Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Compressor

Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows Lyon, July 2007 ISAIF8-0093 Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Comressor Masaya Suzui, Kazuai Inaba and Maoto Yamamoto Deartment of Mechanical Engineering, Toyo University of Science, 1-14-6, Kudanita, Chiyoda-u, Toyo, 102-0073, Jaan Sand erosion is a henomenon where solid articles iminging to a wall cause serious mechanical damages to the wall surface. This henomenon is a tyical gas-article two-hase turbulent flow and a multi-hysics roblem where the flow field, article traectory and wall deformation interact with among others. On the other hand, aircraft engines oerating in a articulate environment are subected to the erformance and lifetime deterioration due to sand erosion. Esecially, the comressor of the aircraft engines is severely damaged. The flow fields of the comressor have strongly three dimensional and unsteady natures. In order to estimate the deterioration due to sand erosion, the sand erosion simulation for a comressor is required under the consideration of the rotor-stator interaction. In the resent study, we aly our three dimensional sand erosion rediction code to a single stage axial flow comressor. We numerically investigate the change of the flow field, the article traectories, and the eroded wall shae in the comressor, to clarify the effects of sand erosion in the comressor. Keywords: sand erosion, axial comressor, rotor/stator interaction, comutational fluid dynamics Introduction The basic researches for sand erosion henomena started centering on Germany in 1930's. Finnie attemted the theoretical analysis on sand erosion, based on the Hertz s contact theory [1]. However, Finnie's model cannot exactly redict the weight loss in high angle imact. Then, Bitter suggested the mechanism of sand erosion which consists of deformation wear and cutting wear [2, 3]. Bitter's model gives the sufficient rediction in any iminging angle for both of the ductile and brittle materials, but this model is too comlex to easily aly for industrial machines. Therefore, Neilson and Gilchrist modified the model to aly for ractical calculation based on Bitter's concet [4, 5]. On the other hand, aircraft engines oerating in a articulate environment are subected to the erformance and lifetime deterioration due to sand erosion. Esecially, the comressor of the aircraft engines is severely damaged. Balan and Tabaoff [6] erformed the exerimental study of sand erosion henomena on a single stage axial flow comressor, and found severe erosion on the leading edge and ressure side of rotor blades, with the increased surface roughness. In recent years, sand erosion henomenon has been simulated numerically to rotect industrial machines from the mechanical damage. In these simulations, however, the change of the flow field and the relating article traectory during the erosion rocess were not taen into account. This treatment is hysically unrealistic. Hence, Masaya Suzui: Graduate Student htt://www.lmfa.ec-lyon.fr/isaif8/

2 Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows we have develoed the numerical rocedure for sand erosion henomenon, including the temoral change of the flow field and the wall shae [7]. This numerical code was successfully alied to a 90-degree bend [8], article searator [9], turbine stator blade [10], and so on. The flow fields in these studies are steady, but the flow field in a comressor has strongly unsteady characters by rotation of the rotor blades. Therefore, it is essential to consider the unsteadiness. In the resent study, we aly our three dimensional sand erosion rediction code to a single stage axial flow comressor. We numerically investigate the temoral change of the flow field, the article traectories, and the eroded wall shae in the comressor, to clarify the effects of sand erosion. Nomenclature C D drag coefficient Gree letters C secific heat at constant ressure α iminging angle D diameter α 0 attac angle at which the tangential comonent of e total energy the reflection velocity comes to be zero F drag force δ Kronecer delta turbulent inetic energy ε turbulent dissiation rate K maximum article velocity at which the collision still is urely elastic φ energy needed to remove unit weight from wall by cutting