IMECE EFFECT OF A NEW VORTEX GENERATOR ON THE PERFORMANCE OF AN AXIAL COMPRESSOR CASCADE AT DESIGN AND OFF-DESIGN CONDITIONS

Transcription

1 Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015 November 13-19, 2015, Houston, Texas, USA IMECE EFFECT OF A NEW VORTEX GENERATOR ON THE PERFORMANCE OF AN AXIAL COMPRESSOR CASCADE AT DESIGN AND OFF-DESIGN CONDITIONS Ahmed M. Diaa Assiut University Assiut, Egypt ahmeddiaa@aun.edu.eg Mahmoud A. Ahmed Assiut University Assiut, Egypt aminism@aun.edu.eg ABSTRACT Secondary flows are noxious to axial compressor performance. To overcome and control those secondary flows, vortex generators are used as a passive control device. Controlling secondary flows will lead to a further improvements in the compressor performance. A new design of vortex generator is considered in this investigation in order to control secondary flows in axial compressor cascade at design and offdesign conditions. Numerical simulations of a threedimensional compressible turbulent flow have been performed to explore the effect of the vortex generators on the reduction of secondary flows. Six different incidence angles are used for the off-design operation investigations. d on the simulation results, the pressure, velocity, and streamline are used to follow up the development of the secondary flows. Thence, total pressure loss coefficient, static pressure rise coefficient, difference in flow deflection angle, and diffusion factor are estimated. Results indicate that vortex generators have a significant effect on the development of secondary flows at off design operation as they cause a reduction in total pressure loss, they also affect the loading behavior of the cascade as they cause a slight change in the cascade deflection, and a slight decrease in the diffusion factor which causes unloading of the blade. Static pressure rise is significantly reduced at negative incidence angles while a slight reduction occurs at positive incidence angles. In a word, the new design of the vortex generator enhances the cascade aerodynamic performance and enlarges the operating range of the cascade towards the positive incidence region. INTRODUCTION Axial compressor gains importance because of its relevance to gas turbine applications in military and commercial airplanes and its usage in stationary power generation. Therefore, early researches have been carried out to enhance its Mohammed F. El- Dosoky Assiut University Assiut, Egypt m_fekry@yahoo.com Omar E. Abdelhafez Assiut University Assiut, Egypt omrhafz@aun.edu.eg overall performance. The secondary flows have noxious effects on the axial flow compressor due to extract energy from the working fluid and increase the flow instability. Therefore, controlling secondary flows will extremely improve the aerodynamic performance of the compressor. The components of the secondary flow in the axial compressor are the endwall boundary layer separation, the horseshoe vortex, the corner vortex, the tip vortex, the endwall crossflow, and the passage vortex. Since the early 1950s, numerous researches were carried out [1 9] to investigate secondary flow phenomena. These investigations played a decisive role in improving the compressor performance. Recently, many researchers investigated the impact of the three-dimensional blades and their endwall boundary layer separation as well as flow separation in the corners of the blade passages on the development of the secondary flows [10-12]. In pursuit of controlling secondary flows, both passive and active methods have been utilized to reduce or overcome the effects of secondary flows in axial compressors. Passive control methods remain the preferable as simple and inexpensive techniques [13,14]. Different configurations of passive flow control devices were used and investigated such as slotted blading in linear cascades [15], vane and plow vortex generators placed on several positions [16], counter rotating and co-rotating rectangular, triangular, and parabolic vane type vortex generators [17 19], cavity as a control of shock wave interactions with the turbulent boundary layer [20], low profile vortex generators to reduce the boundary layer thickness [21], and doublet vortex generators [22]. An extensive review of boundary-layer flow-separation control by micro vortex generators (low profile vortex generators) had been compiled as reported in references [23-24]. Low profile vortex generators are used to energize the low momentum flow near the wall surface without energy expenditure during the momentum transfer from the free-stream flow to the near wall region. Yet,

