodynamic effects of ice play an important role in HPC response, it is important to understand the transient compressor response to improve current FADEC to operate in a more optimized fashion without compromising on the performance and reliability. As ice moves through the compressor, it melts and evaporates thus causing shift in compressor operating line and reduced stall-margin. Compressor stages re-match to operate with an overall reduced stall margin. The dynamic behavior of the compressor is closely related on the ice ingestion rate, amount of ice ingested and the duration. Steady state analysis based on energy balance [8] will provide partial information on TWC through the compressor but it will not provide information on the time response or time scale over which compressor reacts to ice. Understanding the dynamic response and individual stage performance will help in better engine control designs to delay engine stall due to icing. There is still little understanding of transient flow physics in

Subscripts 0 a b c E h i M p sr f c t v,V w x

Stagnation condition Air (continuous phase) Bleed Continuous phase (air) Energy Hub (inner duct) ice Momentum Particle (discrete phase) Particle surface Tip (outer duct) Vapor Water Axial direction

Abbreviations BRM Blade Row Model FADEC Full Authority Digital Engine Control HPC High Pressure Compressor (core) LPC Low Pressure Compressor SCL Super-cooled Liquid Droplets SH25 Specific humidity at compressor inlet TWC Total Water Content, g/m3

INTRODUCTION Commercial aircrafts operate over an extreme range of environmental conditions, with temperatures ranging from 216 K to 322 K and at altitudes up to 12,000 m. Water can exist in liquid state at very high altitudes even at temperatures well below 273.15 K in form of super-cooled liquid droplets (SCL). When an

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core compressor due to ice ingestion [9]. Several experimental initiatives have been recently taken to understand the ice-shed phenomenon in jet engines [10]. But ice-shed from fan and LPC blades is difficult to predict and capture during the measurements. Different forms of ice such as glaze and rime have different material properties which will also determine the shed signature. Engine operating conditions (fan and HPC speeds) can affect the ice-shed frequency. The present work addresses some of these uncertainties and variability during icing events through physics based numerical modeling. The key contribution of this study is to develop the capability to predict compressor stage dynamics in case of ice-shed events and determine compressor sensitivity towards ice-shed time duration and ice amount at HPC inlet (SH25). This paper is organized as follows: Numerical Method section describes the governing equations, flow and ice particles coupling method and the compressor used for the ice-shed study. Numerical Results and Analysis section covers the icing simulations performed at different HPC operating speed lines and discusses the HPC sensitivity towards ice shed amount and duration. The Conclusions section provides the learnings from the present study and addresses the future work.

FIGURE 1. Schematic of the compressor model. Flow solved along mean pitch line radius (rm ), blades and bleed flows modeled as source terms in governing equations (Dhingra et al., 2011)

Equation 1 shows the coupled mass, momentum and energy conservation equations solved for continuous and discrete phases. The right hand side of the equation represents the source terms to model bleed flow, blade rows and discrete phase. An additional species conservation equation needs to be solved for water vapor fraction (q or SH) to incorporate the vapor generation. q is defined as m˙ vapor /m˙ dryair which is same as specific humidity (SH). Total energy and total enthalpy for continuous phase are given by Eqs. 2 and 3 respectively.

NUMERICAL METHOD This work builds on the model developed to study reduced order transient compressor response in an earlier work by Dhingra et al. [11] and Kundu et al. [12]. The literature on reduced order and lumped compressor models has been reviewed in Dhingra et al. [11]. Kundu et al. [12] reviews previous work related to icing models. The present physics based model used to simulate HPC icing is described in more detail in Kundu et al. [13]. The present reduced order model can capture stage-wise transient response and also models air bleeds. The compressor is assumed to operate at constant mechanical speed but the corrected speed might change as ice melting and evaporation affects flow properties. The governing equations, modeling assumptions and limitations are summarized in the following section for completeness. The unsteady Euler equations are solved along the compressor mean pitch line ( ∂∂r = 0). The flow-field is assumed to be axi-symmetric, thus averaged in circumferential direction ( ∂∂θ = 0). The compressor axis lies along x-axis. The rotor and stator blades are modeled as source terms using steady state forces based on steady stage characteristics (required as an input to the solver) at a constant HPC speed. Figure 1 shows the compressor model schematic where individual blade rows and gaps are resolved. Station 25 is HPC inlet and 3 represents HPC exit. The grid along the compressor axis is refined enough to resolve the blade rows. The blades and bleed flows are modeled as source terms and are calculated by using steady-state stage characteristics [11]. The source terms are distributed between leading and trailing edges of the blade.

