Numerical Computations on Flow Past Omar Airfoil

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NUMERICAL COMPUTATIONSON AN OMAR 4-ELEMENT

CONFIGURATION

by

Sabharish M

2nd year,B.Tech Chemical Engineering

National Institute ofTechnology,Trichy

Indian Institute of Science-Bangalore,India

July, 2008


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ABSTRACT

Omar 4 element CFD computations

The flow over a multi-element airfoil is computed usingSpalart Allmaras Turbulence model and SGS implicit scheme.The obtained results are checked with the results obtained atthe wind tunnel tests conducted in the Boeing research windtunnel in Seattle. The deviations found from the experimentalresults are found to be attributable to the separation that

occurs at high angles of attack and improper grid generationtechnique and to the deficiencies in the wake profilecomputations. The computation of the slat flow fieldrepresents a key roadblock to successful prediction of multi-element flows.


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TABLE OF CONTENTS

List of Figures..........................................................................iiList of Tables...........................................................................vAcknowledgements................................................................viChapter I: Introduction............................................................1

1.1Challenges facing CFD...................................................21.2Multi-Element................................................................21.3High-Lift Physics ......................................................3

1.3.1Advantages of multi-element .3Chapter II: Omar Airfoil...........................................................6Chapter III: Grid gnration.....................................................9Chapter IV :Code HIFUN15Chapter V :Code Validation .17Chapter VI :Results..34Chapter VII :Conclusion...65

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LIST OF FIGURES

Number. ......P

age

1. 1.The three approaches of fluid dynamics......2

2. Challenges faced by CFD...3

3. Basic Airfoil...................................................................3

4. .Model C, Omar 4- element airfoil.........8

5. The 4 elements of the airfoil..........................................8

6. .NLR airfoil profile.............10

7. Stagnation region..........................................................21

8. The jump factor from the boundary layer to the

triangular cells ............................................................13

9. RAE airfoil meshed. Mach number=0.729,

=2.79,Re=6.5106............................................18

10.Stagnation region of RAE airfoil; Mach number=0.729,

=2.79, Re=6.5106..19

11.Trailing edge of RAE; Mach number=0.729,

=2.79,Re=6.5106................................................20

12.Mach contour of RAE; Mach number=0.729,

=2.79,Re=6.5106 ...............................................21

13.RAE Streamlines; Mach number=0.729,

=2.79,Re=6.5106.........................................22

14.RAE pressure contour; Mach number=0.729,

=2.79,Re=6.5106...............................................23

15.Comparison of Cp distribution on RAE airfoil obtained

frome experiment and CFD..........24

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29. Mesh structure near the transition region of slat-

trailing..................................................,39

30. Mesh structure near the 90 bend, of the main

element.................................................40

31. Mesh structure near the transition region of the

main...................................................41

32. Mesh structure at the transition region of the flap1

trailing.............................................42

33. Mesh structure at the trailing edge of the last

flap..................................................4334. The mach contours at an angle of attack of -10

...................................................................44

35. The mach contours at an angle of attack of 0

....................................................................45

36. The mach contours at an angle of attack of

14........................................................... 46

37. The mach contours at an angle of attack of 15

...................................................................47

38. The pressure contours at an angle of attack of -10

...................................................................48

39. The pressure contours at an angle of attack of 0

......................................................................49


..............................................................50


...............................................................51

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42. The streamline plot of the flow past the airfoil at an

angle of attack of -10

..52


angle of attack of 0

..53


angle of attack of 14

..54

45. The streamline plot of the flow past the airfoil at anangle of attack of 15

..55

46. Cp distribution at -10 angle of attack; Mach number:

0.201............................................56

47. Cp distribution at 0 angle of attack; Mach number:

0.201............................................56


0.201............................................57


0.201.............................................57

50. SFC distribution at -10 angle of attack; Mach

number: 0.201............................................58

51. SFC distribution at 0 angle of attack; Mach

number: 0.201............................................58


number: 0.201...........................................59

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number: 0.201.............................................59

