Investigation of Corner Separation in a Linear Compressor Cascade ...

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

GT2015-42902

INVESTIGATION OF CORNER SEPARATION IN A LINEAR COMPRESSOR CASCADE USING DDES 1,2

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Yangwei Liu , Hao Yan , Lipeng Lu 1. National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, P.R. China 2. Collaborative Innovation Center of Advanced Aero-Engine, Beihang University, Beijing 100191, P.R. China * Email: [email protected]

ABSTRACT Delayed Detached Eddy Simulation (DDES) method, compared with the RANS method, can more accurately predict the complexity and unsteadiness naturally associated with the compressor flow. DDES method, which incorporates a simple modification into the initial detached eddy simulation (DES) introduces kinematic eddy viscosity into turbulence model to take both effects of grid spacing and eddy-viscosity field into considerations. An attempt is made in the present paper to apply DDES for investigating the flow field in a compressor cascade. Three-dimension (3D) corner separation, which is also referred as corner separation, have been identified as an inherent flow feature of the corner formed by the blade suction surface and endwall of axial compressors. The flow visualization and the quantification of passage blockage expose that corner separation contribute most to the total passage blockage. In order to accurately predict 3D corner separation by employing CFD and increase the performance in compressor routine design by controlling such phenomenon, this paper tries to figure out its mechanism and investigate the turbulence flow field by using DDES method. Numerical simulations are conducted under different incidences in a linear PVD compressor cascade. The results show passage vortex starting at mid-chord position in cascade develops into dominant secondary vortex and obviously enhances corner separation in the PVD cascade. DDES method, which can capture intensive vortex flow and predict complicated flow at the separation region, also illustrates the corner vortex breaks into small stripe vortices which mix with the mainstream flow at the blade trailing edge. The total pressure loss is high in the corner separation region.

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INTRODUCTION Three-dimension (3D) separations, which are also referred as corner separation, have been identified as an inherent flow feature of the corner formed by the blade suction surface and endwall of axial compressors [1]. In compressors, the high loading needs more turning angle achieved in blade passage, thus the flow is much more susceptible to separate [2]. The 3D corner separation may lead to deleterious consequences, such as passage blockage, limiting on static pressure rise, a considerable total pressure loss and reduction in compressor efficiency, and eventually stall and surge especially for highly loaded compressor [3]. Many institutions and researchers have studied 3D corner separation in compressor cascade. Among them, Schulz et al.[4-6], Gallus et al.[7], Hah et al.[8], Gbadebo et al.[9-12] studied the effect of secondary flow on corner separation. Gao et al.[13] studied the corner separation by using steady and unsteady RANS simulation, referring the experiment of Ma et al.[14]. Some researchers also studied such problem and tried to control the corner separation by boundary layer suction[15,16]. The corner separation is so important for compressor cascade that it should be accurately predicted by using advanced CFD method. In the recent decades, numerical simulation based on Reynolds-Averaged Navier-Stokes equations (RANS) has been developing rapidly and RANS is widely used in turbomachinery engineering. However, turbulence model is still a weakness in RANS to accurately predict complicated flow field in turbomachinery [17], such as the 3D corner separation, especially when massive separation or intensive unsteadiness occurs. Large Eddy Simulation (LES) is much more accurate, but is very expensive in terms of computational resources for simulating the complex three-dimensional flowfields in turbomachinery [18].

