Numerical Analysis of the Tip Leakage Flow Field in a Transonic Axial Compressor with Circumferential Casing Treatment

Numerical Analysis of the Tip Leakage Flow Field in a Transonic Axial Compressor with Circumferential Casing Treatment G. Legras 1, N. Gourdain 2 and I. Trebinjac 1 1. LMFA Ecole Centrale de Lyon / Université Lyon 1 / INSA, 69134, Ecully, France. 2. CERFACS, Computational Fluid Dynamics Team, 31057, Toulouse, France. The current paper reports on numerical investigation aimed at advancing the understanding of the influence of circumferential casing grooves on the tip leakage flow and its resulting vortical structures in a transonic axial compressor rotor near stall operating point. The results and conclusions are based on steady state 3D numerical simulations of the well-known compressor NASA Rotor 37. The numerical simulations carried out on the casing treatment configuration reveal an important modification of the vortex topology at the rotor tip clearance. Circumferential grooves limit the expansion of the tip leakage vortex perpendicular to the blade chord, but generate a set of several secondary tip leakage vortices due to the interaction with the leakage mass flow. Based on these observations, a closer look into the tip leakage properties has been carried out. Keywords: transonic axial compressor, casing treatment, circumferential groove, tip leakage vortices. Introduction The continuing design trend toward increased thrust-toweight ratio engines has led to highly loaded compressors with greatly reduced blade and stage count. With increased blade loading, it is critical to maintain a suitable operating range. Engine designers use a large surge margin which is detrimental regarding efficiency and pressure ratio at nominal operating point. For transonic compressor rotors, the tip leakage flow is known to be responsible for the occurrence of instabilities such as rotating stall or surge inception. It rolls-up into a tip leakage vortex which disturbs the main flow, especially at highly loaded operating points. Indeed, several experimental and numerical studies have shown that the tip leakage vortex interacts with the endwall boundary layer and the shockwave in the passage [1,2,3]. The abrupt change of the core vortex downstream the shock-wave somewhat corresponds to a vortex breakdown which blocks the passage flow near the tip gap region. Casing treatments, which consist of slots, grooves or cavities within the rotor casing, are commonly known to have the potential of bringing substantial stability and surge margin improvement. A large number of casing treatments have been investigated: slot-type [4], selfrecirculating bridge [5]. Among them, casing grooves are one of the simplest axisymmetric configurations since they are often viewed as a way of recovering surge margin during the starting phase of a compressor. The basic idea generally advocated for employing circumferential grooves is to provide a means for the fluid to exit the flow path where the blade loading is severe and the local pressure high. The fluid migrates circumferentially, and re-enters the flow path at a location where the pressure is more moderate [6]. The beneficial action on the surge margin decrease has been based on the fact that grooves block or weaken the rolling-up mechanism of the tip leakage vortex resulting on a delay of the vortex breakdown [7] and a reposition further towards the blade trailing edge. The vortex swirl rate then decreases and the vortex breakdown can potentially be avoided. Moreover, the effectiveness of grooves can be measured by how much they reduce flow incidence on the pressure side of the leading edge [7]. A different point of view proposed by Shabbir and Adamczyk [8] showed that circumferential grooves generate axial force due to a radial transport of axial momentum that partially balances the net axial pressure force at the casing in the tip gap region. The purpose of the current investigations aimed at advancing the influence of the tip clearance vortices topology and the tip leakage flow properties induced by circumferential casing grooves on the transonic axial compressor NASA Rotor 37. Compressor model Investigated compressor rotor The present numerical investigation was performed in the transonic compressor NASA Rotor 37. This rotor has been chosen for this investigation since it is known for the occurrence of blade tip located rotating stall phenomena at operating points close to surge [4]. Hence, this rotor is suitable for a successful application of casing treatments. The specification of the rotor is summarized in Table 1. Extensive CFD results and comparison with experiments may be found in references [9]. Investigated casing treatment The investigated casing treatment consists of six circumferential grooves. The first groove starts at around 5% upstream of the rotor leading edge. Each groove is 3mm wide (10.9% of rotor tip axial chord) with a gap of 1.5 mm between each groove. The height to width ratio is 0.7:1. The area covered by casing treatment represents