54. y + distribution at -10 angle of attack; Mach

number: 0.201............................................60

55. y + distribution at 0 angle of attack; Mach

number: 0.201............................................60


number: 0.201.............................................61


number: 0.201.............................................6158. Density Residue vs Number of iterations distribution

at -10 angle of attack; Mach number:

0.201..............62

59. Density Residue vs Number of iterations distribution

at 14 angle of attack; Mach number:

0.201..............62

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L i s t o f T a b l e s

2. Comparison of results obtained from NLR 20 Chords and

NLR 150 chords...33

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ACKNOWLEDGMENTS

The author thanks Associate Professor Dr.Balakrishnan.N for

his assistance and invaluable inputs in the course of this

undertaking. In addition, special thanks to Mr.Ravindra whose

familiarity with the needs and ideas in the grid generation of

Omar 4- element configuration was valuable. The author also

acknowledge Mr.Kiran, Mr.Arjun, Mr.Ganesh, Mr. Anand,

Mr.Karthik, Mr. Partha Mondal and others in the CAD Lab for

their help and invaluable discussions .

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C h a p t e r 1

INTRODUCTION

OverviewComputational fluid dynamics,

called as CFD in short constitutes a new third approach inthe philosophical study of the whole of fluid dynamics. In the

seventeenth century, the foundations for experimental fluiddynamics were laid in France and England. The eighteenthand the nineteenth centuries saw the gradual development ofthe theoretical physics involved in fluid flow. However, withthe advent of high-speed computers and the availability ofaccurate numerical algorithms for solving these physicalproblems on computers has just revolutionized the way wework on fluid dynamics.

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Fig.1.The three approaches of fluid dynamics [1].

Multi-element

The prediction of high-Lift (multi-element airfoil) flow fieldscurrently represents a difficult challenge for thecomputational fluid dynamics (CFD) and turbulencemodelling community. Even in two dimensions state of the

art CFD codes fail to predict the trends with Reynoldsnumber, angles of attack. Without the capability of toconsistently predict trends using CFD, aircraft designersmust depend on heuristic techniques and wind tunnelexperiments, which themselves present additional difficultieswhen attempting to scale the results up to the flightReynolds numbers. The flow around a multi-element airfoil isextremely complex. Variations in angle of attack anddifferent flap / slat settings often present very different anddistinct challenges. For example, for typical landingconfigurations, viscous effects can dominate compressibility

effects near stall, whereas for take-off configurationscompressibility can dominate the flow physics. Also flapseparation is often seen at low or moderate angles of attack,whereas stall is often caused by an unloading of the aftportion of the main element due to rapidly spreading andmerging shear layers and wakes over the flap.

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Due to the fact that predicting the onset and progression ofseparated flow with angle of attack, including the effects ofReynolds number (Re), still remains an elusive goal in theCFD. Multi-element airfoils and wings are generally associatedwith separated flow; along with a host of other flow physicsthat can be difficult to model accurately (see Fig. 1). Also, theexperimental uncertainties also tend to increase for highangle of attack near stall. As a result, it is currently notpossible to prdict the Cl,max accurately at high angle ofattack near the stall angle.

Fig 2.Physics of high lift systems.

1.3. Physics of High-Lift Systems:

Some of the physics pertinent to the high-lift flows are asshown in fig.2. Separated flow exists between the coveregions of slat and the main element of the airfoil which mightbe unsteady. There is a possible transition along the shearlayers starting from the cusps. A fresh boundary layer is

initiated by each element of the airfoil with its own transitionregion. As can be seen the flow over the top of the airfoil canhave some curvature, and shock/boundary layer interactionsare possible. Boundary layer separation is also possible.

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Although high-lift devices work essentially because theymanipulate the inviscid flow, viscous effects are crucial aswell. Some of the viscous features that can affect 2D multi-element systems include: 1) boundary layer transition, (2)shock/boundary layer interactions, (3) viscous wakeinteractions, (4) confluent wakes and boundary layers, and (5)separated flows.Some other flow aspects of high-lift flow physics are, highervelocities are needed over the upper surface of the wing if wehave to get more lift but higher velocities mean greaterdecelerations in the rear and a greater possibility ofseparation.

