University of Khartoum

Faculty of Engineering

Mechanical Engineering Department

Numerical simulation of vortex trapped Airfoil

A thesis submitted in partial fulfillment of the requirements for the degree of B.Sc. in Mechanical Engineering

Presented by: Suhaib Salah El-Tayeb Awad

Supervised by: Dr. Obai Younis Taha

August 2015

ACKNOWLEDGEMENT

I’m greatly indebted and thankful to Dr. Obai Younis Taha for her unlimited support, helpful instructions and closed supervision throughout the year.

And also I want to thank prof.Mohammed Hashim Siddig for his great tips and helps.

And I’d like to thank Dr.Ali Seory for the great CFD course and being very helpful.

In addition great thank for Eng.Ahmed Alrayah hassan.

Lastly for my brother Eng.Ammar Mohammed Ahmed For their technically support and advising.

I

DEDICATION

To my lovely mother, Dear father, my brothers and sisters whom suffered very much till I have finished successfully my task.

II

ABSTRACT

The main objective of this research is to study the characteristics of a smoothing section (airfoil) after work on (NACA23012).

Vortex trapped is located in the front of the Airfoil section with depth of 50% on a round shape and circular vertical shape, research focused on the study of the influence of flow separation widget and vortex and bubbles formed and also the distribution of pressure at Airfoil Section for both laminated and turbulent flow cases. Also the lift and drag results from these adjustments are compared with the base type account. It was discussed according to results that taken from Application of Computation fluid dynamic ( CFD ).

Research has been reached that the angular vortex trapped gives the highest value for the coefficient of lift while notes a rise in the value of the coefficient of drag it is imperative to conduct further studies to reduce the coefficient of drag.

III

الملخص

ان الهدف االساسى من هذا البحث هو دراسة خصائص المقطع االنسيابى )الجنيح( بعد عمل قطعة على المقطع االنسيابى االساسى (NACA23012(.

القطعة أجريت في الجزء األمامي من المقطع االنسيابي بعمق 50% على شكل دائري عمودي و دائري مائل, البحث ركز على دراسة تأثير القطعة على انفصال السريان والدومات المتكونة وايضا توزيع الضغط حول المقطع االنسيابى المقطوع في حالتي السريان الصفائحي و المائر. حيث تم حساب الرفع والمقاومة الناتجة عن هذه التعديالت ومقارنتها مع النوع االساسى. تمت مناقشة تأثيرات القطعة بناء على النتائج التى اخذت من برنامج تحسيب حركة الموائع عمليات (CFD(

الذي تم استخدامه في عمليات التحسيب.

من البحث تم الوصول الى ان القطعة الدائرية المائلة تعطي أعلى قيمة لمعامل الرفع بينما يالحظ وجود ارتفاع في قيمة معامل االحتكاك لذا البد من اجراء المزيد من الدراسات لتقليل معامل االحتكاك.

IV

TABLE OF CONTENTS

ACKNOWLEDGEMENT ...... I DEDICATION ...... II ABSTRACT ...... III IV ...... الملخص TABLE OF CONTENTS ...... V LIST OF ABBREVIATION AND SYMBOLS ...... VII LIST OF FIGURES ...... VIII LIST OF TABLES ...... X Chapter One : INTRODUCTION ...... 1 1.1 DEFINITION: ...... 2 1.2 CHARACTERISTICS OF THE AIRFOIL: ...... 2 1.3 NACA SERIES: ...... 3 1.4 Objective:...... 9 Chapter Two : LITERATURE REVIEW ...... 10 2.1 HISTORY AND DEVELOPMENT: ...... 11 Chapter Three : METHODOLOGY...... 19 3.1 Introduction to CFD: ...... 20 3.1.1 What is Computational Fluid Dynamics? ...... 20 3.1.2 The History of CFD ...... 20 3.2 How does a CFD code work? ...... 21 3.2.1 Pre – processor ...... 22 3.2.2 Solver ...... 24 3.2.3 Post – processor ...... 30 3.3 Governing Equations: ...... 31 3.3.1 Conservation of mass (Continuity Equation) ...... 32 3.3.2 Conversion of momentum (Navier Stokes Equations ...... 33 3.4 Turbulence Models ...... 34

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3.4.1 RANS-based turbulence models ...... 34 3.4.2 Two equation turbulence models ...... 35 3.4.3 The k equation ...... 35 3.4.4 The ℇ equation: ...... 35 Chapter Four : RESULTS ...... 37 4.1 Computational Domain ...... 38 4.2 Mesh Dependence Study: ...... 39 4.3 Final Results: ...... 42 4.3.1 Pressure distributions for turbulent flow : ...... 42 4.3.2 Pressure distributions for laminar flow : ...... 46 4.3.3 Velocity Streamlines: ...... 48 4.3.3.1 Velocity Streamlines of turbulent flow: ...... 48 4.3.3.2 Velocity Streamlines of laminar flow: ...... 50 4.3.3.3 Static Pressure: ...... 51 4.4 Lift and Drag Coefficients: ...... 55 4.4.1 Aerodynamic Coefficients tables: ...... 55 4.4.1.1 Coefficients at turbulent flow: ...... 55 4.4.1.2 Coefficients at laminar flow: ...... 56 4.4.2 Aerodynamic Coefficients Charts: ...... 57 4.4.2.1 Coefficients at turbulent flow: ...... 57 4.4.2.2 Coefficients at laminar flow: ...... 59 Chapter Five : CONCLUSION AND RECOMMENDATIONS ...... 61 5.1 Conclusion: ...... 62 5.2 RECOMMENDATIONS: ...... 63 REFERENCES: ...... 64 APPENDICES ...... 65

VI

LIST OF ABBREVIATION AND SYMBOLS

퐶푙 Lift coefficient

퐶푑 Drag coefficient 푞̅ Dynamic pressure 푐 Airfoil chord g Gravity k Turbulence kinetic energy 푙 Lift force p Pressure t Airfoil thickness

 Density u Velocity

 Angle of attack

 Viscosity

 Vorticity

 Turbulence dissipation rate Is the friction velocity at the nearest wall. u* y is the distance to the nearest wall and  is the local kinematic viscosity of the fluid.