2 this leads to an overwhelmed stronger adverse pressure gradient and therefore avoids or delays the flow separation. In case of turbulent flow over a 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 reduction in the drag effect [25]. Furthermore, vane type with height (h/δ) of 0.8 achieved the largest pressure recovery [26]. An experimental comparison between two passive methods for controlling shock induced separation on a turbulent flat plate boundary layer was carried out by McCormick [22]. A doublet wedge type vortex generator with h/δ=0.36 was used versus passive cavity (porous wall with a shallow Cavity underneath). It is 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 reduction increased. Recently, experimental and numerical studies of the effect of two vortex generator types with different configurations on the performance of the compressor cascade were conducted by Hergt et al. [27]. They concluded that using different types of vortex generators results in significant reduction in cascade losses and loading, which in turn shifts the compressor operating range towards higher positive incidence angle. They also achieved a total pressure loss reduction by 9% at design operation. Moreover, vortex generators have a significant effect on the cascade deflection and a remarkable enhancement of the cascade stall range. However the static pressure rise due to inserting a vortex generator was nearly unaffected. Diaa et al [28-29] 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 12%. d on the literature survey of the research work related to the current subject, the suggested curved surface design of vortex generator is inspired from Wheeler's doublet VG [30] that was used in several applications on flat plates. It was found that using doublet VG significantly enhances the mixing process between the low and high momentum streams. In addition, the total pressure recovery was found to be increased, and the onset of separation was delayed or eliminated. Further modification on the curved side VG design is added by including rounded nose rather than sharp nose. The new design achieved the highest total pressure recovery of about 20.7%. More details can be found in the article. fig.1. The design parameters and the operating conditions of the cascade are summarized in Table 1. FIGURE 1 COMPRESSOR BLADE PROFILE. TABLE 1 DESIGN PARAMETERS AND OPERATING CONDITIONS Mach number at inlet M1 = 0.66 Inlet flow angle β1=132 Turning angle Δβ = 38 Stagger Angle βst =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 Computational domain Computational domain and its boundaries are shown in fig.2. The non-slip boundary condition is applied at the walls representing the top boundary, the bottom boundary (Endwall), and the blade surfaces demonstrating the suction and pressure sides including the leading and trailing edges. Periodic boundary conditions are applied on the domain sides. The pressure outlet boundary condition is defined at the outlet plane. NUMERICAL METHODOLOGY BASELINE COMPRESSOR CASCADE In the present work, a linear high speed compressor cascade that was reported by the research group of Hergt et al. [24] is used. Their compressor cascade was designed by MTU Aero Engines with the profile shown in Figure 2 Boundary conditions of the computational domain (a top view showing inlet, outlet, blade suction and pressure surfaces, and periodic boundaries. Fully developed flow is adopted at the inlet with an average Mach number of 0.66, while the inlet flow angle is varied as will be shown later. 2 Copyright 2015 by ASME

3 Numerical solution The investigated numerical cases present the effect of the vortex generators on the cascade performance at design and offdesign conditions. Therefore, six different sets of vortex generators are investigated at six different incidence angles (i) ranging from i=+6⁰ to i= - 6⁰ with step of 2⁰. Commercial solver ANSYS FLUENT is used as a CFD tool to solve steady Reynolds-averaged Navier Stokes fully coupled with transition shear stress transformation (SST) turbulence model. The transition SST model is used in this simulation because of its ability to accurately capture the transition and separation flows. Three-dimensional grid is constructed using structured mesh of H-O-H topology as shown in fig.3. The second criteria is performed based on the value of residual of different quantities to be less than or equal to 5.0E- 5. The last one is based on calculations of Grid Convergence Index (GCI) as reported by Roache[31]. The GCI measures the percentage of the deviation between the computed values and the asymptotic values. It specifies the error band and how far the solution is from the asymptotic value. Also, it shows how much the solution would change with grid refinement. A small value of GCI indicates that the computation is within the asymptotic range. Therefore, Three different meshes with , , are selected to determine GCI. Table 2 shows the GCI values for axial velocity and static pressure. For the axial velocity, the GCI is found to be 0.53% for the highest grid size, in addition for the static pressure the