Investigations of Double Surface Co-Flow Jet Transonic Airfoil

Transcription

1 University of Miami Scholarly Repository Open Access Theses Electronic Theses and Dissertations Investigations of Double Surface Co-Flow Jet Transonic Airfoil Luchen Wang University of Miami, Follow this and additional works at: Recommended Citation Wang, Luchen, "Investigations of Double Surface Co-Flow Jet Transonic Airfoil" (2019). Open Access Theses This Open access is brought to you for free and open access by the Electronic Theses and Dissertations at Scholarly Repository. It has been accepted for inclusion in Open Access Theses by an authorized administrator of Scholarly Repository. For more information, please contact

2 UNIVERSITY OF MIAMI INVESTIGATIONS OF DOUBLE SURFACE CO-FLOW JET TRANSONIC AIRFOIL By Luchen Wang A THESIS Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Master of Science Coral Gables, Florida May 2019

3 c 2019 Luchen Wang All Rights Reserved

4 UNIVERSITY OF MIAMI A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science INVESTIGATIONS OF DOUBLE SURFACE CO-FLOW JET TRANSONIC AIRFOIL Luchen Wang Approved: Ge-Cheng Zha, Ph.D. Professor of Mechanical and Aerospace Engineering Xiangyang Zhou, Ph.D. Professor of Mechanical and Aerospace Engineering Weiyong Gu, Ph.D. Professor of Mechanical and Aerospace Engineering Guillermo Prado, Ph.D. Dean of the Graduate School

5 WANG, LUCHEN (M.S., Mechanical and Aerospace Engineering) Investigations of Double Surface Co-Flow Jet Transonic Airfoil (May 2019) Abstract of a thesis at the University of Miami. Thesis supervised by Professor Ge-Cheng Zha. No. of pages in text. (72) The objective of this thesis is to investigate the double surface Co-Flow Jet (CFJ) on the transonic supercritical RAE2822 airfoil. Configurations are explored to improved CFJ airfoil performance, such as aerodynamic efficiency C L and lift coefficient ( L ) D C. All the configurations are simulated and verified using the in-house CFD code, FASIP. The Reynolds Averaged Navier-Stokes (RANS) equations with one-equation Spalart- Allmaras (SA) turbulence model is used. A 5th order weighted essentially nonoscillatory (WENO) scheme with a low diffusion Riemann solver is utilized to evaluate the inviscid fluxes. A 2nd order central differencing scheme matching the stencil width of the WENO scheme is employed for the viscous terms. It is shown that CFJ can significantly enhance the aerodynamic performance of RAE2822 transonic supercritical airfoil. The standard CFJ airfoil has an injection slot near the leading edge and a suction slot near the trailing edge on the airfoil suction surface. A small amount of mass flow is sucked into the airfoil near the trailing edge, energized by a micro-compressor located inside the airfoil, and in the tangential direction near the leading edge. For the double surface CFJ airfoil proposed in this paper, an additional injection slot is placed on the pressure surface of the airfoil, and the suction slot remains on the airfoil upper surface. By adding additional injection

6 to the traditional CFJ, lift coefficient C L is further improved, while aerodynamic efficiency ( L ) D C is mostly kept same as the standard CFJ airfoil achieved. The jet along the lower surface of the airfoil reduces the local velocity which increase the pressure and lift. The baseline RAE2822 airfoil and the standard CFJ RAE2822 airfoil at a different angle of attacks (AoA) were simulated and compared for the reference. For the freestream condition of M = 0.729, Re = and AoA from 1 to 5.5, the New CFJ RAE2822 airfoil is able to increase C L by % and ( L ) D C by 0.83% at peak ( L ) D C point compared to the standard airfoil. Different momentum coefficient is also studied. A low total C of will increase the C L from to , and increase of 5.489%,a high total C of will increase the C L from to 1.136, and an increase of 11.76%. The double surface airfoil provides a different approach to enhance the perfomance of transonic airfoils.

7 Dedicated to my beloved parents and girlfriend, for their love, support, encouragement and inspiration. iii

8 Acknowledgements I would like to express my gratitude to my advisor, Dr. Ge-Cheng Zha for his continuous academic guidance throughout my studies in the CFD Lab. I am grateful to my colleagues from the CFD lab for all their help and support. I thank Dr. Yan Ren for help on the trade study and outlining the structure of this thesis. I also thank Yang Wang for helping me to design the injection slot. This paragraph is dedicated to Purvic Patel and Jeremy Boling, who joined the CFD Lab with me even though you both already had your Master s degree. Thanks for all the pleasant movie time and serious brainstorming time we shared. Many thanks to Kewei Xu, for his kindness and letting me live in his living room. Thanks to the loud noise his door makes when he opens it, I was able to wake up earlier than usual and have more time to devote to my work. And finally, I extend special gratitude to my beloved family for their unconditional love and financial support, which allowed me to chase my dream without burden. University of Miami May 2019 Luchen Wang iv

9 Table of Contents LIST OF FIGURES vii LIST OF TABLES xiii List of Symbols xiv 1 INTRODUCTION Background Supercritical Airfoil Co-Flow Jet Flow Control Transonic Co-Flow Jet Active Flow Control Aft Co-Flow Jet GOVERNING EQUATIONS The Navier-Stokes Equations Spalart-Allmaras Turbulence Model CFJ AIRFOIL PARAMETERS 17 v

10 3.1 Lift, Drag and Moment Calculation Jet Momentum Coefficient Power Coefficient Corrected Aerodynamic Efficiency TRANSONIC 2-D CO-FLOW JET AIRFOIL DESIGN Trade Study Results and Discussion Convergence Study C Distribution Optimization Lower Injection Slot Open Location Lower Injection Slot Width Aerodynamic Behavior of Double Surface CFJ Angle of attack Flow Field Comparison CONCLUSIONS 69 BIBLIOGRAPHY 71 vi

11 List of Figures 1.1 Baseline and CFJ airfoil Attached flow of CFJ NACA 6415 airfoil at AoA=25 measured by PIV in experiment, C of 0.06, M=0.1 (Plot adopted from [1]) Measured drag polars of discrete CFJ airfoils at mass flow ṁ = 0.06 kg/s (Plot adopted from [1]) Computed power coefficient compared with experiment at M=0.03 and C = 0.08 (Plot adopted from [1]) General (top) and zoomed-in (bottom) view of O-type structured mesh in size for baseline airfoil Comparison of pressure coefficient C P between simulation and experiment at M=0.729, α= The convergence history of L 2 Norm relative error for the baseline RAE2822 airfoil cases General (top) and zoomed-in (bottom) view of O-type structured mesh in size for standard CFJ airfoil Comparison of pressure coefficient between standard CFJ airfoil simulations at M=0.729, α=2, C = vii