VII

LIST OF FIGURES

Figure (1.1) airfoil ...... 2 Figure (1.2) airfoil characteristics ...... 3 Figure (1.3) NACA 4412 ...... 4 Figure (1.4) Modern airfoil ...... 7 Figure (1.5) Vortex shedding & trapped vortex...... 7 Figure (1.6) Sequence of flow separation ...... 8 Figure (2.1) Vortex trapped experience ...... 17 Figure (3.1) geometry drawing steps and boundaries description ...... 22 Figure (3.2) geometry drawing steps and boundaries description for trapped vortex...... 23 Figure (3.3) geometry drawing steps and boundaries description for trapped vortex...... 23 Figure (3.4) Basic airfoil solver ...... 24 Figure (3.5) Setup Steps “General” ...... 25 Figure (3.6) Models ...... 25 Figure (3.7) Check Solver ...... 26 Figure (3.8) Choose Material ...... 26 Figure (3.9) Boundary Conditions ...... 27 Figure (3.10) Reference values ...... 27 Figure (3.11) Solution Methods ...... 28 Figure (3.12) Solution Controls & Under-Relaxation Factors ...... 28 Figure (3.13) Monitors & Set of Error ...... 29 Figure (3.14) Solution Initialization & Initial Guess ...... 29 Figure (3.15) Run Calculation & Output Results ...... 30 Figure (3.16) Final Results ...... 31 Figure (4.1) Computational Domain ...... 38 Figure (4.2) Blocks ...... 39 Figure (4.3) Edge Sizing ...... 39 Figure (4.4) Domain mesh ...... 40 Figure (4.5) Mesh generation for basic airfoil ...... 40 Figure (4.6) Domain mesh for angular vortex trapped ...... 41 Figure (4.7) Mech Generation for angular vortex trapped ...... 41

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Figure (4.8) Mesh Generation for vertical vortex trapped ...... 42 Figure (4.9) pressure coefficient of base airfoil at 15o angle of attack ...... 43 Figure (4.10) pressure coefficient of angular vortex trapped at 15o angle of attack ...... 44 Figure (4.11) Pressure coefficient of vertical vortex trapped at 15o angle of attack ...... 45 Figure (4.12) pressure coefficient of base airfoil at 15o angle of attack ...... 46 Figure (4.13) pressure coefficient of angular vortex trapped at 15o angle of attack ...... 47 Figure (4.14) pressure coefficient of vertical vortex trapped at 15o angle of attack ...... 47 Figure (4.15) Velocity Streamlines of base airfoil at 15o angle of attack ...... 48 Figure (4.16) Velocity Streamlines of vertical vortex trapped at 15o angle of attack ...... 49 Figure (4.17) Velocity Streamlines of angular vortex trapped at 15o angle of attack ...... 49 Figure (4.18) Velocity Streamlines of base airfoil at 15o angle of attack ...... 50 Figure (4.19) Velocity Streamlines of vertical vortex trapped at 15o angle of attack ...... 50 Figure (4.20) Velocity Streamlines of angular vortex trapped at 15o angle of attack ...... 51 Figure (4.21) Static pressure of base airfoil at 15o angle of attack ...... 52 Figure (4.22) Static pressure of vertical vortex trapped at 15o angle of attack ...... 52 Figure (4.23) Static pressure of angular vortex trapped at 15o angle of attack ...... 53 Figure (4.24) Static pressure of base airfoil at 15o angle of attack ...... 53 Figure (4.25) Static pressure of vertical vortex trapped at 15o angle of attack ...... 54 Figure (4.26) Static pressure of angular vortex trapped at 15o angle of attack ...... 54 Figure (4.27) drag coefficient of base & modified airfoil ...... 57 Figure (4.28) lift coefficient of base & modified airfoil...... 58 Figure (4.29) lift to drag coefficient of base & modified airfoil...... 58 Figure (4.30) drag coefficient of base & modified airfoil...... 59 Figure (4.31) lift coefficient of base & modified airfoil ...... 59 Figure (4.32) lift to drag coefficient of base & modified airfoil...... 60

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LIST OF TABLES

Table (4.1) lift & drag coefficients of base airfoil ...... 55 Table (4.2) lift & drag coefficients of angular vortex trapped...... 55 Table (4.3) lift & drag coefficients of vertical vortex trapped ...... 56 Table (4.4) lift & drag coefficients of base airfoil...... 56 Table (4.5) lift & drag coefficients of angular vortex trapped...... 56 Table (4.6) lift & drag coefficients of vertical vortex trapped...... 57

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Chapter One

INTRODUCTION

1

1.1 DEFINITION:

In essence, an airfoil is a two-dimensional tear-drop shape that is round in the front and sharp in the back, when extruded into the third dimension and moved through air, generates useful forces or minimizes parasitic forces. As any shape travels through the air it can generate both a retarding force and a lifting force. Those forces are a function of the cross-sectional shape. For example, if you take the cross-sectional shape of a wing, it would have an elongated teardrop shape. This is called an airfoil. In Europe the spelling is sometimes airfoil and sometimes it's even called a profile. With proper selection, you can choose airfoils to either create lift or minimize the drag (e.g. plane wings, propellers, pumps and turbines etc...)(1).

Figure (1.1) airfoil

1.2 CHARACTERISTICS OF THE AIRFOIL:

Airfoil geometry can be characterized by the coordinates of the upper and lower surface. It is often summarized by a few parameters such as defined below:  The chord line, defined as the straight line connecting the leading to the trailing edge.  The chord, denoted by c, defined as the distance between the leading and the trailing edge.

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• The camber line, defined as the locus of points located halfway between the upper and lower surface of the airfoil.  The camber, defined as the maximum distance between the camber line and the chord line. When the camber vanishes, the airfoil is symmetric.  The airfoil thickness distribution along the camber line. The angles of attack, denoted by α, define as the angle subtended between the oncoming flow and the chord line of the airfoil(3).

Figure (1.2) airfoil characteristics

1.3 NACA SERIES:

Twelve years after the Wright Brothers' first 1903 flight, the US government decided to create and fund an organization that would be a central clearinghouse of information regarding research into flying machines. So on March 3, 1915, Congress created the National Advisory Committee for Aeronautics often called the NACA. The official purpose of the NACA was to put in place an organization independent of commercial interests that would study the scientific problems of flight. After the great space race started in the late 1950's, the NACA Organization was ended and the National Aeronautics & Space Administration was born (NASA) (3). 3

The NACA engineers didn't limit their designs to one particular size, so they made all of the parameters a function of Chord length. Each airfoil can be scaled up or down and still have geometric similarity. The ultimate product of his theory was the production of several NACA airfoils "series”, the most popular of which were the NACA 4-Digit, NACA 5-Digit and NACA 6-Digit series; so here below some of the characteristics of these series: I. NACA 4-Digits series: The camber line of 4-Digit sections was defined as a parabola from leading edge to position of maximum of camber, then another parabola back to the trailing edge. For example NACA 4412: 4 4 1 2 Max camber in position of max max thickness in % of % of chord camber in 1/10 of chord chord

Figure (1.3) NACA 4412

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II. NACA 5-Digits series: These sections had the same thickness distribution, but used a camber line with more curvature near the nose. For example NACA 23012: 2 3 0 1 2 max camber in position of max camber in max thickness in% of % of chord 2/100 of chord chord

III. NACA 6-Digits series: These sections were generated from a more or less prescribed pressure distribution and were meant to achieve some laminar flow. For example: NACA 64-215: 6 4 - 2 1 5 six series location of a modification where ideal lift max type minimum the back slope are coefficient in 1/10 thickness pressure straight& trailing is of chord in % of in 1/10 of chord thick chord

To ensure a high lift-to-drag ratio, wings of modern airplanes are thin and streamlined. However, the tendency to design commercial aircrafts of ever-larger dimensions, or innovative configurations as Blended-Wing-Body airplanes requires innovative solutions in the field of wing structures. In order to carry a larger load, having a thick wing would be beneficial. The drawback of wings composed of these type of airfoils is their low efficiency caused by the high drag coefficients shown already present at low/moderate incidences. As a matter of fact, these airfoils are generally affected by an early flow separation phenomenon, even at relatively small angles of attack. Now days, many research activities aim at investigating systems dedicated to the control of flow separation control.

