IMECE BOUNDARY LAYER CONTROL OF AN AXIAL COMPRESSOR CASCADE USING NONCONVENTIONAL VORTEX GENERATORS

Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015 November 13-19, 2015, Houston, Texas, USA IMECE2015-52310 BOUNDARY LAYER CONTROL OF AN AXIAL COMPRESSOR CASCADE USING NONCONVENTIONAL VORTEX GENERATORS Ahmed M.Diaa Assiut University Assiut, Egypt ahmeddiaa@aun.edu.eg Mahmoud A. Ahmed Assiut University Assiut, Egypt aminism@aun.edu.eg Mohammed F. El- Dosoky Assiut University Assiut, Egypt mffe1 @ aun.edu.eg Omar E. Abdel-Hafez Assiut University Assiut, Egypt omrhafz@aun.edu.eg ABSTRACT Boundary layer control plays a decisive role in controlling the performance of axial compressor. Vortex generators are well known as passive control devices of the boundary layer. In the current study, two nonconventional types of vortex generators are used and their effects are investigated. The used vortex generators are doublet, and wishbone. Three dimensional turbulent compressible flow equations through an axial compressor cascade are numerically simulated. Comparisons between cascade with and without vortex generators are performed to predict the effect of inserting vortex generator in the overall performance of the axial compressor. Results indicate that using vortex generators leads to eliminate or delay the separation on the blade suction surface, as well as the endwall. Furthermore, the effects of the vortex generators and their geometrical parameters on the aerodynamic performance of the cascade are documented. In conclusion, while the investigated vortex generators cause a slight increase in the total pressure loss, a significant reduction in the skin friction coefficient at the bottom endwall is found. This reduction is estimated to be about 46% using doublet and 32% using wishbone. INTRODUCTION The importance of axial compressors due to its relevance to gas turbine applications has motivated many researchers toward enhancing its overall performance. Controlling the secondary flow phenomena associated with the flow in compressor cascades will significantly improve the aerodynamic performance of compressors. This is due to the fact that secondary flows are extracting energy from the fluid and increasing the flow instability. Endwall boundary layer separation, horseshoe vortex, corner vortex, tip vortex, endwall crossflow, and passage vortex are secondary flow components in the cascade. Many researchers investigated the impact of three-dimensional blades and endwall boundary layer separation as well as flow separation in corners of blade passages on the development of secondary flows [1-3]. In order to control the secondary flows, both passive and active methods have been applied to reduce or overcome the effects of secondary flows in axial compressors. It was found that the passive control methods remain the preferable techniques because of their simplicity and cost effectiveness [4-5]. Numerous types of passive flow control devices were investigated such as slotted blading in linear cascades [6], vane and plow vortex generators placed on several positions [7], cavity as a control of shock wave interactions with the turbulent boundary layer [8], low profile vortex generators to reduce the boundary layer thickness [9], doublet vortex generators [10], and wishbone vortex generator [11]. An excellent comprehensive review of boundary-layer flow-separation control by a passive method and their applications had been compiled by [12-13]. There are numerous other reported studies on the control of separation in turbulent boundary layers using low profile vortex generators. In such devices, the mechanism of flow control is to energize the low momentum layers near a solid surface without adding extra energy through the momentum transfer from the outer (freestream) flow to the near wall region. Yet, this leads to an overwhelmed stronger adverse pressure gradient and hence avoid or delay the flow separation. In case of turbulent flow 1 Copyright 2015 by ASME

over flat plate, experimental results indicated that the vane and wheeler type of vortex generators can efficiently reduce the flow separation. Using the vortex generator height (h/δ) of 0.1 to 0.4 was fairly efficient with much reduce in the drag effect [14]. It was reported that flow control by means of vane type vortex generator arrays is robust with respect to changes in the pressure gradient and changes of separation point [15]. In addition, the van type with height (h/δ) of 0.8 attained the largest pressure recovery [16]. McCormick [16] experimentally compared between two passive methods for controlling shock induced separation on a turbulent flat plate boundary layer. A doublet wedge type vortex generator with h/δ=0.36 was used versus passive cavity (porous wall with a shallow Cavity underneath). He reported that the low profile vortex generators