CGI value is 0.51% for the finest grid. Table 2 shows the calculation of the GCI for different mesh size. As listed in Table 2, successive grid refinement results in a reduction in GCI. Therefore, the solution of the finest grid (826,000) cells is grid independent. Table 2: grid convergence index for static pressure and axial velocity GCI 21 GCI 32 Φ=static pressure 6.4% 0.51% Φ=axial velocity 3.78% 0.53% FIGURE 3 THREE DIMENSIONAL MULTI-BLOCK MESH WITH ENLARGED TOP VIEW OF THE MESHING AROUND THE BLADE AND TWO MAGNIFIED VIEWS OF MESHING AROUND LEADING AND TRAILING EDGES. In the present study several criteria are used to measure the grid convergence. The first one is the grid independency tests which are shown in Figs. 4, and 5. Solution with grid independency is reached by testing four different meh sizes ranging from 0.4 to 1.6 million cells. As shown in fig.4. Solution with grid independency is reached at a mesh of 0.8 million cells. Figure 5 shows the grid convergence test using the velocity contours at the exit plane. This test is carried out by using different grid size starting with a coarse grid with 0.4 Million cells up to a fine grid with 1.6 million cells. It is shown that the values of velocity contours is not subjected to a significant change beyond the 0.8 Million cells grid, and that is another reason to adopt this grid in the present simulation. Figure 4 Mass averaged velocity at exit plane (located 40% of chord length behind trailing edge) of different mesh size starting from 0.4 to 1.8 million cells. Figure 5 velocity contour lines (m/s) at exit plane for different grid sizes ( Million cells). 3 Copyright 2015 by ASME

4 Therefore, the present simulation is performed using 0.8 million cells to get results that independent of the grid size and to reduce the computational time. The minimum cell height near the walls is adopted to have y+<1, which is considered to capture and resolve the boundary layer at the blade surfaces and enwalls. To conclude, a new design of vortex generator (VG) is inserted into the flow passage of a compressor blade cascade, and its effect on the compressor cascade performance is investigated for both design and off-design conditions. For the off design conditions incidence angle will be varied from i= - 6⁰ to i= +6⁰ with step 2⁰. The new VG is shown in fig.6. Two main configurations of the new VG are investigated. First one is having a sharp edged nose as shown in five stets A, B, C, D, and E with different geometrical dimensions. The second configuration is set F which has a rounded edge nose. Four different ratios of r/δ= 0.25, 0.5, 0.75 and 1.0 are investigated, but the only reported results in this manuscript is the case with r/δ=0.5; since it achieves the highest performance relative to the others. The six different sets with different geometrical dimension ratios are summarized in Table 3. FIGURE 7 COMPARISON BETWEEN THE MEASURED ISENTROPIC MACH NUMBER DISTRIBUTION [27] AND THE PRESENT SIMULATION. Another validation comparison is carried out using the mass-flow averaged spanwise pressure loss distribution of the base case as shown in fig. 8. The figure shows a good qualitative agreement with maximum deviation of 7% near the bottom end wall. FIGURE 6 TWO CONFIGURATIONS OF THE NEW VORTEX GENERATOR, (A) WITH SHARPED EDGE NOSE AND (B) WITH ROUNDED EDGE NOSE. Table 3 Summary of vortex generators geometrical ratios represented in set A, B, C, D, E and F. Set h/δ w/h e/h r/δ A 3 B 4 C D 6 E 6 5 F 0.5 FIGURE 8 COMPARISON BETWEEN THE TOTAL PRESSURE LOSS DISTRIBUTION AT A PLANE LOCATED AT 40% OF CHORD LENGTH BEHIND THE TRAILING EDGE [27], AND THE PRESENT SIMULATION. VALIDATION In order to validate the current results, a comparison with Hergt's [27] results is performed. Isentropic Mach number distribution on the blade profile at midspan is compared with isentropic Mach number calculated from the experimental work by Hergt [27] as shown in fig. 7. The Figure shows a good qualitative and quantitative agreement with Hergt's results. RESULTS AND DISCUSSION In this section, the numerical results with vortex generators at both design and off-design conditions are presented and discussed. In particular, The study focuses on the streamlines at blade suction surface and other performance parameters such as, total pressure loss coefficient, flow deflection angle, static pressure 4 Copyright 2015 by ASME