     ∂ m˙ b ρc uA ρc A ∂ x + SV  f A + A ∂ p + u ∂ m˙ b + S  2   ρc uA   x M ∂x ∂x  ∂ (p + ρc u )A  ∂   ∂ m˙ b ρc vθ A +  ρc uvθ A  =    f A + v θ θ  ∂x    ∂x  ∂t   ρc EA   ρc uHA    w˙ s + ∂∂m˙xb Hc + SE ρc qA ρc uqA ∂ m˙ v 

∂x

1 Ec = ec + (u2 + v2θ ) 2

Hc = E +

p ρ

(1)

(2)

(3)

Dry and humid air follow the ideal gas assumption where the following relations are valid: p = ρRT ; p = (γ − 1)ρe; γ = C p (T )/Cv (T ).The specific heat ratios for dry and humid air are function of temperature and the correlations can be found in Walsh and Fletcher [14]. Particles melt, evaporate, break and splash as they move through the compressor as shown in Fig. 2. Particles can melt partially and have water film with ice core. Water droplets splash

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as they strike the blade leading edge. GE empirical models based on test data are used for modeling particle fragmentation and water droplet splash.

of vapor depends on local air properties, where the vapor mass flux equation can be written as Eq. 8. The aerodynamic drag acting on the particle FD can be calculated from Eq. 9. Equation 10 relates the temperature change to the heat exchange between ice and air. The heat transfer coefficient h in Eq. 10 and mass transfer coefficient hm in Eq. 8 are based on GE empirical correlations obtained from experiments. The blockage in the cross-sectional area due to the presence of discrete phase is also taken into account.

FIGURE 2. Schematic showing ice fragmentation, melting and water splash as they impinge on blades along the compressor

1 N m˙ v dx ∑ p

SM = u p SV − fD (u − u p )

SE = SV H p +

fD =

m pCP,p

NFD dx(u − u p )

(7)

(9)

dm f dTp dmv = hπD2p (Tair − Tp ) + Lv +Lf dt dt dt

(10)

RH = SH

(p/Psat ) (0.622 + SH)

(11)

Relative humidity is calculated after each time step from water vapor fraction (q or SH) which is used to calculate the rate of vapor generation. The lower order model is based on some approximations and assumptions and thus have limitations as follows: • Flow is averaged in radial and circumferential (azimuthal) directions, therefore ice migration in radial direction and non-symmetric effect in circumferential direction are not captured in the current formulation. • Ice-crystals are assumed to be spherical; therefore the varying particle drag due to non-spherical shape is not captured. This assumption can be relaxed by incorporating the particle shape effects in the discrete phase transport equations. • Any ice accretion or water film building on airfoils is neglected. The ice volume fraction is small enough so that particle-particle interaction can be neglected. • Ice-shed impulse response is fast enough to assume the constant speed line for the current study. Therefore, the engine thrust loss due to stall cannot be predicted. • Heat exchange between ice and metal surface is not taken into account.

(5)

(6)

du p 1 = ρcCD A p u − u p (u − u p ) = FD dt 2

The relative humidity (RH) and specific humidity (SH) of air can be related by Eq. 11 (Eq. F2.10 in [14]):

(4)

∂ Q˙ p − fD (u − u p )u p ∂x

(8)

mp

The source terms due to icing are obtained by including the drag force acting on ice particles and energy transfer between the continuous and discrete phase. Equations 4, 5 and 6 show the expressions for mass, momentum and energy source terms for the discrete phase. The source term for the mass represents the generation of vapor and its addition to continuous (air) phase. The aerodynamic drag acting on the particle and the force due to vapor generation constitutes the momentum source. The heat transfer between continuous and discrete phase, change in kinetic energy of particles and vapor enthalpy are contributors to the energy source term. Equation 7 shows the drag acting on N particles.

SV = −

dmv = −hm (ρv,sr f c − RH%ρv )πD2p dt

Lagrangian particle tracking is done by solving the coupled continuous and discrete phase equations. The rate of generation

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Some of these limitations can be relaxed as needed. Current implementation is able to capture the key thermodynamic effects due to the ice-crystal ingestion in compressor.

near peak efficiency. Ice shed duration and TWC are parameterized to study the correlation between compressor response and icing properties. The next section presents the simulation and analysis for iceshed events performed at two compressor speed-lines.