were found to be significantly suppressing the shock induced separation and improve the boundary layer characteristics downstream the shock whereas the mass-averaged total pressure loss increased. In case of turbulent flow over backward facing ramp [18], wheeler doublet and wishbone type vortex generators were used to control flow separation. They concluded that both wheeler doublet and wishbone type achieved the best effect in separation control when their heights (h/δ) varied in the range of 0.1 to 0.2. Kerho [11] uses wishbone VG to control the laminar separation, and he reported that h/δ=0.3 caused the highest drag reduction during his investigation. Diaa et al [19-20] have investigated the effect of the curved side vortex generators as a control device with axial compressor cascade, they reported a reduction of total pressure loss of 20.7%. Based on the above literature review, it is found that the Wishbone and Doublet VGs are effectively used to eliminate the separation and reduce the pressure loss on flat plates [11, 18]. Moreover, the influences of Wishbone and Doublet VGs on axial compressors have not been investigated yet. Therefore, the objective of the present study is to explore the effect of both Doublet and Wishbone VGs on the boundary layer characteristics and consequently the resulting secondary flow losses, the total pressure loss, and the skin friction on the endwall. This study will provide the researchers with the opportunity to evaluate the visibility of using such configurations as a boundary layer control devices to improve the performance of axial compressors. at the computational domain sides. One pitchwise computational domain is adopted where the blade is centered in the middle of the domain. The vortex generator is placed on the bottom endwall upstream the blade leading edge. The pressure outlet boundary condition is defined at the outlet plane. The fully developed flow is implemented at the inlet with an average Mach number of 0.66 and inlet angle (β 1) of 132. Table 1 Design operation parameters of the compressor cascade. Mach number at inlet M 1 = 0.66 Inlet flow angle β 1=132 Turning angle Δβ = 38 Stagger Angle β st =105.2 Blade chord C = 40 mm Blade span L = 40 mm Pitch to chord ratio S/C = 0.55 Endwall boundary layer thickness δ = 4 mm Figure1. Computational domain and its boundaries. VORTEX GENERATORS Two types of vortex generators (doublet and wishbone) are investigated as a boundary layer control device. Schematic sketch of ddoublet and wishbone VGs are shown in Fig.2, and their geometrical parameters are summarized in Table 2. NUMERICAL APPROACH AXIAL COMPRESSOR BLADE A transonic axial compressor cascade, that was designed by MTU aero-engines and used by Hergt et.al [21], is used in this study. The design parameters are summarized in Table 1. COMPUTATIONAL DOMAIN The computational domain and its boundaries are shown in Fig.1. Non-slip boundaries are considered at the bottom and top endwalls and the blade sides, as well as vortex generator surfaces. In addition, a periodic boundary condition is applied Figure 2. Schematic sketch of doublet (left) and wishbone (right) vortex generators with geometrical parameters. Table 2 Geometrical parameters of Doublet and Wishbone VGs. VG h/δ e/h w/h t 1/h t 2/h Doublet 0.4 5 6 Wishbone 0.4 5 6 0.8 1.2 2 Copyright 2015 by ASME

NUMERICAL SIMULATION To investigate the effect of inserting different types of vortex generators on the boundary layer, the Reynoldsaverage Navier Stokes equations coupled with transitional shear stress transformation (SST) turbulence model are numerically solved using the commercial solver ANSYS FLUENT. A three dimensional multiblock grid is constructed using a structured mesh. Solution free of grid dependency is attained by testing four different mesh sizes ranging between 0.4 and 1.6 million cells as shown in Fig.4. The Solution independent of the grid is reached at a grid size of 0.8 million cells or more. Therefore, the present simulation is performed using one million cells to guarantee that the results are independent of the grid size along with a reasonable computational time. In fact, many quantities are investigated such as velocity, total pressure, and total pressure loss coefficient. For the sake of brevity, only one figure is included to clarify the grid independency results. Figure 5. Mesh details of the two vortex generator cases, Doublet (Top), and wishbone (Bottom). Figure 4. Variation of mass averaged velocity at exit plane (located 40% of chord length behind trailing edge) with different mesh size starting from 0.4 to 1.8 million cells. The minimum cell height near the walls is adopted to have y+<1, which is considered to capture and resolve the boundary layer on the blade surfaces and enwalls. Mesh details for the two types of VGs are shown in Fig.5. VALIDATION The predicted