81.5% of the rotor tip axial chord. Number of blades 36 Tip radius at leading edge 252 mm Aspect ratio 1.19 Hub-tip radius ratio 0.70 Tip solidity 1.288 Tip clearance 0.356 mm Rotational speed 17188.7 rpm Tip speed 454 m/s (17188.7 rpm) Total pressure ratio 2.106 Mass flow (corrected) 20.19 kg/s Choke mass flow 20.93 kg/s Table 1. Design parameters of the NASA Rotor 37. Numerical model and boundary conditions In order to save computational time, a single-passage, steady analysis is carried out both with and without casing treatment. This simplification is based on the assumptions that the flow is identical within all the 36 blade passages. All results presented in this paper are performed with the elsa software [10] developed by ONERA and CERFACS which solves the 3D Reynolds-Averaged Navier-Stokes (RANS) equations using a cell-centered finite volume approach on multi-block structured meshes. The code also allows for the use of the chimera method to account for complex geometries such as technological effects found in turbomachinery. Computations are run with a 2 nd order centered Jameson scheme for the estimation of convective fluxes. The time marching algorithm is performed by a backward Euler scheme coupled with LU decomposition, the SSOR technique and scalar dissipation. The two-equation model proposed by Wilcox based on a k-ω formulation is used to model turbulence. Moreover, the compressor flow is assumed to be fully turbulent (R e ~ 5.10-6 ). Concerning the boundary conditions, a spatial periodicity is applied on the lateral faces. An axial injection boundary condition is used upstream and a throttle condition coupled with a simplified radial equilibrium is applied downstream. At solid boundaries, an adiabatic wall condition is imposed. Meshing strategy Meshing used for this rotor is based on a multi-blockstructured strategy. Two meshes were generated. The first one corresponds to the smooth wall configuration (1.56 million points) and is based on a O3H topology. The mesh used for the casing treatment configuration is based on the smooth wall mesh at which chimera blocks, modelling the casing grooves, has been added (2.26 million points). The computational grid employed in the simulations is illustrated in Figure 1. Both meshes have 89 grid points in the span-wise direction with 25 grid points in the tipclearance gap (excluding grooves). In the blade-to-blade direction, 41 grid points are used. The tip region is discretized with an O-H type mesh. The casing grooves were meshed using H chimera blocks. The mesh is stretched towards the solid boundaries in order to reach a resolution of y + lower than 1. Figure 1. Computational grid (every 2 nd nodes) for NASA Rotor 37 (top left), close to the leading edge (right) and details of the chimera block of the casing treatment (bottom left). Results and Discussion Validity of numerical simulations Measured and calculated performances at design speed are presented in Figure 2 for both the smooth wall and the casing treatment configurations over the experimental operating range. The numerical simulations of the smooth wall case represent the measured characteristics fairly well, with a good agreement for the pressure ratio. Simulations and experiments locate the operating point of maximum efficiency at the same normalized mass flow. However, the simulation under-predicts the overall efficiency too low (up to 1.5 percent of maximum efficiency). Results of blade-to-blade and radial distributions are in good agreement with the experiment (not presented in the paper). Therefore, it was considered that the numerical model is able to reveal all important flow mechanisms occurring in the tip clearance flow field which are essential for understanding the influence of casing treatments. Regarding the performances of the casing treatment configuration, results show insignificant differences with the smooth wall case. The aim of the present paper is to highlight the vortical mechanisms induced by circumferential grooves. For that purpose, the last stable point which has been experimentally measured has been chosen for comparisons between the smooth and the casing treatment cases. Therefore, the changes in overall performances induced by the grooves are not investigated here.