wear l c eroded cavity length µ viscosity coefficient M mass ν inetic viscosity coefficient n material arameter decides α 0 ρ density static ressure ψ P roduction rate of Pr Prandtl number Ω vorticity Re Reynolds number S strain rate Subscrits t time C cutting T static temerature D deformation U velocity f fluid V iminging velocity article W eroded weight t turbulent x Cartesian coordinate T total energy needed to remove unit weight from wall by deformation wear Numerical Procedures The comutational rocedures for the rediction of sand erosion henomenon are as follows: (1) Calculate the turbulent flow field (2) Calculate the article traectories (3) Judge the collisions against a wall (4) Estimate the amount of erosion (5) Change the wall shae (6) Return to (1), if the wall shae is changed. These rocedures are reeated iteratively, until the comutational time reaches the rescribed terminal time. Normally, since the sand erosion henomenon needs a long eriod, and the time scale is much longer than that of the flow field, the change of flow field could be regarded as a quasi-steady state. Therefore, steady state flow distributions are thought to be valid for each eroded geometry and at every instance. This means that in the resent study sand erosion henomenon is mimiced as series of quasi-steady states. However, in a comressor stage, rotor rotation brings about strong unsteadiness which must be considered. Hence, we store the data of temoral flow field corresonding to a rotor-stator blade osition, and use it to calculate article traectories. Gas-hase Numerical redictions have been carried out with a finite difference technique. The gas-hase is considered to be a continuum hase, while the article-hase is a disersed one. The article-hase that is assumed to be of low concentration has no influence on the gas-hase (i.e. one-way couling). The gas-hase flow is assumed to be three-dimensional, comressible and turbulent. It is calculated by the Eulerian aroach, based on the Favre-averaged Navier-Stoes equations (i.e. RANS aroach). The governing equations with the standard -ε turbulence model (Launder-Salding, 1974) are exressed as follows, (Continuity equation): ρ + ( ρu ) = 0 (1) t i

Masaya Suzui et al. Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Comressor 3 (Favre-Averaged Navier-Stoes equation): ( ρu ) ( ) i + ρu iu + δ i t (2) 2 = ( µ + µ ) S ρδ t i i 3 (Energy equation): ( ρe) + {( ρe + ) U } t t T = ( + ) S 2 U + C + µ (3) µ µ µ ρ δ t i i i 3 Pr Prt U U i 2 U U U i Si = + δ, i Ω i = (4) i 3 i (-ε model): µ t ( ρ) + ( ρu ) µ + σ = t (5) + ρ P ε t ( ρε ) + ( ρεu ) ( ) µ t ε = µ x x + σ ε ε + ρ ( C ε ) ε 1P Cε 2 2 U i P = υt Si δ i 3 2 υ t = C (8) µ ε where C µ = 0. 09, σ = 1. 0, σ = 1. 3, C = 1. 44, ε ε 1 C = 1.92. ρ, U,, T and e denote the averaged comonent of density, velocity, ressure, temerature and total ε 2 energy of fluid. and ε are turbulent inetic energy and its dissiation rate. Since standard -ε model excessively redict turbulence energy roduction for irrotational strain, Kato-Launder s modification (1993) was adoted. Then, P was modified as follows, ~ Ω ~ 2 2 U P = S ~ υ (9) t S 3 ( S S S S ) ~ 1 S = +, Ω ~ = 1 Ω Ω (10) i i ii i i 2 2 The governing equations were discreted using Yee-Harten s second-order uwind TVD scheme (1987) for the inviscid terms, second-order central difference scheme for the viscous ones, and 4-stage Runge-Kutta method for the time integration. Particle-hase The article-hase is treated by the Lagrangian aroach, in which articles are traced in time along their traectories through the flow field. In the resent study, (6) (7) the following assumtions are made for reducing the comutational load: Particle is sherical and non-rotating. Particle-article collision is neglected. The article-hase has no influence on the gas-hase. The force acting on a article is only a drag. Under these assumtions, the equation of the article motion is described using a relative velocity of the gas-hase to the article. du i = F( U ) fi U i U fi U i dt (11) 3C D ρ f F = 4ρ D (12) where U, ρ and D are density, velocity and diameter of a article. F denotes drag force, and the drag coefficient C D is defined by calculating the relative article Reynolds number based on the relative velocity between the gas-hase and the article as follows, 0. ( 1+ 0.15 Re ) ( Re < 1000) ( Re > 1000) 24 687 C = Re (13) D 0.4 D U U fi i Re = (14) υ where ν is inetic viscosity of gas-hase. Finally the article traectory is calculated by integrating the following equation in time with the lea flog method. Erosion estimation dx dt i = U (15) It is well nown that Finnie [1] had an imortant role to the early analysis of sand erosion. And Bitter [2, 3] suggested that sand erosion damage due to article imacts can be considered to be searate mechanisms, that is, deformation wear due to the velocity normal to the surface and cutting wear due to the tangential velocity. The total volume loss W T is the sum of the volume losses due to deformation wear W D and cutting wear W C. W = W + W (16) T D C However, since Bitter s theoretical wor is exhaustive and extremely intricate, it is too difficult to emloy his model in ractical alications. Therefore, the simler relations based on the Bitter s model were roosed by Neilson and Gilchrist [4, 5], in which the weight losses W D and W C can be rewritten as, 1 2 M ( V sinα K ) W 2 D = (17) ψ i

4 Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows 1 2 2 MV cos α sin nα 2 ( α < α ) 0 φ W C = (18) 1 2 2 MV cos α 2 ( α α ) 0 φ π α 0 = (19) 2n where M is total mass of articles, α and V are the attac angle and the iminging velocity of a article. K is the threshold value of the velocity comonent normal to the surface, below which no deformation wear taes lace. α 0 is the attac angle at which the tangential comonent of the reflection velocity comes to be zero (see Fig. 1). n is constant and deends on a surface material. ψ and φ reresent the energy needed to remove the unit weight of material from the wall by deformation and cutting wear, resectively. Using the exeriment by Neilson and Gilchrist [4, 5], these arameters were confirmed to redict sand erosion. In the resent study, the above-described Neilson-Gilchrist erosion model is emloyed because of the simlicity. However, the geometrical information of eroded surface, that is, the length and deth of the cavity removed, cannot be obtained from the Neilson-Gilchrist erosion model, because Eq. (17) and (18) describes only the weight loss of the surface material. Thus, the eroded surface geometry damaged by one article, which consists of the deformation wear (the volumes of A) and the cutting wear (that of B), is assumed as shown in Fig. 2. Considering the concet of Neilson-Gilchrist model, this assumtion is reasonable, and the modeled cavity is similar to the exerimental observation by Bitter [2, 3]. The weight losses due to deformation wear W D and cutting wear W C can be geometrically exressed as follows, using the symbols in Fig. 2, 3 3 D cos θ + 2 W = D ρπ cosθ (20) 2 3 2 D 1 W C = ρlc θ sin 2θ (21) 2 2 The following rocedure is adoted to calculate the erosion length l c. (1) W D and W C are obtained by the Neilson-Gilchrist erosion model. (2) Substituting W D into Eq. (20), θ is calculated. (3) Substituting W C and θ into Eq. (21), the erosion length l c is estimated. In order to reroduce a sand erosion henomenon in a 3-D comutational field, we suggest the erosion line aroach. In this aroach, an erosion cavity is aroximated by a line with the length l c, taing into account that the width of erosion cavity is sufficiently small, comared with the three-dimensional grid sacing on a wall surface. Figure 3 exlains our definition for an erosion line. Erosion line aroach is summarised below. (1) Erosion line l c is laid on the surface in the comutational domain (see Fig. 3). (2) The length occuied by each grid cell is calculated. (3) Partial weight loss is assigned in each bloc in roortion to the artial length l c (i). (4) If the artial weight loss on a bloc exceeds the critical value, the bloc in the wall dros out. The droed cell region is newly treated as the flow field instead of a solid wall. This change of the surface geometry indicates the evolution of a sand erosion henomenon. It should be noted that blocs in a wall and the weight of each bloc are set rior to a calculation. Fig. 1 Schematic of article imact against wall Fig. 2 Modeled erosion cavity Fig. 3 Erosion line aroach The comutational grid consists of two regions, that is, in a flow field and within a solid wall. The bloc height in the wall is uniform and is same as the minimum one in the flow field.

