secondary flow control in an axial compressor cascade using vortex ...

Assiut University

Faculty of Engineering

SECONDARY FLOW CONTROL IN AN AXIAL COMPRESSOR CASCADE USING VORTEX GENERATORS: NUMERICAL SIMULATION A THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science In Mechanical Engineering Department of Mechanical Engineering Faculty of Engineering Assiut University Assiut, Egypt Submitted by Eng. Ahmed Mohamed Diaaeldien Ahmed Darwish Demonstrator – Department of Mechanical Engineering Faculty of Engineering – Assiut University Assiut, Egypt February 2016

SECONDARY FLOW CONTROL IN AN AXIAL COMPRESSOR CASCADE USING VORTEX GENERATORS: NUMERICAL SIMULATION A THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science In Mechanical Engineering Department of Mechanical Engineering Faculty of Engineering Assiut University Assiut, Egypt Submitted by Eng. Ahmed Mohamed Diaaeldien Ahmed Darwish Demonstrator – Department of Mechanical Engineering Faculty of Engineering – Assiut University Assiut, Egypt February 2016 Supervisors committee Prof. Omar Alanwar Abdelhafez

_______________________

Prof. Mahmoud Amin Ahmed

_______________________

Dr.Mohammed Fekry El-dosoky

_______________________

ii

‫ِْ‬ ‫َ ْ‬ ‫ِاَّل‬ ‫ِ إ‬ ‫لم‬ ‫الع‬ ‫ِن‬ ‫ُم م‬ ‫ِيت‬ ‫ُوت‬ ‫َا أ‬ ‫َم‬ ‫و‬ ‫َقل ا‬ ‫ِيًل(‪)83‬‬ ‫اَّلسراء –اآلية ‪83‬‬

‫‪iii‬‬

Dedication To my parents. To my brothers. To my wife.

iv

Acknowledgment I would like to acknowledge some of the people that have been involved both directly and indirectly in making this work possible. My parents, who gave me the values and lessons in life and the motivation to accomplish goals that I had not thought possible. My wife, Reda who has always looked out for me, and given me her continuous support and care. Thank you. My advisors, and supervisors Prof. Omar Abelhafez, Prof. Mahmoud Amin, and Dr. Mohammed El-Dosoky for giving me this opportunity. Their guidance, motivation and patience have proved invaluable in helping me complete this work, but it was their belief in me that ultimately led to its conclusion. My friends and colleagues in Assiut University for helping when needed but more importantly, who brought out the lighter side of research work. Ahmed Diaa.

v

ABSTRACT Axial flow compressors have a limited operating range due to the difficulty of controlling the secondary flows. Therefore, new designs of vortex generator (VG) are considered in the current investigation to control the secondary flow losses and consequently enhance the compressor’s performance. Those new designs are curved side VG with sharp nose edge, curved side VG with rounded nose edge, wishbone VG, and doublet VG. In order to estimate the performance of the compressor cascade with

the

suggested

vortex

generators,

a

three

dimensional

compressible flow with transitional shear stress transformation (SST) turbulence model is simulated using a commercial software ANSYS Fluent 14. A transonic compressor cascade designed by MTU aeroengines is used in the current study. The operating conditions of this cascade are used in setting the boundary conditions of the computational domain. Based on the simulation results, the pressure, velocity, and streamline contours are presented to track the development of secondary flows and their effects on the compressor cascade performance. Thus, the total pressure loss and static pressure rise coefficients, blade deflection angles, and diffusion factors are evaluated. The results of simulating the suggested four VGs show that: a) Using curved side vortex generator (CSVG) with sharp nose edge using different geometrical parameters leads to a maximum reduction in total pressure loss of about 18.3% at design operational conditions. b) Using the rounded nose edge VG causes an increase in the total pressure loss reduction up to 20.7%

vi

c) Using both sharp nose and rounded nose VG leads to a reduction in total pressure loss coefficient at off design conditions at incidence angles in the range from i=+4 to -4 deg. , this causes a widening of the operating range of the cascade. d) Using wishbone and doublet VGs are only investigated at design operation. Although they cause a slight increase in total pressure loss, they also cause a reduction in skin friction coefficient at the bottom endwall. Furthermore, there is a slight reduction in static pressure rise while there is an increase in dynamic pressure. To benefit from the increase in the dynamic pressure, a further research is needed in order to get the design that recover the dynamic pressure into static pressure.

vii

Table of contents

Dedication ................................................................................. iv Acknowledgment........................................................................ v ABSTRACT ................................................................................ vi Table of contents ..................................................................... viii List of figures ............................................................................. x List of tables ............................................................................ xiv Nomenclature........................................................................... xv 1 INTRODUCTION .................................................................... 3 1.1 Introduction ..................................................................................... 3 1.2 Literature review .............................................................................. 3 1.3 Objectives and methodology ............................................................. 4

2 COMPUTATIONAL PROCEDURE ........................................... 11 2.1 Compressor cascade ....................................................................... 11 2.2 Computational domain and boundary conditions ............................ 12 2.3 Numerical solution .......................................................................... 13 2.4 Validation ....................................................................................... 17

3 Results and discussion ......................................................... 23 3.1 Part 1: Curved side VG at design conditions ..................................... 23 3.1.1 Effect of vortex generator on the cascade performance .............. 24 3.1.2 Influence of Vortex Generators on the Development of Secondary Flows……………………………………………………………………………………………. .. 25 3.1.3 Influence of Vortex Generators on Total Pressure Loss Coefficient………………………………………………………………………………………. 33 3.1.4 Influence of Vortex Generators on Cascade Deflection ............... 49 3.1.5 Influence of Vortex Generators on Static Pressure Rise Coefficient ………………………………………………………………………………………………………..50 3.1.6 Influence of Vortex Generators on Diffusion Factor.................... 52 3.1.7 Summary .................................................................................. 54 3.2 Part 2: Curved side vortex generators at off-design conditions ........ 55 3.2.1 Effect of vortex generator on secondary flows ........................... 55 3.2.2 Effect of vortex generator on total pressure loss coefficient ....... 59 viii

3.2.3 Effect of vortex generator on flow turning angle ........................ 62 3.2.4 Effect of vortex generator on the diffusion factor ....................... 64 3.2.5 Effect of vortex generator on static pressure rise ....................... 66 3.2.6 Summary .................................................................................. 67 3.3 Part 3: Non-conventional VGs .......................................................... 68 3.3.1 Effect of vortex generators on the vorticity magnitude .............. 68 3.3.2 Effect of vortex generators on the streamlines across blade ....... 72 3.3.3 Effect of vortex generators on suction surface streamlines ........ 75 3.3.4 Total Pressure loss contours ..................................................... 78 3.3.5 Effect of vortex generators on friction coefficient ...................... 79 3.3.6 Future work .............................................................................. 80 3.3.7 Summary .................................................................................. 81

4 Conclusions ......................................................................... 83 References ............................................................................... 86 Appendix.................................................................................. 92 Arabic summary ..................................................................... 119

ix

List of figures Figure 1-1 Secondary flow structure reported by Kang et al [14]. .................. 6 Figure 2-1 Blade profile of transonic compressor cascade designed by MTU aero engines[23]. .......................................................................... 11 Figure 2-2 Compressor cascade parameters. ................................................... 12 Figure 2-3 Computational domain with the inserted VG. ................................ 13 Figure 2-4 Mesh of the Base case. ...................................................................... 14 Figure 2-5 Mass flow averaged turbulent kinetic energy (k, m2/s2) with different number of cells. ............................................................. 15 Figure 2-6 Mass flow averaged integrated velocity at exit angle with different no of cells. ...................................................................... 15 Figure 2-7 Mass flow averaged integrated TPLC at exit angle with different no of cells. ...................................................................................... 16 Figure 2-8 Velocity contour lines in (m/s) at exit plane of different grid sizes (0.4, 0.8, 1.2, and 1.8 Million cells). ............................................. 16 Figure 2-9 Experimental and calculated numerical Mis distribution at midspan of reference cascade. ..................................................... 17 Figure 2-10 Total pressure loss contours calculated at a plane located at 40% of chord behind the trailing edge, (a) present simulation , (b) experimental TPLC reported by Hergt et al [23]. ................ 18 Figure 2-11 Velocity vectors at exit plane located at 40% of chord behind the trailing edge. .................................................................................. 19 Figure 2-12 Comparison between the predicted mass flow averaged total pressure loss distribution of the present study and Hergt's[23] simulation. ..................................................................................... 19 Figure 2-13 Simulated streamlines on suction side and endwall (a) present simulation ,(b) Hergt et al simulation[23]. ................................. 21 Figure 3-1 Curved Sides’ Vortex Generator Geometry, (a) without round nose, (b) with round nose. ........................................................... 23 Figure 3-2 Calculated static pressure contours and streamlines on the blade suction side of the reference case and set A with h/δ ranged from 0.1 to 0.5. .............................................................................. 25 Figure 3-3Calculated static pressure contours and streamlines on blade suction side of reference case and set B with h/δ ranged from 0.1 to 0.5. ....................................................................................... 27

x

Figure 3-4 Calculated static pressure contours and streamlines on blade suction side of reference case and set C with h/δ ranged from 0.1 to 0.5. ....................................................................................... 28 Figure 3-5 Calculated static pressure contours and streamlines on the blade suction side of the reference case and set D with h/δ ranged from 0.1 to 0.5. .............................................................................. 29 Figure 3-6 Calculated static pressure contours and streamlines on blade suction side of reference case and Set E with e/h=8, 6, 5, and 4. ........................................................................................................ 31 Figure 3-7 Calculated static pressure contours and streamlines on blade suction side of reference case and set F with h/δ ranged from 0.1 to 0.5. ....................................................................................... 31 Figure 3-8 Velocity vectors on suction side for reference case and set D for h/δ=0.3, 0.4, and 0.5. .................................................................... 32 Figure 3-9 Total pressure loss contours of reference case and set A with h/ δ ranged from 0.1 to 0.5, where w/h=3, and e/h=6. .................... 35 Figure 3-10 Total pressure loss contours of reference case and set B with h/ δ ranged from 0.1 to 0.5, where w/h=4, and e/h=6................... 36 Figure 3-11 Total pressure loss contours of reference case and set C with h/ δ ranged from 0.1 to 0.5, where w/h=5, and e/h=6................... 36 Figure 3-12 Total pressure loss contours of reference case and set D with h/ δ ranged from 0.1 to 0.5, where w/h=3, and e/h=6................... 37 Figure 3-13 Total pressure loss contours of reference case and set E with e/h=4, 5, 6, and 8 where h/δ=0.4, and w/h=6. .......................... 38 Figure 3-14 Total pressure loss contours of reference case and r/δ=0.25,0.5,0.75, and 1 where h/δ=0.4, w/h=6, and e/h=5. ... 39 Figure 3-15 Spanwise total pressure loss coefficient distribution for set A with different h/δ values.............................................................. 41 Figure 3-16 Spanwise total pressure loss coefficient distribution for set B with different h/δ values. ............................................................. 42 Figure 3-17 Spanwise total pressure loss coefficient distribution for set C with different h/ δ values. ............................................................ 43 Figure 3-18 Spanwise total pressure loss coefficient distribution for set D with different h/ δ values. ............................................................ 44 Figure 3-19 Spanwise total pressure loss coefficient distribution for set E with different e/h values. ............................................................. 45