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A hybrid RANS-LES model, referred as Detached Eddy Simulations (DES) was proposed by Spalart in 1997 [19]. In the DES approach, the unsteady RANS models are employed in the near-wall regions, while the RANS mode switches to LES method where the turbulence length scale exceeds the grid dimension. Therefore the grid resolution is not as demanding as pure LES, and the cost of the computation is considerably cut down. So the computation cost in DES is much less than LES and mainly maintaining the numerical accuracy of LES at the same time. However, the grid control is inadequate in some cases when the boundary layers are thick, so Delayed Detached-eddy Simulation (DDES) was proposed by Spalart et. al.[20,21]. DDES incorporates a simple modification into the initial DES (DES97) by introducing kinematic eddy viscosity into the model parameter d to take the effects of both grid spacing and eddy-viscosity field into considerations. This approach narrows the grey area between RANS and LES, especially in separating cases. In this paper, the 3D corner separation in compressor cascade is investigated by using DDES method. The development of secondary flow is investigated and complicated vortices in corner separating region are discussed. Time-averaged results show the main total pressure loss concentrated in the corner separating region. The unsteady feature of corner separation is analyzed detailedly. The DDES results show 3D corner separation in compressor cascade is an unsteady phenomenon with active turbulence fluctuation and the streamwise normal Reynolds stress contribute most to the mainstream field. The turbulence velocity spectra and anisotropy invariant map are utilized to study the turbulence flow field.

Table1. Geometric parameters of cascade[9-12] Characteristic Value chord(mm) 151.5 s/c 0.926 h/c 1.32 t/c 0.1 camber angle 42.0deg Stagger angle 15.0deg Rec(inlet) 2.3×105 5.23 δ(mm) 2.2 Computational Grids

In the simulation, one-blade passage is selected to investigate the separation. Periodic boundary conditions are set on the two sides of flow passage. Hexahedral structural meshes are generated in O4H topology, shown in Fig.2. As the blade is symmetric between the hub and tip without clearance, in order to reduce computation quantity, the computational domain is reduced to half span with symmetric condition set on the passage top surface. The grid scale based on the chord in the spanwise, pitchwise, and streamwise are ∆x/c < 0.012 ， ∆y/c < 0.0057, ∆z/c < 0.012 respectively. The y + adjacent to the wall is smaller than 0.8 with total mesh number about 5.0 million for the half-span computational domain. The inlet locates at 1.5chord upstream of the blade leading edge and the whole computation domain is about 3.5chord in the streamwise direction.

2 COMPUTATIONAL PROCEDURE 2.1 Cascade Description A linear compressor cascade from Cambridge University is used as computational geometrical model to investigate the corner separation [9-12]. The test rig consists of five modern prescribed velocity distribution (PVD) cascades, Fig.1. Surface mounted tufts were used for the experimental flow visualization on the cascade. The geometric, flow, and inlet boundary layer integral parameters for the cascade are summarized in Table1.

Fig.2 Mesh of PVD cascade

Fig.1 Pictorial view of PVD cascade [9-12]

Fig.3 Velocity profile at inlet

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where P1 and P01 are the reference static and total pressure at inlet, while P0 is static pressure at the local point. 𝑉1 is mainstream velocity at inlet and ρ is density at inlet.

2.3 Numerical method DES method is created to address the challenge of high– Reynolds number, massively separated flows, which must be addressed in such fields as aerospace and ground transportation, as well as in atmospheric studies[21]. This method can accurately predict the complexity and unsteadiness naturally associated with the compressor flow. In 2006, Spalart proposed DDES method, which incorporates a simple modification into the initial DES. DDES introduces kinematic eddy viscosity into SA turbulence model to take both effects of grid spacing and eddy-viscosity field into considerations. In order to study the evolvement of secondary vortex in compressor cascade, DDES method based on SA model is used in this paper. The governing equations of the DDES-SA model differ from those of the SA model in RANS method. In the SA based DDES, the length scale d in the SA model is replaced by d̃ = d − fd max⁡(0, d − ⁡ CDES ∆), where ∆≡ max⁡(∆x, ∆y, ∆z) fd = 1 − tanh⁡([8rd ])3 rd ≡

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TIME-AVERAGED RESULTS OF DDES Comparing with RANS results, DDES method can give better results. Fig.4 and Fig.5 shows the blade surface static pressure distribution at 54.0% and 89.0% span respectively. Both the RANS method and DDES method can give reasonable results at 54.0% span, as the separating flow is not obvious at blade middle span. At the meanwhile, the difference between the RANS method and experimental results at 89.0% span indicates RANS method is not suitable to calculating flow fields where there is large separation flow, as corner separating flow appears at 89.0% span. The DDES method gives better results at 89.0% span, which confirms the simulation could reflect the real flows in compressor cascade.

vt + v √Ui,j Ui,j κ2 d2

vt is the kinematic eddy viscosity, v is the molecular viscosity, Ui,j is the velocity gradients and κ is Karman constant. With this new formula, d̃ depends not only on the grid, but also on the eddy-viscosity field. The new model can “refuse” LES mode if function fd indicates that the point is well inside a boundary layer, as judged form the value of rd .