Energy Balance across compressor Given T3 suppression due to wet conditions and compressor exit dry and wet flow conditions, the TWC at compressor inlet can be calculated from a simple energy balance equation across compressor [8]:

m˙ aC p (T )∆T3 = m˙ p hi,T1−0oC + L f + hw,0oC−(T3 ,p3 )




NUMERICAL RESULTS AND ANALYSIS The following section presents the simulation results for icesheds and characterizes the compressor dynamic response based on the ice-shed parameters: ∆ticeshed and SH at HPC inlet. Icecrystals and SCL can freeze on metal surfaces and build up ice on fan and stator vanes as shown in Fig. 3. Ice eventually sheds from these surfaces entering HPC, sometimes as big chunks.

(12)

where hi,T1−0oC is the specific enthalpy required to bring the ice crystals from T 1 to the melting point. hw,0oC−(T3 ,p3 ) is the specific energy required to bring water to the compressor discharge condition (T 3, p3). Air mass flow rate m˙ a is available from engine data. Equation 12 is valid when compressor has attained steady state and it assumes that all ice has evaporated at HPC exit. This formulation, however, cannot capture the potential impact of transient nature of T3 drop. Simulation Setup A representative 10 stage commercial high-bypass turbofan engine HPC has been used for the present study. Air (customer and turbine cooling air) is bled out after stages 4 and 7. The amount of ice equivalent to stage 4 air bleed percentage is extracted from the main flow after fourth stage. Simulations are performed at flight idle (65% Nc) and approach idle (82% Nc) corrected HPC speeds. Without loss of generality, RosinRammler distribution is used to represent ice-crystal size distribution at HPC inlet with Median Volume Diameter (MVD) of 150 microns. The sensitivity study around particle size has been previously performed in Kundu et al. [12]. The ice-crystal temperature at compressor inlet is taken as -17.15 degC to represent realistic ice-crystal conditions in convective clouds. The TWC range is taken from the available test data to represent cloud water content [8]. The steady ice ingestion study presented in Kundu et al. [13] has shown the stage re-matching in presence of humidity where front stages unload (choke) and rear stages throttle. The presence of ice and water in front stages lead to lower air density. Two factors effect the air density in rear stages. Temperature drop due to heat exchange between air and discrete phase lead to increase in air density while addition of water vapor leads to decrease in air density. Due to cooling evaporation, there is net increase in air density leading to higher loads. Therefore, compressor stall initiates in rear stages and moves upstream along the compressor eventually leading to surge. This is different from the stall usually initiated from the front stage operating at higher loading

FIGURE 3. Ice-accumulation regions shown upstream of HPC. Ice accumulation on fan, LPC and strut blades causes ice-shed event resulting in instantaneous ice ingestion into HPC. Ice-crystals shown by blue circles. Rotating blades shown in grey and stators shown in black.

The ice-shed simulations are performed at two compressor operating speeds for different ice-shed amounts and duration to represent realistic shedding time scales. Operating Point: Approach Idling (82% Nc) Table 1 shows the list of ice-shed cases simulated at 82% Nc. A value of ∆ticeshed = 5 ms corresponds to ice ingestion duration of 5 ms while ”Continuous” refers to steady ice ingestion at the given SH25. Time duration of 5 ms is of the similar order as flow through time. An initial steady ice ingestion study was performed to determine the SH threshold for compressor stall in case of continuous ice ingestion. Then the ice-shed time and SH was varied to simulate broader range of ice-shed possibilities ranging from very short period of shed to a steady ice ingestion. Table 1 also lists the compressor stall behavior in each ice-shed case. Compressor is able to operate at the steady ice ingestion at lower SH25 (Run 1) while it stalls at higher SH25 ingested for a short period of time (Run 7). It can be inferred from these

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TABLE 1.

Run No.