1.3.1. Advantages of multi-element:There are five primary effects of properly designed gaps inthe multi-element airfoil which give them an advantage overthe single-element, they are

1) Slat effect: The velocity circulation on the upstreamelements reduces the pressure peaks on thedownstream elements and the boundary layers are ableto better negotiate the resulting lowered adversepressure gradient.

2) Circulation effect: The downstream elements cause aflow inclination that induces greater circulation andhence greater lift.

3) Dumping effect: The trailing edge of an upstreamelement is in a region of higher velocity thanfreestream, and hence there is a higher dischargevelocity of the boundary layer into the wake. This highvelocity reduces the pressure rise impressed on theboundary layer and hence reduces the possibility ofseparation.

4) Off-pressure recovery: The wakes of upstream

elements, formed from boundary layers dumped athigher-than-freestream velocity, decelerate out ofcontact with the wall which is more efficient thandeceleration with the contact of the wall.

5) Fresh boundary layer effect: Each new element has itsown fresh boundary layer, and thin boundary layers can

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withstand adverse pressure gradients than the thickones.

The mechanisms responsible for limiting the maximum liftattainable on multi-element wing configuration are not wellunderstood. For a typical three-element airfoil the mainelement carries the maximum load followed by the flap andthe slat. The lift on the main and the slat increases withincreased incidence, whereas the lift on the flap generallydecreases with increasing incidence because, the pressuresuction peak becomes more moderate.

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C h a p t e r 2

Omar airfoil:The Two-Dimensional Wind

Tunnel Tests of the NASA supercritical airfoil with varioushigh-lift systems was given by NASA to The Boeing Companyin May, 1971. Data was taken at a Reynolds number of 2.83million for various configurations, ranging from one elementto five elements. They were named as model A for oneelement, model B for two element, model C for four element,model E for five element. Boundary layer control was done bymeans of tangential blowing on the sidewall turntables usedto maintain as 2-D a flow as possible. The double-slotted flapwith slat configuration (4 elements) is discussed here.Boundary layer separation was present at some conditions.

Fig.3. Basic airfoil

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Fig.4. Model C, Omar 4 element.

Fig.5. The 4 elements of the airfoil.

Testing facilities:Wind tunnel: The tests were conducted at the Boeingresearch wind tunnel (BWRT) which is located in Seattle, USA.

The BWRT is a single-return closed-circuit wind tunneldesigned and built as a two-Dimensional high-lift test facility.The test section of BWRT is 0.9144m wide and 2.4384 highand has a length of 6.0961m. the contraction ratio of thetunnel bell mouth is 12.1 to1.

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C h a p t e r 3

Grid Generation

In the present case the grids were generated by using thecommercially available grid generation software called

Gambit. The co-ordinates of the airfoil are imported and arejoined by using a spline (NURBS) and the airfoils profile likethe one shown in fig.6. is obtained. The co-ordinates must bejoined in such a way that the angularity of the airfoil ismaintained. Usually the edges are chosen such that the arclength of the edges at the nose of the airfoil is about tenpercent of the total chord length, which is the distancebetween the leading edge and the trailing edge of the airfoil.The generated profile is smooth as shown in fig for a two-element airfoil.

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Fig.6.The NLR airfoil profile

The airfoil is scaled by about a lakh times. This is done so thatthe edges of the airfoil are in proper shape. A face of theairfoil is made. Circles with a radius of a 2 chord length, 20chord length and 150 chords are drawn. The chord length ofthe airfoil is defined as the distance between its leading edge

and its trailing edge. The circle is subtracted from the faces ofthe slat, main, vane and flap of the airfoil as our work requiresonly exterior fluid flow. The mesh edges (Points) for all theedges are formed in such a way that the number of points inthe critical regions like the stagnation region of the airfoil ismaximum as shown in fig.7.