Fig.4 Time-averaged pressure coefficient at 54.0% span

The commercial CFD software Fluent 6.3.26 is used to make numerical simulation. Dual time step method is applied with an outer iteration physical-time step of 1.0×10-5 second and 50 inner iterations per physical time step. The pressurebased implicit solver is chosen. The central-differencing scheme is used for the convection terms and the viscous terms of each governing equation to minimize the numerical diffusion. According to the experiment, the velocity of main flow is set as 23.0m/s with nature boundary layer velocity profiles at inlet, as shown in Fig. 3. The turbulent intensity is set as 1.5% at inlet. 2.4 Definitions of Flow Field Parameters There are two important performance parameters in compressors. One is static pressure coefficient which is defined as: P − P1 Cp = 1 2 ρV 2 1 The other one is total pressure loss which is defined as: P01 − P0 Yp = 1 2 ρV 2 1

Fig.5 Time-averaged pressure coefficient at 89.0% span Fig.6 is the time-averaged total pressure loss at 50.0% chord downstream of the trailing edge at different incidences. The total pressure loss core locates at the corner separating region, which indicates the corner separation contributes most to the loss in the cascade. There is also a small area of high total pressure loss region beside the corner separation region,

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which is caused by the wake. With increase of incidence, the effects of wake becomes more obvious and the interations between wake and corner separation becomes stronger.

Fig.7 Iso-surface of Q = 5000 (a)i=-7deg (b)i=0deg Fig.6 Time-averaged total pressure loss coefficient at 50.0% chord downstream 4

VORTEX STRUCTURES IN THE CASCADE In order to detect the location of vortex core in the corner separation region, the vorticity criterion Q is used. ⁡Q is defined as: 1 Q = (Ωij Ωij − Sij Sij ) 2 where Ωij is the vorticity tensor, Sij is the shear strain tensor. Q represents the local balance between the shear strain rate and vorticity magnitude[22,23]. Fig.7 shows the iso-surface of Q = 5000 at 0 ° incidence. The horseshoe vortex which formed at the blade leading edge bifurcated into suction side leg and pressure side leg. The pressure side leg vortex runs towards the suction surface of adjacent blade because of pitchwise pressure gradient and merges into the passage vortex gradually. The passage vortex becomes the main secondary vortex in the cascade. The passage vortex core is closed to the endwall. At approximate 35% chord position, the corner separation begins to form. At this position the effect of passage vortex on corner separation is not obvious. With air flowing downstream, the core of passage vortex moves towards blade suction surface. At blade rear part, many stripe vortices concentrate at the corner region in the cascade. These stripe vortices are the large scale vortex coherent structures in the corner separation region. These large scale vortices are on the outer edge of the corner region and the velocity is relatively high. At meanwhile, there are many small vortices piling in the corner region. These small vortices originate from the endwall or shed from blade trailing edge and the velocity is relatively low. Different value of Q can help to figure out the various scales of vortices. In Fig.8 values of Q reaching at 100000 and 2000000 respectively, both large scale vortices and small scale vortices in the corner separating region can be captured. In Fig.8, the velocity of large

(a) Q=100000

(b) Q=2000000 Fig.8 Iso-surface of Q

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scale vortices is relatively high and these vortices are bent like hairpins, referring as hairpin vortices in this paper. At the same time, there are many small scale vortices inside the corner separating region. The velocity of small scale vortices near the endwall is low and many small vortices are generated from the end wall or shedding from blade surface and rolled up near the blade trailing edge. The streamwise vorticity magnitude contour at various chord shows development of horseshoe vortex clearly, Fig.9. Besides the pressure side leg of horseshoe vortex at the leading edge(red line at pressure side), the suction side leg one(blue line) dissipates quickly near the blade suction surface as the rotating direction is opposite to the main secondary vortex in the cascade. The suction side leg of horseshoe vortex also induces a small vortex (red line at suction side) which has opposite rotating direction. The small vortex develops and finally shed from the suction surface. Fig.10 Contour of Streamwise vorticity magnitude at the trailing edge of the blade