Ice shed simulations at 82% Nc

SH25

∆ticeshed (ms)

Stall Observed

1

1

Continuous

N

2

1.5

Continuous

Y

3

1.75

5

N

4

1.75

10

Y

5

1.75

Continuous

Y

6

2

5

N

7

3

5

Y

for shorter period of time. Run 3 doesn’t stall while run 4 does. Compressor is able to recover to its dry state in run 3 before last stage stalls. Runs 6 and 7 shed ice for 5 ms at SH = 2% and 3% respectively. Run 7 stalls as it goes well past the T3 drop threshold of 20% and the compressor is not able to recover. Therefore, it can be safely assumed the compressor will not stall if maximum T3 drop is less than the threshold T3 drop. But past the threshold T3 drop, ice-shed parameters (SH and duration) determine the compressor dynamics.

values that both SH and ice-shed duration are important to determine the compressor response. Next, the stage-wise compressor behavior in these runs has been analyzed. The percent T3 drop as a function of time is plotted for runs 1 to 7 in Fig. 4. It is defined as a function of time (K/K) in Eq. 13: %T 3drop (t) =



T 3 (t) − T 3dry /T 3dry × 100

(13)

The horizontal axis is physical time normalized with compressor flow-through time. Compressor flow-through time is calculated as the time taken by air at HPC inlet to reach HPC exit. Water freezing point at STP (273.15 K) is well below the highest %T3 drop reported on Fig. 4. Ice ingestion starts at 6 flow-through times after the compressor has reached a steady dry state. The particle speed at HPC inlet is taken as one tenth of the air speed which increases along the compressor as air exerts force on the particles. The stall in these runs is characterized by the steep drop in mass flow through the compressor. As stages re-match in presence of discrete phase, the stall margin on rear stages keep reducing until a point where the stage moves beyond its stall limit. If this happens, the stage can initiate compressor stall. The stall point is not characterized by only the T3 drop. Several observations are made on this figure. Run 1 (SH = 1%, blue line) stabilizes after 5-6 flow through times to a constant T3 drop of nearly 13%. Run 2 (green dash line) leads to stall after reaching a T3 drop of nearly 20%. This number can be treated as the threshold of T3 drop the compressor can digest without stall in a continuous ice-ingestion case. Low frequency oscillations are observed in this case with time period of nearly 0.8 flow through time. When SH is further increased to 1.75% for continuous ice-ingestion, the compressor shows similar transients near stall as for run 2 with same oscillation frequency. This shows that the compressor dynamics near stall in closely related to its through flow time scale. Ice-shed runs 3 and 4 ingest ice

FIGURE 4. Transient %T3 drop for icing events listed in table 1. Compressor operating at 82% Nc.

The stage-wise compressor response to ice-shed is analyzed by observing the transient static pressure and temperature behavior along the compressor. The normalized static pressure with respect to its dry value is plotted against normalized time at each rotor inlet for runs 1 and 6. Figure 5(a) shows the compressor stage matching for SH = 1% steady ice ingestion. Middle stages (5-7) have suffered the highest pressure drop as they move towards choke. Figure 5(b) shows static pressure variation with respect to its dry run value along the compressor for run 6 in Table 1. The transient pressure drop for last stage is nearly 6% while the middle stages drop by 18%. As the compressor recovers to its dry state, the pressure over-shoots due to inertial effects. As the operating point moves to its dry conditions after the ice-ingestion is stopped, there is a time-lag between the change in flow properties and the compressor response. In the present model, the operating point traverses on the steady state characteristics and this results in an overshoot before the steady dry conditions are

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reached. Experiments (GE Engine certification tests) have reported this overshoot as well which might indicate higher flow angles to the blade and hence higher loading.

the front stages and heat exchange between the discrete and continuous phase is not sufficient to show a significant temperature drop. Therefore, local air density remains almost constant in front stages while it increases in rear stages due to higher temperature drop. Last stage sees around 14% drop in T3 with respect to its dry value. Figure 6(b) plots the temperature variation for SH = 2% and ice-shed duration of 5 ms. It can be observed that the rate at which temperature drops is similar and slower for all stages as compared to the recovery where front stages recover at a slower pace as compared to back stages. This attributes to the compressor response time to the ice particles as they enter the HPC at a slower speed than the flow Mach number. Figures 7(a) and 7(b) show the transient ice-shed response on the steady state compressor maps for front and back stages respectively. The red circle on the plots show the dry operating point.The axial force coefficient, Ψ(= fx /(0.5ρU 2 )), is plotted against the axial flow coefficient, φx (= ux /U). As explained earlier, the front stages unload and move to a higher flow coefficient due to stage-matching while rear stages throttle and load to lower stall margin. Figure 8 show the unloading the recovery path on one of the stages. The black squares show the transient path on the compressor map. Dry operating point is shown by red circles. The overshoot can be seen in the transient. For the runs listed in table 1, the corresponding TWC can be calculated from steady energy balance Eq. 12. Table 2 shows the computed SH25e values. The sub-script e represents the SH values calculated from energy balance equation across compressor. The maximum T3 drop has been used as an input to Eq. 12. It is observed that the steady equation consistently over predicts SH25e at HPC inlet. Maximum T3 is an instantaneous compressor response to the ice-shed and will not represent both SH and ice-shed duration. As concluded from Fig. 4, both these parameters are important in determining the initiation of compressor stall. The transient model provides higher degrees of freedom to find more reliable ways to predict compressor behavior during icing.