numerical results are compared with the available results reported by Hergt et.al [21]. Isentropic Mach number distribution along the blade surfaces (suction and pressure) at the midspan is plotted against the isentropic Mach number calculated from the experimental work by Hergt [21] as shown in fig. 6. The comparison shows a good agreement between Hergt's and the present results. Figure 6. Mach isentropic distribution over the blade profile (at midspan) of the present simulation and Hergt et. al[21]. RESULTS AND DISCUSSION In this section, the effect of the two types of VGs on the vortex structure within the flow passage as well as the separation lines distribution along suction blade surface as well as the bottom endwall are presented and discussed. Effect of vortex generators on the flow vorticity In order to track the changes of the vorticity magnitude by using the vortex generators, four measurement planes are used and placed at different positions along the blade. The four 3 Copyright 2015 by ASME

planes are A, B, C and D placed at 20%, 40%, 60%, and 80% of chord length respectively. The vorticity contours along the blade chord are shown in fig. 7 for all studied cases. First for base case (without VG) at plane A, as shown in fig.7-a, The vorticity is noticed to have the highest value near the top and bottom walls due to the endwall boundary layer. Plane B shows a growth in the vorticity magnitude near the blade walls and a slight increase in the vorticity near the corner of the blade suction surface and both enwalls. Further development in the vorticity is observed at suction surface in plane C. This increase in the vorticity is considered to be an indicator for the passage vortex formation and propagation affecting the separation from the suction surface. Plane D shows a reduction in the vorticity strength near the endwall with an increase in the vorticity diffusion area. This occurs due to the endwall boundary layer growth and the mixing of the low momentum flow with the main passage flow. When wishbone VG is inserted in fig.7-b, vorticity contours suffer from some changes in the value and distribution along monitored planes. At plane A, a spot area of high vorticity is noticed above the observed vorticity in the base case. This circular area indicates the suction side component of the wishbone's generated vortex. For plane B, an increase in the spot area of the high vorticity is noted which points to the interaction between the generated and the passage vortices. At plane C, a slight reduction in the generated vortex strength is noted; along with a reduction in the vorticity magnitude near the blade suction surface. This smear in the vortex strength approves that the wishbone's generated vortex reduces the passage vortex strength. Plane D shows a further stretching of the generated vortex with lower vorticity magnitude, while the occupation area of high vorticity near the bottom endwall and the suction surface is slightly reduced. This refers to a further mixing of the low momentum fluid of the endwall, and blade suction surface boundary layer and the high momentum fluid. When doublet VG is inserted in fig.7-c, plane A shows the appearance of circular high vorticity area similar to that generated with doublet VG. The circular area is more shifted toward the mid flow passage due to the high deflection of the generated vortex along the VG side and the double length in streamwise direction of the VG. At plane B, the track area of the vorticity is increased and becomes close to the suction surface due to mixing of the low momentum fluid with high momentum fluid supported with the cross flow from the pressure to suction side. In plane C, more reduction in the vorticity magnitude is registered. At the same plane, a reduction in bottom endwall vorticity is noticed because of a continued mixing. A slight deformation is noticed in the vorticity area adjacent to the suction surface. By reaching plane D, vorticity at the corner region between bottom endwall and suction surface is diminished. In addition, a further reduction in vorticity magnitude is observed at the bottom endwall. Figure 7. Vorticity magnitude contours at different planes A, B, C, and D for the a-base case (without VG), b-wishbone VG, and c-doublet VG. 4 Copyright 2015 by ASME