xi

Figure 3-20 Spanwise total pressure loss coefficient distribution for set F with different r/δ values. ............................................................. 45 Figure 3-21 TPLC contours for reference case and set F of r/δ=0.5 with (i) passage vortex, and (ii) the generated suction side vortex, at exit plan. ........................................................................................ 46 Figure 3-22 Normalized total pressure loss coefficient for sets A, B, C, and D. ........................................................................................................ 47 Figure 3-23 Normalized total pressure loss coefficient for set E. .................. 48 Figure 3-24 Normalized total pressure loss coefficient for set F.................... 49 Figure 3-25 Normalized cascade deflection coefficient for sets A, B, C, D, E, and F. .............................................................................................. 50 Figure 3-26 Normalized static pressure rise coefficient for sets A, B, C, D, E, and F. .............................................................................................. 52 Figure 3-27 Normalized diffusion factor for sets A, B, C, D, E, and F. .............. 53 Figure 3-28 Skin friction lines on the suction surface for base case (without vg) and sets a, b, c, d, and f at design operation ( i=0 [deg.]). ... 58 Figure 3-29 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 Base, D, E and F cases. ............................... 60 Figure 3-30 Total pressure loss factor with different inlet flow angles for sets A, B, C, D, E, and F[%]. ................................................................... 61 Figure 3-31 Normalized difference of flow turning angle at midspan for sets A, B, C, D, E, and F with various inlet flow angles [%]. ............... 64 Figure 3-32 Diffusion factor for case A, B, C, D, and E with different inlet flow angles [%]. ..................................................................................... 65 Figure 3-33 Static pressure rise coefficient for set A, B, C, D, E, and F with different inlet flow angles [%]. .................................................... 66 Figure 3-34 Doublet (left) and wishbone (right) vortex generators with geometrical parameters. .............................................................. 68 Figure 3-35 Vorticity magnitude contours at different planes A, B, C, and D for the base case (without VG), case with wishbone VG, and case with doublet VG. ............................................................................ 70 Figure 3-36 Streamlines at measurement planes A, B, C, and D for Base, Wishbone, Doublet cases. ............................................................. 73 Figure 3-37 Streamlines on Bottom endwall and the Suction surface for Base, Wishbone, and Doublet cases ...................................................... 77

xii

Figure 3-38 Total pressure loss contours at exit plane for Base, Wishbone, and Doublet cases. ........................................................................ 79 Figure 3-39 Skin friction contours at bottom endwall for Base, Wishbone, and Doublet cases. ........................................................................ 80

xiii

List of tables Table 2-1 Compressor cascade design parameters and operating conditions. ................................................................................. 12 Table 3-1 Different parameters values for CSVG used in sets A, B, C, D, E, and F ....................................................................................... 24 Table 3-2 Geometrical parameters of Doublet and Wishbone VGs. ...... 68

xiv

Nomenclature Latin symbols AL BF C CB Cf Cp DF e h i k L M P r S SP w x,y,z SL CF

:Attachment line : Bluntness factor : Chord length :Circulation bubble :Friction coefficient : Static pressure coefficient : Diffusion factor : Vortex generator's length : Vortex generator's height : Incidence angle :Turbulent kinetic energy : Span : Mach number : Pressure (total or static) :Rounded nose radius : Pitch :Separation point : Vortex generator's width : Cartesian coordinated : Separation line : Cross flow

Greek symbols β δ ζ ζ* ν σ τ Subscripts is s t Base VG θ n 1

: flow angle : Boundary layer thickness : Integrated total pressure loss coefficient :Local total pressure loss coefficient : Relative velocity : Solidity : Wall shear stress : Isentropic : Static pressure : Total pressure : Base case without vortex generator : Case with vortex generator : Tangent component : Normalized : At inlet xv

2 : At measurement plane Abbreviations CFD :Computational fluid dynamics CSVG :Curved side vortex generator DNS :Direct numerical simulation DOC :Direct operating costs LES :Large eddy simulation NTPLC :Normalized total pressure loss RANS :Reynold average Navier-stokes SFC :Specific fuel consumption TPLC :Total pressure loss coefficient VG :Vortex generator

xvi

Chapter 1 Introduction

Chapter 1 Introduction

2

Chapter 1 Introduction 1 INTRODUCTION 1.1 Introduction Axial compressor as one of the main components in the gas turbine and the aircraft engine is an essential element in energy production in the coming decades. A further increase in the efficiency of axial compressor is, therefore, necessary to reduce COX and NOX emissions from gas turbines. The current high level of development of modern turbomachinery, has very ambitious rates, and requires the use of the latest techniques and methods in the design of the individual turbomachinery components, such as axial compressor in order to increase its efficiency. In addition, the economic requirements needed by the airlines and power plant operators should be considered. For instance, the fuel consumption which plays a central role, as well as the procurement and maintenance costs are considered over the lifetime, especially for aircraft.

Therefore, it is necessary to use simple,

maintenance-free as possible methods to increase efficiency. In a compressor stage, there are numerous sources of loss that cause entropy creation. The sources of loss can be categorized as 2D and 3D. The possible 2D sources are: (i) blade boundary layers, (ii) trailing edge mixing, (iii) flow separation, and (iv) shock waves. The total 2D loss for a compressor can be examined through cascade tests or 2D computational methods, but there are no general correlations that can be applied to all cases. All compressor blades will suffer from boundary layer and trailing edge mixing loss. The aforementioned losses are strongly dependent on the blade surface pressure 3

Chapter 1 Introduction distribution. Well-designed compressor blades should not suffer from flow separation losses at their design operating conditions. However, at off-design conditions, when the diffusion levels on the blade surfaces become too high, the flow can separate leading to excessive loss and possible stall or surge. Shock wave losses are only present in compressor stages with supersonic inlet flow. The main 3D loss sources in a compressor are (i) end wall boundary layer, (ii) horse shoe, passage, and corners vortices, and (iii) tip leakage flow. However, in practice, it is difficult to isolate these sources of loss as they interact strongly and the total 3D loss is often simply described as loss due to secondary flow. 1.2 Literature review Secondary flow is a major obstacle arising in an investigation of the performance of axial compressors. An early definition of secondary flow given by Herzig et al.[1], “ any motion of boundary layer fluid having components of motion normal to the through flow direction”. Also, Kumar and Govardhan [2]defined the secondary flow as “the three-dimensional vortical flow structures that developed in blade passages due to high turning of the flow and non-uniform inlet total pressure profile”. The reason of secondary flow initiation is the boundary layer flow along the end wall which contains span wise velocity gradients[3]. When the boundary layer flow is turned, transverse velocity components are introduced. These secondary flows, created at the endwall and blade junction, extract energy from the fluid which would 4

Chapter 1 Introduction otherwise be used to rotate the blades or produce thrust. If these secondary flows can be weakened, more energy would be available for torque and thrust production. Separation of the boundary layer in the compressor’s blade passage is caused by the unfavorable pressure gradient in the flow direction as well as the crosswise variation of the pressure gradient across the flow passage[4,5]. A cross flow is motivated within the curvature of the flow passage due to the pressure difference on both the blade surfaces. As the flow propagates through the curved passage, a crosswise pressure gradient is created[4]. Fluid in the boundary layer near the wall is moving with a lower velocity than that outside the boundary layer, therefore, particle paths in boundary layer have a larger curvature than the outside paths[3].Thus, the tendency of the local boundary layer to separate increases, especially with the existence of the pressure gradients. Moreover, the crosswise flow, which occurs perpendicular to the main flow outside the boundary layer establishes a secondary flow, causing a transfer of low momentum boundary layer fluid into the center of the blade passage. As a result, frictional losses increase as high momentum fluid is brought near to the walls[3,6]. Since the early 1950’s a lot of researches were carried out to investigate, analyse, and reduce the effects of secondary flows and separation on turbomachines and on compressors in particular[4–12]. The endwall boundary layer separation as well as the flow separation in the corners of blade passages, the horseshoe vortex, the 5

Chapter 1 Introduction corner vortex, the tip vortex, the endwall cross flow, and the passage vortex are the main components of the secondary flow in the cascade as shown in Fig.1-1[2,13,14]. These secondary flows extract energy from the fluid and increase the flow instability [13]. Therefore, controlling the secondary flows is of crucial importance in order to improve the aerodynamic performance of compressors.

Figure 1-1 Secondary flow structure reported by Kang et al [14].

Boundary layer control can be used to delay the transition from laminar to turbulent boundary layer which reduces the skin friction, or it may be used to delay boundary layer separation along the blade suction side which increases the allowable blade loading [15].

6

Chapter 1 Introduction Many flow control techniques [16,17] have been investigated in order to reduce or overcome the effects of the secondary flow and to control flow separation. Those flow control techniques can be classified according to Gad-el-Hak as [16,18]: (i) Passive control which requires no auxiliary power[19–31]. (ii) Active control which involves energy expenditure[32–51]. Passive control methods were commonly used, Estruch-Samper et al [19] used micro vortex generator (with diamond arrangement) to control axisymmetric high speed laminar boundary layer separation. Ortmanns et al [20] implemented vortex generator with cambered profile to reduce cross-passage flow in compressor stator end-walls. Joubert and Le Pape[21] utilized a row of co-rotating deployable vortex generators ( vane type) located at the leading edge of an airfoil in order to control static stall. Mdouki and Gahmousse[22] used slotted blading in linear cascade configuration to increase allowable blade loadings and to enlarge the stable operating range for highly loaded compressor, Hergt et al [23] used various configuration of vortex generators (vane and plow vortex generator) placed on several positions, achieving a reduction in the total pressure loss up to 9%. Seo[24] employed a cavity as a control of shock wave interaction with turbulent boundary layer, also he reduced the total pressure loss as well as the strength of shock wave. Meyer [25] used single vortex generator placed in each corner between the wall and the compressor blade which reduced the corner separation significantly. Sahin[26], and Lengani et al [27] implemented low profile vortex generator (low profile vortex generator refers to vortex generators with height less 7

Chapter 1 Introduction than boundary layer thickness) on the end-walls to reduce secondary flow losses and to control turbulent boundary layer separation. Wheeler [28] investigated the doublet vortex generator to delay separation [29]. Micro vortex generators were found to be effective in reducing the separation zone as reported by Lu et al [30]. Lee et al [31] used various VG geometries in order to control normal shock boundary layer. Boundary layer suction is a famous active flow control technique that was investigated by many researchers[39–46]. Moreover, vortex generator jets were also used as an active flow separation control method [32–38]. It was noted that oscillatory blowing jets can delay separation from a symmetrical airfoil and this method is called periodic excitation [47–50].Plasma actuator was also used as an active technique of flow separation control [51]. Moreover, a lot of research has been done on the shape of threedimensional blades and non-axisymmetric endwall design which represent a major impact on the secondary flow and consequently a significant loss reduction due to load redistribution can be obtained[52,53]. As mentioned above, Vortex generators (VGs) were commonly used as a passive device to reduce the effects of secondary flow and the total pressure loss by either mixing the boundary layer or turning the flow. This role is mainly dependent on the ratio between the boundary layer thickness and characteristic’s dimensions of the used VGs[22,29]. Different geometrical configurations of vortex generators were 8

Chapter 1 Introduction previously used on compressors [22–25]. Results indicated that a significant improvement in the compressor’s performance was achieved due to using vortex generators. 1.3 Objectives and methodology In the present work, new designs of vortex generators are investigated. The new designs are: 1-Curved side vortex generator (CSVG) with sharp nose edge, 2-Curved side vortex generator with rounded nose edge, 3-Wishbone vortex generator and 4-Doublet vortex generator. They are placed in the endwall region near the leading edge of the compressor blade. This study is conducted in order to investigate the effect of inserting the vortex generators with varying dimensions on the secondary flow losses. The study is carried out by solving numerically the Reynolds-averaged Navier–Stokes equations with fully coupled turbulence model equations using the commercial flow solver ANSYS FLUENT. The results of the secondary flow losses without vortex generator are compared with the available measured values reported by Hergt et al[23] for validation purpose. Then, the study is devoted to assess the effects of inserting the vortex generator with different geometrical ratios inside the flow passage on the total pressure loss, the boundary layer separation, the streamlines foot print on blade and endwall surfaces, the vortex structure inside flow passage, the static pressure rise, and the blade deflection angle.