(a) SH25 = 1%, continuous ice ingestion

Operating Point: Flight Idling (65% Nc) The ice-shed simulations are performed near flight idling conditions. The steady ice-ingestion shows that the compressor is able to ingest more ice as compared to 82% Nc in terms of SH before stall. It should be noted that the physical mass flow rate through HPC is lower at 65% Nc as compared to 82% Nc. The ice-shed duration is varied around 10% SH to further understand compressor dynamics. Table 3 shows the list of six ice-shed runs simulated at 65% Nc. The run at lowest SH of 8% does not show stall. SH = 10% run stall when ice is ingested for more than 20 ms but is able to recover to its dry condition for shorter ice-shed duration. Figure 9 shows the transient percent T3 drop for all six cases described before. Horizontal axis is normalized with respect to

(b) SH25 = 2%, ice-shed duration = 5 ms

FIGURE 5. Transient static pressure PS change along the compressor for continuous ice ingestion and ice-shed event. Compressor operating at 82% Nc.

Figure 6(a) plots the transient temperature along the compressor for continuous ice-ingestion at SH = 1%. The gradual drop in temperature along the compressor can be observed with nearly no effect in front two stages. The ice has not melted in

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(a) Front stages of axial compressor

(a) SH25 = 1%, continuous ice ingestion

(b) Rear stages of axial compressor

FIGURE 7. Transient compressor stage wise matching in case of iceshed, optimal operating point recovered after humid air leaves the compressor. SH25 = 2%, ice-shed duration = 5 ms. Black squares track the dynamic compressor response. Red circles show the dry operating point.

(b) SH25 = 2%, ice-shed duration = 5 ms

FIGURE 6. Transient temperature along the compressor for continuous ice ingestion and ice-shed event. Compressor operating at 82% Nc.

pressor stalls. The individual stage work load play an important role in compressor stage-matching during icing. Figure 10(a) shows the static pressure change for each stage as a function of normalized time. Stage 10 (red dash curve) operates at higher pressure with respect to its dry value while other stages are operating at lower static pressures. Middle stages (5 7) show highest pressure drop which is consistent with the observations made for 82% Nc. Middle stages have all three phases of water present: ice, water droplets and vapor. Figure 10(b) shows

compressor flow-through time and ice ingestion starts at the normalized time of 3. The first case shows that the compressor is able to sustain at much larger T3 drop (nearly 25%) when smaller amount of ice is ingested. For an higher SH25, compressor is able to recover until 22% T3 drop beyond which the compressor stalls. The compressor behavior is different from 82% Nc in terms of the threshold T3 drop and also the SH at which com-

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TABLE 3.

Run No.

Ice-shed simulations at 65% Nc

SH25

∆ticeshed (ms)

Stall Observed

1

8

Continuous

N

2

10

5

N

3

10

10

N

4

10

15

N

5

10

20

Y

6

12

10

Y

FIGURE 8. Stage matching in presence of ice: operating point move towards choke and recovering to its dry state after ice-shed. SH25 = 2%, ice-shed duration = 5 ms. Black squares track the dynamic compressor response. Red circles show the dry operating point. TABLE 2. SH25e calculated from energy balance across compressor for icing simulations at 82% Nc

Run No.

SH25

%T3 drop (Maximum)

SH25e (Eq. 12)

1

1

16

2.1

2

1.5

21

3.96

3

1.75

21

3.96

4

1.75

22

4.19

5

1.75

24

4.55

6

2

23

4.27

7

3

27

5.19

FIGURE 9. Transient %T3 drop for icing runs listed in table 3. Compressor operating at 65% Nc.