Proceedings of the 9th International Symposium on Experimental and 0,90 2,18 0,89 2,14 Isentropic efficiency Total pressure ratio 2,16 2,12 2,10 2,08 2,06 2,04 2,02 2,00 Experimental data 1,98 Smooth wall Casing treatment 1,96 19,0 19,5 0,88 0,87 0,86 0,85 0,84 0,83 20,0 20,5 21,0 0,82 19,0 Mass flow (kg/s) 19,5 20,0 20,5 21,0 Mass flow (kg/s) Figure 2. Comparison between the measured and the computed compressor maps for the solid wall case and the casing treatment case at design speed. Analysis of the tip clearance vortices topology at the measured stall point It is crucial to identify the vortex structure for the purpose of revealing details of the tip clearance flow field in the compressor rotor. To match this goal, the q-criterion (eq. 1) and the relative helicity H (eq. 2) are chosen for the vortices detection. q= ( 1 2 Ω S 2 2 ) destructuration leads to the large blockage effect near the tip in the rotor passage which deflects the main flow to the neighboring channel. This result has been notably shown by Wilke et al. [4]. A secondary vortex noted T2 in Figure 3.a. is generated by the interaction of the tip leakage vortex with the casing boundary layer. This induced vortex develops close to the beginning of the tip leakage vortex and is parallel to it until it interacts with the shock-wave with more moderate impact than the tip leakage vortex T1. A third vortex T3 can also be observed at the suction side and is generated by the interaction of the passage shock with the suction side boundary layer. It disconnects from the blade around 55% of the blade chord. (1), where Ω and S represent respectively the symmetric and antisymmetric parts of the velocity gradient tensor. rr (2), H = ξ.w r r where ξ and w denote respectively vectors of the relative vorticity and the relative flow velocity. The magnitude of the helicity H can assess the local zone where rotational is preponderant. Figure 3 and Figure 4 show a blade-to-blade view at 96% of the rotor blade span of the q-criterion and helicity for both smooth wall and casing treatment simulations. It can be observed in the smooth wall simulation shown in Figure 3.a. the formation of a main vortex, denoted T1, known as tip leakage vortex. This vortex is generated by the interaction of the tip leakage flow (driven by the pressure gradient between the pressure and the suction sides at rotor blade tip) and the incoming flow. Then, the tip leakage flow rolls-up into a longitudinal vortex, rotating in the opposite blade rotation (red region of helicity in Figure 4.a.). It develops close to the leading edge, but detaches further on from the suction side. The vortex is then linearly carried out in the channel by the main flow with a trajectory angle relative to the blade s camber line around 16 and is continuously provided in fluid by the tip leakage gap. It moves towards the pressure side of the neighboring blade until it interacts with the bow shock-wave detached from the leading edge [4]. Then, the vortex core structure abruptly expands downstream of the shock-wave which is highlighted by the deficit of helicity (Figure 4.a.). This observation corresponds to some features of a bubble vortex breakdown. This a) Smooth casing b) Casing treatment Figure 3. q-criterion cartographies with relative Mach number contours noted at 96% of the rotor blade span. a) Smooth casing b) Casing treatment Figure 4. Helicity cartographies noted at 96% of the rotor blade span. Concerning the casing treatment simulation, Figure 3.b. shows a more complex vortex topology at the rotor tip clearance than the smooth wall case. The results highlight the development of the tip leakage vortex T1 close to the leading edge, in agreement with the results found on smooth casing configuration. However, the trajectory angle relative to the blade s camber is reduced to 13.7. It can be explained by a less intensive tip leakage flow which limits the expansion of the vortex T1 perpendicular to the blade chord. One assumption concerning the decrease in intensity could be attribute to a new distribution of the leakage flow momentum along the blade chord due to local augmentation of the tip gap surface (smooth tip gap surface S1 + cavities surface S2 in