Masaya Suzui et al. Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Comressor 5 Comutational Conditions The comutations were carried out for the single stage axial flow comressor measured by Balan and Tabaoff [6]. The design secifications of the comressor are listed in Table 1. The comressor blade is NACA65 (10)-10 airfoils [11]. The comressor does not have any guide vanes, and the rotor diameter is constant for the axial direction. Figure 4 shows the schematic of the target comressor stage. The test conditions are listed in Table 2. In the resent study for the simlicity, it was assumed that the ti clearance was 0 and that the ti and hub walls rotated with rotor blades. Table 1 Design secifications Airfoil NACA65 (10)-10 Chord length 50.8 [mm] Asect ratio 0.75 Solidity 2 diameter 300 [mm] Rotating seed 9000 [rm] Pressure ratio 1.1 Mass flow rate 3.67 [g/s] using erosion model. In the rebound at end walls, article imingement is treated as erfect elastic imingement. Fig. 4 Schematic of axial flow comressor stage (a) 2D section of rotor and stator Table 2 Oeration conditions Rotating seed 5000 [rm] Inlet total ressure 1.013 10 5 [Pa] Inlet total temerature 288.15 [K] Mass flow rate 1.360-2.000 [g/s] Figure 5 lots the comutational grid used in the resent simulation. The grid numbers in the flow fields were 900,000, and those within the blade walls were 300,000. Thus, the total grid number was 1,200,000. The region around the rotor blade was comuted in relative coordinate system, on the other hand, the region around the stator blade was treated in absolute coordinate system. The boundary conditions were imosed as follows. At the inlet boundary, flow angle, total ressure and total temerature were fixed. At the exit, static ressure was secified. On the blade surfaces, non-sli and adiabatic conditions were imosed. On the end walls, sli and adiabatic conditions were used. The turbulent quantities were decided by the wall function. At the side boundaries, eriodic condition was used (comutational domain was 1 itch). The materials of solid articles and the wall were assumed to be alumina and aluminum, resectively. The article diameter was 165 µm. The total mass of the inlet articles is 25 g. In the article traectory calculation, the rebound velocity at the blade surface is estimated by (b) Rotor main grid (c) Rotor sub grid Fig. 5 Comutational grids

6 Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows Results and Discussion Change of flow field Figures 6 and 7 deict Mach number and static ressure contours at midsan of clear blades. In the case with mass flow rate of 1.75 [g/s], inlet Mach number is 0.14 and the maximum Mach number is 0.28. Consequently, these are subsonic cascade. Furthermore, inlet and outlet static ressure are resectively 9.985 10 4 and 1.025 10 5 [Pa]. As not shown here, but searation vortexes are confirmed on the rotor and stator blade root. Static temerature and turbulent inetic energy contours at midsan of clear blades are shown in Figs. 8 and 9. It is clear that the wae of rotor blade is choed by the stator blade. The develoment of the boundary layer is romoted around the region where the wae of rotor blade iminges on the stator ressure side. The fluid which has high turbulent inetic energy asses the stator blades assage eriodically. It is confirmed that reresentative rotor/stator interaction is reroduced in our comutation. Figure 10 illustrates the comarison of the vorticity contours on rotor blade ressure side before and after erosion. Since the surface of the ressure side is severely rough, as shown later, the velocity disturbances generated on the ressure side is remarable. Thus, the irregularity of vorticity becomes high after erosion. Static ressure contours at the leading edge of the clear and eroded rotor blade surface are exhibited in Fig. 11. Similarly to the vorticity, static ressure becomes nonuniform. Static ressure on the ressure surface is smaller than that of the uneroded blades, additionally. This is because the boundary layer thicness becomes thic due to the growth of surface roughness, and then the freestream velocity between the blades increases. Eroded surface Figure 12 shows the change of the blade surface due to sand erosion. Severe erosion occurs around the leading edge and on the ressure surface. The ressure side of the rotor blade suffers from severe damage over wide region esecially. The ti is severely eroded rather than the hub. On the rotor blade suction surface, a little wear is confirmed around the leading edge. And no erosion occurs on the downstream region from the mid chord. Moreover, the suction side of the stator blade ees a clear surface. These results would be affected by the interactions among iminging velocity, angle and frequency. The reasons why the eroded surface is formed will be discussed in the following sub sections. Fig. 6 Mach number contour at midsan Fig. 7 Static ressure contour at midsan Fig. 8 Static temerature contour at midsan Fig. 9 Turbulent inetic energy contour at midsan