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Fig.7. Stagnation Region

The mesh edges ideally must be such that the jump factorfrom one edge to the other is small as shown in fig.8.On anaverage the slat, vane and flap can contain around 200-250points and the main element around 350 -400 points andmore points must be pumped into regions where bends arepresent and at the nose of the airfoil. The 150 chords circle isthe far-field which is far away from the airfoil that the effectdue to the airfoils presence is negligible. The far-field waschosen as 150 choed instead of the 20 chord as it was feltthat the effect due to the airfoil was beyond the 20 chord

circle and more accurate results were obtained . Theboundary layers are created. The height of the boundary layercan be guessed by the following formulae.

Height of the boundary layer = (5/Re)

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The boundary layer padding around the airfoil must besmooth and uniform. The boundary layers at the trailingedges must be adjusted and the jump must be small as shownin fig.

Fig. The boundary layer.

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Fig.8.The jump factor from the boundary layer to the

triangular cells.

The mesh edges are drawn for the circles with the 2 chordcircle, the 20 chord circle, the 150 chord circle. The sizefunction is a tool which is used so that the jump factor fromthe boundary layer is gradual as shown in fig.20. Mesh thefaces. The growth of the cells must be gradual as shown infig.. The size functions are given and adjusted to the variousedges till proper cells are obtained. Similarly the sizefunctions are defined for the 2 and 20 chord circles and theface meshing was done for these faces.

The quality of the grid is checked and the equi-angle skewmust be less than or equal to 0.8 and the aspect ratio must beless than 3000. The boundary conditions are provided. Themesh is exported from the grid generating software.

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C h a p t e r 4

Code HIFUN

HIFUN which stands for High resolution Flow Solver forUnstructured Meshes is a in-house code of ComputationalAero Dynamics Lab (CAD), Indian Institute Of Science (iisc),Bangalore, India. It is a code based on cell centered finitevolume technique. It gives fast, accurate and robust solutionsfor flows ranging from subsonic to hypersonic. Flux at theinterface is computed using schemes like Roe, Vanleer, HLLC,AUSM and AUSM-plus. Second order accuracy is obtained byreconstructing using diamond path reconstruction techniqueor least squares or green gauss procedure. To havemonotonocity at the face interface, the reconstructedgradients are limited by Venkatakrishnan limiter. To attain thesteady state quickly, convergence acceleration procedureslike SGS implicit procedure is used. Turbulent flows aremodeled by using Baldwin Lomax 0 equation mode and 1equation mode of Spalart Allmaras. The HIFUN can take cellsof various shapes like polyhedrons, pyramid, tetrahedral etc in3 dimensional and quadrilaterals and triangles in 2dimensional grids and these shapes can be usedinterchangeably.

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C h a p t e r 5

Code Validation:

Two standard test cases were done before starting the mainproject of omar-4-Element. The first test case is that of thetransonic flow past a RAE airfoil.

RAE:

RAE is a single-element airfoil. The flow that is taken for thiscase is trans-sonic in nature. It is one of the most computedsingle-element airfoil.

The test conditions are given below

Mach Number = 0.729 Angle of attack = 2.79 Reynolds Number = 6.5106

The various plots obtained are as given below

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Fig.9.RAE airfoil meshed. Mach number=0.729,

=2.79,Re=6.5106

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Fig.11 Trailing edge of RAE; Mach number=0.729,

=2.79,Re=6.5106

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Fig.12.Mach contour of RAE; Mach number=0.729,

=2.79,Re=6.5106

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Fig.13.RAE Streamlines; Mach number=0.729,

=2.79,Re=6.5106

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Fig.14.RAE pressure contour; Mach number=0.729,

=2.79,Re=6.5106

The comparison of the results obtained from theexperiments and that obtained from CFD is as shown

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Fig.15. Comparison of Cp distribution on RAE airfoilobtained from experiment and CFD.

Fig.16. Comparison of sfc Distribution on RAE airfoilobtained from experiment and CFD.