Fig.9 Contour of streamwise vorticity magnitude A slice cut at blade trailing edge shows there are many vortices with different rotating directions in the corner separation region in Fig.10. Further studying shows theses vortices changes at different transient cases, which indicate the corner separation is an unsteady phenomenon in the cascade, the unsteady character of corner separation will be discussed in the next part in the paper. Part of the area in Fig. 10 is magnified in Fig.11 and the streamlines shows the rotating directions of the vortices clearly. The red part represents the positive vortex rotating direction along streamwise, while the blue part is the negative rotating direction. The rotating directions between two adjacent vortices are opposite. The vortices in the corner separating region may induce each other. The interactions between vortices lead to strong energy transportation in the region. This is one of reasons that make

Fig.11 Streamlines on part of slice at the trailing edge of the blade the turbulence fluctuation very active in the corner region. Comparing with vortices in the corner region, the passage vortex is relative “steady” in compressor cascade. The location of passage vortex doesn’t change with time obviously. The location and strength of streamwise vorticity change at different transient cases, which illustrate the active turbulent stripe vortices in the corner. As the vortices rotating direction is opposite with each other, these stripe vortices lead to active turbulence fluctuation in the corner, which lead to main total pressure loss in the cascade.

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5 UNSTEADY CHARACTERS SEPARATION REGION

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CORNER

In order to study the unsteady characters in the corner separation region, several monitor points are set in the cascade, Fig.13. In Fig.13, P1 locates at the mainstream, P3 locates at the corner separation region and P4 is just at the exit of the blade passage. The pressure fluctuation data of 3 monitor points are transformed to pressure spectra by using fast Fourier transformation (FFT) method. As shown in Fig.14, the pressure fluctuation of these points is mainly located in the low frequency region. The amplitude fluctuation scale of P3 and P4 increases and additional frequencies appears comparing with P1. This indicates the corner separation has very obvious unsteady characters in the cascade passage. The peak amplitudes of P3 and P4 both appear at 216Hz, which shows the main unsteady period is 1/216s. As the physical time interval is 0.00001s, one main unsteady period is about 460 time steps in DDES simulation.

Fig.14 Pressure spectra of three monitor point structures from iso-surface of Q criteria, but also from contour of vorticity magnitude from Fig.17. There are many eddies in the corner separating region, some of eddies comes from the shedding vortex of the trailing edge while the others originate from blade suction surface. Eddies shedding from the trailing edge deform and break along the flow and finally dissipate due to fluid viscosity. Eddies from the suction surface is caused by the shear between the mainstream and corner separating region. They break along the flow, moves toward to blade suction surface and finally disappear with the shedding eddies from the trailing edge. From iso-surface of Q at different time in one period, Fig.18, development of hairpin vortices and small scale vortices can be observed. The hairpin vortices, the dashed circle captures one of them, are stretched flowing downstream with relatively high speed. The swept of these high speed vortices transforms the kinetic energy to the smaller scale vortices, so the corner separation is the region where the energy transportation is active. From the figures, the development of small vortices can also be observed (solid circle). Some of them evolving from endwall are rolled up into the separating region. These vortices constitute the complex flow phenomenon in corner separating region. From the analysis above, the corner separation is made by many large scale hairpin vortices outside the corner separation region and small vortices inside the region. The unsteady features of these vortices and eddies contribute a lot to the unsteady phenomenon in corner separation region and also leads to great total pressure loss in the cascade.