12 4.6 The convergence history of L 2 Norm relative error for the standard CFJ RAE2822 airfoil cases General (top) and zoomed-in (bottom) view of O-type structured mesh in size for double surface CFJ airfoil Comparison of pressure coefficient between standard CFJ airofoil simulations at M=0.729, α=2, C = The convergence history of L 2 Norm relative error for the current CFJ RAE2822 airfoil cases Coefficient of lift C L contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection Power coefficient P C contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection Corrected aerodynamic efficiency ( L D ) C contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection Corrected aerodynamic efficiency productivity ( L2 D ) C contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection The double surface CFJ transonic airfoil with different lower injection slot opening location Aerodynamic coefficients for different lower injection slot location under different C Isotropic mach distribution comparison between the different location of double surface CFJ designs at same C viii

13 4.17 The double surface CFJ transonic airfoil with x-axis force and drag coefficient in pressure term along location change The current CFJ transonic airfoil with different suction slot width arrangement Aerodynamic coefficients for different lower injection slot width under different C The baseline RAE2822 airfoil, the standard CFJ RAE2822 airfoil and the double surface CFJ airfoil Double surface CFJ airfoil upper (top) and lower (bottom) injection velocity versus angle of attack for different jet moment Double surface CFJ airfoil upper (top) and lower (bottom) Injection Suction AoA for different jet moment Aerodynamic coefficients of the baseline, standard CFJ airfoil and double surface CFJ for angle of attack changing from 1 to The drag polar curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to The corrected drag C D + C P polar curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to The aerodynamic performance L D curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to ix

14 4.27 The corrected aerodynamic performance curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at C = Mach contours comparison between the baseline, standard CFJ and double surface CFJ airfoil at C = Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at C = Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at C = Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at peak efficiency condition with C = Mach contours comparison between the baseline, CFJ and double surface CFJ airfoil at peak efficiency condition with C = Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at peak efficiency condtion with C = Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at peak efficiency condtion witht C = x

15 4.36 Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at maximum lift cases Mach contours comparison between the baseline,standard CFJ and double surface CFJ airfoil at maximum lift condition Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at maximum lift condition Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at at maximum lift condition Shock entropy increase distributions at locations above surface(lss) for the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at the peak efficiency condition X-component of wake velocity distribution at one chord length downstream location(dl) for the baseline airfoil, standard CFJ airfoil and the double surface CFJ airfoil at the peak efficiency condition Shock entropy increase distributions at locations above surface(lss) for the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at the maximum lift condition X-component of wake velocity distribution at one chord length downstream location(dl) for the baseline airfoil, standard CFJ airfoil and the double surface CFJ airfoil at the maximum condition Entropy increase contours comparison at C =0.003 cases xi

16 4.45 Entropy increase contours comparison at peak aerodynamic efficiency Entropy increase contours comparison at the maximum lift cases xii

17 List of Tables 4.1 Baseline RAE2822 airfoil aerodynamics coefficients comparison between simulation and experiment The standard CFJ airfoil aerodynamics coefficients comparison between mesh size Double surface CFJ airfoil aerodynamics coefficients comparison between mesh size Aerodynamics coefficients comparison between the baseline airfoil, the CFJ airfoil and the double surface CFJ airfoil Corrected aerodynamics coefficients comparison between the baseline airfoil, the standard CFJ airfoil and the double surface CFJ airfoil.. 50 xiii

18 LIST OF SYMBOLS a, c speed of sound, γp/ρ A, B, C Jacobian matrix of inviscid flux E, F, G in ξ, η, ζ direction C speed of sound in generalized coordinates, c lξ 2 + l2 η + lζ 2 C C D C L C m C p C x, C θ, C r C t dq dw de D absolute velocity vector Drag coefficient Lift coefficient Pitch moment coefficient specific heat capacity at constant pressure absolute velocities in x, θ, r direction tip chord of the compressor rotor head added to system total work done of the system change in total energy of system source term of Navier-Stokes equations in generalized coordinates E, F, G inviscid flux vectors in ξ, η, ζ direction e e x, e y, e z F total energy per unit mass unit normal vector in reference xyz sum of fluid force acting on the structure or on a finite control volmue xiv

19 F b F s I I o J L body force acting on a finite control volmue surface force acting on a finite control volmue identity matrix rothalpy Jacobian of the coordinate transformation, (ξ,η,ζ) (x,y,z) reference or characteristic length l, m, n normal vector on ξ, η, ζ surface with its magnitude equal to the elemental surface area and pointing to the direction of increasing ξ, η, ζ l t grid moving velocity L, M, N Jacobian matrix of viscous flux R, S, T in ξ, η, ζ m M pseudo time marching step reference Mach number, V a M ξ n N D contravariant Mach number in ξ direction, M ξ = U C physical time marching step number of nodal diameter p, P static pressure p o, P o P r R total pressure Prandtl number gas constant R, S, T viscous flux vectors in ξ, η, ζ direction R e S S v T Reynolds number, ρ V L Wing span length S-A turbulence model source term static temperature, or period xv

20 T T o t surface stress vector, σ n total temperature time U, V, W contravariant velocities in ξ, η, ζ direction V freestream reference velocity u, v, w relative velocities in x, y, z direction u + dimensionless velocity, u/u τ u τ friction velocity, τ w /ρ V V relative velocity vector cell volume x, y, z cartesian coordinates in moving frame of reference X, Y, Z cartesian coordinates in fixed frame of reference y + - Greek Symbols - dimensionless wall normal distance, uτ y ν θ, r, x Cylindrical coordinates S t γ Change of entropy, C p ln T o T o Rln P o P o physical time step specific heat ratio viscosity DES turbulent eddy viscosity determined by DES, DDES or IDDES ν ν ρ τ ik kinematic viscosity working variable of the S-A model related to turbulent eddy viscosity fluid density shear stress in Cartesian coordinates xvi

21 τ w ϕ fluid shear stress at the wall surface position vector in reference xyz ξ, η, ζ generalized coordinates - Subscripts - b i computational domain outer boundary computational domain inner boundary i, j, k indices reference point - Abbreviations - AoA BC CF D CF J F V S LDE LE LHS RAN S RHS S A T E W EN O ZNMF Angle of Attack Boundary Condition Computational Fluid Dynamics Co-Flow Jet Flux Vector Splitting Low Diffusion E-CUSP scheme Leading Edge Left Hand Side Reynolds Averaged Navier-Stokes equations Right Hand Side Spalart-Allmaras (S-A) one equation turbulence model Trailing Edge Weighted Essentially Non-Oscillatory scheme Zero-net mass flux xvii

22 CHAPTER 1 Introduction 1.1 Background From the first powered flight to the supersonic fighters roaring in the sky, aircraft have evolved. These milestones are credited to the scientists and engineers who are seeking a way to push the capabilities of flight to its physical limits. Scientists first proposed the idea of backward-swept wings when the jet engine was developed in 1940s, in order to delay the sudden rise of drag. Looking ahead to the 1960 s, the concept of supercritical airfoils was proposed. This change in airfoil shape enabled aircraft to maintain efficient performance when approaching transonic conditions. Nevertheless, the supercritical airfoil has seen few improvements in recent decades. This does not mean work was stopped by these same engineers and scientists. Eager to enhance the performance of aircraft, researchers developed various active flow control techniques like circulation control, laminar flow control and boundary layer control. Some of these techniques have already been practically applied and have proven their worth at subsonic conditions [2], but few methods have the ability to also gain benefits in the transonic regime. 1