9

Chapter 2 Computational procedure


10

Chapter 2 Computational procedure 2 COMPUTATIONAL PROCEDURE 2.1 Compressor cascade In the present work, a linear high speed compressor cascade that was reported by the research group of Hergt et al. [23] is used. Their compressor cascade was designed by “MTU Aero Engines” with the profile shown in Fig.2-1. The design parameters and the operating conditions of the cascade are summarized in Table 2-1. In addition, the inlet and staggered angles of the compressor cascade are shown in Fig.2-2.

Figure 2-1 Blade profile of transonic compressor cascade designed by MTU aero engines[23].

11

Chapter 2 Computational procedure Table 2-1 Compressor cascade design parameters and operating conditions[23]. Mach number at inlet, [-]

M1 = 0.66

Inlet flow angle, [deg.]

β1=132°

Turning angle, [deg.]

Δβ = 38°

Stagger Angle,[deg]

βst =105.2 °

Blade chord, [mm]

c = 40 mm

Blade span, [mm]

L = 40 mm

Pitch to chord ratio, [-]

S/c = 0.55

Endwall boundary layer thickness, [mm]

δ = 4 mm

Figure 2-2 Compressor cascade parameters. 2.2 Computational domain and boundary conditions The computational domain used in the present work is depicted in Fig.2-3. The non-slip boundary condition is applied at the walls 12

Chapter 2 Computational procedure representing the top boundary, the bottom boundary (Endwall), and the blade surfaces demonstrating the suction and pressure sides including the leading and trailing edges.

Figure 2-3 Computational domain with the inserted VG. Periodic boundary conditions are applied on the domain sides. The pressure outlet boundary condition is defined at the outlet plane which is located at 200% of chord behind trailing edge. The fully developed flow is adopted at the inlet with an average Mach number of 0.66 and inlet angle (β1) of 132°. Turbulence intensity is set to be 1% at the inlet and 3% at the exit [23]. 2.3 Numerical solution In order to investigate the effect of inserting vortex generators with varying dimensions on secondary flow losses, the Reynoldsaverage Navier–Stokes with fully coupled turbulence model equations 13

Chapter 2 Computational procedure are numerically solved using the commercial flow solver Fluent-14. The three dimensional multiblock grid is constructed using a structured mesh of H-O-H topology as shown in Fig.2-4. Five different numbers of grids are selected in order to investigate the effect of grid size on the computed results. Figures 2-5, 2-6, 2-7, and 2-8 present the effect of grid size on the flow averaged turbulent kinetic energy, the mass flow averaged velocity, the total pressure loss coefficient(TPLC), and the velocity contours at exit plane (which is located at 40% of chord length behind trailing edge).

Figure 2-4 Mesh of the Base case.

14


Figure 2-5 Mass flow averaged turbulent kinetic energy (k, m2/s2) with different number of cells.

Figure 2-6 Mass flow averaged integrated velocity at exit angle with different no of cells.

15


Figure 2-7 Mass flow averaged integrated TPLC at exit angle with different no of cells.

Figure 2-8 Velocity contour lines in (m/s) at exit plane of different grid sizes (0.4, 0.8, 1.2, and 1.8 Million cells).

16

Chapter 2 Computational procedure Based on these figures, it is found that there is no grid dependency after 0.8 million cells. Therefore, the present simulation is performed using 0.8 million cells to get free grid independent results and to reduce the computational time and with minimum y+~1 near the walls, which is considered to capture and resolve the boundary layer at the blade surfaces and enwalls. 2.4 Validation The numerical results are validated first by comparing between the isentropic Mach, Mis, distribution at midspan calculated from the numerical and the experimental results of Hergt et al [23] as shown in Fig.2-9. Comparison indicates that a good agreement exists between the present simulation and the experimental results, since the maximum deviation is found to be less than 3.4 %.

Figure 2-9 Experimental and calculated numerical Mis distribution at midspan of reference cascade. 17

Chapter 2 Computational procedure Also, the total pressure loss contours as shown in Fig.2-10(a) are compared with the experimental results reported in Fig.2-10(b)[23]. It is worth mentioning that the values of total pressure loss are calculated and measured at a plane placed at 40 % of chord length behind the trailing edge. Comparison shows a good agreement between the present results and those measured and predicted by Ref.[23]. Furthermore, the position of the vortices I, II, and III shown in fig.2-10(b) are captured in the present simulation with certainty and plotted using the velocity vectors as shown in the Fig.2-11.

(a)

(b)

Figure 2-10 Total pressure loss contours calculated at a plane located at 40% of chord behind the trailing edge, (a) present simulation , (b) experimental TPLC reported by Hergt et al [23].

18


Figure 2-11 Velocity vectors at exit plane located at 40% of chord behind the trailing edge. Furthermore, the total pressure loss distribution is compared with the results obtained by Hergt et al [23] at the same plane (exit plane) as shown in Fig.2-12.

Figure 2-12 Comparison between the predicted mass flow averaged total pressure loss distribution of the present study and Hergt's[23] simulation. 19


Based on Fig.2-12, a reasonable agreement is observed between the present and Hergt’s simulations[23]. The maximum deviation is less than 4% away from the endwall, while it reaches about +9% near the endwall.

It was reported by Hergt [23] that the calculated total

pressure loss near the endwall is under-predicted from the measured value, consequently the difference between the present results and measured by Hergt [23] is expected to be much less than 9%. Thereby the simulated numerical model is able to predict the time-averaged blade loading with adequate engineering accuracy as appropriate boundary conditions are applied. Moreover, streamlines at the endwall and blade suction side have been verified by comparing the present calculations with Hergt et al[23] measurements. Figure2-13 shows the generated vortices that could be identified by separation lines: the suction side separation line identifies the horse-shoe vortex that propagates toward the blade suction side forming a laminar separation line. The endwall separation line identifies the corner vortex on the suction side. On the other hand, the blade separation line identifies the passage vortex and its separation from the blade suction surface. A comparison between the present results and those obtained by Hergt et al[23] is shown in Fig.213. The qualitative comparison shows a reasonable similar streamlines and consequently, secondary flow components.

20


(a)

(b)

Figure 2-13 Simulated streamlines on suction side and endwall (a) present simulation ,(b) Hergt et al simulation[23].

21


Chapter 3 Results and discussion

22

Chapter 3 Results and Discussion 3 Results and discussion In this chapter the results of the investigated VGs is divided into three parts. The three parts are as follow:  Part 1: Curved side VG at design condition.  Part 2: Curved side VG at off-design conditions.  Part 3: Non-conventional VGs. In each part the vortex generator parameters and the simulation results are shown and discussed. 3.1 Part 1: Curved side VG at design conditions Numerical simulations for six sets of curved side vortex generators (CSVGs) with and without a rounded nose are performed in order to find their effects on the development of secondary flows. The dimensions of studied sets of vortex generators named A, B, C, D, E, and F are summarized in Table 3-1. All tested CSVGs have the geometrical parameters shown in Fig.3-1. The vortex generator’s height to boundary layer thickness h/δ is varied from 0.1 to 0.5 for each set which is defined as low profile vortex generators [29].

Figure 3-1 Curved Sides’ Vortex Generator Geometry, (a) without round nose, (b) with round nose.

23

Chapter 3 Results and Discussion Table 3-1 Different parameters values for CSVG used in sets A, B, C, D, E, and F e/h

w/h

h/δ

6

3 4 5 6 0.1 0.15 0.2 0.25 0.3 0.4 0.5

Set A

x

x

Set B

x

Set C

x

Set D

x

x x x e/h

Set E

Set F

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

w/h

h/δ

4

5 6

8

6

0.4

x

x x

x

x

x

e/h

w/h

h/δ

5

6

0.4

x

x

x

r/δ 0.25 0.5 0.8 x

x

x

1 x

3.1.1 Effect of vortex generator on the cascade performance

The effects of inserting the vortex generators on cascade performance are discussed in the following five subsections. The first one depicts the influence of vortex generators on the development of secondary flows. The second subsection describes the influence of vortex generators on the total pressure loss coefficient. The influence of vortex generators on cascade deflection is shown in the third subsection. The fourth subsection illustrates the influence of vortex generators on the static pressure rise coefficient. In the last subsection, the influence of vortex generators on the diffusion factor is presented.

24

Chapter 3 Results and Discussion 3.1.2 Influence of Vortex Generators on the Development of Secondary Flows

Streamline patterns are used to display the separation lines and the foot print for the secondary flows that occur and their positions on the suction surface for the different sets of vortex generators. Figures 3-2 to 3-7 illustrate the streamline and the static pressure contours on the suction side for different configurations of vortex generators of A, B, C, D, E, and F. Figure 3-2 shows the streamline for the reference case (without VG) and set A where h/δ varies between 0.1 and 0.5 in step of 0.1. Form Fig.3-2, the inspection of the reference set and other sets indicate that at h/δ=0.1, streamlines show how separation lines are shifted along the suction surface. The cross flow from the endwall is moved toward the leading edge where a new separation line beside the formation of a separation bubble are observed.

Figure 3-2 Calculated static pressure contours and streamlines on the blade suction side of the reference case and set A with h/δ ranged from 0.1 to 0.5. 25

Chapter 3 Results and Discussion They occur in the position between the cross flow and the corner separation which is shifted slightly downstream. Increasing h/δ to 0.2 indicates that streamlines at the corner separation is shifted downstream, and endwall cross flows are still developed and formed towards the leading edge. For h/δ=0.3, streamlines show a further movement of the corner separation towards the trailing edge and a separation line is noticed near the corner separation region. Thus causing the endwall cross flow to be deflected in the downstream direction. At h/ δ=0.4, streamlines show a noticeable displacement of the corner separation downstream, and so leading the endwall cross flow is to be translated in the downstream direction as well. In addition the growth of previous formed separation lines occurs. Finally at h/ δ=0.5, streamlines show regression of the corner separation towards the trailing edge, and at the same time the endwall cross flow deflects in the downstream direction, as well as the separation line near the corner region disappears. Similarly, Fig.3-3 shows the streamline contours for the reference case and set B where h/δ varies between 0.1 and 0.5 in intervals of 0.1. Comparisons between the reference set and other sets indicate that at h/δ=0.1, streamlines shows how separation lines move at the suction surface. The cross flow from the endwall moves toward the leading edge where a new separation line occurs. In addition, the formation of a separation bubble in position between cross flow and corner separation is observed, while the corner separation is slightly translated downstream. Further increase of h/δ to 0.2 indicates that Streamlines move to the corner separation downstream and the 26

Chapter 3 Results and Discussion endwall cross flow is still developed and formed towards the leading edge.