NLR:

One of the most computed multi-element configurations hasbeen the NLR-7301, a two-element flapped configuration

tested in the NLR 3_2m low-speed wind tunnel in the 1970s.This configuration was designed with moderate flap angle(20.1) so that no flow separation would occur on the flap. It isrepresentative of a typical take-off flap setting. The flow thatis taken for this test case is subsonic in nature.

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The test conditions are given below

Mach Number = 0.185 Angle of attack = 13.1 Reynolds Number = 2.51106

The various plots obtained are as given below

Fig.17.NLR 20 chords; Mach number=0.185, =13.1,Re=2.5110Machnumber=0.185,=13.1,Re=2.51106

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Fig.18.NLR 20 chords, critical region; Mach number=0.185,=13.1,Re=2.51106

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Fig.19. NLR Trailing Edge; Mach number=0.185,

=13.1,Re=2.51106

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Fig.20. NLR 20 chords, mach contours; Mach number=0.185,

=13.1,Re=2.51106

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Fig.21.NLR 20 chords, pressure contours, Mach

number=0.185, =13.1,Re=2.51106

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Fig.23.NLR 150 chords, Mesh; Mach number=0.729,

=2.79,Re=6.5106

The comparison of the results obtained fromthe experiments and that obtained from CFD is as shown

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Fig.24. Comparison of Cp distribution on airfoil obtained fromexperiment and CFD.

Fig.25. Comparison of SFC Distribution on airfoil obtained fromexperiment and CFD

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Parameter NLR 20chords NLR 150chords

Lift Co-efficient Cl 3.295

3.299

Drag Co-efficient Cd

0.071

0.06078

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C h a p t e r 6

Results:

The flow over a multi- element airfoil is computed by usingthe Spalart Allmaras turbulence model under the conditionsgiven below and the following results has been obtained. Theresults are compared with that of the experimental valuesobtained from the Boeing wind tunnel at Seattle. The results

which have been obtained are fairly decent. The stalling anglehas been obtained correctly but the values are over predicted.

The test conditions areMach number : 0.201Reynolds number : 2.83 106

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Fig.26. Generated mesh. The total number of cells:

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Fig.27. Omar 4 element airfoil.

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Fig.28. Mesh structure near the nose of the slat.

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Fig.29. Mesh structure near the transition region of

slat-trailing edge and nose of the main element.

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Fig.30. Mesh structure near the 90 bend, of the main element.

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Fig.31 Mesh structure near the transition region of

the main elements trailing edge and nose of the flap1.

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Fig.32. Mesh structure at the transition region of theflap1 trailing region and the flap2 nose.

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Fig.33. Mesh structure at the trailing edge of the last

flap.

The mach contours of the airfoil at angles of attack of-10, 0, 14, 15 are as follows

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Fig.34. The mach contours at an angle of attack of

-10 .

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Fig.35. The mach contours at an angle of attack of 0 .

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14 .

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15 .

The pressure contours of the airfoil at angles of attack of -10, 0, 14, 15 areshown in figure.

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Fig.38. The pressure contours at an angle of attack

of -10 .

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of 0 .

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of 14 .

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Fig.41.The pressure contours at an angle of attack of

15.

The streamlines of the flow past the airfoil at angles of attackof -10, 0, 14, 15 are as follows

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Fig.42. The streamline plot of the flow past the airfoil

at an angle of attack of -10 .

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Fig.43. The Streamlines plot of the airfoil at angle of attack of0.

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Fig.44. The streamline plot of the flow past the airfoil

at an angle of attack of 14 .

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Fig.45. The streamline plot of the flow past the airfoilat an angle of attack of 15 .