Figure 5) compared to the smooth casing configuration. This will be further investigated in the next section. Further in the channel, the vortex T1 interacts with the blade passage shock leading to the occurrence of a stagnation region. Moreover, Figure 3.b. shows the development of five secondary vortices noted T2_CT that do not appear on the smooth casing simulations. These vortices develop close to the blade suction side at axial positions where the 2 nd to the last casing grooves are implemented. More precisely, each vortex develops at approximately mid-distance between the grooves leading and trailing edges. Clearly, the occurrence of these vortices is related to the interaction of the grooves with the tip leakage flow. The alternation of area non-covered/covered by grooves along the axial chord leads to intensive/non-intensive tip leakage mass flow. Each discontinuity in the tip leakage mass flow leads to the development of new tip leakage vortices (the mechanisms of the T2_CT development are the same than the vortex T1). Then, the secondary vortices T2_CT are carried out by the main flow. The T2_CT vortices trajectory coming from the 2 nd to the last grooves are respectively 18, 25, 25, 15 and 13.7 (Figure 3.b). In consequence, the first four secondary vortices interact with the main vortex T1 whereas the last one is transported in the channel. It can also been observed in Figure 3.b. that the 3 rd secondary vortex is much larger than the others due to the dual effect of the 4 th groove s influence and the interaction between the shock-wave and the boundary layer of the suction side. A third type of vortex noted T3_CT in Figure 3.b. develops in the middle of the blade-to-blade leading edge distance. The position of this vortex suggests that it is generated by the interaction between the first groove and the casing boundary layer. Driving mechanisms In order to understand the driving mechanisms of the casing grooves leading to strong modification of the tip flow field, it is helpful to analyze the important properties of the tip leakage flow inside the gap with and without casing treatment. A pressure-based phenomenon Since the tip leakage flow is mainly seen as a pressure driven phenomenon, it is interesting to compare the distribution of static pressure inside the rotor tip gap (Figure 6) in combination with the evolution of leakage mass flow along the tip chord length (Figure 7) in order to quantify the groove s impact on the leakage flow intensity. In fact, it is well known that higher the pressure difference is the more intensive the tip leakage flow will be. For convenience, the integration of the leakage mass flow in Figure 7 is done on the S1 surface (Figure 5). For the smooth casing configuration, after a short transient phase at the leading edge of the rotor blade an almost constant pressure difference (around 40000 Pa) between the pressure and suction side establishes over 45% of the tip chord length resulting in a constant leakage mass flow (around 1.15 10-4 kg.s -1 ). After the shock, at around 50% of the tip chord length, this pressure difference then disappears leading to a decrease in the tip leakage mass flow. The total leakage mass flow passing through the tip gap is around 6.10-3 kg.s -1. Figure 5. Surfaces considered for the tip leakage mass flow estimation. a) Local tip leakage mass flow. Figure 6. Distribution of static pressure at mid-gap over the tip axial chord. b) Evolution of tip leakage mass flow over the tip axial chord. Figure 7. Comparison of the tip leakage mass flow computed on the S1 surface (Figure 5). Regarding the casing treatment configuration, results in Figure 6 and Figure 7.a. show a strong influence of the circumferential grooves with an oscillating behavior of the distribution of pressure and leakage mass flow compared to the smooth wall solution. In Figure 6, the static pressure on the pressure side oscillates around the smooth wall solution. Maximums of static pressure occur at the grooves leading edge whereas minimums are located at the grooves trailing edge. At suction side, static pressure oscillates in phase around a mean value higher than the smooth wall solution. In consequence, casing grooves are capable to significantly reduce the pressure difference along the tip chord compared to the smooth casing case. In this casing treatment configuration, it results in a large reduction by 21.3% of the cumulated tip leakage mass flow over the S1 area (Figure 7.b.). Moreover, the leakage mass flow oscillates with a phase displacement along the blade tip chord (Figure 7.a.) around a mean value decreased by 25% compared to the

