Modeling of Compressor Performance Deterioration Due to Erosion *

This paper presents the results of a simulation of compressor performance deterioration due to blade erosion. The simulation at both design and off-design conditions is based on a mean line row by row model, which incorporates the effects of blade roughness and tip clearance. The results indicate a pronounced effect of blade erosion on the compressor adiabatic efficiency and a lesser effect on the pressure ratio. The loss in performance is mainly caused by the increased blade surface roughness and was highest at 100% speed.


INTRODUCTION
Aircraft engines are often exposed to ingestion of sand or runway gravel, causing the erosion of fan and compressor blades. This leads to increased blade surface roughness and tip clearances with a subsequent degradation in performance [Hamed, Tabakoff and Wenglarz (1988), Tabakoff (1988)].
In addition severe erosion damage can change the blade leading edge characteristics and reduce the blade chord, which can further deteriorate the performance Tabakoff (1983, 1984), and Batcho, Moller, Padova and Dunn (1987)].
Several investigators have developed performance deterioration models for compressors based on the "stage stacking" method. In this approach changes were introduced in the individual corn-This paper was originally presented at ISROMAC-6. Corresponding author.
pressor stage characteristics to reflect the effects of erosion [Batcho, Moller, Padova and Dunn (1987), Tabakoff, Lakshminarasimha and Pasin (1990)], and fouling [Muir, Saravanamutto and Marshall (1989), Aker and Saravanamutto (1989)] on the stage pressure, work and efficiency. Using thin airfoil theory, Batcho et al. [1987] modeled the reduction in a compressor stage pressure ratio due to the increased tip clearance and reduced chord caused by erosion, and compared their predictions with experimental results for dust eroded aircraft gas turbine engine. Tabakoff et al. [1990] Milner et al. (1975) to include the effects of chord reduction due to erosion. The results showed that erosion caused both pressure and mass flow rate to decrease, this reduction was found to be a function of both the compressor speed as well as the location of th stage where erosion occurred.
In general, the individual stage characteristic curves which are required in the "stage stacking" method are not available in the open literature. Therefore in the present investigation, a mean line method was developed to model the effects of erosion on compressor performance. Mean line methods are based on resolution of velocity triangles for each blade row and the application of loss correlations to establish the pressure and temperature rises through the stage [Casey (1987), Miller and Wasdell (1987)]. In the present investigation the effects of increased surface roughness and tip clearance due to erosion are introduced into the loss model. This model could generally be applied to predict the compressor stage performance, given the blade inlet and exit metal angles, blade stagger, camber, chord, solidity, thickness to chord ratio, and hub and tip diameters.

MODEL DESCRIPTION
The mean line performance model is based on the use of empirical correlation's for the incidence and deviation angles and pressure losses, which are separated into, profile, annulus, secondary and tip clearance losses [Casey (1987), Miller and Wasdell (1987)]. In the present study the NASA SP-36 [Johnsen and Bullock (1965)] correlation is used for incidence angle and Carter's model [Horlock (1973)] is used to calculate the flow deviation angle.
The loss model developed by Koch and Smith [Koch and Smith (1976)] is used for design point operation, whereas Swan's method [Swan (1961)] is used for off-design loss predictions. It is assumed that the secondary losses are not affected by erosion and are given by following equation [Horlock (1973)]: as (0.072/cr) (cos 2 2/COS/3m) (tan 2 tan 1 )2.

EFFECT OF INCREASED SURFACE ROUGHNESS
Balan and Tabakoff Tabakoff (1983, 1984)] conducted an experimental study in which they measured compressor cascades and single stage compressor performance after various amounts of sand were ingested. Both the cascade and compressor performance deteriorated with increased sand ingestion. They attributed the loss of performance to the following changes, which were characterized in their reported results:  (1983,1984) indicated an initial sharp rise in cascade losses with increased sand mass ingestion up to 0.10Kg/cm2, then the losses remained practically unchanged up to a sand mass ingestion of 0.32 Kg/cm2, before increasing sharply again. The following correlation for drag on a fully rough flat plate [Mills and Hang (1983)] was used to model the effects of increased surface roughness in the calculation of the profile losses due to the boundary layer development on the blade surface.
Cd (2.625 0.618 loge(ks/c)) -257. (2) The equivalent sand grain roughness, ks was taken to be equal to 6.2 times the center line average roughness [Koch and Smith (1976)], and the center line average surface roughness of smooth blades was taken as Ra=0.371 lam [Kramer and Smith (1978)]. The contribution of the surface roughness to the profile loss is calculated from the following relation: CO CdCr(cos/1)2/(COS/m) 3. (3)

EFFECT OF INCREASED TIP CLEARANCE
The loss in efficiency due to increased tip clearance is modeled using the empirical correlation of Lakshminarayana (1970). The increase in the rotor tip clearance due to erosion was taken to be equal to 1% of the blade height based on the experimental data of Balan and Tabakoff (1984).
In the model, the flow conditions at the blade row exit are iterated from the assumption of an initial exit axial velocity and the upgraded loss calculations. The exit conditions of each blade row constitute the input conditions to the next blade rOW.

RESULTS AND DISCUSSIONS
The compressor performance simulation were performed for a single stage axial compressor with NACA 65 airfoils. The performance parameters for stage 23B-20 of Britsch et al. (1979) Figure 3 shows the effects of increasing blade surface roughness on the stage pressure ratio. The model predicts a small drop in the pressure ratio at 100% and 90% speeds that diminishes at 70% speed. Figures 4 and 5 are expanded views of the pressure ratio plotted against the mass flow rate for 100% and 90% speeds. As seen in both these figures the loss in pressure ratio increases with increased mass flow and can reach 0.5% in the case of surface roughness corresponding to moderate erosion (case A). Figures 6 and 7 present the effect of surface roughness on adiabatic efficiency. One can see that the roughess has a far greater effect, on I. 00 FIGURE 3 Effect of surface roughness on pressure ratio. Economic and environmental factors are creating ever greater pressures for the efficient generation, transmission and use of energy. Materials developments are crucial to progress in all these areas: to innovation in design; to extending lifetime and maintenance intervals; and to successful operation in more demanding environments. Drawing together the broad community with interests in these areas, Energy Materials addresses materials needs in future energy generation, transmission, utilisation, conservation and storage. The journal covers thermal generation and gas turbines; renewable power (wind, wave, tidal, hydro, solar and geothermal); fuel cells (low and high temperature); materials issues relevant to biomass and biotechnology; nuclear power generation (fission and fusion); hydrogen generation and storage in the context of the 'hydrogen economy'; and the transmission and storage of the energy produced. As well as publishing high-quality peer-reviewed research, Energy Materials promotes discussion of issues common to all sectors, through commissioned reviews and commentaries. The journal includes coverage of energy economics and policy, and broader social issues, since the political and legislative context influence research and investment decisions.