5 rise coefficient, and diffusion factor which will clarify the effect of VG on the cascade performance. Effect of vortex generator on secondary flows In order to determine the separation lines, secondary flow components such as the footprint of the propagation of the passage, corner, and horseshoe vortices are considered. The limiting streamlines on the blade suction surface are used to trace the changes in the separation lines after using vortex generator. In Fig.9, streamlines at blade suction surface with and without vortex generators show the position of both the separation lines, the attachment lines and the recirculation volumes. For base case without vortex generator, the passage vortex is firstly separated from the endwall and then reattached to the suction surface at AL1. The separation line SL1 indicates the separation of the passage vortex from the suction surface followed with reverse flow over the blade which is originated near the midspan towards SL1, and then the flow is separated from the blade surface by the passage vortex as mentioned before. In addition, separation line SL2 indicates the separation of the corner vortex along the blade suction surface, while AL2 shows the reattachment of the corner vortex with the blade surface. For cases, where VGs are used, the vortex structure inside the flow passage is affected by the two generated counter rotating vortices. For case A, SL1, and AL1 are both moved toward the trailing edge which is an indicator for the deflection of the passage vortex into the flow direction. This deflection is due to one of the generated vortices near the suction side, also, SL2 and AL2 disappeared from the streamlines of this case. Reverse flow on the blade surface is decreased for case A, as shown in Fig. 8. As w/h increased for design B, no significant changes in the position and distribution of the streamlines are identifiable. Further increase in w/h, as in case C, causes a larger deflection of the passage vortex which is indicted by the movement of SL1 and AL1 downstream towards the trailing edge. Reverse flow on the suction side is diminished. Another increase in w/h for case D yields a disappearance of SL1 and AL1, furthermore, the reverse flow also disappeared, these changes due to increasing w/h are attributed to a more strength generated vortex by inserting the VG.. In addition, the movement of the separation lines also indicates to an increase in stretching rate of the vortex control region with higher w/h values. Streamlines behavior of case E is similar to that caused by case F; therefore it is not reported here. In case F with the rounded nose edge, separation and attachment lines SL1 and AL1 are vanished. In addition, reverse flow is noted on the blade surface. On the top half of the blade surface, for base case a circulation bubble CB is noticed in the upper and lower half of the blade span. After using VG, a circulation bubble CB1 is noticed on the upper half of the blade span suction surface. This circulation bubble is formed by the interaction of the cross flow driven by the adverse pressure gradient at the top wall corners and midspan and the streamwise flow. FIGURE 9 SKIN FRICTION LINES ON THE SUCTION SURFACE FOR BASE CASE (WITHOUT VG) AND CASE A, B, C, D, AND F AT DESIGN OPERATION ( i=0 [deg.]). Effect of vortex generator on total pressure loss coefficient Total pressure loss coefficient (TPLC) is known as a compressor performance parameter which is used to judge the loss behavior of the flow. TPLC is calculated from the following equation: pt1 pt 2( y, z) TPLC( y, z) (2) p p Figure 10 shows local TPLC contours at exit plane (which is located 40% of chord length downstream the trailing edge) at design and off design. From this TPLC contours, it is clear that at high negative and positive incidence angles (when i=-6 and +6[deg.]) TPLC is increased when using VG in comparison with the base cascade. By decreasing incidence angle to i=-4 t1 s1 5 Copyright 2015 by ASME

6 and +4[deg.] a slight decrease in TPLC is noted in all cases with VG compared with the base case. Further reduction in TPLC is gained by decreasing the incidence angle to i=-2 and +2[deg.].Therefore using VG will decrease the total pressure loss over a range of incidence angles between i=-4⁰ to +4⁰. Total pressure loss factor (TPLF) represents the difference of total pressure loss coefficient (between case with VG and the base case) normalized by the total pressure loss coefficient of the base case as stated in equation 3. To calculate the TPLF, the local value of TPLC(y,z) in equation 2 is integrated in the spanwise direction and pitch wise directions for base and all VG cases. TPLCVG TPLC TPLF (3) TPLC Figure 11 Total pressure loss factor with different incidence angles for set A, B, C, D, E, and F[%] Figure 10 TPLC contours measured at exit plane (located at 40% of chord length behind trailing edge) at incidence angles i=-6, +4,-2, +2, +4, and +6 [deg.] for, D, E and F cases. Figure 11 shows the TPLF for all cases. At design condition, for cases A to D, where β1=132 deg., it is noticeable that by increasing w/h the TPLF is reduced which indicates a reduction in the total pressure loss in comparison with the base case. This is due to the increase of the stretching rate of the generated vortices. The TPLF ranges from -5.3% to % for case