23 1.2 Supercritical Airfoil 2 Research has shown that with the traditional airfoils of the 1950 s and 60s, the aircraft is not able to easily to reach Mach 0.9 without a large increase in drag. Flow over the suction surface of a traditional airfoil accelerates the flow to supersonic speed, terminating in a strong shock wave, which increases wave drag. However, the supercritical airfoil has a flatter suction surface, pushing the shock wave downstream. This results in a weaker shock and less wave drag, which allows for speed flows compared to conventional airfoils. The supercritical airfoil was first suggested by K.A. Kawalki in Germany. This airfoil has a flattened suction surface, a thin downwardcurved trailing edge, and a larger radius leading edge compared to a laminar airfoil. Supercritical airfoils feature four main benefits: Higher drag divergence Mach number Shock waves on supercritical airfoils are moved further downstream than traditional airfoils The shock induced boundary layer separation is reduced More efficient wing designs are allowed For a subsonic airfoil, flow over the suction surface of an airfoil can become locally supersonic but slows down to match the pressure at the trailing edge of the lower surface without a shock. Comparatively, for a transonic airfoil, a shock is created to recover pressure in order to match the pressure at the trailing edge. This shock leads transonic wave drag, and induces separation, which has negative effects on the airfoil s performance.

24 3 A shock is formed, which raises pressure to the critical value, where the local flow speed will be sonic. The position of this shock is determined by the geometry of the airfoil if no circulation control applied. A supercritical airfoil can minimize and push the shock wave as far downstream as possible, thus reducing drag. Compared to a typical airfoil section, the supercritical airfoil creates more lift due to its more even pressure distribution over the upper surface. 1.3 Co-Flow Jet Flow Control The Co-Flow Jet (CFJ) active flow control was developed by Zha et al. [3]. The CFJ flow control method is able to achieve lift enhancement, drag reduction and stall margin increment at low energy expenditure. The CFJ airfoil has an injection slot near the leading edge and a suction slot near the trailing edge on the airfoil upper surface as sketched in Fig A small amount of mass flow is withdrawn into the airfoil near the trailing edge, pressurized and energized by a pumping system inside the airfoil, and then injected near the leading edge in the direction tangential to the main flow. The whole process does not add any mass flow to the system. And hence CFJ airfoil is a zero-net mass-flux (ZNMF) flow control. The CFJ system is a self-contained high lift system with no moving parts. The fundamental mechanism of the CFJ airfoil is that the turbulent mixing between the jet and main flow energizes the wall boundary-layer, which dramatically increases the circulation, augmenting lift, and reducing the total drag (or generates thrust) by filling the wake velocity deficit. The CFJ airfoil has a unique low energy expenditure mechanism because the jet gets injected at the leading edge suction peak location, where the main flow pressure

25 is the lowest and makes it easy to eject the flow, and the flow is sucked at near the trailing edge, where the main flow pressure is the highest and makes it easy to 4 withdraw the flow. The turbulent shear layer between the main flow and the jet causes strong turbulence mixing, which enhances lateral transport of energy from the jet to main flow and allows the main flow to overcome severe adverse pressure gradient and remain attached at a high angle of attack. Figure 1.1: Baseline and CFJ airfoil. Figure 1.2: Attached flow of CFJ NACA 6415 airfoil at AoA=25 measured by PIV in experiment, C of 0.06, M=0.1 (Plot adopted from [1]). Fig. 1.2 adopted from [1] is the PIV measured velocity field of the CFJ-NACA airfoil at the AoA of 25 and C of 0.06, which has the flow attached and a higher speed within the wake than in the freestream. In this case, thrust is generated. The baseline NACA-6415 airfoil has massive flow separation at this AoA. Fig. 1.3 shows the wind tunnel test results of several CFJ airfoils at Mach number of 0.1. The CFJ airfoil achieves a C Lmax of about 5, more than 3 times higher than the baseline airfoil. It also obtains an enormous thrust coefficient of about 0.8. A CFJ wing is hence can be used as a distributed thrust system.

26 5 Figure 1.3: Measured drag polars of discrete CFJ airfoils at mass flow ṁ = 0.06 kg/s (Plot adopted from [1]). Figure 1.4: Computed power coefficient compared with experiment at M=0.03 and C = 0.08 (Plot adopted from [1]). Fig. 1.4 from [1] shows the computed power coefficient compared with the experiment. The power coefficient decreases with the increase of AoA up to 15 and then rises at higher AoA. It is because when the AoA is increased and the flow still remains attached, the airfoil LE suction effect becomes stronger with lower static pressure in the region of the injection jet, and hence less power is needed to generate the jet with the same momentum coefficient. However, when the AoA is beyond the separation value, the boundary layer is deteriorated with large energy loss and the suction power is significantly increased. More information on CFJ airfoil can be found in [1, 3 13] 1.4 Transonic Co-Flow Jet Active Flow Control Previous research has shown the capability and effectiveness of the CFJ airfoil in subsonic conditions. The idea to make CFJ work in the transonic regime comes in response to the performance enhancement of supercritical airfoils compared to tra-

27 ditional subsonic airfoils. A similar breakthrough in performance would allow for 6 more efficient cruise. The working principle is sill that of the subsonic CFJ [12], however the CFJ airfoil is able to gain higher performance at higher Mach number due to lower compressibility effects [12]. Starting with the design of subsonic CFJ and making appropriate adjustments for a supercritical airfoil, the CFJ airfoil is able to increase efficiency under transonic flow conditions. The main shock wave is also pushed more downstream than the baseline supercritical airfoil. In addition, increasing the circulation around the airfoil [12] helps the CFJ design generate a higher lift coefficient; an increase in C L and ( L ) D C by 17.7% and 14.5% respectively at the peak aerodynamic efficiency point. Ignoring aerodynamic efficiency, the CFJ airfoil obtained 25.6% C L rise, from 0.93 to 1.16, at the point of maximum lift coefficient. Liu has noted that the separation caused by the shock wave-boundary layer interaction is reduced. The relationship between CFJ airfoil geometry and its performance was also specifically demonstrated in this study. These results give insight into the fundamentals of transonic CFJ airfoils and provide a starting point for future designs. 1.5 Aft Co-Flow Jet The Aft-CFJ design places both injection and suction downstream of the main a shock wave; a configuration created by Fernandez, J. Hoffmann and G. Zha [14]. Ideally, it results in an enlarged supersonic region that increase performance of the airfoil. They provide a detailed trade study of the design origins and its performance. The Aft-CFJ airfoil was based on the baseline RAE2822 airfoil. The simulation was performed at Re = and M =0.729 by using in-house CFD program, FASIP.