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As a scientific discipline and as a technological curiosity, flow control is perhaps more hotly pursued by scientists and engineers than any other area in fluid mechanics (5). The ability to manipulate a flow field to effect a desired change is of immense practical importance. An external wall-bounded flow, such as that developing on the exterior surface of an aircraft or a submarine, can be manipulated to achieve transition delay, separation postponement, lift increase, skin-friction and pressure drag reduction, turbulence augmentation, heat transfer enhancement, or noise suppression.

By preventing separation, lift is enhanced, stall is delayed, pressure recovery is improved and form drag is reduced. Future possibilities for aeronautical applications of flow separation control include providing structurally efficient alternatives to flaps or slats; cruise application on conventional takeoff and landing aircraft including boundary-layer control on thick span loader wings; as well as cruise application on high-speed civil transports for favourable interference wave-drag reduction, increased leading edge thrust, and enhanced fuselage and upper surface lift. In fact, many of the remaining gains to be made in aerodynamics appear to involve various types of flow control, including separation flow control.

It is well to know that the maximum lift of an airfoil is associated with the separation of the boundary layer on its suction side. Thus the Numerical prediction of the maximum lift must deal with the pressure distribution of an airfoil section with partly separated flow and with the interaction between this pressure distribution and the boundary layer.

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Figure (1.4) Modern airfoil

Figure (1.5) Vortex shedding & trapped vortex

7

Figure (1.6) Sequence of flow separation

Geometric optimization of lifting surfaces during flight has the potential to enhance aircraft performance for a wide range of flight maneuvers. Shorter takeoff and landing distances, slower takeoff and landing speeds, lower fuel consumption , and longer range are just a few examples of performance characteristics that can be enhanced by optimizing the geometry of lifting surfaces during flight. A wide range of methods have been employed using devices such as flaps, slats, spoilers, and drooped leading edges. These

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systems are designed to maximize aerodynamic performance for limited flight maneuvers/conditions relying on traditional aerodynamic concepts that utilize attached flows (4). The airfoil should be able to function at high angles of attack without stalling. If we couple these desired parameters, a multitude of airfoil designs can be developed, each having its own aerodynamic characteristics tailored to a specific flight condition.

1.4 Objective:

The main objective of this research is study of the effect of vertical and angular vortex trapped on separation of boundary layer and lift coefficient and drag coefficient.

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Chapter Two

LITERATURE REVIEW

10

2.1 HISTORY AND DEVELOPMENT:

The earliest serious work on the development of air foil section began in the late 1800’s. H.F.Phillips patented a series of airfoil shapes in 1884 after testing them in one of the earliest wind tunnels. At nearly the same time Otto Lilienthal had similar ideas, after measuring shapes of bird wings in his book “Bird flight as the basis of aviation”. A wide range of airfoils was developed based primarily on trial and error. A successful section such as the Clark.Y in 1922 and Gőttingen 398,387 in 1919 were used as the basis for family of sections tested by NACA in early 1920’s. In 1939, Eastman Jacobs at the NACA in langely designed and tested the first laminar flow airfoil sections, illustrates, that the concept is practical for some applications. All these investigations were made at low value of Reynolds Number; therefore, the airfoils developed may not be the optimum ones for full-scale application (4).

More recently a number of airfoils have been tested in the variable-density wind tunnel at values of the Reynolds Number. These days’ airfoils are usually designed especially for their intended applications.

Advanced flow control techniques are nowadays required in order to improve the performances of modern aircraft. An interesting but not greatly investigated flow control strategy is the so-called “trapped vortex cell” control, from here on referred to as TVC. This technique requires a properly shaped cavity positioned along the span wise direction on the upper surface of the airfoil. Under certain flow conditions, a steady, large vertical structure forms in the cavity creating a recirculating region closed by the dividing streamline. The idea of trapping a vortex is not new as it was first mentioned by Ringleb

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(1961). Following this work, several applications of the trapped vortex concept for flow control have been studied (3).

Adkins (1975) demonstrated experimentally that the pressure recovery in a short diffuser could be strongly enhanced by a stabilized trapped vortex. There are also two known examples of flight testing, namely the Kasper wing, (see Kasper (1974)) and the EKIP aircraft, (see Savitsky et al (1995)) (4).

More recently, several investigations, theoretical, numerical and experimental, have been carried out in the framework of the EU project VortexCell2050. Savelsberg and Castro (2008) studied experimentally the flow inside a large aspect ratio cylindrical cell. In this case, the flow in the cavity, driven by the shear layer forming in the opening, showed a nearly solid body rotation although the mean velocity profile was significantly distorted into an S shape due to three dimensional effects. This span wise modulation of the transversal velocity was also observed in a large eddy simulation performed by Hokpunna and Manhart (2007). Donelli et al (2009) simulated the vortex cell flow as purely two dimensional and presented a comparison between several approaches. The authors concluded that the Prandtl-Batchelor model produces similar results to RANS simulations, which in turn compare favourably to experimental results. Iollo and Zannetti (2001) have shown that a trapped vortex can have a limited stability region. The authors demonstrated that, under certain conditions, the vortex is unstable and cannot be kept trapped if some control in the cavity region is not exerted. For this reason different control strategies have been proposed and tested. De Gregorio and Fraioli (2008) have demonstrated experimentally, by means of PIV measurements on a cavity located on an airfoil that a coherent vortex formed only if suction was applied in the cavity region (4).

Most of the work on cavity flows has focused on simpler geometries, e.g. rectangular cavities. Although this is not a suitable shape for trapping a vortex on a wing, the

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fundamental flow mechanisms observed in such a configuration are still important for a flow control application. Rockwell and Naudascher (1979) provide a comprehensive review of the subject. Maull and East (1963); Rockwell and Knisely (1980); Faure et al (2009); Migeon (2002); Larchevˆeque et al (2007) have investigated the flow complexity in rectangular cavities highlighting a three dimensional organization of the flow. Br`es and Colonius (2008) investigated rectangular cavity flows through direct numerical simulations. The authors evidenced the presence of complex three-dimensional global instabilities with a spanwise wavelength nearly equal to the cavity depth that oscillate at a much lower value than the two-dimensional Rossiter instabilities. Moreover, the three dimensional instabilities were strictly related to the centrifugal instability mechanism.