smooth wall solution. The amplitudes of oscillations are all the more high that the pressure difference of the smooth wall solution is great. Before the shock-wave, the tip leakage mass flow covered by the 2 nd to the 4 th grooves oscillates around a mean value of 8.5 10-5 kg.s -1 (-26% compared to the smooth wall solution) with amplitudes of 3 10-5 kg.s -1 (corresponding to 35% of this mean value). After the shock, results clearly show a moderate impact of the two last grooves compared to the others: the leakage mass flow oscillates around a mean value of 7 10-5 kg.s -1 (- 24% compared to the smooth wall case) with amplitudes of 1 10-5 kg.s -1 (15% of this mean value). Minimums of leakage mass flow are located at mid-gap of each groove, which confirms the previous observation that leakage mass flow discontinuities lead to the development of secondary vortices (T2_CT). Maximums of leakage mass flow are located between two consecutive grooves and reach the smooth wall solution. To sum up, in areas which are not covered, the tip leakage develops like in the untreated case: the leakage mass flow is intensive with the same magnitude than the smooth wall case (Figure 7.a.). However, in areas which are covered by grooves, the leakage mass flow is distributed over a higher surface (increased in the radial direction compared to the smooth wall case) leading to a decrease of the mass flow intensity through the S1 surface. Based on the previous observations, the grooves impact clearly depends on the static pressure distribution of the smooth wall configuration and the grooves dimensions. Since the tip leakage intensity is known to be related to the momentum through the tip gap (especially in the tangential direction), it is interesting to analyze the momentum distribution through the gap in order to connect with the change in leakage mass flow. Comparisons of the momentum distributions Figure 8 presents the comparison of the momentum along the blade tip axial chord for both configurations. For the smooth wall configuration, it clearly appears that the global momentum (Figure 8.d.) is mainly driven by the tangential component of the relative velocity (Figure 8.b.). After a short transient phase at the leading edge of the rotor blade, the tangential momentum reaches a constant value over 45% of the tip axial chord length, in agreement with the constant value of pressure difference observed in Figure 6. Moreover, the leakage flow is mainly supersonic in this area. After the shock at 50% of the axial chord length, the tangential momentum reaches a lower constant values resulting from the pressure difference decrease. The tip leakage flow then becomes subsonic. Regarding the radial momentum, results in Figure 8.a. show low positive value whereas axial momentum is mainly negative (Figure 8.b.). Furthermore, results suggest that the tip leakage flow is directed in the opposite axial direction to the main flow before passing the shock whereas it turns more perpendicular to the main flow after the shock. a) Radial momentum b) Tangential momentum c) Axial momentum d) Global momentum Figure 8. Comparison of the momentum along the tip axial chord for the smooth wall and the casing treatment simulations. As in the smooth wall case, the leakage flow in the casing treatment configuration is mainly driven in the tangential direction (Figure 8.b. and Figure 8.d). However, the tangential momentum oscillates in phase with the pressure distribution. High level of tangential momentum occurs at the groove leading edge where peaks of static pressure are great compared to the mean value, whereas lower levels are located at the groove trailing edge. From results shown in Figure 8.b., peaks of tangential momentum are the greatest at the 3 rd and 4 th grooves trailing edge. This leads to intensive mass flow momentum which is in agreement with the large trajectory angle (25 ) of the secondary vortices. In contrary, the 2 nd, 5 th and 6 th grooves, peaks are moderate which results in lower angle values (18, 15 and 13.7 ). Concerning the radial direction of the momentum (Figure 8.a), grooves annul the mean impact along the tip chord. Indeed, it oscillates around a mean value of 0 in the envelope defined by the radial momentum of the smooth wall case solution and in the opposite phase observed in the tangential momentum. Maximums reach values of the smooth wall solution, whereas minimums reach the opposite value of maximums. In combination with the analysis on the static pressure, it seems that fluid enters the grooves near the grooves trailing edge at blade pressure side, and re-enters in the flow path at suction side at position near the grooves leading edge. Between two consecutive grooves, the radial momentum decreased linearly. Regarding the axial momentum, grooves are able