Figure 3-3Calculated static pressure contours and streamlines on blade suction side of reference case and set B with h/δ ranged from 0.1 to 0.5. Furthermore, at h/ δ=0.3 streamlines also show a movement of the corner separation towards the trailing edge, and the endwall cross flow is deflected in the downstream direction. At h/ δ=0.4, streamlines show a noticeable displacement of the corner separation downstream, and the endwall cross flow is also translated in the downstream direction. Finally, at h/ δ=0.5 streamlines show regression of the corner separation towards the trailing edge, and at the same time the endwall cross flow is similarly deflected in the downstream direction.

27

Chapter 3 Results and Discussion Figure 3-4 shows the streamline contours for the reference case and set C where h/δ varies between 0.1 and 0.5 in interval of 0.1. Comparisons between the reference set and other sets indicate that at h/δ=0.1, streamlines show a translation of corner separation in the downstream direction towards the trailing edge. As the endwall cross flow propagates towards the leading edge, a separation bubble is noted between the endwall cross flow and the corner separation.

Figure 3-4 Calculated static pressure contours and streamlines on blade suction side of reference case and set C with h/δ ranged from 0.1 to 0.5. However, at h/δ=0.2, no significant changes in streamlines are noted. At h/δ=0.3, streamlines also show a translation of the corner separation towards the trialing edge, and a formation of a separation 28

Chapter 3 Results and Discussion line between the endwall cross flow and the corner separation. At h/δ=0.4, streamlines show a significant movement of the corner separation downstream towards the trailing edge, and the endwall cross flow is deflected in a downstream direction. However, the separation line formed in the previous case disappears. Finally, at h/δ=0.5, streamlines show that the corner separation is at 0.85 of chord (downstream) which is significantly translated, and the endwall cross flow is deflected in the downstream direction as well.

Figure 3-5 Calculated static pressure contours and streamlines on the blade suction side of the reference case and set D with h/δ ranged from 0.1 to 0.5. Figure 3-5 shows the streamline contours for the reference case and set D where h/δ varies between 0.1 and 0.5 in intervals of 0.1. Comparisons between the reference set and other sets indicate that at 29

Chapter 3 Results and Discussion h/δ=0.1, the cross flow is slightly reduced meanwhile it propagates in the span direction, while separation lines do not display significant changes. Though, at h/δ=0.2, no significant changes in streamlines are noted. At h/δ=0.3, streamlines show a translation of the corner separation towards the trialing edge, a formation of laminar separation line between the endwall cross flows, a corner separation, and a turbulent reattachment line. At h/δ=0.4, streamlines are significantly moved from the corner separation region towards the trailing edge, and the endwall cross flow is deflected in the downstream direction. However, the separation line formed in the previous case disappeared. Finally, at h/δ=0.5, streamlines show that the corner separation is at 0.85 of chord (downstream) which is significantly translated, and the endwall cross flow is also deflected in the downstream direction. Figure 3-6 shows the streamline contours for the reference case and set E where e/h varies between 4 and 6 in step of 1. Comparisons between the reference set and other sets indicate that streamlines are shown for all values of e/h, and the cross flow is slightly reduced. Then again, separation lines do not have significant changes. Figure 3-7 shows the streamline contours for the reference case and set F where r/δ varies between 0.25 and 1 in intervals of 0.25. Comparisons between the reference set and other sets indicate that while streamlines are shown for all values of r/δ, it is obvious that the cross flow slightly reduces; meanwhile separation lines do not witness significant changes.

30

Chapter 3 Results and Discussion

Figure 3-6 Calculated static pressure contours and streamlines on blade suction side of reference case and Set E with e/h=8, 6, 5, and 4.

Figure 3-7 Calculated static pressure contours and streamlines on blade suction side of reference case and set F with h/δ ranged from 0.1 to 0.5. 31

Chapter 3 Results and Discussion To conclude, for all those sets, the pressure side effects the development of the passage vortex and its propagation which in turn affects the flow structure on the blade suction side. As a result of inserting the vortex generators, the passage vortex is lifted from the endwall and swept downstream which travels the separation line on the blade suction surface towards the trailing edge of sets A, B, C, and D. Increasing h/δ results in the downstream movement of this separation line as noted in the previous figures. For set E, increasing e/h leads to the increase of the downstream movement of the separation line on the blade suction surface. A similar trend is observed by increasing r/δ as set F. For further explanation, Fig.3-8 shows the velocity vectors (plotting of a unified velocity vector length for clarity purposes) on the suction side for the reference case and set D for h/δ=0.3, 0.4, and 0.5.

Figure 3-8 Velocity vectors on suction side for reference case and set D for h/δ=0.3, 0.4, and 0.5. 32

Chapter 3 Results and Discussion Figure 3-8 shows how the deflected passage vortex affects the velocity vectors and consequently the separation lines. It is obviously shown that a downstream translation of the blade separation line occurs. This translation increases for h/δ=0.4 where the separation line is almost eliminated and the suction side flow is developed in the main flow direction. Furthermore, it is clear that the endwall cross flow is redirected to the main flow direction by increasing r/δ, which is also due to the deflected passage vortex. 3.1.3 Influence of Vortex Generators on Total Pressure Loss Coefficient

Total pressure loss coefficient (TPLC) is usually used as an indicator for losses that take place in a cascade. Reducing pressure losses tends to increase the cascade efficiency and consequently enhances the compressor performance. TPLC (ζ*) refers to local mass averaged total pressure loss coefficient (TPLC) and it can be defined as the following:

*

pt 1  pt 2 ( y , z ) p t 1  p s1

3-1

Where: Pt1 is the total pressure at the inlet, and Pt2(y,z) is the total pressure at the exit plane while, Ps1 is the static pressure at the inlet. TPLC is estimated as a function of (y, z) based on the calculated values at a plane downstream of the trailing edge at the distance of 0.45 of the chord (C). This plane is defined as the exit plane where variables computed at this plane take the index 2.

33

Chapter 3 Results and Discussion 3.1.3.1 Total Pressure Loss Coefficient Contours

Figures 3-9 to 3-12 show the total pressure loss contours for sets A, B, C, and D respectively.

For each set, the total pressure loss

contours are depicted for different values of h/δ varied from 0.1 to 0.5 in intervals of 0.1 along with the contours for the reference case. As reported earlier, the reference case is related to the flow in the compressor cascade without the vortex generator. By comparing the TPLC for reference case and those for different values of h/δ, the results show two different trends. Firstly, a slight reduction in TPLC values are observed for h/δ ranged from 0.1 to 0.3. Secondly, further increase of h/δ beyond 0.3 results in a significant reduction in TPLC. This is most likely due to the effect of increasing h/δ which strengthens the generated vortices and consequently increases the mixing of high momentum fluids with low ones. This process enriches the boundary layer velocity and therefore exhibits more resistance to separate from the suction side. Furthermore, increasing h/δ leads to an increase of the mean stream wise momentum of the boundary layer till h/δ=0.4, nevertheless beyond this value further increase in h/δ has no effect in TPLC reduction. This is due to energizing the lower part of the boundary layer velocity profile, since it is more crucial to reduce the tendency of the flow to separate. From Figs. 3-9 to 3-12, increasing w/h leads to a significant increase in TPLC. This is attributed to the increase in stretching rate of the generated vortices as w/h increases. This increase is most likely related to the bluntness factor (BF) as defined by Equation 3-2. Increasing w leads to an increase in BF and consequently increases stretching rate and vortex strength. The strong 34

Chapter 3 Results and Discussion generated vortex becomes more powerful to depart and reduce the effects of the swept pressure leg of the horse shoe vortex by the cross flow towards the suction side. The relationship between Bluntness Factor (BF) and geometrical parameters of vortex generators can be written as:

BF 

1 r w a    2 e  a e

(2)

3-2

Where: r is the nose radius, “a” is the distance from the nose head along the CSVG surface to the maximum thickness, “w” is the width of vortex generator, and “e” is the length of vortex generator as shown in Fig.3-1.

Figure 3-9 Total pressure loss contours of reference case and set A with h/ δ ranged from 0.1 to 0.5, where w/h=3, and e/h=6. 35


Figure 3-10 Total pressure loss contours of reference case and set B with h/ δ ranged from 0.1 to 0.5, where w/h=4, and e/h=6.

Figure 3-11 Total pressure loss contours of reference case and set C with h/ δ ranged from 0.1 to 0.5, where w/h=5, and e/h=6.

36


Figure 3-12 Total pressure loss contours of reference case and set D with h/ δ ranged from 0.1 to 0.5, where w/h=3, and e/h=6. Figure 3-13 shows the TPLC for the reference case and set E where e/h is equal to 4, 5, 6, and 8, while h/δ=0.4, and w/h=6. As shown in Fig.313, the reduction in TPLC increases from e/h=4 to 5. Further increase in e/h from 5 to 8 leads to a decrease in TPLC. The reason is that the increase of e/h leads to a reduction in bluntness factor as in Equation 3-2, and consequently a reduction in stretching rate and vortex strength. This trend can be attributed to the effects of parameter “e” on both BF and “a”. When the parameter “e” increases the BF decreases, on the other hand as “e” increases, “a” increases which can increase or decrease the BF. Therefore, the results show that the reduction gained in TPLC increases by increasing “e/h” up to 5. Any further increase of e/h beyond the value of 5, the reduction in TPLC decreases due to the weakness of the generated vortices and consequently the reduction in its stretching rate. 37


Figure 3-13 Total pressure loss contours of reference case and set E with e/h=4, 5, 6, and 8 where h/δ=0.4, and w/h=6. Figure 3-14 shows the TPLC for the reference case and set F with r/δ = 0.25, 0.5, 0.75, and 1.0, where h/δ=0.4, w/h=6, and e/h= 5. It was found that a significant reduction in TPLC occurs with increasing r/δ from 0.25 to 0.5. Further increase of r/δ beyond 0.5 results in a decrease of TPLC. This is attributed to the increase of the bluntness factor which is a correlation on the effect of wing shape on the horseshoe vortex stretching rate as reported by Fleming et al [54]. In rounded nose vortex generator the parameter “e” affects the blunt nose shape which controls the vortices strength through the bluntness factor “BF” [55,56].

38


Figure 3-14 Total pressure loss contours of reference case and r/δ=0.25,0.5,0.75, and 1 where h/δ=0.4, w/h=6, and e/h=5. Moreover, as the vortex generator nose radius increases, the timemean vortex size and strength increase as reported by [54]. These strong generated vortices enhance the performance of the compressor cascade till r/δ≈0.5. Further increase in r/δ leads to stronger vortices with larger vortex stretching rate which increases the energy loss and in turn reduces the enhancement degree. 3.1.3.2 Total Pressure Loss Coefficient Distribution

The integration of local total pressure loss coefficient (ζ) distribution is calculated as a function of Z/L by integrating the mass averaged TPLC from y = 0 to y = S for each value of Z/L with a constant Δ Z.