Cavity flows are also characterized by self-sustained oscillations, occurring in a broad range of incoming flow parameters and cavity geometries, as shown by Rowley et al (2001). Two main types of oscillations have been observed: The shear-layer mode and the wake mode. The shear-layer mode, associated with the spatial instability of the vorticity layer bounding the cavity, is usually described in terms of the acoustic feedback process introduced by Rossiter (1964). It is characterized by a Strouhal number St = f L=Ue, based on the cavity length L and on the free-stream velocity Ue, of the order of unity, according to the Mach number. The wake mode oscillation, observed experimentally by Gharib and Roshko (1987) and in numerical simulations by Rowley et al (2001) and Suponistsky et al (2005), is dominated by a low frequency large scale vortex shedding, similar to the shedding of vortices in the wake of bluff bodies. Such a regime is associated with large amplitude fluctuations and with an increase of the cavity drag. It is characterized by a Strouhal number of the order of 0.07.

Other studies have focused their attention on the effects of d-type roughness on the structure of a flat plate turbulent boundary layer, in order to obtain skin friction drag reduction. d-type roughness, which consists of sparsely spaced two dimensional square

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grooves whose size is much lower than the boundary layer, has been experimentally demonstrated to reduce the turbulent skin friction drag by Choi and Fujisawa (1993). The authors found that the near wall structure of the turbulent boundary layer was modified by a vortex in the cavity, which absorbed and reorganized the incoming near wall turbulence downstream of the cavity.

The TVC flow control technique lacks the support of experimental data regarding its effectiveness in controlling the flow over a wing profile. Olsman and Colonius (2011) recently published a paper on this subject, although the Reynolds number of their experiment was almost two orders of magnitude lower than that of the present experiment and no control was operated in the cavity. Using two dimensional direct numerical simulations and dye flow visualizations, the authors studied the complex flow physics arising from the interaction of the cavity flow with the external flow. The interaction developed into several cavity flow regimes. According to the angle of attack, the authors highlighted the first and the second shear layer mode. These oscillations generated vortices which delayed separation. Moreover, at specific incidences the authors suggested the possibility of a higher lift to drag ratio for the airfoil with the cavity.

The experimental results obtained in the wind tunnel investigation performed on a wing equipped with a trapped vortex cavity are reported. The main objective of the investigation was to assess the effects of the TVC flow control technique on the aerodynamic performance of the airfoil and to compare it with a conventional boundary layer suction system. The experiments also focused on investigating the complex unsteady phenomena taking place in the cavity trapping the vortex. The paper is organized as Follows: The lift and drag characteristics of the controlled configuration are shown and compared with the clean airfoil configuration and with the classical boundary layer suction

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configuration. Some selected static pressure distributions and wake velocity profiles are then shown and discussed. Finally, results of the analysis of the unsteady pressure measurements taken inside and outside the cavity region are discussed, to give some insight into the unsteady flow dynamics taking place.

More recently, several investigations, theoretical, numerical and experimental have been carried out in the framework of the EU project VortexCell2050, which had the objective of advancing the state-of-the-art of the technology of control by trapped vortex cells. Particular emphasis was given to study the characteristics of the vortex flow. In fact, one issue regarding this control technique concerns the inherent instability of the trapped vortex as a two dimensional flow. Theoretical work on trapped vortices, Chernyshenko et al. [2003], Zannetti [2006], Bunyakin et al. [1998], has shown that a trapped vortex is usually unstable.

A three dimensional instability of the flow was also identified in both experimental and numerical investigations. For example Savelsberg and Castro [2008] studied experimentally the flow inside a large aspect ratio cylindrical cell. In this case, the flow in the cavity, driven by the shear layer forming in the opening, showed a nearly solid body rotation, with low turbulence level in the vortex core. These authors noticed a significant distortion into an “S” shape of the mean velocity profile, which the authors attributed to three dimensional effects. In fact, they observed a span wise modulation of the entire cells flow, which they suggested to be due to a natural three-dimensional instability. Further work by the same authors, Tutty et al. [2012], confirmed their hypothesis.

This span wise modulation was also observed in a large eddy simulation performed by Hokpunna and Manhart [2007]. The authors argued that the three-dimensionality of the

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flow is due to an inviscid instability of the vortex core, and also showed the appearance of a marked span wise modulation of the Reynolds stresses along the cavity span. However, no specific indication of the effects of such three dimensional instability on the effectiveness of the TVC control technique was given by the above authors.

Nevertheless, the problem of stability of the trapped vortex flow directly leads to the problem of its control. A first solution is passive control of the flow which can be realised by careful design of the cavity geometry. For example, Chernyshenko et al. [2008] set up an evolutionary algorithm to search in the space of cavity geometries for that which reduces internal secondary separation of the cell’s flow, which is an undesirable feature of this flow. Active control of the cavity flow has been also investigated. De Gregorio and Fraioli [2008] have investigated experimentally, by means of PIV measurements, the effectiveness of a cavity located on an airfoil.

The upstream interior part of the cavity was porous, in order to allow suction of the flow. Unfortunately, their setup did not allow to measure lift and drag of the controlled airfoil, since the airfoil was embedded on the bottom surface of the wind tunnel. Nevertheless, the effectiveness of the control was assessed by considering the size of the region of separated flow downstream of the cavity. The authors observed that, in passive conditions, i.e. no suction, the sole presence of the cavity yielded performances poorer than that of a clean airfoil, with a large separation region starting from the cavity cusp. By gradually increasing the suction, they observed the formation of a coherent vortex in the cavity, accompanied by partial flow reattachment and by a decrease of the separation region downstream of the cell itself.

A further investigation of the TVC technique is the wind tunnel testing of a thick airfoil equipped with a TVC control device, performed by Lasagnaet al. [2011]. This work is briefly discussed here, since it is the most relevant work for this project (5).

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Figure (2.1) Vortex trapped experience

The airfoil chosen was a thick NACA0024 profile. Several configuration were tested and compared: the baseline NACA0024 profile, (B), the same profile but with a classical boundary layer suction system, (BS), and a NACA0024 profile equipped with a TVC, as in figure. The latter configuration featured a porous cavity surface, in order to apply suction in the cavity region, similarly to what performed by De Gregorio and Fraioli [2008], resulting in the configurations TVC, no suction, and TVCS, with suction. Aerodynamic coefficients were measured by integration of the static pressure distribution, for the lift, and by momentum balance, for the drag. Tests were mainly performed at a chord-based Reynolds number of 106. The lift coefficient results of the four configurations tested are reported. The results indicates that the TVC configuration with no suction, i.e. passive control, yields virtually no improvements, since the lift coefficient is essentially the same of the B configuration, if not worse. However, when suction is applied to the trapped vortex 17

cell the lift increases, by a small amount at small-to-medium incidences, and by a larger, but not exceptional, amount at high incidences. In any case, in terms of lift, the performance of the TVCS configuration were never superior to that of the classical boundary layer suction system, BS, neither at low nor at high incidences. The explanation provided by Lasagna et al. [2011] for the larger lift observed at high incidences for the TVCS, and BS, configurations is the delay of flow separation on the upper surface of the airfoil, mainly due to the suction applied in this region, in spite of the way this suction was applied, i.e. at the wall of the clean airfoil, or in the cavity region (2).