Effect of vortex generators on the streamlines across blade Streamlines at the measurement planes A, B, C, and D are used to track the propagation of the vortices inside the flow passage between the blade suction and pressure surfaces as shown in Fig.8. For base case (without VG), as shown in fig.8-a, plane A has no vortex formation. As the flow is propagating toward plane B, the pressure side horse shoe vortex which is driven by the pitchwise pressure gradient toward the suction surface, is observed above the bottom endwall. Further movement toward plane C, the lower passage vortex is appeared, it is also noticeable, the appearance of the corner vortex in the junction between the bottom endwall and the suction surface. At plane D, the passage vortex is lifted from the bottom endwall toward the midspan due to the cross flow effect. A magnified view near the corner between suction surface and bottom endwall shows the propagation of the corner vortex. By inserting wishbone VG, the pressure side generated vortex starts to appear near the bottom endwall at the periodic boundary. This early appearance of pressure side vortex provides more mixing at the bottom endwall boundary layer. For plane B, the pressure side generated vortex continues its propagation which is noticeable in the streamlines fig.8-b. At plane C, the passage vortex appears near the lower suction surface. It is slightly deflected toward the blade suction surface. For plane D, lower passage vortex has been shifted slightly toward the midspan. A magnified view of the corner vortex is presented with using the wishbone VG. The view shows that no significant change to the corner vortex is attained. It is shown in fig.8-c that by using doublet VG, changes in the streamlines are observed on the tracked panes. At plane A, the pressure side generated vortex is more identifiable than that of wishbone VG associated with a higher strength generated vortex. Therefore, an energetic mixing of the bottom endwall boundary layer with the main stream flow is achieved. It is also noted that the generated vortex is slightly shifted toward the periodic boundary (near the center of the flow passage). As the flow propagates toward plane B, the generated vortex is converted and propagated. This is causing additional mixing of the bottom endwall boundary layer. At plane C, passage vortex is noticed to be slightly deflected from the blade suction surface toward the flow passage, due to the initially high strength of the generated pressure side vortex. Another thing to be noticed at this plane is the diminished corner vortex because of the energized bottom endwall boundary layer. Moving to plane D, a further deflection is caused for the passage vortex toward the flow passage away from the blade suction surface. Effect of vortex generators on limited suction surface streamlines Figure.9 shows the surface streamlines at the blade suction surface and the bottom endwall. The streamlines are used to track the location and growth or decay of the separation lines which represent the footsteps of the secondary flow structure. Figure 8 streamlines at measurement planes A, B, C, and D for a-base, b-wishbone, c-doublet cases. 5 Copyright 2015 by ASME

For base case, as shown in fig.9-a, node N at 35% of chord length indicates the origin of the corner vortex. Suction side corner vortex is separated from the blade suction surface at the separation line SL, and re-attached to it at the attachment line AL. Corner vortex footprint is also shown at the bottom endwall where it is separated at SL2 and re-attached at AL2. In addition, passage vortex which is driven by the pressure gradient between the blade surfaces is identified by the separation line SL1 where it is separated from the blade suction surface, and then reattaches to it at AL1. A circulation bubble CB is noticed at the end of attachment line AL1. Cross flow and reverse flow regions are identified by CF and RF respectively. The cross flow is driven by the high pressure at the corner region toward the midspan. While the adverse pressure gradient on the blade suction surface causes the revers flow RF. By inserting wishbone VG, as shown in fig.9-b,node N is moved downstream toward the trailing edge (at 40% of chord length), because the generated vortex converted the horseshoe vortex in the downstream direction. In addition, the separation and the attachment lines of the corner vortex SL and AL have slightly been moved toward the trailing edge. The movement of the corner vortex over the bottom endwall is indicated by SL2 and AL2. The area between SL2 and AL2 is larger than the same area at the base case, which indicates a growth in the suction surface boundary layer at the lower corner In other words, the generated vortex has not affected the corner vortex; in contrast an increase in the corner vortex is attained. For the passage vortex, a slight deflection in the downstream direction is noticed, which could be identified by the movement of SL1 and AL1 Also, a further movement of circulation bubble CB in the downstream direction is noticed. Consequently, the generated vortex causes a slight deflection of the passage vortex in the downstream direction. Another circulation bubble CB1 appears on the suction surface due to the interaction between the cross flow driven by the adverse pressure gradient at the lower corner and the streamwise flow. Cross flow region CF is