39

Chapter 3 Results and Discussion h

 

s

    y, z  

z 0 s 0 h

2

(y, z) u 2 (y, z)dydz 3-3

s

 

2

(y, z) u 2 (y, z)dydz

z 0 s 0

Where: ζ is defined as the integrated local total pressure loss coefficient, and s is defined as the pitch which is the distance between two adjacent blades. For sets A, B, C, D, E, and F, the total pressure loss coefficient distribution at the exit plane from the endwall till the midspan is shown in Figs. 3-15 to 3-20. It was found that for all investigated sets, the mass average of TPLC at Z/L = 0 is approaching unity.

Figure 3-15 shows two distinct trends. Firstly, at Z/L 0.25, the TPLC is 40

Chapter 3 Results and Discussion slightly less than the corresponding TPLC for the reference case except at the VGs with h/δ ranging from 0.1 to 0.25 where it is slightly higher than those of the reference case. When Z/L lies between 0.14 and 0.25, TPLC values for reference case and for VGs with h/δ =0.1, 0.2 and 0.3 are almost the same.

Figure 3-15 Spanwise total pressure loss coefficient distribution for set A with different h/δ values

Similarly, Fig. 3-16 shows two distinct trends. For Z/L0.25, the TPLC for all h/δ cases is slightly less than the corresponding TPLC for the reference case except at h/δ =0.1, and 0.15

41

Chapter 3 Results and Discussion where the corresponding values of TPLC is slightly higher than that of the reference case. Figure 3-17 shows that at Z/L 0.2, the TPLC for all h/δ cases is slightly less than the corresponding TPLC for the reference case except at h/δ =0.1, and 0.15 where TPLC is slightly higher than those of the reference case.

42

Chapter 3 Results and Discussion Figure 3-18 shows at Z/L 0.32, the TPLC is slightly less than the corresponding TPLC for the reference case except at h/δ=0.1, and 0.15 where the TPLC is slightly higher than those of the reference case.

Figure 3-17 Spanwise total pressure loss coefficient distribution for set C with different h/ δ values.

43


Figure 3-18 Spanwise total pressure loss coefficient distribution for set D with different h/ δ values. Figure 3-19 shows that the TPLC distribution is reduced compared to the reference case along the span for e/h=4, 5, while it’s slightly reduced for e/h=8. For e/h=6, it is reduced at Z/L< 0.06, and increased until Z/L=0.3, then it is reduced again. The highest reduction in TPLC occurs at e/h=5. Figure 3-20 shows that the TPLC is reduced for all values of r/δ from 0.25 to 1. The highest reduction in TPLC occurs with r/δ=0.5 which is the highest of all sets. The reason of the change in TPLC distribution is attributed to the interaction between the secondary flow which affects the formation and developing of passage vortex (i), and the generated suction side vortex (ii). These two vortices are shown for the reference case and a vortex generator of set F at r/δ=0.5 as shown in Fig.3-21.

44


Figure 3-19 Spanwise total pressure loss coefficient distribution for set E with different e/h values.

Figure 3-20 Spanwise total pressure loss coefficient distribution for set F with different r/δ values.

45

Chapter 3 Results and Discussion The outcome of this interaction is reflected as changes in TPLC distribution along the span with detectable reduction in TPLC values for all sets. Near the Suction side, the generated vortex energizes the lower momentum fluid (in the boundary layer) and consequently reduces or delays the onset of separation.

Figure 3-21 TPLC contours for reference case and set F of r/δ=0.5 with (i) passage vortex, and (ii) the generated suction side vortex, at exit plan. 3.1.3.3 Normalized Total Pressure Loss Coefficient

Normalized TPLC is defined as:

n 



 Re f



 VG   Re f  Re f

3-4

It is calculated for all sets by integrating the mass-averaged TPLC value across the exit plane and subtracting it from the integrated massaveraged TPLC for the reference case. Figure 3-22 presents the variation of ζn versus h/δ for sets A, B, C, and D. From Fig.3-22, for set A the ζn reduces by 2.3% at h/δ=0.1. As h/δ increases, the reduction in ζn increases from 3% at h/δ=0.15 to about 5.3% at h/δ=0.4 then decreases to about 3.7% at h/δ=0.5. 46


Figure 3-22 Normalized total pressure loss coefficient for sets A, B, C, and D. A Similar trend is observed for set B where ζn is reduced by 1.9% at h/δ=0.1. As h/δ increases, the reduction in ζn increase from 3.25% at h/δ=0.15 to about 6.67% at h/δ=0.4 then decreases 5.82% at h/δ=0.5. For set C, the ζn is reduced by 1.7% at h/δ=0.1. As h/δ increases, the reduction in ζn increase from 3.73% at h/δ=0.15 to about 7% at h/δ=0.4 then decreases to 5.1% at h/δ=0.5. Finally for set D, the ζn is reduced by 1% at h/δ=0.1. As h/δ increases, the reduction in ζn increases from 3.4% at h/δ=0.15 to about 12.6% at h/δ=0.4 then it is reduced to 5.1% at h/δ=0.5. Figure 3-23 presents the variation of ζn versus e/h for set E. As shown in Fig.3-23, ζn is about 13.4 % at e/h=4. As e/h increases, ζn reaches to 18.6 % at e/h=5 and then reduces to about 5.73% at e/h=8. 47


Figure 3-23 Normalized total pressure loss coefficient for set E. The effect of varying the vortex generator nose radius r/δ on the NTPLC is shown in Fig.3-24. Based on this figure, ζn is about to 18.62% at r/δ=0. Increasing r/δ to 0.5 results in an increase of ζn to 20.7%, while further increase in r/δ to 1.0 leads to a decrease in ζn to 15.8%. In conclusion the NTPLC reaches 20.7% for set F with r/δ=0.5. This value of 20.7 % is the best achievable reduction in a NTPLC among all tested cases.

48


.

Figure 3-24 Normalized total pressure loss coefficient for set F.

3.1.4 Influence of Vortex Generators on Cascade Deflection

Cascade deflection (ε) is calculated as follow:

  1  2

3-5

Figure 3-25 shows the variation of the percentage of deflection angle εn=Δε/εRef versus h/δ for sets A, B, C, and D. Based on Fig.3-25, deflection is slightly changed for all sets between h/δ=0.1-0.5. However, for set D a significant reduction is observed between h/δ=0.4 and 0.5. As shown in Fig.3-25, set E has a slight change in deflection occurring by varying e/h. It is noted that the deflection increases by increasing the value of e/h. For set F, the deflection change is ranged from 0 to -0.5 % with r/δ =0.25, 0.5, 0.75, and 1.These results are

49

Chapter 3 Results and Discussion important for multistage compressors, since the change in deflection angle causes an off design operation with incidence angle for the next stages. However, using vortex generators does not lead to a significant change in deflection and consequently the incidence angle changes will slightly affect the performance of subsequent stages.

Figure 3-25 Normalized cascade deflection coefficient for sets A, B, C, D, E, and F. 3.1.5 Influence of Vortex Generators on Static Pressure Rise Coefficient

Static pressure rise coefficient, Cp is defined as:

Cp 

Ps 2  Ps1 Pt1  Ps1

3-6

Where: pt1 is the total pressure at the inlet; pt 2 is the total pressure at the exit; p s1 is the static pressure at the inlet; and p s 2 is the static 50

Chapter 3 Results and Discussion pressure at the exit. Fig.3-26 shows the variation of the normalized change of the static pressure rise coefficient Cpn=(CpVG-CpRef)/CpRef at mid span versus h/δ for sets A, B, C, and D. As shown in Fig. 3-26, Cpn is decreased for all sets. This reduction almost remains constant for set A, while it increases for sets B, C, and D. The percent of change in Cp n has the minimum reduction of 2.7% at set D with h/δ=0.1 and the maximum reduction of -11.6% at set D with h/δ=0.5. For set E, as shown in Fig.3-26, increasing e/h from 4 to 8 leads to a decrease in the reduction of Cpn from -12 to -8 %. For set F, as shown in Fig.3-26, the reduction in normalized change of the static pressure rise coefficient is almost constant with various r/δ values. This reduction in static pressure with the increase in exit total pressure means that there is a considerable increase in the dynamic pressure when using the vortex generators. To benefit from the increase in the dynamic pressure, optimization study can be carried out on the suction blade profile to recover part of the dynamic pressure into static pressure.

51


Figure 3-26 Normalized static pressure rise coefficient for sets A, B, C, D, E, and F. 3.1.6 Influence of Vortex Generators on Diffusion Factor

Blade loading is assessed by calculating 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 the following Equation 3-6 [28]:

DF  1 

v 2 v  v1 2v1

3-7

Where: ν1 is the inlet relative velocity at inlet plane, ν2 is the outlet relative velocity at exit plane, Δνθ is the difference of tangential components of inlet and outlet velocity, and σ is the solidity. 52

Chapter 3 Results and Discussion Figure 3-27 shows the variation of the normalized difference of the diffusion factor DFn=(DFVG-DFRef)/DFRef for sets A, B, C, and D versus h/δ at midspan. The Diffusion factor is used as an indicator of probability of separation occurrence. Based on Fig.3-27, as h/δ increases, the diffusion factor is decreased for all sets except for set C at h/δ=0.4, and set D at h/δ=0.5 where the diffusion factor is slightly increased. Reduction of the normalized diffusion factor as a percentage varies from 0.5% for set C with h/δ=0.4 to 5.5% for set C with h/δ=0.5. The reduction in the diffusion factor causes a reduction in the flow tendency to separate which may be reflected in the delay or for some sets leading to eliminate separation on the suction surface.

Figure 3-27 Normalized diffusion factor for sets A, B, C, D, E, and F.

53

Chapter 3 Results and Discussion For set E, as shown in Fig.3-27, the diffusion factor reduction is almost constant -2%. This behavior is also similar to set F, as shown in Fig.3-27. From literature, values of DF in excess of 0.6 are thought to indicate blade stall [57]. In this study, the DF for all cases including the reference case is about 0.35. 3.1.7 Summary

New designs of vortex generators are considered in the current investigation in order to control the secondary flow losses in compressor cascades and enhance the compressor’s performance. Six different sets of vortex generators with varying geometrical parameters and designs are numerically investigated. The flow in the compressor cascade is a 3-d compressible turbulent flow with an inlet Mach number of 0.66 and an inlet blade angle (β1) of 132°. Numerical simulations are performed using a numerical solver Fluent-14. The flow through the compressor cascade is invistigated without and with vortex generators placed on the endwall region near the leading edge of the cascade blade. In light of the current study, some important observations can be made: 1. Vortex generators have a significant impact on secondary flow losses such as improving the location of separation lines by its moving toward the trailing edge, and reducing the corner vortices. 2. A significant reduction in the NTPLC of up to 20.7% is accomplished using the curved surface vortex generator with a rounded nose of r/δ=0.5, w/h=6, e/h=5, and h/δ=0.4. 54

Chapter 3 Results and Discussion 3. Using vortex generators results in reduction of the diffusion factor of about -2.0 %. This will enlarge the safe margin of operating conditions without stall. 4. Inserting vortex generators has insignificant effect on the change of deflection and consequently there is no induced incidence angle that can affect the next stage. However, there is a slight reduction of static pressure rise which leads to an increase of dynamic pressure. To benefit from the increase in the dynamic pressure, a further investigation is needed in order to recover part of the dynamic pressure into static pressure.