28 7 Several trade studies were conducted in order to achieve the final design for the Aft-CFJ airfoil. The final peak efficiency configuration for the Aft-CFJ RAE-2822 is obtained with injection slot location at 67% chord length, C = and AoA=1.9. CFJ creates a lower pressure area downstream of shock wave [14]. The idea is to reduce the normal shock wave speed, and push the shock further downstream. Results indicate an increased supersonic region, leading to a higher C L compared to the baseline RAE2822 airfoil. Another advantage of the Aft-CFJ design is providing lower power consumption compared to the traditional CFJ [14]. Therefore, the design is able to bring a higher aerodynamic efficiency over the baseline RAE2822 airfoil of about 5.26%. However, aerodynamic efficiency is 6.64% lower when compared to the tradition CFJ RAE2822 airfoil. This study examines a novel design compared to the traditional CFJ airfoil. Although the efficiency and lift gains are seen compared to the baseline, supercritical airfoil, the results did not compete with the standard transonic CFJ airfoil design.

29 CHAPTER 2 Governing Equations Navier-Stokes equations are the governing equations for fluid flow, which are a system of unsteady and non-linear partial differential equations for the conservation of mass, momentum, and energy. This chapter describes the governing equations compressible aerodynamics in detail. 2.1 The Navier-Stokes Equations Following the derivation of Knight et al. [15], the filtered compressible Navier- Stokes equations in Cartesian coordinates can be expressed as: Q t + E x + F y + G z = 1 Re ( E v x + F v y + G v z ) (2.1) where t is time,re is the Reynolds number. The variable vector Q, inviscid flux vectors E, F, G, and the viscous fluxes E v, F v, G v are given as the following. 8

30 9 Q = ρ ρũ ρṽ, E = ρ w ρẽ E v = ρũ ρũ 2 + p ρũṽ, F = ρũ w ( ρẽ + p)ũ 0 τ xx + σ xx τ xy + σ xy, F v = τ xz + σ xz Q x Q y ρṽ ρṽũ ρṽ 2 + p, G = ρṽ w ( ρẽ + p)ṽ 0 τ yx + σ yx τ yy + σ yy, G v = τ yz + σ yz Q z ρ w ρ wũ ρ wṽ ρ w 2 + p ( ρẽ + p) w 0 τ zx + σ zx τ zy + σ zy τ zz + σ zz The overbar denotes a regular filtered variable, and the tilde is used to denote the Favre filtered variable. In above equations, ρis the density, u, v, w are the Cartesian velocity components in x, y, z directions, p is the static pressure, and e is the total energy per unit mass. The τ is the molecular viscous stress tensor and is estimated as: τ ij = 2 3 ũ k x k δ ij + ( ũ i x j + ũ j x i ), i, j = 1, 2, 3 (2.2) The above equation is in tensor form, where the subscript 1, 2, 3 represent the coordinates, x, y, z, and the Einstein summation convention is used. as: The molecular viscosity = ( T ) is determined by Sutherland law. The σ is the subgrid scale stress tensor due to the filtering process and is expressed

31 10 The energy flux Q is expressed as: σ ij = ρ(ũ i u j ũ i ũ j ) (2.3) where Φ is the subscale heat flux: Q i = ũ j ( τ ij + σ ij ) q i + Φ i (2.4) The q i is the molecular heat flux: Φ i = C p ρ(ũit ũ i T ) (2.5) q i = C p P r T (2.6) x i ρẽ = p (γ 1) ρ(ũ2 + ṽ 2 + w 2 ) + ρk (2.7) where γ is the ratio of specific heats, ρk is the subscale kinetic energy per unit volume. ρk = 1 2 ρ(ũ iu i ũ i ũ i ) = 1 2 σ ii (2.8) In the present calculation, the ρk in Eq.(2.7) is omitted based on the assumption that the effect is small. In generalized coordinates, Eq.(2.1) can be expressed as the following: Q t + E ξ + F η + G ζ = 1 Re ( ) E v ξ + F v η + G v ζ (2.9) where

32 11 Q = Q J (2.10) E = 1 J (ξ tq + ξ x E + ξ y F + ξ z G) (2.11) F = 1 J (η tq + η x E + η y F + η z G) (2.12) G = 1 J (ζ tq + ζ x E + ζ y F + ζ z G) (2.13) E v = 1 J (ξ xe v + ξ y F v + ξ z G v ) (2.14) F v = 1 J (η xe v + η y F v + η z G v ) (2.15) G v = 1 J (ζ xe v + ζ y F v + ζ z G v ) (2.16) where J is the transformation Jacobian. The inviscid fluxes in generalized coordinate system are expressed as: E = ρu ρũu + l x p ρṽu + l y p ρ wu + l z p ( ρẽ + p) U l t p, F = ρv ρũv + m x p ρṽv + m y p ρ wv + m z p ( ρẽ + p) V m t p, G = ρw ρũw + n x p ρṽw + n y p ρ ww + n z p ( ρẽ + p) W n t p where U, V and W are the contravariant velocities in ξ, η and ζ directions.

33 12 U = l t + l V = l t + l x ũ + l y ṽ + l z w V = m t + m V = m t + m x ũ + m y ṽ + m z w (2.17) W = n t + n V = n t + n x ũ + n y ṽ + n z w l, m, n are the normal vectors on ξ, η, ζ surfaces with their magnitudes equal to the elemental surface area and pointing to the directions of increasing ξ, η, ζ. l = ξ J, m = η J, n = ζ J l t = ξ t J, m t = η t J, n t = ζ t J (2.18) (2.19) For simplicity, all the overbar and tilde in above equations will be dropped in the rest of this thesis. Please note that the Navier-Stokes equations, Eq.(2.9), are normalized based on a set of reference parameters. 2.2 Spalart-Allmaras Turbulence Model The transport equation of the Spalart-Allmaras one equation turbulence model is derived by using empiricism, dimensional analysis, Galilean invariance and selected dependence on the molecular viscosity [16]. The working variable ν is related to the eddy viscosity ν t. The transport equation is expressed as D ν = Dt c b1 S ν (1 f t2 ) [c w1 f w c b1 k 2 f t2 ][ ν d ]2 + 1 σ [ ((ν + ν) ν) + c b2( ν) 2 ] + f t1 ( q) 2 (2.20) In generalized coordinate system, the dimensionlessed conservative form of Eq.(2.20) is given as the following:

34 13 1 J ρ ν t + ρ σ + ρ νu ξ + ρ νv η (ν + ν) (m ν) η + ρ νw ζ + ρ σ = 1 Re ( ρ (ν + ν) (l ν) σ ξ (ν + ν) (n ν) ζ + 1 J S ν ) (2.21) where S ν = ρc b1 (1 f t2 ) S ν [ + 1 ρ ( ) ( c Re w1 f w c b1 f ν ) 2 κ 2 t2 d + ρ c σ b2 ( ν) 2 1 (ν + ν) ν ρ] + Re [ ρf σ t1 ( q) 2] (2.22) The eddy viscosity ν t is obtained from: ν t = νf v1 f v1 = χ 3 χ 3 + c 3 v1 χ = ν ν (2.23) where ν is the kinematic viscosity. The production term is: S = S + ν k 2 d 2 f v2, f v2 = 1 χ 1 + χf v1 (2.24) where S is the magnitude of the vorticity. The function f w is given by f w = g( 1 + c6 w3 ) 1/6, g = r + c g 6 + c 6 w2 (r 6 r), r = ν (2.25) w3 Sk 2 d 2 The function f t2 is given by and the trip function f t1 is f t2 = c t3 exp ( c t4 χ 2) (2.26) [ f t1 = c t1 g t exp c t2 ω 2 t U 2 ( d 2 + g 2 t d 2 t ) ] (, g t = min 0.1, q ω t x t ) (2.27)

35 where, ω t is the wall vorticity at the wall boundary layer trip location, d is the distance to the closest wall. d t is the distance of the field point to the trip location, q is the difference of the velocities between the field point and the trip location, x t is the grid spacing along the wall at the trip location. The values of the coefficients are: c b1 = , c b2 = 0.622, σ = 2 3, c w1 = c b1 k 2 + (1 + c b2 )/σ, c w2 = 0.3, c w3 = 2, k = 0.41, c v1 = 7.1, c t1 = 1.0, c t2 = 2.0, c t3 = 1.1, c t4 = 2.0. In S-A one equation turbulence model, the trip point need to be specified before computation. This is not straightforward to do because the exact position of the trip point is not known in most of the cases. Thus, a full turbulent boundary layer is used by setting c t1 = 0 and c t3 = 0. No trip point needs to be specified. It is observed that the S-A one equation turbulence model is sensitive to initial field. If the initial field of ν is set to a small value, e.g. ν < 1, the solution may converge with ν = 0, which is the trivial solution of ν when c t1 = c t3 = 0. This will result in a laminar flow solution. If the initial value is too large ( ν > 3), the computation may diverge. In addition, setting up the initial value of ν also depends on the schemes to be used. In our computation, it is found that it is generally safe to set the initial value of ν to 2. The boundary conditions of ν are given as the following 14 at walls : ν = 0 far field inflow : ν = 0.02 far field outflow : ν is extrapolated Coupled Eqs.(2.9) with the S-A model Eq.(2.21), the conservative form of the governing equations are given as the following:

36 15 Q t + E ξ + F η + G ζ = 1 ( R Re ξ + S η + T ) ζ + D (2.28) where, Q = 1 J ρ ρu ρv ρw ρe ρ ν (2.29) E = ρu ρuu + l x p ρvu + l y p ρwu + l z p (ρe + p) U l t p ρ νu, F = ρv ρuv + m x p ρvv + m y p ρwv + m z p (ρe + p) V m t p ρ νv, G = ρw ρuw + n x p ρvw + n y p ρww + n z p (ρe + p) W n t p ρ νw (2.30)

37 16 R = 0 l k τ xk l k τ yk l k τ zk l k β k ρ (ν + ν) (l ν) σ, S = 0 m k τ xk m k τ yk m k τ zk m k β k ρ (ν + ν) (m ν) σ, T = 0 n k τ xk n k τ yk n k τ zk n k β k ρ (ν + ν) (n ν) σ (2.31) D = 1 J (2.32) S ν where, U, V, W are defined as in Eq.(2.17). β k = u i τ ki q k (2.33) The shear stress τ ik and total heat flux q k in Cartesian coordinates is given by [( ũi τ ik = ( + DES ) + ũ k x k x i ( q k = P r + DES P r t ) 2 ] 3 δ ũ j ik x j (2.34) ) T x k (2.35) where is from Sutherland s law. For DES family in general, the eddy viscosity is represented by DES (= ρ νf v1 ).

38 CHAPTER 3 CFJ Airfoil Parameters This chapter describes the definitions of parameters that are used to measure the CFJ implementation and to evaluate the performance of CFJ airfoil. 3.1 Lift, Drag and Moment Calculation The momentum and pressure at the injection and suction slots produce a reactionary force, which is automatically measured by the force balance in wind tunnel testing. However, for CFD simulation, the full reactionary force needs to be included. Using a control volume analysis, the reactionary forces can be calculated using the flow parameters at the injection and suction slot opening surfaces. Zha et al. [4] give the following formulations to calculate the lift and drag due to the jet reactionary force for a CFD simulation. By considering the effects of injection and suction jets on the CFJ airfoil, the expressions for these reactionary forces are given as : F xcfj = (ṁ j V j1 + p j1 A j1 ) cos(θ 1 α) (ṁ j V j2 + p j2 A j2 ) cos(θ 2 + α) (3.1) F ycfj = (ṁ j1 V j1 + p j1 A j1 ) sin(θ 1 α) + (ṁ j2 V j2 + p j2 A j2 ) sin(θ 2 + α) (3.2) 17

39 18 where the subscripts 1 and 2 stand for the injection and suction respectively, and θ 1 and θ 2 are the angles between the injection and suction slot surfaces and a line normal to the airfoil chord. α is the angle of attack. The total lift and drag on the CFJ airfoil can then be expressed as: D = R x F xcfj (3.3) L = R y F ycfj (3.4) where R x and R y are the surface integral of pressure and shear stress in x (drag) and y (lift) direction excluding the internal injection and suction ducts. Let us introduce the CFJ reactionary forces components in the x and y direction for the injection (inj subscript) and suction (sub subscript) as : F xinj = (ṁ j V j1 + p j1 A j1 ) cos(θ 1 α) (3.5) F xsuc = (ṁ j V j2 + p j2 A j2 ) cos(θ 2 + α) (3.6) F yinj = (ṁ j1 V j1 + p j1 A j1 ) sin(θ 1 α) (3.7) F ysuc = (ṁ j2 V j2 + p j2 A j2 ) sin(θ 2 + α) (3.8) The total pitching moment of the CFJ airfoil can be expressed as: M z = M z + F xinj.l yinj + F yinj.l xinj F xsuc.l ysuc F ysuc.l xsuc (3.9) where M z is the pitching moment generated by the airfoil surface pressure and shear stress excluding the internal injection and suction ducts. L xinj and L yinj, respectively L xsuc and L ysuc, are the moment arm in x and y direction for the injection, respectively suction. By convention, we define a pitch up moment as a positive moment and a pitch down moment as a negative moment. For the CFD simulation, the total lift, drag and moment are calculated using Eqs. (3.3), (3.4) and (3.9) respectively.