Fig.13 Location of monitor point The pressure perturbation and transformation can be clearly observed in Fig.15. The pressure fluctuation remains near the blade trailing edge. The positive pressure fluctuation and negative pressure fluctuation appears in sequence. Because of the shedding vortex at the trailing edge and shedding eddies from the corner separation, pressure fluctuations originate near the trailing edge and expand downstream. The shedding eddies are a cluster of hairpin vortices and small scale vortices at the corner region. The black dashed lines show the pressure perturbation propagation. From the contour of velocity in Fig.16, eddies shed from the corner separation region continuously and there are small vortex structures in these eddies, which has been analyzed in former part. Shedding eddies are one of reasons that lead to the unsteady phenomenon in the corner separation in cascade. The turbulence coherent structures exist both in the corner separating region and the shedding eddies from the corner separating region. We can not only figure out such coherent

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Fig.15 Static pressure perturbation distributions at 10.0% span at several transient cases

Fig.16 Contour of velocity at 10.0% span at several transient cases

Fig.17 Contour of vorticity magnitude at 10.0% span at transient cases

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6 TURBULENT CHARACTERS IN THE CORNER REGION In the separating region, the flow experienced strong shear and deformation, especially in the outer edge of the corner separating region. The mainstream flow with high velocity interacted strongly with the low velocity separating flow in the corner, resulting in high shear strain rate, Fig.19. In the contour of resolved turbulence kinetic energy, Fig.20, the high turbulent kinetic energy region appears at the corner separation region. The high velocity mainstream flow transports high kinetic energy flow to the low velocity corner separation region, which also leads to active turbulence fluctuation. The helicity can represent the energy backscatter in the whole turbulent flow field [24]. It is found that when the relative helicity density is strong, the energy backscatter is stronger than the forward dissipation. From contour of helicity in compressor cascade, energy backscatter is a common phenomenon in the cascade, Fig.21. The area of high-helicity speckle is larger in the corner separating region and the energy backscatter is obvious at that region. The streamlines in the cascade show large vortex structures exist in the corner separation region and the helicity density is different from other place in the cascade. This phenomenon indicates the helicity corresponds to the fluid rotation in the corner region.

Fig.19 Shear strain rate

Fig.20 Resolved Turbulent kinetic energy at 80% chord Fig.18 Iso-surface⁡Q = 300000 at several transient cases

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According to Wilcox[25], the Kolmogorov -5/3 law is so well established that numerical predictions are regarded with skepticism if they fail to reproduce it. Fig.23 shows normalized energy spectra of velocity fluctuations computed in the mainstream monitor point P2, referring in Fig.13. The spectral density and frequency are normalized using the inflow mainstream velocity and blade chord. Energy spectra predict an inertial subrange that is typically described with slope of -5/3.

Fig.21 Contour of helicity density in cascade The Reynolds stress at 80% chord is shown in Fig.22. The high Reynolds stress region remains at the corner separating region, which indicates the active turbulent fluctuation in the corner. Comparing with spanwise Reynolds normal stress() and pitchwise Reynolds normal stress(), the streamwise normal Reynolds stress() makes greatest contribution to the turbulence fluctuation, and it has major effect on the mainstream. The distribution of shear stress differs from each other and the strength of shear stress is obviously lower than the normal stress. As the streamwise turbulence fluctuation contributes greatly to the mainstream, the high valued area of and at the corner region is larger than the area of .

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(b)

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Fig.23 One-dimensional frequency spectra of velocity fluctuations at P2 The anisotropy invariant map (also referred to as the Lumley triangle), which was initially proposed by Lumley [26], has proven to be a useful and popular tool to study the structure of the turbulence. The second(η) and third(ξ) invariants of the non-dimension tensor ij should settle in the triangle for real physical turbulence flow. Isotropic turbulence is found at the origin point, and from this point two limiting lines are found where the flow is assumed to be axisymmetric. The curve edge of the triangle represents 2D turbulence. In this paper, the invariants η and ξ are calculated from three lines extracted from 20% span, Fig.24. The results show all the points locate in the triangle range. According to A.J. Simonsen’s research results[27], the location of stress invariants determines the shape of turbulence. In Fig.25, many points distribute near the right lines of the triangle which indicate the turbulence shape is rodlike, some points locates near the left lines of the triangle, which indicate the turbulence shape is disklike.