to significantly decrease the magnitude level compared to the smooth wall case. The axial momentum oscillates in phase with the leakage mass flow: maximums reach values around 0 whereas minimums reach the smooth wall solution. Compared to the smooth wall solution, grooves modify the direction of the leakage flows: in area covered by grooves the leakage flow is directed more perpendicular to the main flow whereas the tip leakage behavior is the same as the smooth wall case in area not covered. Entropy level A good representation of the main impact of grooves in terms of losses is obtained through the entropy. Comparison of the circumferential averaged solution of entropy for both the smooth wall and the casing treatment configurations (not presented) has shown insignificant difference except near the tip gap region. Figure 9 presents the relative difference of entropy between the two cases near the blade rotor tip. A small region of higher entropy production (0.5% of relative difference) appears in the casing treatment solution. This zone is located at 99% of the rotor blade span and expands from the 2 nd to the 4 th grooves. This production of higher entropy can be related to the interaction of the secondary vortices T2_CT with the main tip leakage vortex T1 and also to the interactions of the detached shock and the casing boundary layers with the 1 st groove. In contrary, the two last grooves have a moderate impact on the leakage flow and thus a small influence on the entropy production. Figure 9. Comparison of the relative difference of entropy production near the blade tip region between the meridional smooth wall and the casing treatment solutions. Conclusion A numerical investigation has been made to examine the effect of six circumferential grooves on the tip leakage flow at operating condition close to surge of the transonic compressor NASA Rotor 37. An analysis of the tip clearance vortices topology reveals that grooves limit the expansion of the tip leakage vortex perpendicular to the blade chord by reducing the momentum involved in its rolling-up mechanisms. This observation explains the delay of the rotating stall onset currently observed with this kind of casing treatment geometry. This analysis also highlights the occurrence of secondary tip leakage vortices developing at mid-distance between the grooves leading and trailing edges. A comparison of distributions of static pressure and flow momentum through the tip gap has been carried out for both configurations in order to quantify the grooves impact. The analysis reveals that grooves significantly reduce the pressure difference across the tip gap leading to a favorable reduction of the tip leakage mass flow involved in the rolling-up process of the tip leakage vortex. Moreover, grooves impact is all the more important that the pressure difference between the suction and pressure surfaces in the smooth wall solution is great. Such considerations are based on an inviscid approach, and the effects of 3D boundary layer separation have to be taken into account for a deeper analysis which is currently done in order to find reliable guidelines which help to dimension circumferential grooves for a specific compressor. References [1] Yamada K., Funazaki K. and Furukawa M. The Behavior of Tip Clearance Flow at Near-Stall Condition in a Transonic Axial Compressor Rotor, Proceedings of ASME Turbo Expo, paper 2007-27725, 2007. [2] Hofman, W., and Ballmann, J. Tip Clearance Vortex Development and Shock-Vortex Interaction in a Transonic Axial Compressor Rotor. AIAA 2002-0083, 2002. [3] Hoeger, M., Fritsch, G., and Bauer, D. Numerical Simulation of the Shock Tip Leakage Vortex Interaction in a HPC-Front Stage. ASME J. Turbomachinery, 120, pp. 131-140, 1998. [4] Wilke I., Kau H.-P. and Grignole G. Numerically aided Design of a High-Efficient Casing Treatment for a Transonic Compressor. Proceedings of ASME Turbo Expo 2005, paper GT2005-68993, 2005. [5] Hathaway M. Self-Recirculating Casing Treatment Concept for Enhanced Compressor Performance. Proceeding of ASME Turbo Expo 2002, paper GT2002-30368, 2002. [6] Wilke I.and Kau H.-P. A Numerical Investigation of the Influence of Casing Treatments on the Tip Leakage Flow in a HPC Front Stage. Proceedings of ASME Turbo Expo 2002, paper GT2002-30642, 2002. [7] Rabe D.C. and Hah C. Application of Casing Circumferential Grooves for Improved Stall Margin in a Transonic Axial Compressor. Proceedings of the ASME Turbo Expo, GT-2002-30641, 2002. [8] Shabbir A. and Adamczyk J.J. Flow Mechanism for Stall Margin Improvement due to Circumferential Casing Grooves on Axial Compressors. Transactions of the ASME, Vol. 127 pp. 708-717, 2004 [9] Dunham J. ed. 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