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Chapter Three

METHODOLOGY

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3.1 Introduction to CFD:

Computational Fluid Dynamics (CFD) was developed over 40 years ago by engineers and mathematicians to solve heat and mass transfer problems in ,vehicle aerodynamics, chemical engineering , nuclear design and safety, ventilation and industrial design .whilst the fundamental equations of fluid motion that formed the basis of such codes had been well known since the 19th century, their solution for problems with complex geometry and boundary conditions required the development of efficient numerical solution techniques and the ability to implement these on digital computers. The development of this technology in the 1950s and 1960s made such research possible, and CFD was one of the first areas to take advantage of the newly emergent field of scientific computing. In the process, it was soon realized that CFD could be an alternative to physical modeling in many areas of fluid dynamics, with its advantages of lower cost and greater flexibility. Computational fluid dynamics is therefore an area of science made possible by, and intrinsically linked to, computing. Its development has paralleled that of computer power and aeronautics availability, and as we move in to an age of cheap, powerful desktop computing it is now possible, with a little knowledge, to run large and complex 3D simulations on an average personal computer. However, most research advances in CFD continue to originate in the aeronautics and industrial design communities as a result of the significant investment levels available in these areas.

3.1.1 What is Computational Fluid Dynamics? Computational Fluid Dynamics (CFD) is a computer-based for simulating the behavior of systems involving fluid flow, heat transfer, and other related physical processes. It works by solving the specified known conditions on the boundary of the region.

3.1.2 The History of CFD

Computers have been used to solve fluid flow problems for many years. Numerous programs have been written to solve either specific problems, or specific classes of 20

problems. From 1950, 1960 to the mid-1970’s, the complex mathematics required to generalize the algorithms began to be understood, and general purpose CFD solvers were developed. These began to appear in the early 1980’s and required what were then very powerful computers, as well as an in-depth knowledge of fluid dynamics, and large amounts of time to setup simulations. Consequently, CFD was a tool used almost exclusively in research. Recent advances in computing power, together with powerful graphics and interactive 3D manipulation of models have made the process of creating a CFD model and analyzing results much less labor intensive, reducing time and, hence, cost. Advanced solvers contain algorithms which enable robust solutions of the flow field in a reasonable time. As a result of these factors, Computational Fluid Dynamics is now an established industrial design tool, helping to reduce design timescales and improve processes throughout the engineering world. CFD provides accost-effective and accurate alternative to scale model testing, with variations on the simulation being performed quickly, offering obvious advantages.

3.2 How does a CFD code work?

CFD codes are structured around the numerical algorithms that can be tackle fluid flow problem in order to provide easy access to their solving power all commercial CFD packages include sophisticated user interface to input problem parameters and to examine the results. Hence all codes contain three main demands :

1. A pre – processor. 2. A solver. 3. A post – processor.

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3.2.1 Pre – processor Pre – processing consist of the input of a flow problem to a CFD programs by means of an operator – friendly interface and the subsequent transformation of this input into a form suitable for use by the solver, the user activities at pre – processing involve:

- Definition of geometry of the region of interest: the computational domain. - Grid generation the sub-division of the domain into a number of smaller, non – over lapping sub – domains: a grid or (mesh) of cells (or control volumes or elements). - Section of the physical and chemical phenomena that need to be modeled. - Definition of fluid properties. - Specification of appropriate boundary condition at cells which coincide with or touch the domain boundary.

The solution to a flow problem (velocity, pressure, temperature…etc) is defined at nodes inside each cell. The accuracy of a CFD solution is governed by the number of cells in grid. In general the larger number of cells the better solution accuracy.

Optimal meshes are often non-uniform: finer in areas where large variation occur from point to point and coarser in regions with relatively little change.

Figure (3.1) geometry drawing steps and boundaries description

22

Figure (3.2) geometry drawing steps and boundaries description for trapped vortex.

Figure (3.3) geometry drawing steps and boundaries description for trapped vortex.

23

3.2.2 Solver There are three distinct streams of numerical solution techniques:

- Finite difference. - Finite element. - Finite volume.

Numerical methods that form the basis of the solver perform the following steps:

- Approximation of the unknown flow variables by means of a simple functions - Discretization by substitution of the approximations into the governing flow equation and subsequent mathematical manipulations.

Solution of the algebraic equation.

Figure (3.4) Basic airfoil solver

24

Figure (3.5) Setup Steps “General”

Figure (3.6) Models

25

Figure (3.7) Check Solver

Figure (3.8) Choose Material 26

Figure (3.9) Boundary Conditions

Figure (3.10) Reference values

27

Figure (3.11) Solution Methods

Figure (3.12) Solution Controls & Under-Relaxation Factors 28

Figure (3.13) Monitors & Set of Error

Figure (3.14) Solution Initialization & Initial Guess 29

Figure (3.15) Run Calculation & Output Results

3.2.3 Post – processor

As in pre – processing a huge amount of development has recently taken place in the post – processing filed. Owing to the increased popularity of engineering workstations, many of which have outstanding graphics capabilities, the leading CFD package are now equipped with versatile data visualization tools these include :

- Domain geometry and grid display. - Vector plots. - 2D and 3D surface plots. - Particle tracking - View manipulation (translation, rotation, scaling….etc). - Color postscript output. 30

Figure (3.16) Final Results

3.3 Governing Equations:

A flow is completely determined if the velocity vector 푣⃗ and the thermodynamic properties, the pressure p, the density ρ, and the temperature T are known everywhere in the flow field. These six quantities, the three velocity components, and the three thermodynamic variables have to be provided for the description of the flow. This can be done by solving the conservation equations for mass, momentum, and energy and the thermal equation of state, which connects the thermodynamic variables with each other. If the latter change markedly, the dynamic shear viscosity, the thermal conductivity k, and the specific heat c also have to be prescribed as a function of pressure and temperature. Liquids can be considered as incompressible and their density ρ can be assumed to be constant. This assumption also holds for gases flowing at low speeds. The conservation laws are presented in the form of partial differential equations; their solution requires the prescription of initial and boundary conditions. A flow is completely determined if the velocity vector 푣⃗ and the thermodynamic properties, the pressure p, the density ρ, and the temperature T are known everywhere in the flow field. These six quantities, the three velocity components, and the three thermodynamic variables have to be provided for the 31

description of the flow. This can be done by solving the conservation equations for mass, momentum, and energy and the thermal equation of state, which connects the thermodynamic variables with each other. If the latter change markedly, the dynamic shear viscosity, the thermal conductivity k, and the specific heat c also have to be prescribed as a function of pressure and temperature. Liquids can be considered as incompressible and their density ρ can be assumed to be constant. This assumption also holds for gases flowing at low speeds. The conservation laws are presented in the form of partial differential equations; their solution requires the prescription of initial and boundary conditions.