40 3.2 Jet Momentum Coefficient 19 A parameter,the jet momentum coefficient C, is used to quantify the jet intensity. It is defined as : ṁv j C = 1 ρ 2 V 2 S (3.10) where ṁ is the injection mass flow, V j the injection velocity, ρ and V denote the free stream density and velocity. S is the planform area. 3.3 Power Coefficient The CFJ can be implemented by mounting a pumping system inside the wing that withdraws air from the suction slot and blows it into the injection slot. The power consumption can be determined by the jet mass flow and total enthalpy change as the following : P = ṁ(h t1 H t2 ) (3.11) where H t1 and H t2 are the total enthalpy in the injection cavity and suction cavity respectively, P is the Power required by the pump and ṁ the jet mass flow rate. Introducing the pump efficiency η and total pressure ratio of the pump Γ = P t1 P t2, the power consumption can be expressed as : P = ṁc pt t2 (Γ γ 1 γ 1) (3.12) η where γ is the specific heat ratio equal to 1.4 for air. The power consumption can be expressed as a power coefficient below: P P c = 1 ρ 2 V S 3 (3.13)

41 3.4 Corrected Aerodynamic Efficiency 20 The conventional airfoil aerodynamic efficiency is defined as : L D (3.14) For the CFJ airfoil, the ratio above still represents the pure aerodynamic relationship between lift and drag. However since CFJ active flow control consumes energy, the ratio above is modified to take into account the energy consumption of the pump. The formulation of the corrected aerodynamic efficiency for CFJ airfoils is : ( L D ) c = L D + P V (3.15) where V is the free stream velocity, P is the pumping power, and L and D are the lift and drag generated by the CFJ airfoil. The formulation above converts the power consumed by the CFJ into a force P V which is added to the aerodynamic drag D. If the pumping power is set to 0, this formulation returns to the aerodynamic efficiency of a conventional airfoil.

42 CHAPTER 4 Transonic 2-D Co-Flow Jet Airfoil Design 4.1 Trade Study Results and Discussion It is already proven that both subsonic and transonic CFJ airfoil configurations dramatically improve the airfoil performance not only on lift coefficient but also on the aerodynamic coefficient [2, 12]. However, both cases only used activate flow control technique on suction surface (upper surface) which is associated with higher velocity and lower static pressure. Since the current improvement is focus on optimizing, it is interesting to think about a different approach-to increase the local static pressure and to reduce the flow velocity on pressure surface (lower surface) Convergence Study The baseline RAE2822 airfoil and the standard CFJ RAE2822 airfoil is used, as the new design adopted suction surface desgin of Liu and Zha [12]. The maximum thickness of RAE2822 supercrtical airfoil is 12.1% at 37.9% chord and the maximum camber is 1.3% at 75.7% chord. As the free-stream condition of M = 0.729, Re = and various AoA from 1 to 5.5, which based on AGARD report, experiment Case 9 [?]. All the mesh size used is identical to the pape [12] for verifi- 21

43 22 cation reason. O-type structured grids with mesh size in circumferential and radial direction are applied for mesh dependency study. A slight large size, , O-type structured grids is used for the double surface CFJ airfoil due to an additional injection. Figure 4.1: General (top) and zoomed-in (bottom) view of O-type structured mesh in size for baseline airfoil

44 Figure 4.2: Comparison of pressure coefficient C P between simulation and experiment at M=0.729, α=3.19. Table 4.1: Baseline RAE2822 airfoil aerodynamics coefficients comparison between simulation and experiment Case C L C D Experiment mesh mesh mesh mesh mesh

45 Figure 4.3: The convergence history of L 2 Norm relative error for the baseline RAE2822 airfoil cases Figure 4.2 indicates that pressure coefficient C P distributions of all baseline meshes fit very well with the experiment result. The L 2 Norm convergence history shows in Figure 4.3 is able to tell residuals of all mesh size simulations are at least reduced 7 orders of magnitude after 8000 iterations. Table 4.5 points out that mesh size large than are all converged with difference less than 1% in lift coefficient and drag coefficient. The mesh size of is chosen for baseline airfoil in order to keep mesh size consistency with standard CFJ airfoil and double surface airfoil.

46 25 Figure 4.4: General (top) and zoomed-in (bottom) view of O-type structured mesh in size for standard CFJ airfoil

47 Figure 4.5: Comparison of pressure coefficient between standard CFJ airfoil simulations at M=0.729, α=2, C = Table 4.2: The standard CFJ airfoil aerodynamics coefficients comparison between mesh size Case C L C D C M P C mesh mesh

48 Figure 4.6: The convergence history of L 2 Norm relative error for the standard CFJ RAE2822 airfoil cases In addition, the standard CFJ airfoil C =0.006 is also calculated under same free stream condition like the baseline airfoil. Mesh size refinement study of size and is performed. The CFJ airfoil convergence history, shown in Table 4.2, indicates mesh size and convergence difference are less than 1.2% at all marked parameters. Therefore, the mesh size is chosen for the standard CFJ airfoil.

49 28 Figure 4.7: General (top) and zoomed-in (bottom) view of O-type structured mesh in size for double surface CFJ airfoil

50 29 Figure 4.8: Comparison of pressure coefficient between standard CFJ airofoil simulations at M=0.729, α=2, C = Table 4.3: Double surface CFJ airfoil aerodynamics coefficients comparison between mesh size Case C L C D C M P C mesh mesh

51 30 Figure 4.9: The convergence history of L 2 Norm relative error for the current CFJ RAE2822 airfoil cases The mesh refinement study on the double surface CFJ airfoil C =0.003 is calculated under the same flow condition as the baseline airfoil for mesh size and The CFJ airfoil convergence history, shows in Table 4.3, indicates mesh size and convergence difference are less than 1.2% at all marked parameters. The reason there is a sudden jump on L 2 Norm at iteration is due to the right hand side order scheme switched from 1st order MUSCL to 3rd order-weno. Consequently, size is picked for the current design C Distribution Optimization The standard CFJ airfoil configuration has only one CFJ set which can be easily controlled by assign only one C. However, in the new design, an additional injection will be located on pressure surface of the airfoil which require an additional C assign

52 31 to this injection. A parametric study is carried out in order to find the best optimized C distribution between upper injection C and lower injection C. Different C from to for the injection on suction surface (upper injection) and a different C from to is given to injection located in pressure surface (lower injection). Note that C = is the lowest number can be assigned to the lower injection. Any lower C will create any separation due to the high static pressure on the lower airfoil surface. Figure 4.10: Coefficient of lift C L contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection

53 32 Figure 4.11: Power coefficient P C contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection Figure 4.12: Corrected aerodynamic efficiency ( L D ) C contour plot for current CFJ RAE2822 airfoil design with different C on upper and lower injection

54 33 Figure 4.13: Corrected aerodynamic efficiency productivity ( L2 D ) C RAE2822 airfoil design with different C on upper and lower injection contour plot for current CFJ Figure 4.10 demonstrates the C L distribution contour between the upper injection C and the lower injection C. As both C increasing, the C L is increasing as well. However Figure 4.13 states the best aerodynamic efficiency ( L ) D C locate at lowest C point. This is due to rise of energy consumption while the C increased. Although a higher C will induce a higher C L, the aerodynamic efficiency will largely decrease. Therefore, C = will be employed as optimized point for lower injection Lower Injection Slot Open Location Since the double surface CFJ design have an injection in the pressure surface and the static pressure will be varied along the pressure surface, it is interesting to know where is the best location to place the injection. In this subsection, the relationship between lower injection location and aerodynamic efficiency will be studied.