ature drop is directly related to amount of ice melting and water evaporation within each stage. Figure 11(b) shows the transient temperature variation during an ice-shed event where the compressor recovers to its dry state after ice-shed. The maximum temperature drop increases along the compressor and the recovery rate is faster for rear stages as compared to front stages. This is primarily due to the reason that ice particles move slower in front stages as compared to rear stages and hence the recovery rate trend. This observation is consistent with 82% Nc trend as shown in Fig. 6(b). Figures 12(a) and 12(b) show the transient ice-shed response on the steady state compressor maps for front and back stages

static pressure response at each stage inlet with respect to time for SH25 = 10% and ice-shed duration of 10 ms. The pressure drop is highest for middle stages and the overshoot during recovery to dry state is highest for stage 6. Pressure at stage 10 inlet is higher from its dry value during the transient which is different from the transient behavior observed for the ice-shed at 82% Nc. Figure 11(a) shows the stage-wise temperature variation during continuous ice-ingestion. The trend is predictable with temperature drop increasing from front to rear stages. This temper-

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(a) SH25 = 8%, continuous ice ingestion (a) SH25 = 8%, continuous ice ingestion

(b) SH25 = 10%, ice-shed duration = 10 ms (b) SH25 = 10%, ice-shed duration = 10 ms

FIGURE 10. Transient static pressure (PS) change along the compressor for continuous ice ingestion and ice-shed event. Compressor operating at 65% Nc.

FIGURE 11. Transient total temperature (TT) along the compressor for continuous ice ingestion and ice-shed event. Compressor operating at 65% Nc.

respectively. The red circle on the plots show the dry operating point. Similar trend as observed at 82%Nc in Fig. 7 is obtained. The SH25e at HPC inlet is calculated for all runs using the steady energy balance Eq. 12 and the values are listed in table 4. The SH25e values correspond to maximum T3 drop observed during the transient. As seen in table 4, the SH25 is overpredicted from energy balance equation at 65% Nc, a similar observation was made at 82 %Nc. It can be seen that SH25e for run 1 is higher than other runs but the compressor doesn’t stall. The steady ice-ingestion results in gradual drop in T3 thus allowing stages to re-match without stalling. Run 4 and 5 give

similar numbers for SH25e but run 5 stalls while run 4 does not. Therefore, the transient behavior provides us better insight in determining stall characteristics.

CONCLUSIONS The paper presents the numerical study of transient compressor response in case of icing events at different compressor speeds. Compressor stages re-match to operate at a reduced stall

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TABLE 4. SH25e calculated from energy balance across compressor for icing simulations at 65% Nc

Run No.

SH25

%T3 drop (Maximum)

SH25e (Eq. 12)

1

8

26

25.69

2

10

22

20.24

3

10

23

21.98

4

10

23

22.28

5

10

24

22.28

6

12

24

22.88

(a) Front stages of axial compressor

in determining the TWC in convective clouds but the estimation can significantly vary if the transient T3 drop is due to an instantaneous icing event. The present lower-order model is able to capture the key icing physics and the transient compressor behavior well within model simplifications. Compressor operates at much higher front stage loading near take-off conditions. An ice-shed analysis near design point can be performed to evaluate compressor operability range near cruise conditions where icing events are more probable. Further understanding of the time scales of these events will help in determining the control response to trigger thrust loss abatement techniques. The model is capable of predicting the effect of ice particle size and shape on compressor dynamics. The effect of ice properties (rime or glaze) and its temperature can be incorporated in a future study.

(b) Rear stages of axial compressor

FIGURE 12. Transient compressor stage wise matching in case of ice-shed at 65%Nc, optimal operating point recovered after humid air leaves the compressor. SH25 = 10%, ice-shed duration = 10 ms. Black squares track the dynamic compressor response. Red circles show the dry operating point.

ACKNOWLEDGMENT Authors would like to acknowledge the contributions made by Reema Kundu (Georgia Tech.) and J V R Prasad (Georgia Tech.) in development of the icing solver. Technical discussions with Peter Szucs (GE Aviation) are greatly appreciated. Authors wish to thank the General Electric Company for giving permission to publish this paper. This work has been funded by GE Aviation.

margin and reduced efficiency under wet conditions making it susceptible to stall in an ice-shed event. Simulations have been performed for different amount of ice at HPC inlet at 82 %Nc and 65 %Nc. From the present simulations, it can be concluded that the amount of ice ingested, its ingestion rate and duration have coupled effect on compressor dynamics. These parameters cannot be separately evaluated. It has been observed that compressor might be able to sustain smaller amount of ice ingested over a longer period of time as compared to instantaneous iceshed event with larger amount of ice entering the compressor. The steady energy balance across the compressor can be useful

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