A and D respectively. For case E a further reduction in TPLF is attained with value of %.The highest reduction is reached using case F with rounded nose edge, where the TPLF value is- 20.7%. At off-design condition, it is clear that TPLF increases with the increase of incidence angle, for negative incidence angle i=-6 deg. (β1=126 deg.) there is no reduction in total pressure loss attained in all cases, instead an increase in the total pressure loss is achieved by using vortex generator relative to the base case. At negative incidence angles, the two generated vortices will not have the same strength as at design condition. The pressure side generated vortex is strong, but the suction side generated vortex is far too weak. This non-symmetric strength of the two generated vortices will cause an opposed effect on losses reduction, since the weaker vortex will not be able to mix low and high momentum flows properly. By decreasing the incidence angle to i= - 4 where β1=128 deg., the non-symmetric strength still exists but with smaller difference between the generated vortices, and this is the reason why TPLF is slightly reduced at this operating point. Furthermore at i= -2 β1=130 deg. TPLF is further reduced for all cases, the highest reduction is reached at case E with value of %. At positive incidence angles the effect is reversed where the suction side generated vortex is stronger than that of the pressure side. TPLF is increased for all cases at i=+2 where β1=134 deg., and the uppermost value of TPLF reduction at this incidence angle occurs at case E with value of %. TPLF is further increased with i=+4 where β1=136 deg., for all cases. At i=+6 deg., where β1=138, all cases have an increase in pressure loss which is noted by the positive vale of TPLF for all cases at this incidence angle. Therefore, at design conditions, case F causes the highest reduction in TPLF; nevertheless, at offdesign operation case E yields higher reduction in TPLF than this caused by case F. Consequently, optimization of the best case to be used to cover a wider range of operation with the highest reduction in pressure losses is still needed. 6 Copyright 2015 by ASME

7 Effect of vortex generator on flow turning angle Flow turning angle is computed from Equation 4. In order to track the change in flow deflection by using vortex generators, the difference of the flow turning angle will be normalized by flow turning of the base case as shown in Equation 5. (4) 1 2 VG The normalized difference of flow turning angle is shown at midspan for base case and all VG cases in Fig. 12. At design operation, the flow turning angle is either decreased or increased by using VG where the maximum reduction is of % with the case C and the maximum increase of 0.38% with the case D. Consequently, a slight change is noticed in the flow turning angle for all cases at this point of operation. At off-design condition, a high negative incidence angle i= - 6 deg., causes an increase in the flow turning angle with value of 1.8 % at case A, slight change in this value is noted for other cases. As negative incidence decreases to i= -4 deg., flow turning is increased to 1.2% at case B. Further decrease in incidence angle to i= -2 deg. flow turning is lowered to 0.53 % at case B. At positive incidence angles, the change in flow turning angle is lower than that caused by negative incidence. At i= +2 deg, a slight increase in flow turning angle is identifiable with intermediate value of 0.32 % at case B. By increasing the positive incidence to i= +4 deg, further increase in flow turning is attained with middle value of 0.45% at case A. Highest positive incidence angle of i=+6 deg results in an increase flow turning with central value of 0.63% at case A.Consequently, using VG has no significant effect on the flow turning angle at design and off-design operation. Effect of vortex generator on the diffusion factor Blade loading is assessed by the diffusion factor (DF) which relates to the peak velocity on the suction surface of the blade to the velocity at the trailing edge. The Diffusion factor can be defined by Equation 6[33]. 2 DF 1 (6) (5) Figure 12 Normalized difference of flow turning angle at midspan for case A, B, C, D, E, and F with various incidence angles [%]. The Diffusion factor is used as an indicator of the probability of stall, since the increase of DF leads to more possible separation [34]. Figure14 shows variation in DF for all cases at the entire operating range. For sets A, B, C, D, and E, diffusion factor decreases over the whole operating range and it almost remains constant except for i=+6, where DF increases. For set F, diffusion factor is slightly increased for both positive and negative incidence angles as shown in Fig.13. The first two terms of the diffusion factor defined by Eq. 6 represent the deceleration of the flow, while the