3.3.1 Conservation of mass (Continuity Equation) The mass of a flowing medium remains constant in a time-dependent volume, bounded by the closed surface 휕𝜌 + 훻. (𝜌푉⃗⃗) = 0 … … … … … … … … … … … … … … … … … … … … . . … . (3 − 1) 휕푡

Or

휕𝜌 휕(𝜌푢) 휕(𝜌푣) + + = 0 … … … … … … … … … … … … … … (3 − 2) 휕푡 휕푥 휕푦

The change of mass per unit time in the control volume is expressed by partial derivative 휕휌 ; the mass flow through its surface is given by the expression 훻. (𝜌푉⃗⃗). 휕푡

32

3.3.2 Conversion of momentum (Navier Stokes Equations

Cauchy’s equation:

휕 (𝜌푣⃗) + 훻 ∗ (𝜌푉⃗⃗ 푉⃗⃗) = 𝜌푔⃗ + 훻⃗⃗. 𝜎 … … … … … . . . . (3 − 3) 휕푡 푖푗

Where:

𝜎푖푗 is the stress tensor which can be separated into the pressure stress and viscous stresses.

σxx σxy σxz −p 0 0 τxx τxy τxz σ σ σ τ τ τ σij=[ yx yy yz] = [ 0 −p 0 ] + [ yx yy yz] … … . (3 − 4) σzx σzy σzz 0 0 −p τzx τzy τzz

Since for reasons of symmetry, and after the stress-strain relations substituted in the momentum equations, the Navier-Stokes equations are obtained

X-component of the compressible Navier – Stokes Equation:

퐷푢 휕푝 휕 휕푢 휕 휕푢 휕푣 휕 휕푢 휕푤 𝜌 = − + [2휇 + 휆̃(훻. 푣⃗)] + [휇 + ] + [휇 + ] … … . (3 − 5) 퐷푡 휕푥 휕푥 휕푥 휕푦 휕푦 휕푥 휕푧 휕푧 휕푥

Y-component of the compressible Navier – Stokes Equation:

퐷푣 휕푝 휕 휕푣 휕 휕푣 휕푤 𝜌 = − + [2휇 + 휆̃(훻. 푣⃗)] + [휇 + ] + 𝜌푔 … (3 − 6) 퐷푡 휕푦 휕푦 휕푧 휕푧 휕푧 휕푦 푦

Z-component of the compressible Navier – Stokes Equation:

33

퐷푤 휕푝 휕 휕푤 휕 휕푢 휕푤 휕 휕푣 휕푤 𝜌 = − + [2휇 + 휆̃(훻. 푣⃗)] + [휇 + ] + [휇 + ] + 𝜌푔 … (3 퐷푡 휕푧 휕푦 휕푧 휕푥 휕푧 휕푥 휕푦 휕푧 휕푦 푧 − 7)

Incompressible Navier – Stokes Equation:

퐷푣⃗ 𝜌 = −훻푝 + 𝜌푔⃗ + 휇훻2푣⃗ … … … (3 − 8) 퐷푡

3.4 Turbulence Models

Turbulence modeling is a key issue in most CFD simulations. All practical engineering flows are turbulent and hence need to be modeled.

3.4.1 RANS-based turbulence models The smart Reynolds decomposition has left us with the so called closure problem which means that the number of unknowns is greater than the number of equations; the additional unknowns are the Reynolds stresses which have to be modeled. For incompressible turbulent flow, all variables are divided into a mean part (time averaged) and fluctuating part. For the velocity vector this means that 푢̃푖 is divided into a mean part 푈푖and a fluctuating part 푢푖so that 푢̃푖 + 푈푖 + 푢푖 . Time averaging yields: 휕푈 푖 = 0 … … … … … … … … … … … … . . … (3 − 9) 휕푥푖 2 휕푈푖 휕푝 휕 푈푖 휕휏푖푗 푈푗 = − + 휈 2 − … … . . . … (3 − 10) 휕푥푗 휕푥푖 휕푥푗 휕푥푗 Where the turbulent stress tensor (also called Reynolds stress tensor) is given by:

휏푖푗 = 푢̅̅푖̅푢̅̅푗 … … … … … … … … … … … … . . . . (3 − 11)

34

3.4.2 Two equation turbulence models Two equations turbulence models include two additional transport equations (turbulent kinetic energy k-equation and turbulent dissipation -equation) to represent the turbulent properties of the flow. This allows the turbulence model to account for convection and diffusion of turbulent energy(5).

3.4.3 The k equation The turbulent kinetic energy is the sum of all normal Reynolds stresses:

1 푘 = (푢̅̅̅̅2̅ + ̅푢̅̅̅2̅ + ̅푢̅̅̅2̅) … … … … … … … … … … … … … … … … … … . . (3 − 12) 2 1 2 3

K-equation is derived directly by setting the indices i = j in the equation that govern the Reynolds stresses, i.e.

2 휕푘 휕푘 휕푢푖 휕푢푖 휕푢푖 휕 푝 1 휕 푘 + 푈푗 = −푢̅̅푖̅푢̅̅푗 − 푣 − {푢푗( + 푢푖푢푖)} + 푣 … . . (3 − 13) 휕푡 ⏟ 휕 푥푖 ⏟ 휕푥 푗 ⏟ 휕 푥 푗 휕 푥 푗 ⏟휕푥 푗 𝜌 2 ⏟ 휕푥 푗 휕 푥푗 퐶 푃 휀 퐷 퐷 표푓 퐾

Where (C) denotes convection, (P) denotes turbulent production, (휀) denotes turbulent dissipation, and (D) denotes diffusion. The above equations can be symbolically written as follows:

퐶 = 푃 + 휀 + 퐷 … … … … … … … … … … … … … … … … … . (3 − 14)

3.4.4 The ℇ equation:

Two quantities are usually used in eddy-viscosity model to express the turbulent viscosity. In the (K – ℇ) model, (K) and (ℇ) are used. The turbulent viscosity is then computed from

푘2 푣 = 퐶 … … … … … … … … … … … … … … … … … . . (3 − 15) 푡 휇 휀

35

Where 퐶휇 = 0.09 An exact equation for the transport equation for the dissipation 휀 =

휕푢´ 휕푢´ 푣 푖 푖 can be derived, but it is very complicated and at the end many terms are found to 휕푥푗 휕푥푗 be negligible. It is much easier to look at the (k) equation, and to setup a similar equation for (ℇ). The transport equation should include a convective term, (C), a diffusion term, (D), a production term, (P), and a dissipation term, (ℇ), i.e.