The pressure distributions at angles of attack -10,0 14,15 areshown in fig.46,47,48,49

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Fig.46. Cp distribution at -10 angle of attack; Machnumber: 0.201

Fig.47. Cp distribution at 0 angle of attack; MachNumber : 0.201 and Reynolds number:

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Fig.48. Cp distribution at 14 angle of attack; MachNumber: 0.201 and Reynolds number:

Fig.49. Cp distribution at 15 angle of attack; MachNumber: 0.201 and Reynolds number:

The Distribution of Skin friction Coefficient atvarious angles of attack is as shown

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Fig.50. SFC distribution at -10 angle of attack; Machnumber: 0.201 and Reynolds number:

Fig.51. SFC distribution at 0 angle of attack; Machnumber: 0.201 and Reynolds number:

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The distribution of y + at various angles of angles ofattack is as shown

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Fig.54. y + distribution at -10 angle of attack; Machnumber: 0.201 and Reynolds number:

Fig.55. y + distribution at 0 angle of attack; Machnumber: 0.201 and Reynolds number:

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The plot between Density residue, Nutlida Residue vs numberof iterations at angles of attack of -10 and 14 are as shown

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Fig.58. Density Residue vs Number of iterationsdistribution at -10 angle of attack; Mach number: 0.201 andReynolds number:

Fig.59. Density Residue vs Number of iterationsdistribution at 14 angle of attack; Mach number: 0.201 andReynolds number:

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Lift and Drag

One of the primary benefits of usin computational methods indeveloping high-lift multi-element airfoils is to get some ideaof the effects of changing gap/overhang between the variouselements and to determine the effects of Reynolds number onairfoil performance. Determining gap/overhang effects cansignificantly reduce configuration optimization time in thewind tunnel by narrowing the element position matrix, thussaving time and money. Determining Reynolds numbereffects is necessary for prediction of the airfoil performance atflight Reynolds numbers. When calculating lift and dragchanges it is very important to predict the sign and

magnitude of the change improves or degrades airfoilperformance which drives the optimization process. Themagnitude is important because it determines the amount ofperformance improvement or degradation associated with agiven change. When calculating lift and drag changes it isimportant to predict the sign and magnitude correctly. Thesign is critical as it determines whether a change improves ordegrades the airfoil performance which drives theoptimization process. The magnitude is important as itdetermines the amount of improvement or degradationassociated with a change.

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Fig. The variation of experimental and CFD results ofLift coefficient at different angles of attack.

Fig. the variation of experimental and CFD results ofDrag coefficients at different angles of attack.

It can be noted that the stalling angle has been predicted inaccordance with the experimental results. But the liftcoefficients has been somewhat over predicted especially athigh angles of attack one can find a significant deviation with

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C h a p t e r 7

Conclusion

The flow over a multi-element configuration has beencomputed by using Spalart Allmaras turbulence model andSGS implicit scheme. The Cp distributions and the variation ofLift coefficient and Drag coefficient at different angles ofattack has been presented here. Deviations in Lift coefficientswith that of experimental results have been found at highangles of attack while deviations in drag coefficients havebeen found at negative angles of attack. The Lift coefficienthas been over-predicted at high angles of attack, while theDrag coefficient has been under predicted at negative angleof attack. Based on the computed results and theexperimental results the following conclusions are made,

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The over prediction of the Lift coefficient can beattributed to the separation occurs near the stallingangle of the airfoil.

The cells generated doest capture the wake properly,and various techniques like adaptation etc must beemployed to increase the cell count in critical regions.

The usage of local time stepping caused unsteadinessfor flows at high angles of attack and the unsteadinessis also felt after exceeding certain CFL numbers. So forhigh angles of attack the global time stepping must beused.

The flow field over the slat is not well understood and isdifficult to predict.

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R e f e r e n c e s

1. Anderson J.D. Computational Fluid dynamics, the basics

with applications

2. Omar E, Zierten T,Hahn M, Szpiro E, Mahal A.Two-Dimensional Wind tunnel tests of a NASAsupercritical airfoil with various high lift systems, volume II-test data NASA CR-2215, April 1977.

3. Prediction of high lift: review of present CFD capability.Christopher L. Rumsey, Susan X. Ying.

Numerical Computations on Flow Past Omar Airfoil

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Transcript of Numerical Computations on Flow Past Omar Airfoil