third term represents the flow turning [35]. For positive incident angles, the declaration of the outlet flow is increased for almost all sets which increases the deceleration term in the DF equation. It is also noted that flow turning term is slightly decreased at this range of incident angles as shown in Fig.14. The result is a slight increase in the DF at this range of operation. At negative incident angles, flow is less decelerated which allows the deceleration term in the DF equation to decrease. The flow turning term is also highly increased at this region as shown in Fig.14, which is also reflected in the increase of the DF in the negative incident region. Normalized diffusion factor in Equation 7 is used to measure the effect of different cases with VG at different incidence angles on the diffusion factor. DFVG DF DF (7) DF Figure 13 Diffusion factor for case A, B, C, D, and E with different incidence angles [%] 7 Copyright 2015 by ASME

8 Figure 14 Deceleration term, flow turning, and diffusion factor DF with different incidence angles for set F. Effect of vortex generator on static pressure rise Static pressure rise coefficient is calculated form Equation 8 and the normalized difference is calculated as shown in Equation 9. Ps 2 Ps 1 Cp (8) P P t1 s1 CpVG Cp Cp Cp Figure 15 shows the difference in static pressure rise coefficient for all cases. As noticed, at negative incidence angles, the static pressure rise is highly decreased while at positive incidence angles static pressure is slightly decreased. Similar effect is noticed for set F as shown in Fig.15. The rise of Cp at β1=134 is probably attributed to the difference of the axial velocity density ratio (AVDR) between both β1=134 and the other positive incidence angles of 136, 138. It was found that the value of AVDR at β1 of 134 is less than that of 136, and 138. Accordingly, the flow contraction at β1=134 is less than that of 136, and 138. This means that the flow is more decelerated at 134 than that of 136, and 138. Consequently the value of Cp at 134 is greater than that of 136, and 138. As reported in reference [4], the AVDR is defined by Eq. 10 as follows:. 2v x 2 (10) AVDR v 1 x 1 Table 4: AVDR values at different inlet angles Angle Set F Change in AVDR β1= % β1= % β1= % (9) Figure 15 Static pressure rise coefficient for set A, B, C, D, E, and F with different incidence angles [%] CONCLUSIONS Numerical simulations of a three-dimensional compressible turbulent flow have been performed to explore the effect of the vortex generators on the reduction of secondary flows. Six different sets of a new design of vortex generator are used in the current work as a passive boundary layer control device in an axial compressor cascade. The investigation is carried out over a wide operating range of incidence angles at design and off design conditions. The inlet Mach number is of 0.66 with inlet angle of β1=132⁰ at design operation. For off-design operation the flow incidence angle is changed between i= -6 and i=+6 deg. Numerical simulation is performed using commercial software ANSYS FLUENT. The results show that for all investigated configurations, a significant reduction of total pressure loss up to 20.7% by case F is attained in comparison with the base cascade without vortex generator at the design point. In addition, this reduction in total pressure loss occurs at incidence angles of i=±2, ±4 deg with maximum value of 12.8 %, while at i = ±6 deg an increase in total pressure loss is noted. For other investigated performance parameters, the flow turning angle has a slight change for the different operating range angles. Also, a slight decrease in the diffusion factor is noticed for the entire operating range when using vortex generators. Static pressure rise coefficient is rapidly decreased by increasing the negative incidence, while it remain constant at positive incidence angles. Therefore, using this vortex generator reduces the total pressure loss and enlarges the operating range of compressor cascade towards the positive incidence angle region without a significant effect on the flow turning angle and diffusion factor. 8 Copyright 2015 by ASME