55 34 Figure 4.14: The double surface CFJ transonic airfoil with different lower injection slot opening location As showing in Figure 4.14, the double surface CFJ transonic airfoils with injection slot placed at 3%, 5%, 7%, 10%, 20% and 37.9% chord location. The 3% chord length is where the upper injection slot located as well. Note that the 37.9% is the thickest point of the RAE2822.

56 35 Figure 4.15: Aerodynamic coefficients for different lower injection slot location under different C Figure 4.15 indicates the aerodynamics coefficients for each location. Although the C L change between the different injection location barely shown, the C D plots shown significant deference. With the C increased, the C D raised at all locations. Moreover, with the location moved to further downstream the C D increased a lot. On the contrary, the P C decreased. The ( L ) D C plot demonstrates the 3% chord length has the most desirable result.

57 36 Figure 4.16: Isotropic mach distribution comparison between the different location of double surface CFJ designs at same C Figure 4.17: The double surface CFJ transonic airfoil with x-axis force and drag coefficient in pressure term along location change

58 Figure 4.16 presents the isotropic mach distribution for different injection slot 37 locations at total C = It shows that the individual jumps on the pressure surface are caused by the injection of air by the slot at each location. As Eq.(3.3) illustrates drag coefficient can be divided into three components namely viscous term (C DP ), pressure term (C DV ) plus the total injection force in x-axis, F x, thus equation become: C D = C DP + C DV + F x Figure 4.17 indicates the reason why the C D would increase. It is mostly due to the injection reaction force in x-axis. Airfoil curvature changes along the pressure side while the injection slot shooting angle remains the same. This, therefore, makes the injection reaction force applied on airfoil changed while the injection location changed. Although the C DV is increased, the number is simply one magnitude smaller that cannot make up the change of force Lower Injection Slot Width The previous study on standard CFJ airfoil shown injection slot size will affect the coming out jet velocity if the momentum coefficient C is fixed. In order to know the relationship between slot width and CFJ performance, a trade study is been conducted. Three different lower injection slot width, 0.6%, 1% and 1.4% chord length is being studied, meanwhile the upper injection and suction size will remain unchanged. Figure 4.18 shows the double surface CFJ transonic airfoil with the lower injection slot width of 0.6%, 1% and 1.4% chord length respectively.

59 38 Figure 4.18: The current CFJ transonic airfoil with different suction slot width arrangement.

60 39 Figure 4.19: Aerodynamic coefficients for different lower injection slot width under different C Figure 4.19 demonstrates the difference while different size of slot applied to the lower injection. It is clear that the larger the sloth width, the higher the C L. However C D and P C are higher as well, which lead to a lower ( L ) D C. Generally, a higher ( L ) D C is preferred, which means a larger sloth width size is tend to be chosen. However, C L is a essential reference as well, since any C L improvement is also critical. Considering the balance between this two reference parameters, the 1.0% chord width is thereby chosen.

61 Aerodynamic Behavior of Double Surface CFJ Angle of attack After all the study in above, the final design of the double surface CFJ airfoil is finalized. The configuration is shown in figure 4.20 and a study concerns with various angle of attack (AoA) is implemented. The AoA is change from 1 to 5.5 with total C changing from to (δ=0.001). And the lower injection C is fixed at Note that all the cases simulated is assuming pump efficient λ=100% without any efficiency loss. Baseline RAE2822 Standard CFJ RAE2822 Double Surface CFJ RAE2822 Figure 4.20: The baseline RAE2822 airfoil, the standard CFJ RAE2822 airfoil and the double surface CFJ airfoil.

62 41 Figure 4.21: Double surface CFJ airfoil upper (top) and lower (bottom) injection velocity versus angle of attack for different jet moment. Figure 4.21 shows the double surface CFJ airfoil injections velocity V j V versus AoA at different jet momentum coefficient C. The plot on top indicates the upper injection velocity. Likewise the standard CFJ airfoil design, the larger the C is, the faster the jet velocity comes out. And all jets is lower than the free stream velocity Mach= While the increasing of AoA, the jet velocity also growing. The right side plot tells the lower injection velocity. Due to the lower injection C is fixed to

63 , the velocity difference between each case is lower than 1%. In addition, the velocity decreasing as AoA increases from 1 to 5.5 is due to rise of pressure force lower injection has to inject higher pressure flow. It is also explained less efficiency on the relative high AoA. Γ Γ Figure 4.22: Double surface CFJ airfoil upper (top) and lower (bottom) Injection Suction jet moment. AoA for different Figure 4.21 demonstrates the injection/suction total pressure ratio Γ versus AoA. All the cases discussed here have the total pressure ratio greater than 1, otherwise

64 43 the co-flow jet can circulate the flow by itself without using pump driven it. The total pressure of upper injection generally followed the Liu s paper [12]. For all the other C cases, as AoA increases, the total pressure ration of the bottom injection keep rising until AoA=3.5. When the AoA raised up beyond 3.5, flow separation appers around the suction slot and the shock wave translate to upstream caused by the boundary layer separation. The shock wave now interact with boundary layer is oblique shock rather than normal shock. The expansion wave spontaneously formed downstream of the shock wave. Even though the separation appeared, the lower injection also working at high static pressure status and due to the shock wave is pushed closer to suction region, the total pressure tend to weaken or keep in same The reason for upper injection total pressure decreases is because of the oblique shock interacting with the boundary layer [12]. Thus the Γ decreases as the AoA in range of 3.5 to 5.5.

65 44 Figure 4.23: Aerodynamic coefficients of the baseline, standard CFJ airfoil and double surface CFJ for angle of attack changing from 1 to 5.5.

66 Figure 4.23 shows aerodynamic coefficients variation with respect to AoA for baseline and CFJ and double surface CFJ airfoil. Several phenomenons is observed: First of all, the double surface CFJ airfoil performed higher C L than both the CFJ and the baseline airfoil for all AoA and while the C L is increased as C increases. Second of all, for the AoA smaller than 2, the double surface CFJ airfoil generates lower drag than the baseline. However, at all AoA, the drag is still slightly larger than the standard CFJ case. It is because also the third observation, that the P C of double surface CFJ airfoil is higher than the tradition CFJ airfoil at all cases. The high static pressure on pressure surface cost lower injection much higher power to perform. The higher drag coefficient is also caused by the stronger shock wave created by the double surface CFJ. Fourth, the current design is at least able to maintain L D and ( L D ) C when AoA is smaller than 2. For higher AoA, L D and ( L D ) Cdecrease due to increasing drag coefficient C D. Fifth, the double surface CFJ ( L2 D ) C at AoA lower than 2 is higher than standard case. that is benefit from the C L gain in lower AoA. 45

67 46 Figure 4.24: The drag polar curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to 5.5 Figure 4.24 shows the drag polar of the double surface CFJ and CFJ airfoil compared with the baseline airfoil with the AoA vary from 1 to 5.5. It shows the double surface CFJ design increases the lift coefficient compare to standard CFJ, not mention to baseline airfoil, with the same C D at all C conditions. The maximum C L of the new design is increased from to by 11.76%. At AoA higher than 2, the double surface CFJ airfoil has slightly higher C D that the number no larger than 0.5%. The drag increasing is because of the stronger shock wave.