퐶 = 푃 + 퐷 − 휀 … … … … … … … … … … … … … … . . (3 − 16)

The production and dissipation terms in the equation are used to formulate the corresponding terms in the (ℇ) equation. The terms in the (k) equation have the dimension

휕푘 2 휕ℇ 2 ≡ [푚 ⁄ ] whereas the terms in the ℇ equation have the dimension ≡ [푚 ⁄ ]. 휕푡 푠3 휕푡 푠4 1 Hence, we must multiply (P) and (ℇ) by a quantity which has a dimension ⁄푠 .One quantity with this dimension is the mean velocity gradient which might be relevant to the production 푘 1 term, but not for the dissipation. A better choice should be ⁄ℇ ≡ ⁄푠. Hence, we get

ℇ 푃 − ℇ = (퐶 푃 − 퐶 ℇ) … … … … … … … … … . . … . . (3 − 17) 푘 ℇ 1 ℇ 1

The final form of the ℇ transport equation reads:

휕ℇ 휕ℇ ℇ 휕 휕ℇ + 푈푗 = (퐶ℇ 1푃 − 퐶ℇ 1ℇ) + (휈 ) … … … (3 − 18) 휕푡 휕푥푗 푘 휕푥푗 휕푥푗

36

Chapter Four

RESULTS

37

4.1 Computational Domain

There are three cases has been tested numerically for modified and conventional NACA 23012,the trapped were located at upper surface with, vertical trapped and angular trapped Conventional and modified airfoils were then tested numerically at various angles of attack (0o , 5°, 10°, 15°and 20°). Then it checked at turbulent flow (Re =18.2e5) and velocity of 27.4 m/s, and at laminar flow (Re= 4.2e5) and velocity of 7.04 m/s. The simulations were carried out using commercial software packages. All the Pre-processing comprising mesh generation, quality control and setting up of the boundary conditions was done using Ansys. “Ansys14.5” was used for generating meshes for all the airfoil configurations. The meshes were then generated into “FLUENT” a finite volume method based CFD tool which solves the governing equations of conservation of mass and momentum was the flow solver used for the entire numerical analysis. Post processing including generation of plots and figures was performed using FLUENT.

Figure (4.1) Computational Domain 38

4.2 Mesh Dependence Study:

Firstly domain was districted to four blocks at basic airfoil case and to five blocks at vertical and angular vortex trapped as in figure (4-2). Then Edge sizing was used to distribute each edge to 50 part while taking in account that near airfoil distribution is very imperceptible.

Figure (4.2) Blocks

Figure (4.3) Edge Sizing 39

Then we generate mesh for each case “basic airfoil, vertical vortex trapped and angular vortex trapped” as below:

Figure (4.4) Domain mesh

Figure (4.5) Mesh generation for basic airfoil

40

Figure (4.6) Domain mesh for angular vortex trapped

Figure (4.7) Mesh Generation for angular vortex trapped

41

Figure (4.8) Mesh Generation for vertical vortex trapped

4.3 Final Results:

Here is the final results of pressure cofficient , pressure static and velocity streamlines of both turbulent and laminar flow.

4.3.1 Pressure distributions for turbulent flow :

Generally there are set of parameters of the base and modified airfoil have been compared to show that the modification influence over base NACA 23012 and how these modification can improve the aerodynamics characteristics in order to get delay in stall. Pressure distribution around airfoil is an important factor that can be highlighted by comparing between base and modified airfoil. Comparison has been taken for specific angle of attack (15°) for base, angular vortex trapped, vertical vortex trapped airfoil

42

Figure (4.9) pressure coefficient of base airfoil at 15o angle of attack

43

Figure (4.10) pressure coefficient of angular vortex trapped at 15o angle of attack

44

Figure (4.11) Pressure coefficient of vertical vortex trapped at 15o angle of attack

45

The aerodynamic performance of airfoil sections can be studied most easily by reference to the distribution of pressure over the airfoil. Cp is the difference between local static pressure and free stream static pressure, non-dimensionalized by the free stream dynamic pressure. Cp is plotted "upper and lower" with negative values (suction), higher on the plot. (This is done so that the upper surface of a conventional lifting airfoil corresponds to the upper curve.) The Cp starts from about 1.0 at the stagnation point near the leading edge It rises rapidly (pressure decreases) on both the upper and lower surfaces and finally recovers to a small positive value of Cp near the trailing edge.

From figures above we can see clearly that at turbulent flow case that the final results of pressure cofficient and saparation of boundary layer for basic airfoil , vertical vortex trapped and angular vortex trapped are the same so the vortex trapped has no effect on turbulent flow.

4.3.2 Pressure distributions for laminar flow : As in turbulent flow the base , angular vortex trapped and vertical vortex trapped had been tested this time at laminar flow. The results have taken at angle of attack 15o for each airfoil as below:

Figure 1 4.12 pressure coefficient of base airfoil at 15o angle of attack 46

Figure (4.13) pressure coefficient of angular vortex trapped at 15o angle of attack

Figure (4.14) pressure coefficient of vertical vortex trapped at 15o angle of attack 47

From above results we can see that vortex trapped “ vertical or angular “ has an effect on saparation of boundary layer by delay it.

4.3.3 Velocity Streamlines:

A streamline is a path traced out by a mass less particle as it moves with the flow. It is easiest to visualize a streamline if we move along with the body (as opposed to moving with the flow).

4.3.3.1 Velocity Streamlines of turbulent flow: As we’ll see on next figures at turbulent flow vortex dosen’t appear

Figure (4.15) Velocity Streamlines of base airfoil at 15o angle of attack

48

Figure (4.16) Velocity Streamlines of vertical vortex trapped at 15o angle of attack

Figure (4.17) Velocity Streamlines of angular vortex trapped at 15o angle of attack 49

4.3.3.2 Velocity Streamlines of laminar flow: When the flow is laminar we can easier see the vortex that because the boundary layer separate very smoothly and slowly as below:

Figure (4.18) Velocity Streamlines of base airfoil at 15o angle of attack

Figure (4.19) Velocity Streamlines of vertical vortex trapped at 15o angle of attack 50

Figure (4.20) Velocity Streamlines of angular vortex trapped at 15o angle of attack

4.3.3.3 Static Pressure: As we’ll see below there is drop on static pressure for turbulent and laminar flow at each base and modified airfoil.

51

4.3.3.3.1 Static Pressure for turbulent flow:

Figure (4.21) Static pressure of base airfoil at 15o angle of attack

Figure (4.22) Static pressure of vertical vortex trapped at 15o angle of attack

52

Figure (4.23) Static pressure of angular vortex trapped at 15o angle of attack

From above figures, there is no big drop at static pressure that why there is no effect of vortex trapped at turbulent flow.

4.3.3.3.2 Static Pressure for laminar flow:

Figure (4.24) Static pressure of base airfoil at 15o angle of attack 53

Figure (4.25) Static pressure of vertical vortex trapped at 15o angle of attack

Figure (4.26) Static pressure of angular vortex trapped at 15o angle of attack 54

From previous results we can see clearly that at laminar flow the static pressure has small drop at vertical vortex trapped and very big drop at angular vortex trapped.