Masaya Suzui et al. Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Comressor 7 (a) Before erosion (b) After erosion Fig. 10 Vorticity contour of the rotor blade ressure surface S.S. S.S. P.S. P.S. (a) Before erosion Fig. 11 (b) After erosion Static ressure contour of the rotor blade leading edge (a) Rotor ressure surface (b) Rotor suction surface (c) Stator ressure surface Fig. 12 Eroded surface (d) Stator suction surface

8 Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows (a) Bird eye view (b) Side view Fig. 13 Particle traectory (c) To view Particle traectories The tyical article traectories are lotted in Fig. 13. The article traectories around the rotor are shown in relative coordinate system and those around the stator are exhibited in absolute coordinate system. The colors corresond to the article seed (blac: high seed, white: low seed) in each coordinate system. Obviously, the articles reflect around the rotor blade leading edge or ressure side, and most of the inetic energy is consumed by the erosion of the first imact. The article has less inetic energy at the second imact to the suction surface, and thus the mechanical damage on the suction surface is not so severe. When the article velocity becomes small by the article-wall collision in the rotor blades assage, Coriolis and centrifugal forces are dominant, and the article raidly moves towards the ti (Fig. 13(b)). Then, the article goes through the rotor assage with the reeated imacts to the ressure and suction sides and end wall (Fig. 13(c)). On the other hand, the article inflowing into the stator has large velocity due to the rebound on the rotor blade and the rotor rotation. Therefore, most of the article imact to the leading edge of the stator blade at high seed. Note that the article dose not iminge on the downstream region from the mid chord of the ressure side. It is caused from the fact that the article has high circumferential velocity. As same as in the rotor blade assage, the article consumes its inetic energy at the first imact, and flows towards the downstream with reeated imacts to the ressure and suction sides. Imact roerties Figure 14 shows the imact frequency distribution. The imingement to blade surface concentrates around the trailing edge of the rotor blade and the leading edge of the stator blade. And the high imact frequency is found on the ressure surface of the rotor blade and the mid chord region of stator blade suction side. The imact frequency of the ti is much higher than that of the hub. This is caused by the high concentration of articles in the rotor assage due to centrifugal force (Fig. 13(b)). We defined average eroded weight, dividing the total eroded weight by the total imingement number at every grid cell on the blade surface. Figure 15 exhibits the average eroded weight distributions. In the rotor, most of the ressure surface suffers from severe damage due to one article imingement. Additionally, the leading edges of both rotor and stator blade are exosed to high damage imact. The first imact velocity is roortion to the radial osition from the axis because of the rotation, the damage of the ti is severer than that of the hub. Note that the low damage region exists at the ti of the rotor blade. Nevertheless, this does not mean the ti erosion is not severe. This results from that the rebounded article collides against the rotor ti secondarily with low velocity and high angle. Figure 16 indicates average imact velocity, and Fig. 17 illustrates imact angle. These are averaged similarly to average eroded weight. The article iminges to the ressure side of the rotor blade with high velocity. Moreover, the average imact velocity is high at the leading edge and ti. This result matches with the behavior of average eroded weight. The high angle collision occurs frequently on the suction surface of both rotor and stator blade. In addition, the high angle imingement is confirmed at the trailing edge of the rotor blade ressure side. This leads no ronounced erosion on the region. Because weight loss of ductile material at high angle imingement is smaller than that at low angle.