68 47 Figure 4.25: The corrected drag C D + C P polar curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to 5.5 Figure 4.25 is the lift coefficient against the corrected drag coefficient C D + C P. It is showing the higher C L it reached, the higher corrected drag coefficient it get. It is because the C L increment is caused by increased mass flow rate of air in the suction slot, hence it results a higher P C. Besides, the stronger shock wave leads the larger drag coefficient, the C D + C P therefore is raised.

69 48 Figure 4.26: The aerodynamic performance L D curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to 5.5 Figure 4.27: The corrected aerodynamic performance curves of the double surface CFJ airfoil and the tradition CFJ and the baseline airfoil for angle of attack changing from 1 to 5.5

70 49 Figure 4.26 tells the results of L ) verses C D L. And two groups are selected for comparison purpose. The first group is the C =0.003 at AoA=2 as the peak efficiency. The second group is the maximum C L points for each airfoil design. Table 4.4: Aerodynamics coefficients comparison between the baseline airfoil, the CFJ airfoil and the double surface CFJ airfoil Baseline standard CFJ double surface CFJ Improvement α N/A C N/A N/A C L % L % D Baseline standard CFJ double surface CFJ Improvement α N/A C N/A N/A C L % L % D

71 Table 4.5: Corrected aerodynamics coefficients comparison between the baseline airfoil, the standard CFJ airfoil and the double surface CFJ airfoil 50 Baseline standard CFJ double surface CFJ Improvement α N/A C N/A N/A C L % ( L ) D C % Baseline standard CFJ double surface CFJ Improvement α N/A C N/A N/A C L % ( L ) D C % Baseline standard CFJ double surface CFJ Improvement α N/A C N/A N/A C L % ( L ) D C % Figure 4.27 tells the results of ( L D ) C verses C L. And several points are selected for parallel comparison. The first group is the C =0.003 at AoA=2 as the peak efficiency point in Liu s paper [12]. The second group is the C =0.002 at AoA=2 as the peak efficiency point when the pump efficiency is 100%. The third group is the maximum C L points for each airfoil design. A few observation are obtained: 1) Comparing the Liu s peak efficiency point between CFJ and double surface CFJ

72 51 airfoil, the double surface CFJ airfoil had the C L improved by 5.15% with the ( L ) D C loss only %. 2) Comparing the maximum peak efficiency in my simulation, the double surface CFJ airfoil had the C L improved by 5.47% with the ( L ) D C increased 0.83%. 3) Comparing the maximum lift coefficient point the double surface CFJ airfoil had the C L improved from to with lower C. And the ( L ) D C is increased by 2.105% Flow Field Comparison Figure 4.29, 4.33 and 4.37 indicates the Mach contours for the peak efficiency points of the baseline, the CFJ airfoil and the double surface CFJ airfoil with C = It shows clearly that the double surface CFJ airfoil design further expands the supersonic region to a larger area with even higher Mach number. As also showing in the Figure 4.28, 4.32 and 4.36, the surface pressure and isotropic Mach number distributions, while the double surface CFJ airfoil has same peak suction Mach number near the leading edge, it is able to maintain in higher Mach number generally. The larger supersonic region is induced by the higher mass flow rate of the suction, which means the suction sucked shock wake closer. Zoomed-in mach contour is shown in Figure 4.30 and 4.34 The shock wave of the double surface CFJ airfoil case is about 5.5% more downstream than CFJ airfoil. In the Figure 4.30, the boundary layer of double surface CFJ airfoil is slightly smaller than the CFJ case is due the airfoil larger curvature in downstream. The shock wave/boundary-layer interaction is hence interfered. On the contrary, in Figure 4.34, a thicker high momentum layer neat the wall is shown in double surface CFJ airfoil.

73 52 The Mach contours in the trailing edge wake region as shown in Figure 4.31,4.35 and 4.39 also demonstrate the double surface CFJ airfoil is able to smaller the low mach number region. Figure 4.28: Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at C =

74 53 Figure 4.29: Mach contours comparison between the baseline, standard CFJ and double surface CFJ airfoil at C =

75 54 Figure 4.30: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at C =

76 55 Figure 4.31: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at C =

77 56 Figure 4.32: Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at peak efficiency condition with C =

78 57 Figure 4.33: Mach contours comparison between the baseline, CFJ and double surface CFJ airfoil at peak efficiency condition with C =

79 58 Figure 4.34: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at peak efficiency condtion with C =

80 59 Figure 4.35: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at peak efficiency condtion witht C =

81 60 Figure 4.36: Surface pressure distribution and isotropic Mach distribution comparison between the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at maximum lift cases.

82 61 Figure 4.37: Mach contours comparison between the baseline,standard CFJ and double surface CFJ airfoil at maximum lift condition.

83 62 Figure 4.38: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at maximum lift condition.

84 63 Figure 4.39: Shock location and after shock region Mach contour between the baseline, standard CFJ and double surface CFJ airfoil at at maximum lift condition.

85 Figure 4.35 and 4.36 copmares the Mach contours, surface pressure and isotropic Mach number distributions for the maximum lift coefficient cases. The higher C L 64 is caused by the shock wave is moved further downstream. However the surface distributions shows the double surface CFJ case has a stronger shock wave formed before suction. Figure 4.40: Shock entropy increase distributions at locations above surface(lss) for the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at the peak efficiency condition

86 65 Figure 4.41: X-component of wake velocity distribution at one chord length downstream location(dl) for the baseline airfoil, standard CFJ airfoil and the double surface CFJ airfoil at the peak efficiency condition Figure 4.42: Shock entropy increase distributions at locations above surface(lss) for the baseline airfoil, standard CFJ airfoil and double surface CFJ airfoil at the maximum lift condition

87 66 Figure 4.43: X-component of wake velocity distribution at one chord length downstream location(dl) for the baseline airfoil, standard CFJ airfoil and the double surface CFJ airfoil at the maximum condition Figure 4.44: Entropy increase contours comparison at C =0.003 cases.

88 67 Figure 4.45: Entropy increase contours comparison at peak aerodynamic efficiency. Figure 4.46: Entropy increase contours comparison at the maximum lift cases. Figure 4.40 tells entropy increase distribution at peak efficiency point. The distance of 5% and 15% chord length vertically above the suction surface near the chock