9 NOMENCLATURE Symbols AVDR :Axial velocity density ratio c : Chord length Cp : Static pressure coefficient DF : Diffusion factor e : Vortex generator's length GCI :Grid Convergence Index h : Vortex generator's height i : Incidence angle L : Span M : Mach number P : Pressure (total or static) r Rounded nose radius S : Pitch TPLC : Total pressure loss coefficient TPLF : Total pressure loss factor w : Vortex generator's width β : flow angle δ : Boundary layer thickness ν : Relative velocity ρ :Density σ : Solidity Subscripts is : Isentropic 1 : At inlet 2 : At measurement plane s : Static pressure t : Total pressure : case without vortex generator VG : Case with vortex generator θ : Tangent component x : Axial component REFERENCES [1] Herzig, H., Hansen, A., and Costello, G., 1954, A Visulaization study of secondary flows in cascades, Technical Report No. 1163, NACA. [2] Dean, R. C., 1954, Secondary flow in axial compressors, (1949). [3] B. Lakshminarayana, and Horlock, J. H., 1963, Reviw : Secondary Flows and Losses in Cascades and Axial-FLow Turbomachines, Int. J. Mech. sci, 5, pp [4] H. Schlichting, and Das, A., 1966, Recent Research on Cascade-Flow Problems, pp [5] Gessner, B. F. B., 1972, The origin of secondary flow in turbulent flow along a corner. [6] Wisler, D. C., 1985, Loss Reduction in Axial-Flow Compressors Through Low-Speed Model Testing, (3). [7] Dong, Y., 1987, Three-Dimensional Flows and Loss Reduction in Axial Compressors, 109(July 1987). [8] Horlock, J. H., Louis, J. F., Percival, P. M. E., and Lakshminarayana, B., 1966, Wall Stall in Compressor Cascades, Journal of Fluids Engineering, 88(3), pp [9] Greitzer, E. M., 1980, Review Axial Compressor Stall Phenomena, Journal of Fluids Engineering, 102(2), pp [10] Gbadebo, S. a., Cumpsty, N. a., and Hynes, T. P., 2005, Three-Dimensional Separations in Axial Compressors, Journal of Turbomachinery, 127(2), p [11] 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 [12] 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 [13] Lin, J., F., H., Bushnell, D., and Selby, G., 1990, Investigation of several passive and active methods for turbulent flow separation control, 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, American Institute of Aeronautics and Astronautics. [14] Gad-el-Hak, M., 1996, Modern developments in flow control, Applied Mechanics Reviews, 49, pp [15] Mdouki, R., and Gahmousse, A., 2013, EFFECTS OF SLOTTED BLADING ON SECONDARY FLOW IN HIGHLY LOADED COMPRESSOR CASCADE, 8(5), pp [16] Lin, J. C., 1999, Control of turbulent boundary-layer separation using micro-vortexgenerators, 30th AIAA Fluid Dynamics Conference, Norfolk, VA, June 28 July 1, 1999, AIAA Paper. [17] Kuya, Y., Takeda, K., Zhang, X., Beeton, S., and Pandaleon, T., 2009, Flow Separation Control on a Race Car Wing With Vortex Generators in Ground Effect, ASME J. Fluids Eng., 131(12), p. pp [18] Katz, J., and Morey, F., 2008, Aerodynamics of Large-Scale Vortex Generator in Ground Effect, Journal of Fluids Engineering, 130(7), p [19] Van de Wijdeven, T., and Katz, J., 2013, Automotive Application of Vortex Generators in Ground Effect, Journal of Fluids Engineering, 136(2), p [20] 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), pp Copyright 2015 by ASME

10 [21] Sahin, F.., and Arts, T., 2012, Experimental Investigations on the Effects of Low Profile Vortex Generators in a Compressor Cascade, pp [22] MCCORMICK, D. C., 1993, Shock/boundary-layer interaction control with vortex generators and passive cavity, AIAA Journal, 31(1), pp [23] Lin, J. C., 2002, Review of research on low-profile vortex generators to control boundary-layer separation. [24] Lu, F. K., Li, Q., Shih, Y., Pierce, A. J., and Liu, C., 2011, Review of Micro Vortex Generators in High- Speed Flow, (January), pp [25] LIN, J., HOWARD, F., and SELBY, G., 1989, Turbulent flow separation control through passive techniques, 2nd Shear Flow Conference, American Institute of Aeronautics and Astronautics. [26] LIN, J., HOWARD, F., and SELBY, G., 1991, Exploratory study of vortex-generating devices for turbulent flow separation control, 29th Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics. [27] Hergt, A., Meyer, R., Engel, K., 2012, Effects of Vortex Generator Application on the Performance of a Compressor Cascade, Journal of Turbomachinery, 135(2), p [28] Diaa, A., El-dosoky, M., Ahmed, M., Abdel-Hafez, O.,2014, Secondary flow control on axial flow compressor cascade using vortex generators, ASME IMECE 2014, Montreal, Canada, Nov [29] Diaa, A., El-dosoky, M., Ahmed, M., Abdel-Hafez, O., 2015, Boundary layer control of an axial compressor cascade using nonconventional vortex generators, ASME IMECE2015, Houston, Texas, Nov.2015 [30] Wheeler G.O., 1984 Means of maintaining attached flow of a flow medium. US Patent [31] Roache, P. J., 1997, Quantification of Uncertainty in Computational Fluid Dynamics, Annual Review of Fluid Mechanics, 29(1), pp [32] Fleming, J., Simpson, R. L., Devenport, W.J., 1991," An Experimental Study of a Turbulent Wing- Body Junction andwake Flow," VPI&SU Re- port VPI- AOE-179, Va. Polytech. Inst. State Univ., Blacksburg, Va. [33] Lieblein,S. Schwenk, F. C., and Broderick, R. L., 1953," Diffusion Factor for Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor Blade Elements,"NACA RM E53D01. [34] Falck, N. Axial Flow Compressor Mean Line Design,Master thesis, Lund University, Sweden, [35] Dixon, S. L., 2014, Fluid Mechanics and Thermodynamics of Turbomachinery Seventh Edition Fluid Mechanics and Thermodynamics of Turbomachinery. 10 Copyright 2015 by ASME