Fig.22 Reynolds stress at 80.0% chord

Fig.24 Position of lines extracted at 20% span

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2008,Vol.130, pp.031006-10 . [2] Z.N. Wang and X. Yuan, “Unsteady Mechanism of Compressor Corner Separation Over a Range of Incidence Based on Hybrid LES/RANS,” Proceedings of ASME Turbo Expo, 2013. [3] J.D. Denton, “Loss Mechanisms in Turbomachines,” Journal of Turbomachinery, 1993, Vol.115, pp 621-656. [4] H.D. Schulz, and H.D. Gallus, Experimental Investigation of the Three-Dimensional Flow in an Annular Compressor Cascade, Journal of Turbomachinery,1998, Vol:110, pp. 467-478. [5] H.D. Schulz, H.E. Gallus, and B. Lakshminarayana, ThreeDimensional Separated Flow Field in the Endwall Region of an Annular Compressor Cascade in the Presence of Rotor-Stator Interaction: Part 1---Quasi-Steady Flow Field and Comparison With Steady-State Data, Journal of Turbomachinery, 1990, Vol. 112, pp. 669-678. [6] H.D. Schulz, H.E. Gallus, and B. Lakshminarayana, ThreeDimensional Separated Flow Field in the Endwall Region of an Annular Compressor Cascade in the Presence of Rotor-Stator Interaction:Part2---Unsteady Flow and Pressure Field, Journal of Turbomachinery, 1990, Vol.112, pp. 679-688 [7] H.E. Gallus, C. Hah, and H.D. Schulz, Experimental and Numerical Investigation of Three-Dimensional Viscous Flows and Vortex Motion Inside an Annular Compressor Blade Row, Journal of Turbomachinery, 1991 , Vol. 113, pp. 198-206. [8] C. Hah, and J. Loellbach, Development of Hub Corner Stall and Its Influence on the Performance of Axial Compressor Blade Rows, Journal of Turbomachinery, 1999, Vol.121, pp. 67-77. [9] S.A. Gbadebo, T.P. Hynes, and N.A. Cumpsty, “Influence of Surface Roughness on Three-Dimensional Separation in Axial Compressors,” Journal of Turbomachinery, 2004, Vol.126, pp. 455-463. [10] S.A. Gbadebo, N.A. Cumpsty, and T.P. Hynes, “ThreeDimensional Separations in Axial Compressors,” Journal of Turbomachinery, 2005, Vol.127, pp.331-339. [11] S.A. Gbadebo, N.A. Cumpsty, and T.P. Hynes, “Interaction of Tip Clearance Flow and Three-Dimensional Separations in Axial Compressors,” Journal of Turbomachinery, 2007, Vol.129, pp. 679-685. [12] S.A. Gbadebo, N.A. Cumpsty, and T.P. Hynes, “Control of ThreeDimensional Separations in Axial Compressors by Tailored Boundary Layer Suction,” Journal of Turbomachinery, 2008, Vol.130, pp.011004-8. [13] F. Gao, W. Ma, et al., “Numerical Analysis of Three-Dimensional Corner Separation in a Linear Compressor Cascade”, Proceedings of ASME Turbo Expo, 2013. [14] W. MA, X. OTTAVY, et al., “Experimental Study of Corner Stall in a Linear Compressor Cascade”, Chinese Journal of Aeronautics, 2011, Vol. 24, pp.235-242 [15] Liu, Y.W., Sun, J.J., Lu, L.P., “Corner Separation Control by Boundary Layer Suction Applied to a Highly Loaded Axial Compressor Cascade”, Energies, 2014, Vol.7, pp. 7994-8007. [16] C. Gmelin, F. Thiele, et al., “Investigation of Secondary Flow Suction in a High Speed Compressor Cascade”, Proceedings of ASME Turbo Expo, 2011. [17] Liu, Y.W., Yu, X.J., Liu, B.J., “Turbulence models assessment for large-scale tip vortices in an axial compressor rotor”, Journal of

Axisymmetric ξ>0 (Rod like turbulence) Axisymmetric ξ