reduced in the downstream direction, while the reverse flow region RF is shifted toward the midspan leading to a probable increase in the total pressure loss. By inserting doublet VG, as shown in fig.9-c node N is moved towards the trailing edge at 55% of chord length. This large movement due to the high shooting angle of the horseshoe vortex introduced by the vortex generator. The separation and reattachment lines of the corner vortex on the suction surface (SL and AL) no longer exist. In addition, the area between SL2 and AL2 is diminished, which indicates a reduction in suction surface boundary layer growth. Therefore, doublet VG increases the mixing of the endwall boundary layer and reduces the corner separation. However, the area between SL1 and AL1 (which indicates the passage vortex separation and re-attachment lines) is increased and slightly shifted towards the trailing edge leading to an increase in the total pressure loss. No significant changes is noted in the cross flow CF, reverse flow RF, and the circulation bubble CB1. Figure 9 Streamlines on Bottom endwall and the Suction surface for a-base, b-wishbone, and c-doublet cases. 6 Copyright 2015 by ASME

Effect of vortex generator on total pressure loss coefficient Figure 10 shows the total pressure loss coefficient (TPLC) contours at the exit plane (located at 40 % of chord length downstream the trailing edge). TPLC is calculated from Eq. 1 where the subscript 1 indicates the inlet plane, and subscripts 2 indicated the exit plane. Inserting wishbone VG causes an identifiable increase of total pressure loss in comparison with base case. Mass averaged TPLC in case of wishbone VG is increased by 4.3 % (as shown in fig.10-b) compared with the base case. Similar effect on TPLC is noticed when using doublet VG, total pressure loss is increased. The increase in mass averaged TPLC caused by doublet VG reaches a value of 5.2 % over the base case as shown in fig.10-c. Therefore, using doublet and wishbone VGs (as a boundary layer control device) increases the total pressure losses in comparison with the base case. This increase in TPLC for both VGs can be attributed to the angle of injection of the generated vortices due to using rounded nose instead of sharp one. pt1 pt2 TPLC (1) p p t1 s1 Figure 11. Skin friction contours at bottom endwall for a-base, b-wishbone, and c-doublet cases. From this figure, wishbone VG causes a significant reduction in friction coefficient C f in comparison with the Base case, with a value of 32% as in fig.10-b. This reduction in friction coefficient is increased by using Doublet VG to 46% as shown in fig.10-c. This significant reduction in friction coefficient stimulates further investigation to be conducted on those two types of VGs. Figure 10. Total pressure loss contours at exit plane for a-base, b-wishbone, and c-doublet cases. Effect of vortex generators on friction coefficient Both vortex generators cause a significant effect on the skin friction coefficient at the bottom endwall. Skin friction coefficient is calculated from Equation 2. C f w 1 U 2 Skin friction coefficient (C f) contours at bottom endwall for Base, wishbone and doublet cases is shown in Fig.11. 2 (2) FUTURE WORK The investigation will be extended by using different geometrical ratios (for both doublet and wishbone vortex generators) that probably causes a TPLC reduction accompanied with aerodynamic enhancement for the performance of the compressor cascade. CONCLUSION Numerical simulations of a three-dimensional compressible turbulent flow have been performed to explore the effect of non-conventional vortex generators such as Wishbone and Doublet as a boundary layer control devices. The investigation is carried out using a transonic compressor cascade at the design operation with inlet Mach number of 0.66. Numerical simulation is executed using ANSYS FLUENT. The results shows a moderate enhancement effect of the two vortex generators on the cascade secondary flow structure. This appears in shifting the passage vortex initiation towards the 7 Copyright 2015 by ASME

trailing edge and reducing (Doublet VG) or shifting (Wishbone VG) the corner vortex between suction and the bottom endwall surfaces. In addition a significant reduction in friction coefficient at the bottom endwall is achieved by wishbone (up to 32%) and Doublet (up to 46%) vortex generators. However, an increase in total pressure loss is attained by using the two vortex generators with a percentage of 4.3 % with Wishbone, and 5.2 % with Doublet type. More investigation is recommended to study the effect of the various geometrical parameters of the two types in order to reach the optimum geometrical parameters that cause enhancement in the aerodynamic structure of the axial compressor cascade with considerable reduction in the total pressure loss. NOMENCLATURE Symbols A,B,C,D =Measurement planes AL =Attachment line C =Chord CB =Circulation bubble CF =Cross flow C f =Skin friction coefficient e =VG length h = VG height L =Span M =Mach number N =Separation node P = Pressure (static or total) RF =Reverse flow S =Pitch SL =Separation line t =Thickness TPLC =Total pressure loss coefficient U = velocity magnitude VG =Vortex generator w =VG width β =inlet flow angle δ =Boundary layer thickness ρ =Density σ =solidity τ =Wall shear stress Subscripts 1 =inlet plane 2 =exit plane is =isentropic s =static pressure st =stagger t =total pressure REFERENCES [1] Gbadebo, S. a., Cumpsty, N. a.,and Hynes,T.P.,2005, Three- Dimensional Separations in axial compressors, Journal of Turbomachinery, 127(2), p. 331-339. [2]Dorfner, C., Hergt, A., Nicke, E., and Moenig, R., 2011, Advanced Nonaxisymmetric Endwall Contouring for Axial Compressors by Generating an Aerodynamic Separator Part I: Principal Cascade Design and Compressor Application, Journal of Turbomachinery, 133(2), p. 021026. [3] Hergt, A., Dorfner, C., Steinert, W., Nicke, E., and Schreiber, H.-A., 2011, Advanced Nonaxisymmetric Endwall Contouring for Axial Compressors by Generating an Aerodynamic Separator Part II: Experimental and Numerical Cascade Investigation, Journal of Turbomachinery, 133(2), p. 021027. [4] Gad-el-Hak, M., 1996, Modern developments in flow control, Applied Mechanics Reviews, 49, pp. 365 379. [5] J.C. Lin, F.G. Howard, D.M. Bushnell, Investigation of several passive and active methods for turbulent flow separation control, in: AIAA 21st Fluid Dynamics, Plasma Dynamics and Laser Conference, June 18 20 1990, Seattle, WA, AIAA Paper 90-1598. [6] Mdouki, R., and Gahmousse, A. (2013). "Effects of Slotted Blading on Secondary Flow in Highly Loaded Compressor Cascade", Journal of Engineering Science and Technology, 8(5), 540 556. [7] Lin, J. C.,1999," Control of turbulent boundary-layer separation using micro-vortexgenerator s", AIAA Paper 99-3404,30th AIAA Fluid Dynamics Conference, Norfolk, VA, June 28 July 1, 1999. [8] Seo, J. I., Kim, S. D., and Song, D. J.,2002," A Numerical Study on Passive Control of Shock Wave/Turbulent Boundary Layer in a Supersonic Compressor Cascade", The International Journal of Rotating Machinery, 8(6), 423 430. [9] Sahin, F., and Arts, T.,2012," Experimental Investigations on the Effects of Low Profile Vortex Generators in a ompressor Cascade", 9th National Congress on Theoretical and Applied Mechanics, Brussels,pp. 1-9. [10] McCormick DC,1992, "Shock boundary layer interaction control with low-profile vortex generators and passive cavity", AIAA Paper 92-0064, 30th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6 9,1992. [11] KERHO, M., HUTCHERSON, S., BLACKWELDER, R. F., and LIEBECK, R. H., 1993, Vortex generators used to control laminar separation bubbles, Journal of Aircraft, 30(3), pp. 315 319. [12] Lin, J. C.,2002 Review of research on low-profile vortex generators to control boundary-layer separation, Progress in Aerospace Sciences 38 (2002) 389 420 [13] Lu, F. K., Li, Q., Shih, Y., Pierce, A. J., and Liu, C., 2011, Review of Micro Vortex Generators in High-Speed Flow, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition4-7 January 2011, Orlando, Florida. AIAA 2011-31 8 Copyright 2015 by ASME

[14] J.C. Lin, F.G. Howard,1989, Turbulent flow separation control through passive techniques, in: AIAA 2nd Shear Flow Conference, March 13 16 1989,Tempe AZ, AIAA Paper 89-0976, 1989. [15] Ola,L., Kristian,A., Henrik,A.,2010, On the robustness of separation control by streamwise vortices European Journal of Mechanics B/Fluids 29 (2010) 9 17. [16] J.C. Lin, G.V. Selby, F.G. Howard, 1991, Exploratory study of vortex-generating devices for turbulent flow separation control, in: 29th Aerospace Sciences Meeting, January 7 10 1991, Reno, Nevada, AIAA Paper 91-0042. [17] McCormick, D. C., 1993, Shock/Boundary Layer Interaction Control with Vortex Generators and Passive Control, AIAA J., Vol. 93, No. 1, pp 91-96. [18] Lin,J.C., 1999, Control of turbulent boundary layer separation using microvortex generators, AIAA Paper 99-3404, 1999. [19] Diaa, A., El-dosoky, M., Ahmed, M., Abdel-Hafez,O., 2014, Secondary flow control on axial flow compressor cascade using vortex generators, ASME IMECE2014, Montreal, Canada, 14-20 Nov.2014. [20] Diaa, A., El-dosoky, M., Ahmed, M., Abdel-Hafez,O., 2015, Effect of a new vortex generator on the performance of an axial compressor cascade at design and off-design conditions, ASME IMECE2015,Houston, Texas, 13-19 Nov.2015. [21] Smith, F.T,1994, Theoretical prediction and design for vortex generators in turbulent boundary layers, J. Fluid Mech. 270 (1994) 91 131. [22] Hergt, A., Meyer, R., Engle, K., 2012, Effects of Vortex Generator Application on the Performance of a Compressor Cascade, Journal of Turbomachinery, 135(2), p. 02102. 9 Copyright 2015 by ASME