3.2 Part 2: Curved side vortex generators at off-design conditions 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 rise coefficient, and diffusion factor to show the output results. 3.2.1 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, 55

Chapter 3 Results and Discussion 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.3-28, 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 set A, as shown in Fig. 3-28. As w/h increased for design B, no significant changes in the position and distribution of the streamlines are identifiable.

56

Chapter 3 Results and Discussion Further increase in w/h, as in set 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 set D yields a disappearance of SL1 and AL1, furthermore, the reverse flow also disappeared, and this 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 set E is similar to that caused by set F; therefore it is not reported here. In set 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. By 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.

57


Figure 3-28 Skin friction lines on the suction surface for base case (without vg) and sets a, b, c, d, and f at design operation ( i=0 [deg.]). 58

Chapter 3 Results and Discussion 3.2.2 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 Equation 3-1. Figure 3-29 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 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. NTPLC (ζn) 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 in Equation 3-4 in section 3.1.4.3. To calculate the TPLC, the local value of TPLC(y,z) in Equation 3-1 is integrated in the spanwise direction and pitch wise directions for base and all VG cases.

59


Figure 3-29 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 Base, D, E and F cases. Figure 3-30 shows the NTPLC for all cases. At design condition, for sets A to D, where β1=132 deg., it is noticeable that by increasing w/h the NTPLC 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 NTPLC ranges from -5.3% to -12.6 % for set A and D respectively. For set E a further reduction in 60

Chapter 3 Results and Discussion NTPLC is attained with value of -18.6 %.The highest reduction is reached using set F with rounded nose edge, where the NTPLC value is- 20.7%.

Figure 3-30 Total pressure loss factor with different inlet flow angles for sets A, B, C, D, E, and F[%]. At off-design condition, it is clear that NTPLC 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 sets, 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 61

Chapter 3 Results and Discussion 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 NTPLC is slightly reduced at this operating point. Furthermore at i= -2 β1=130 deg. NTPLC is further reduced for all sets, the highest reduction is reached at set E with value of -12.3 %. At positive incidence angles the effect is reversed where the suction side generated vortex is stronger than that of the pressure side. NTPLC is increased for all sets at i=+2 where β1=134 deg., and the uppermost value of NTPLC reduction at this incidence angle occurs at set E with value of -12.8 %. TPLF is further increased with i=+4 where β1=136 deg., for all sets. At i=+6 deg., Where β1=138, all sets have an increase in pressure loss which is noted by the positive vale of NTPLC for all sets at this incidence angle. Therefore, at design conditions, set F causes the highest reduction in NTPLC; nevertheless, at off-design operation set E yields higher reduction in NTPLC than this caused by set 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. 3.2.3 Effect of vortex generator on flow turning angle

Flow turning angle is computed from Equation 3-5. In order to track the change in flow deflection by using vortex generators, the difference 62

Chapter 3 Results and Discussion of the flow turning angle will be normalized by flow turning of the base case as shown in Equation 3-9.

n 

 VG   Base  Base

3-8

The normalized difference of flow turning angle is shown at midspan for base case and all VG cases in Fig.3-31. At design operation, the flow turning angle is either decreased or increased by using VG where the maximum reduction is of - 0.25 % with the set C and the maximum increase of 0.38% with the set D. Consequently, a slight change is noticed in the flow turning angle for all sets 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 set A, slight change in this value is noted for other sets. As negative incidence decreases to i= -4 deg., flow turning is increased to 1.2% at set B. Further decrease in incidence angle to i= -2 deg. Reduces the flow turning angle by 0.53 % at set 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 set B. By increasing the positive incidence to i= +4 deg, further increase in flow turning is attained

with middle value of 0.45% at set A. Highest positive

incidence angle of i=+6 deg results in an increase flow turning with central value of 0.63% at set A .Consequently, using VG has no

63

Chapter 3 Results and Discussion significant effect on the flow turning angle at design and off-design operation.

Figure 3-31 Normalized difference of flow turning angle at midspan for sets A, B, C, D, E, and F with various inlet flow angles [%]. 3.2.4 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 3-7. Normalized diffusion factor in Equation 3-10 is used to measure the effect of different cases with VG at different incidence angles on the diffusion factor.

64


DFn 

DFVG  DF Base DFBase

3-9

Figure 3-32 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.3-32.

Figure 3-32 Diffusion factor for case A, B, C, D, and E with different inlet flow angles [%].

65

Chapter 3 Results and Discussion 3.2.5 Effect of vortex generator on static pressure rise

Static pressure rise coefficient is calculated form Equation. 3-6 and the normalized difference is calculated as shown in Equation 3-11.

Cp n 

CpVG  Cp Base Cp Base

3-10

Figure 3-33 shows the difference in static pressure rise coefficient for all sets. 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.3-33.

Figure 3-33 Static pressure rise coefficient for set A, B, C, D, E, and F with different inlet flow angles [%]. 66

Chapter 3 Results and Discussion 3.2.6 Summary

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 blade angle of β1=132⁰ at design operation. For off-design operation the flow incidence angle is changed between i= -6 and i=+6 deg. The results show that for all investigated configurations, a significant reduction of total pressure loss up to 20.7% by set 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.

67

Chapter 3 Results and Discussion 3.3 Part 3: Non-conventional VGs Two types of vortex generators (doublet and wishbone) are investigated as a boundary layer control device. Doublet and wishbone VG are shown in Fig.3-34; their geometrical parameters are summarized in Table 3-2.

Figure 3-34 Doublet (left) and wishbone (right) vortex generators with geometrical parameters. Table 3-2 Geometrical parameters of Doublet and Wishbone VGs. VG Doublet

h/δ e/h w/h t1/h t2/h 0.4

5

6

‫ــــ‬

‫ــــ‬

Wishbone 0.4

5

6

0.8

1.2

In this section, the effect of inserting the two types of VGs on the vortex structure inside the flow passage as well as the separation lines distribution along the bottom endwall (where the VG is placed) are presented and discussed. 3.3.1 Effect of vortex generators on the vorticity magnitude

In order to track the changes of the vorticity magnitude by using the vortex generators, four measurement planes are used and placed at 68

Chapter 3 Results and Discussion different positions along the blade. The four planes are A, B, C and D placed at 20%, 40%, 60%, and 80% of chord length respectively for base case as well as doublet and wishbone cases. As shown in Fig.3-35 vorticity magnitude is varied along the blade chord for all cases.

69


Figure 3-35 Vorticity magnitude contours at different planes A, B, C, and D for the base case (without VG), case with wishbone VG, and case with doublet VG. 70


For base case(without VG) at plane A vorticity is noticed to have high value top and bottom walls this is due to the endwall boundary layer. Plane B, shows a growth in the vorticity magnitude near the walls and a slight increase in vorticity near the corners of the blade suction surface and both enwalls. Further increase in vorticity is noted at suction surface in plane C, this increase in vorticity is an indicator of the passage vortex which is noted to initiate separation from the suction surface. Plane D, shows a reduction in the vorticity magnitude near the endwall; in addition, an increase in the vorticity diffusion is noticed which is expected because of boundary layer growth, and this also indicates the propagation of the passage vortex. As wishbone VG is inserted, vorticity contours witness some changes in value and distribution along measurement planes. At plane A, a circular area of high vorticity is noticed above the vorticity caused by the bottom boundary layer. This circular area indicates the suction side component of the wishbone's generated vortex. Moving to plane B, an increase in the circular (high vorticity) area is noted which indicates the further stretching of the generated vortex. 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, which means a reduction in the passage vortex strength is attained. Plane D, shows a further stretching of the generated vortex with lower vorticity magnitude, while the high vorticity area around the bottom endwall and the suction surface is slightly reduced , which refers to an 71

Chapter 3 Results and Discussion increase in the mixing of low momentum fluid ( boundary layer of bottom endwall and blade suction surface) and the high momentum fluid. For doublet VG; 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 flow passage (near its center), due to the high deflection of the generated vortex along the VG side. At plane B, the circular area of vorticity is increased; consequently, mixing low momentum fluid (bottom endwall boundary layer) with high momentum fluid (free stream flow). At plane C, the vorticity magnitude is reduced which indicates a reduction in the strength of the generated vortex. At the same plane, a reduction in bottom endwall vorticity is noticed, which is a result of the achieved 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 noticed to be reduced. In addition, a further reduction in vorticity magnitude is noticed at the bottom endwall. 3.3.2 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.3-36.

72


Figure 3-36 Streamlines at measurement planes A, B, C, and D for Base, Wishbone, Doublet cases. 73


For base case (without VG), plane A has no vortex formation noted. As the flow is propagating toward plane B, the pressure side horse shoe vortex which is driven by the pressure gradient toward the suction surface, this vortex is noted above the bottom endwall. Further movement toward plane C indicates the appearance of the passage vortex, it is also noticeable, the appearance of the corner vortex between the bottom endwall and the suction surface. At plane D, the passage vortex is shifted from the bottom endwall toward the midspan. A magnified view near the corner between suction surface and bottom endwall shows the propagation of 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 figure. At plane C, the passage vortex appears near the lower suction surface. Passage vortex is slightly deflected toward the blade suction surface. As for plane D, lower passage vortex has been shifted slightly toward the midspan. Another magnified view of the corner vortex is used for wishbone VG, as shown no significant changes to the corner vortex is attained. Using doublet VG also causes changes in the streamlines on the measurement panes. At plane A, the pressure side generated vortex is more identifiable than in case of wishbone VG. This indicated a higher strength generated vortex. So, mixing the bottom endwall boundary 74

Chapter 3 Results and Discussion layer is achieved. It is also noted that the generated vortex is slightly shifted toward the periodic boundary (near the center of flow passage). As the flow propagates toward plane B, the generated vortex is propagating as well, which causes additional mixing of bottom endwall boundary layer. At plane C, passage vortex is noticed to be slightly deflected from the blade suction surface toward the flow passage, which is due to the effect of the generated pressure side vortex. Another thing to notice at this plane is the diminished corner vortex, which is due to energizing the 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. 3.3.3 Effect of vortex generators on suction surface streamlines

Figure 3-37 shows the surface streamlines at blade suction surface and bottom endwall. The streamlines are used to track the movement and growth or decay in the separation lines which are a result of secondary losses components. For base case (without VG), 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 reattached 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 re-attaches to it at AL1.A circulation bubble CB is 75

Chapter 3 Results and Discussion 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, node N is moved downstream toward the trailing edge (at 40% of chord length), because the generated vortex deflected the horseshoe vortex in the downstream direction. In addition, separation and attachment lines of 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; but in contrast an increase in the corner vortex is attained. For the passage vortex, alight deflection in the downstream direction is noticed, which could be identified by the movement of SL1 and AL1; in addition, a further movement of circulation bubble CB in the downstream direction is also noticed. Consequently, the generated vortex causes a slight deflection of the passage in the downstream direction. Another circulation bubble CB1 appears on the suction surface, this bubble is formed by 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

76

Chapter 3 Results and Discussion direction, while the reverse flow region RF is shifted toward the midspan.