4.4 Lift and Drag Coefficients:

4.4.1 Aerodynamic Coefficients tables:

4.4.1.1 Coefficients at turbulent flow: Table (4.1) lift & drag coefficients of base airfoil.

23012 base airfoil α Cd Cl L/D×10

5 0.0175 0.62 3.5 10 0.0318 1.04 3.26 15 0.058 1.3 2.18644 20 0.286 1.05 0.3663

Table (4.2) lift & drag coefficients of angular vortex trapped.

angle Cd Cl Cl/Cd*10 0 0.006 0.02 0.333333 5 0.037 0.58 1.567568 10 0.09 1.028 1.142222 15 0.096 1.25 1.302083 20 0.3 1.039 0.346333

55

Table (4.3) lift & drag coefficients of vertical vortex trapped

angle Cd Cl Cl/Cd*10 0 0.004 0.018 0.45 5 0.051 0.46 0.901961 10 0.08 1.01 1.2625 15 0.098 1.2 1.22449 20 0.325 1.093 0.336308

4.4.1.2 Coefficients at laminar flow: Table (4.4) lift & drag coefficients of base airfoil.

angle Cd Cl Cl/Cd*10 0 0.0212 0.3318 1.565094 5 0.03 0.46 1.533333 10 0.052 0.68 1.307692 15 0.092 0.89 0.967391 20 0.23 0.7 0.304348

Table (4.5) lift & drag coefficients of angular vortex trapped.

angle Cd Cl Cl/Cd*10 0 0.0613 0.882 1.438825 5 0.081 1.1 1.358025 10 0.0853 1.25 1.465416 15 0.2 1.3 0.65 20 0.4 1.5 0.375

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Table (4.6) lift & drag coefficients of vertical vortex trapped.

angle Cd Cl Cl/Cd*10 0 0.043 0.521 1.211628 5 0.061 0.73 1.196721 10 0.075 0.86 1.146667 15 0.12 1.05 0.875 20 0.31 0.98 0.316129

4.4.2 Aerodynamic Coefficients Charts:

4.4.2.1 Coefficients at turbulent flow:

0.35

0.3

0.25

0.2 base vertical trapped 0.15 angular trapped 0.1

0.05

0 0 5 10 15 20 25

Figure (4.27): drag coefficient of base & modified airfoil

57

1.4

1.2

1

0.8 base vertical 0.6 angular 0.4

0.2

0 0 5 10 15 20 25

Figure (4.28): lift coefficient of base & modified airfoil.

1.8

1.6

1.4

1.2

1 base 0.8 angular 0.6 vertical 0.4

0.2

0 0 5 10 15 20 25

Figure (4.29) lift to drag coefficient of base & modified airfoil.

58

4.4.2.2 Coefficients at laminar flow:

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 0 5 10 15 20 25

Figure (4.30) drag coefficient of base & modified airfoil.

1.6

1.4

1.2

1 base 0.8 vertical 0.6 angular

0.4

0.2

0 0 5 10 15 20 25

Figure (4.31) lift coefficient of base & modified airfoil

59

1.8

1.6

1.4

1.2

1 base

0.8 vertical angular 0.6

0.4

0.2

0 0 5 10 15 20 25

Figure (4.32) lift to drag coefficient of base & modified airfoil.

From above result, the angular vortex trapped airfoil gives best lift coefficient but high drag coefficient as well. So more researches should be done to minimize drag coefficient.

60

Chapter Five

CONCLUSION AND RECOMMENDATIONS

61

5.1 Conclusion:

1- NACA 23012 airfoil had been compared with modified (vortex trapped) types in order to enhance the aerodynamic characteristics of conventional NACA 23012 airfoil and to examine the advantages and disadvantages of the new design concept.

2- This study has been performed on a relatively new family of airfoils which are yet to be researched extensively.

3- Hence the major advantage can be gained from this thesis is the increscent in lift over conventional NACA 23012 airfoil except when angular vortex trapped is located, while Drag-coefficient data indicate that with the introduction of a step; drag increased. This observation is consistent in all the modified airfoil cases studied. High drag generation is an issue to perform more study to reduce it.

4- When the flow is turbulent the results of base airfoil and modified airfoil are almost the same so we don’t need to make a vortex trapped because it makes the structure body very weak.

5- At laminar flow the lift and drag chart show very big variation which is a good sign that vertical and angular vortex trapped has an effect on flow

6- From above discussion the best modification configuration can be specified through these numerical tests is angular vortex trapped airfoil

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5.2 RECOMMENDATIONS:

1- Drag generated with flow over vortex trapped airfoils is very high, so more studies is needed to reduce drag amount.

2- Airfoil with vortex trapped’s thickness is became very week to overcome the aerodynamics forces acting on it, so structural analysis studies is needed to ensure that the stepped airfoil going to stand against aerodynamics forces.

3- Experimental study should be carried out with the same geometry and same condition of computational work to know more about vortex trapped airfoil characteristics.

4- Other types of vortex trapped configuration should be checked using CFD software’s to meet other hidden proprieties of the new concept of design. (i.e. as well as the vortex trapped location is changed, the optimum vortex trapped can be achieved because there are more than step can be located in one side).

63

REFERENCES:

(1) Kline, Richard, "The Ultimate Paper Airplane", Simon and Schuster, New York, NY, 1985. (2) Huang.A, Folk.C, Ho.C.M., Liu.Z, Chu.W.W., Y. Xu, Tai.Y.C., "Gryphon M3 System: Integration of MEMS for Flight Control", MEMS Components and Applications for Industry, Automobiles, Aerospace, and Communication, Conference Proceedings of SPIE Vol. 4559, 2001. (3) H. K. VERSTEEG and W. MALALASEKERA, “An introduction to computational fluid dynamics” The finite volume method. (4) Massy and Ward-Smith, Mechanics of fluids 1998.

(5) Ahmed Alrayah’s research for step airfoil December 2013.

(6) Versteeg, Malalasekera" An-introduction-to-computational-fluid-dynamics” first edition 1995.

64

APPENDICES

65

Figure A-1: Static pressure of base airfoil at 0o angle of attack.

Figure A-2: velocity streamlines of base airfoil at 0o angle of attack

66

Figure A-3: velocity of base airfoil at 0o angle of attack.

Figure A-4: velocity streamlines of base airfoil at 5o angle of attack.

67

Figure A-5: velocity of base airfoil at 5o angle of attack.

Figure A-6: Static pressure of base airfoil at 5o angle of attack

68

Figure A-8: velocity streamlines of base airfoil at 10o angle of attack.

Figure A-9: Static pressure of base airfoil at 10o angle of attack 69

Figure A-10: velocity of base airfoil at 10o angle of attack.

Figure A-11: Static pressure of base airfoil at 20o angle of attack

70

Figure A-12: velocity streamlines of base airfoil at 20o angle of attack.

Figure A-13: velocity of base airfoil at 20o angle of attack.

71

72