Masaya Suzui et al. Numerical Simulation of Sand Erosion Phenomena in Rotor/Stator Interaction of Comressor 9 (a) Rotor ressure surface (b) Rotor suction surface (c) Stator ressure surface Fig. 14 Imact frequency (d) Stator suction surface (a) Rotor ressure surface (b) Rotor suction surface (c) Stator ressure surface Fig. 15 Average eroded weight (d) Stator suction surface (a) Rotor ressure surface (b) Rotor suction surface (c) Stator ressure surface Fig. 16 Average Imact Velocity (d) Stator suction surface (a) Rotor ressure surface (b) Rotor suction surface (c) Stator ressure surface Fig. 17 Average Imact Angle (d) Stator suction surface

10 Proceedings of the 8 th International Symosium on Exerimental and Comutational Aerothermodynamics of Internal Flows Concluding Remars We carried out the numerical simulations for the sand erosion henomena in the rotor/stator interaction of the single stage axial flow comressor. Through the resent study, we obtained the following insights. (1) Since the surface of the ressure side is severely rough, the nonuniformity of the vorticity and static ressure becomes high. This changes the static ressure distribution on the blade. (2) Severe sand erosion occurs on the ressure surface and leading edge of the blades. (3) is deteriorated by sand erosion rather than hub due to high imact velocity. (4) In both of the rotor and stator blades, article-wall collisions reeatedly occur, but the first imacts are dominant and the most imortant to erosion. Acnowledgement This aer owes much to the hel of I. Mizuta and D. Kato in Ishiawaima-Harima Heavy Industries Co., Ltd. In addition, this research was artially suorted by the Ministry of Education, Science, Sorts and Culture, Grant-in-Aid for Scientific Research (C) 16560158. References [1] Finnie, I.: Erosion of surfaces by solid articles, Wear, vol.3,.87-103, (1960). [2] Bitter, J. G. A.: A study of erosion henomena art I, Wear, vol.6,.5-21, (1963). [3] Bitter, J. G. A.: A study of erosion henomena art II, Wear, vol.6,. 169-190, (1963). [4] Neilson, J. H. and Gilchrist, A.: Erosion by a stream of solid article, Wear, vol.11,.111-122, (1968). [5] Neilson, J. H. and Gilchrist, A.: An exerimental investigation into asects of erosion in rocet motor nozzles, Wear, vol.11,.123-143, (1968). [6] Balan, C. and Tabaoff, W.: Axial Flow Comressor Performance Deterioration, AIAA-84-1208, (1984). [7] Kui, J., Toda, K., Yamamoto, M.: Develoment of Numerical Code to Predict Three-Dimensional Sand Erosion Phenomena, FEDSM2003-45017, Proc. ASME FEDSM'03 4TH ASME_JSME Joint Fluids Engineering Conference, Honolulu, (2003). [8] Miyama, T., Naayama, T., Kitamura, O. and Yamamoto, M.: Numerical Prediction of Sand Erosion along Curved Passages, Proc. Third World Conference in Alied Comutational Fluid Dynamics, 27,.53-60, (1996). [9] Kui, J., Toda, K., Yamamoto, M.: Numerical Simulation of Sand Erosion Phenomena in a Particle Searator, Key Engineering Materials, 243-244,. 565-570, (2003). [10] Suzui, M., Toda, K. and Yamamoto, M., Numerical Simulation of Sand Erosion Phenomena on Turbine Blade Surface, Proc. WCCM VI in conunction with APCOM'04, Beiing, (2004). [11] Emery, J. C., Herring, L. J., Erwin, J. R. and Felix, A. R.: Systematic Two-Dimensional Cascade Tests of NACA 65-Series Comressor Blades at Low Seeds, NACA Reort 1368.