Figure 3-37 Streamlines on Bottom endwall and the Suction surface for Base, Wishbone, and Doublet cases 77


By inserting doublet VG, node N is moved towards the trailing edge (at 55% of chord length). This large movement indicates a high deflection of the horseshoe vortex by the generated vortex. 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. Therefore, doublet VG increases the mixing of the endwall boundary layer and reduces the corner separation. Moreover, 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. No significant changes is noted in the cross flow CF, reverse flow RF, and the circulation bubble CB1. 3.3.4 Total Pressure loss contours

Figure 3-38 shows the total pressure loss coefficient (TPLC) contours at exit plane (located at 40 % of chord length). 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 %. 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 %. Therefore, using doublet and wishbone VG (as a boundary layer control device) increases the total pressure losses in comparison with the base case. TPLC is calculated from Equation. 1 where the subscript 1 indicates the inlet plane, and subscripts 2 indicated the exit plane. 78

Chapter 3 Results and Discussion 3.3.5 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 3-12.

Cf 

w 1 U 2 2

3-11

Skin friction coefficient (Cf) contours at bottom endwall for Base, wishbone and doublet cases is shown in Fig.3-39.

Figure 3-38 Total pressure loss contours at exit plane for Base, Wishbone, and Doublet cases. From this figure, wishbone VG causes a significant reduction in friction coefficient Cf in comparison with the Base case, with a value of 32%. This reduction in friction coefficient is increased by using Doublet VG to 46%. This significant reduction in friction coefficient stimulates more investigation to be conducted on those two types of VGs.

79

Chapter 3 Results and Discussion 3.3.6 Future work

The investigation will be extended by using different geometrical ratios (for both doublet and wishbone vortex generators) that causes a TPLC reduction, and aerodynamic enhancement in the performance of the compressor cascade.

Figure 3-39 Skin friction contours at bottom endwall for Base, Wishbone, and Doublet cases.

80

Chapter 3 Results and Discussion 3.3.7 Summary

The results shows a moderate effect of the two vortex generators on the separation on the suction surface and the bottom endwall. Doublet VG causes the corner vortex to be diminished. In contrast, 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. In addition a significant reduction in friction coefficient at the bottom endwall is achieve by wishbone (up to 32%) and doublet (up to 46%) vortex generators. Therefore, the investigation is recommended to be extended to study various geometrical parameters of the two types in order to reach the optimum geometrical parameters that give better control of the boundary layer and enhance the aerodynamic performance of the axial compressor.

81

Chapter 4 Conclusions

Chapter 4 Conclusions

82

Chapter 4 Conclusions 4 Conclusions In this study new designs of vortex generators were used in order to control the secondary flows. In the present study, a numerical simulations were conducted to calculate the change in performance parameters due to the usage of VGs. As shown previously in the results and discussion chapter, the vortex generators effects on the performance are summarized as follow: Concerning the curved side VG with sharp edge nose and rounded nose edge:  Transitional SST turbulence model is capable to capturing the separation and transitions from laminar to turbulent into the flow field.  Six different sets of CSVG were investigated to reach the geometrical parameters values which causes the highest enhancement of the aerodynamic performance of the linear cascade.  The highest enhancement in performance was attained at VG height equals to 40% of the boundary layer thickness.  Curve side vortex generators CSVGs (with sharp nose edge) have a significant impact on secondary flow losses such as improving the location of separation lines by moving them toward the trailing edge, and reducing the corner vortices.  A significant reduction in the normalized total pressure loss (up to 20.7%) is accomplished using the curved surface vortex generator with a rounded nose of r/δ=0.5, w/h=6, e/h=5, and h/δ=0.4. 83

Chapter 4 Conclusions  Using CSVG results in reduction of the diffusion factor of about -2.0%. This will enlarge the safely operating range without stall.  Inserting vortex generators has insignificant effect on the change of deflection and consequently the off design conditions will still be far from reached.  There is a reduction of static pressure rise which leads to an increase of dynamic pressure. To benefit from the increase in the dynamic pressure, a further investigation is needed in order to recover part of the dynamic pressure into static pressure.  At off-design operation, a 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.  At off-design operation, static pressure coefficient is rapidly decreased by increasing the negative incidence, while it remains constant at positive incidence angles, therefore using VG enlarges the operating range of compressor cascade towards the positive incidence angle region. Concerning the wishbone and doublet VGs:  Moderate enhancement on the effect of the two VGs on the cascade secondary flow structure which appears in shifting the passage vortex initiation towards the trailing edge and reducing (in case of Doublet VG) or shifting (in case of wishbone VG) the

84

Chapter 4 Conclusions corner vortex between the suction and the bottom endwall surfaces.  An increase in total pressure loss coefficient is attained by using the two VGs with a percentage of 4.3% with Wishbone, and 5.2% with Doublet type.  A significant reduction in skin friction coefficient at bottom endwall is achieved by Wishbone (up to 32%), and Doublet (up to 46%).  Therefore the investigation is recommended to be extended to study the effect of the various geometrical parameters (of this types of VGs) on the enhancement of the aerodynamic performance of the axial compressor cascade.

85

References

References [1]

Herzig, H., Hansen, A., and Costello, G., 1954, “A Visulaization study of secondary flows in cascades,” Tech. Rep. No. 1163, NACA.

[2]

Kumar, K. N., and Govardhan, M., 2011, “Secondary flow loss reduction in a turbine cascade with a linearly varied height streamwise endwall fence,” Int. J. Rotating Mach., 2011, pp. 1–16.

[3]

Mertz, C., 1954, “A study of the effect of boundary layer control on axial flow compressors stage,” Master’s thesis ,California institute of technology.

[4]

Lakshminarayana, B., and Horlock, J. H., 1965, “Leakage and secondary flows in compressor cascades,” Reports and memoranda No 3483, aeronautical research council,University of Liverpool.

[5]

Lakshminarayana, B., and Horlock, J. H., 1963, “Reviw : secondary flows and losses in cascades and axial-flow turbomachines,” Int. J. Mech. sci, 5, pp. 287–307.

[6]

Lampart, P., 2009, “Investigation of endwall flows and losses in axial turbines. Part i. Formation of endwall flows and losses,” J. Theor. Appl. Mech., 47(2), pp. 321–342.

[7]

Horlock, J. H., Louis, J. F., Percival, P. M. E., and Lakshminarayana, B., 1966, “Wall stall in compressor cascades,” J. Fluids Eng., 88(3), pp. 637–648.

[8]

Greitzer, E. M., 1980, “Review—Axial Compressor Phenomena,” J. Fluids Eng., 102(2), pp. 134–151.

[9]

Schlichting, H., and Das, A., 1966, “Recent Research on CascadeFlow Problems,” J. Basic Eng., pp. 221–228.

Stall

[10] Dong, Y., 1987, “Three-Dimensional Flows and Loss Reduction in Axial Compressors,” 31st International Gas Turbine Conference and Exhibit, Dusseldorf, Germany. [11] Wisler, D. C., 1985, “Loss Reduction in Axial-Flow Compressors Through Low-Speed Model Testing,” 29th International Gas Turbine Conference and Exhibit, Netherlands. [12] Gessner, B. F. B., 1972, “The origin of secondary flow in turbulent flow along a corner,” J. Fluid Mech., 58, pp. 1–25. 86

References [13] Gbadebo, S. a., Cumpsty, N. a., and Hynes, T. P., 2005, “ThreeDimensional Separations in Axial Compressors,” J. Turbomach., 127(2), p. 331. [14] Kang, S., and Hirsch, C. H., 1991, “Three Dimensional Flow in a Linear Compressor Cascade at Design Conditions,” International Gas Turbine and Aeroengine Congress and Exposition, Orlando, FL, 1991, pp. 3–10. [15] Sinnette, J. T., and Costello, G. R., 1951, “Possible application of blade boundary-layer control to improvement of design and offdesign performance of axial-flow turbomachines,” Technical Note 2371, Lewis Flight PropulsionLaboratory, Cleveland, Ohio. [16] Gad-el-Hak, M., 1996, “Modern developments in flow control,” Appl. Mech. Rev., 49, pp. 365–379. [17] 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. [18] Gad-el-Hak, M., 2000, Flow control passive, active, and reactive flow managment, Cambridge university press. [19] Estruch-Samper, D., Vanstone, L., Hillier, R., and Ganapathisubramani, B., 2014, “Micro vortex generator control of axisymmetric high-speed laminar boundary layer separation,” Shock Waves, 25(5), pp. 521–533. [20] Ortmanns, J., Pixberg, C., and Gummer, V., 2011, “Numerical investigation of vortex generators to reduce cross-passage flow phenomena in compressor stator end-walls,” Proc. Inst. Mech. Eng. Part A J. Power Energy, 225(7), pp. 877–885. [21] Joubert, G., Le Pape, a., Heine, B., and Huberson, S., 2013, “Vortical Interactions Behind Deployable Vortex Generator for Airfoil Static Stall Control,” AIAA J., 51(1), pp. 240–252. [22] Mdouki, R., and Gahmousse, A., 2013, “Effects of slotted blading on secondary flow in highly loaded compressor cascade,” J. Eng. Sci. Technol., 8(5), pp. 540–556. [23] Hergt, A., Meyer, R., and Engel, K., 2012, “Effects of Vortex Generator Application on the Performance of a Compressor Cascade,” J. Turbomach., 135(2), p. 021026. 87

References [24] 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,” Int. J. Rotating Mach., 8(6), pp. 423–430. [25] Meyer, R., Bechert, D. W., and Hage, W., 2003, “Secondary flow control on compressor blades to improve the performance of axial turbomachines,” 5th European Conference on Turbomachinery, Fluid Dynamics and Thermodynamics , Prague. [26] Sahin, F. ., and Arts, T., 2012, “Experimental Investigations on the Effects of Low Profile Vortex Generators in a Compressor Cascade,” 9th National Congress on Theoretical and Applied Mechanics, Brussels, pp. 9–10. [27] Lengani, D., Simoni, D., Ubaldi, M., Zunino, P., and Bertini, F., 2011, “Turbulent boundary layer separation control and loss evaluation of low profile vortex generators,” Exp. Therm. Fluid Sci., 35(8), pp. 597–616. [28] Wheeler, G. O., 1991, “Low drag vortex generators.” [29] Lin, J. C., 2002, “Review of research on low-profile vortex generators to control boundary-layer separation,” Prog. Aerosp. Sci., 38(4-5), pp. 389–420. [30] 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 Exposition, Orlando, Florida, pp. 1–16. [31] Lee, S., Loth, E., and Babinsky, H., 2011, “Normal shock boundary layer control with various vortex generator geometries,” Comput. Fluids, 49(1), pp. 233–246. [32] Scholz, P., 2010, “Experimental and Numerical Investigations on the Control of Airfoil Stall using Vortex Generator Jets,” Aerospace, (July), pp. 1–17. [33] Godard, G., Foucaut, J. M., and Stanislas, M., 2006, “Control of a decelerating boundary layer. Part 2: Optimization of slotted jets vortex generators,” Aerosp. Sci. Technol., 10(5), pp. 394–400. [34] Ortmanns, J., and Kähler, C. J., 2007, “The effect of a single vortex generator jet on the characteristics of a turbulent boundary layer,” Int. J. Heat Fluid Flow, 28(6), pp. 1302–1311. 88

References [35] Sullerey, R. K., and Pradeep, a. M., 2004, “Secondary Flow Control Using Vortex Generator Jets,” J. Fluids Eng., 126(4), p. 650. [36] Casper, M., Scholz, P., and Radespiel, R., 2011, “Separation Control on a High-Lift Airfoil using Vortex Generator Jets at High Reynolds numbers,” 41st AIAA Dynamics conference and Exhibit, Honolulu,Hawaii, pp. 1–11. [37] Zheng, X., Zhou, S., Hou, A., Jiang, Z., and Ling, D., 2006, “Separation control using synthetic vortex generator jets in axial compressor cascade,” Acta Mech. Sin., 22(6), pp. 521–527. [38] Johnston, J. P., and Nishi, M., 1990, “Vortex generator jets - Means for flow separation control,” AIAA J., 28(6), pp. 989–994. [39] Peacock, R. E., 1971, “Boundary-Layer Suction to Eliminate Corner Separation in Cascades of Aerofoils Boundary-Layer Suction to Eliminate Corner Separation in Cascades of Aerofoils,” University Engineering Department, Cambridge, Aeronautical research council reports and memoranda, Report No. 3663. [40] Gbadebo, S. a., Cumpsty, N. a., and Hynes, T. P., 2008, “Control of Three-Dimensional Separations in Axial Compressors by Tailored Boundary Layer Suction,” J. Turbomach., 130(1), p. 011004. [41] Shuang, G., Shaowen, C., Yanping, S., Yufei, S., and Fu, C., 2010, “Effects of Boundary Layer Suction on Aerodynamic Performance in a High-load Compressor Cascade,” Chinese J. Aeronaut., 23(2), pp. 179–186. [42] Zhang, Y., Chen, H., and Fu, S., 2012, “A Karman-Vortex Generator for passive separation control in a conical diffuser,” Sci. China Physics, Mech. Astron., 55(5), pp. 828–836. [43] Karanth, K. V., and Sharma, N. Y., 2009, “CFD Analysis of a Centrifugal Fan for Performance Enhancement using Converging Boundary Layer Suction Slots,” World Acad. Sci. Eng. Technolody, 36, pp. 381–387. [44] Chen, W. L., Lien, F. S., and Leschziner, M. A., 1998, “Computational prediction of flow around highly loaded compressor cascade blades with non-linear eddy viscosity models,” Int. J. Heat Fluid Flow, 19, pp. 307–319. [45] Liesner, K., Meyer, R., and Schulz, S., 2012, “Non-symmetrical boundary layer suction in a compressor cascade,” J. Theor. Appl. 89

References Mech., 50(2), pp. 455–472. [46] Liu, Y., Sun, J., and Lu, L., 2014, “Corner Separation Control by Boundary Layer Suction Applied to a Highly Loaded Axial Compressor Cascade,” Energies, 7, pp. 7994–8007. [47] Seifert, A., Bachar, T., Koss, D., Shepshelovich, M., and Wygnanskil, I., 1993, “Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation,” AIAA J., 31(11), pp. 2052–2060. [48] Greenblatt, D., and Wygnanski, I. J., 2000, “The control of flow separation by periodic excitation,” Prog. Aerosp. Sci., 36, pp. 487– 545. [49] Liu, F. E. I., Wang, J., and Wu, K., 2008, “Numerical analysis of controlling separation in axial cascades by excitation of periodical incoming wake,” (1), pp. 21–34. [50] Cerretelli, C., and Kirtley, K., 2009, “Control With Fluidic Oscillators,” J. Turbomach., 131, pp. 1–9. [51] Roupassov, D. V, Nikipelov, A. A., Nudnova, M. M., and Starikovskii, A. Y., 2009, “Flow Separation Control by Plasma Actuator with Nanosecond Pulsed-Periodic Discharge,” AIAA J., 47(1). [52] 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,” J. Turbomach., 133(2), p. 021026. [53] 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,” J. Turbomach., 133(2), p. 021027. [54] Fleming, J. L. L., Simpson, R. L. L., Cowling, J. E. E., and Devenport, W. J. J., 1993, “An experimental study of a turbulent wing-body junction and wake flow,” Exp. Fluids, 14(5), pp. 366–378. [55] Rood, E. P., 1984, “The governing influence of the nose radius on the unsteady effects of large scale flowstructure in the turbulent wing and plate junction flow.,” ASME Forum Un- steady Flow, (15), pp. 7–9. 90

References [56] Mehta, R. D., 1984, “Effect on a wing nose shape on the flow in a wing/body junction.,” Aerosp. J, 88, pp. 456–60. [57] Lieblein, S., Schwenk, F. C., and Broderick, R. L., 1953, “Diffusion factor for estimating losses and limiting blade loadings in axialflow-compressor blade elements,” NACA research memorandum, Lewis Flight Propulsion Laboratory Cleveland, Ohio.

91

Appendix Published work

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

‫‪Arabic summary‬‬

‫التحكم في السريان الثانوي في ريش الضاغط الموجه باستخدام مولدات‬

‫الدوامات ‪ :‬محاكاة عددية‬

‫الملخص باللغة العربية‬

‫الضواغط المحورية لها حدود تشغيل وحدود للكفاءة بسبب صعوبة التحكم في التيارات الثانوية‪.‬‬ ‫لذلك‪ ،‬سيتم دراسة استخدام تصميم جديد من المولدات الدوامية في للسيطرة على تدفق الثانوي‬ ‫وبالتالي انخفاض الضغط الكلي الذي قد يؤدي في النهاية لتعزيز أداء الضاغط‪ .‬التصميمات‬ ‫المقترحة لمولدات الدوامات هي ‪ 4‬تصميمات كاالتي ‪:‬‬ ‫‪ -1‬المولد ذو االضالع المنحنية ذو االنف المستقيم ‪.‬‬ ‫‪ -2‬المولد ذو االضالع واالنف المنحني‪.‬‬ ‫‪ -3‬المولد على شكل عظمة الترقوة)‪.(wishbone‬‬ ‫‪ -4‬المولد المزدوج ‪.‬‬ ‫ومن اجل دراسة تأثير تلك المولدات تم اجراء محاكاة عددية باستخدام الحاسب لمعرفة مدى تاثير‬ ‫المولدات الدوامية على التيارات الثانوية والفواقد الناتجة عنها ‪.‬وتتم المحاكاة العددية لسريان ثالثي‬ ‫االبعاد لمائع قابل لالنضغاط ‪ .‬وبناء على تلك المحاكاة العددية يتم رسم توزيع كنتوري للسرعة‬ ‫والضغط االستاتيكي وخطوط السريان في مناطق مختلفة داخل الوسط الحسابي لمتابعة تاثير‬ ‫المولدات الدوامية على السريان الثانوي بين متوالية ريش الضاغط‪ .‬كما يتم حساب الفقد فى‬ ‫الضغط الكلي ومعامل الضغط االستاتيكي لمتابعة هذا التاثير وما يترتب عليه وقد كانت النتائج‬ ‫كاالتي ‪:‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬

‫‪‬‬

‫عند استخدام المولد ذو االنف المستقيمة سبب انخفاض للفقد في الضغط الكلي بمقدار‬ ‫‪ % 18.3‬عتد التشغيل في حالة التصميم‪.‬‬ ‫استخدام المولد ذو االنف الدائري سبب انخفاض في الضغط الكلي بمقدار ‪ % 20.7‬غند‬ ‫التشغيل في حالة التصميم‪.‬‬ ‫استخدام المولدين ذو االنف المستقيم والدائري بعيدا عن حالة التصميم ادي النخفاض في‬ ‫الفواقد في الضغط الكلي عند مقدار انحراف للمائع عند الدخول من ‪ 4-‬درجات الي ‪4+‬‬ ‫درجات ‪.‬‬ ‫المولد الدوامي على شكل عظمة الترقوة والمولد المزدوج تم دراسة تاثيرهم عند الحالة‬ ‫التصميمية فقط ووجد انهما يسببان انخفاض في معامل االحتكاك على الحائط السفلى الذي‬ ‫يثبت عليه متوالية ريش الضاغط‬ ‫‪119‬‬

‫‪Assiut University‬‬

‫‪Faculty of Engineering‬‬

‫التحكم في السريان الثانوي في ريش الضاغط الموجه باستخدام مولدات‬ ‫الدوامات ‪ :‬محاكاة عددية‬ ‫رسالة مقدمة من‪:‬‬

‫المهندس‪ /‬أحمد محمد ضياء الدين أحمد درويش‬ ‫المعيد بقسم الهندسة الميكانيكية – كلية الهندسة– جامعة أسيوط‬ ‫كجزء تكميلى للحصول على درجة‬

‫ماجستيرالعلوم‬ ‫فى الهندسة الميكانيكية‬ ‫كلية الهندسة‪ -‬جامعة أسيوط‬

‫فبراير ‪2016‬‬ ‫لجنة االشراف ‪:‬‬ ‫أ‪.‬د‪ .‬عمر محمد االنور عبدالحافظ‬ ‫أ‪.‬د‪ .‬محمود أمين أحمد‬ ‫د‪.‬محمد فكري فرح الدسوقي‬

‫‪Assiut University‬‬

‫‪Faculty of Engineering‬‬

‫التحكم في السريان الثانوي في ريش الضاغط الموجه باستخدام مولدات‬ ‫الدوامات ‪ :‬محاكاة عددية‬ ‫رسالة مقدمة من‪:‬‬

‫المهندس‪ /‬أحمد محمد ضياء الدين أحمد درويش‬ ‫المعيد بقسم الهندسة الميكانيكية – كلية الهندسة– جامعة أسيوط‬

‫كجزء تكميلى للحصول على درجة‬

‫ماجستيرالعلوم‬ ‫فى الهندسة الميكانيكية‬ ‫كلية الهندسة‪ -‬جامعة أسيوط‬

‫فبراير ‪2016‬‬

secondary flow control in an axial compressor cascade using vortex ...

secondary flow control in an axial compressor cascade using vortex ...

Suggest Documents

Numerical Investigation of Secondary Flow In An Axial Flow ... - ijcer

Performance Investigation of Axial-Flow Compressor

Separation control using synthetic vortex generator jets in axial ...

Flow Simulations of an Axial Transonic Compressor Stage

Effect of blade sweep on inlet flow in axial compressor

Flow Control in Twin Air-Intakes using Vortex Generators - wseas.us

Elliptic instability in a Rankine vortex with axial flow - IRPHE

Design optimization of axial flow compressor blades ... - Springer Link

Design and Optimization of a Multi-Stage Axial-Flow Compressor ...

Axial Flow Compressor Design Optimization: Part II ...

Secondary Air Interaction with Main Flow in Axial ... - Semantic Scholar

Vortex sinks with axial flow - Institute of Fluid Dynamics & Turbulence

Simulation of 3D Multistage Axial Compressor Using ...

Evolution of the Tip Leakage Vortex in an Axial ...

Flow Separation Control By Trapped Vortex

Solution of Turbine Blade Cascade Flow Using an Improved Panel ...

Life Cycle Assessment of an axial air compressor ... - CiteSeerX

Multi-objective optimization of an axial compressor blade - Springer Link

Life Cycle Assessment of an axial air compressor ... - CiteSeerX

design optimization of an axial flow compressor for industrial gas turbine

Structural and Conceptual Design Analysis of an Axial Compressor for ...

Life Cycle Assessment of an axial air compressor ... - CiteSeerX

Dimensional Transonic Cascade Flow Fields Using ...

numerical analysis of secondary flow topologies of low-speed axial