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MASTER'S THESIS

Validation of Aerodynamic Non-conformance Definitions

Andreas berg

Master of Science in Engineering TechnologySpace Engineering

Lule University of TechnologyDepartment of Engineering Sciences and Mathematics

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Abstract

Non-conformances are effects related to the difference between the nominal design of an aircraftengine component and the finished manufactured product. At the aerothermodynamicsdepartment at Volvo Aero, a number of definitions are used to classify the non-conformancesand their impact on the engine performance.

The main objective of this thesis has been to validate the defined definitions limits for local non-conformances (bumps) positioned on the outlet guide vanes of a turbine rear frame, using CFD,and derive a correlation for calculation the drag coefficient of the bumps. The project wasdivided into two parts; a flat plate analysis and a real geometry analysis.

The definition of a local non-conformance is based on the height of the bumps in relation to the boundary layer thickness at that location. The flow over a flat plate has been studied with andwithout bumps at a wide range of Reynolds numbers to see how different bump sizes affects the

shape and size of the boundary layer. The added drag to the plate due to the presence of the bumps has been calculated and compared to the bump-free cases to see if a correlation was possible to derive.

From the flat plate simulations it was found that the lower limit of 10 % and the upper limit of 99% of the defined borders are valid. The lower limit can however be rectified due to an increase of just 11 % of the boundary layer thickness for bumps with a height of 40 %. A correlation wasderived that calculates the drag coefficient of the bumps with an error of 5 % between thecorrelation calculation and the CFD results.

The real geometries that were analyzed were representative of the regular vanes and mount vanesof a turbine rear frame. The boundary layer thickness has been calculated for both nominal vanesand for vanes with non-conformances (bumps) to determine the effect of the bumps on the boundary layer and ifits possible to compar e the results with the flat plate.

The boundary layer thickness on the suction peak was found to be 3.1 mm on the regular vaneand 3.3 mm on the mount vane. However, the method used for calculating the boundary layerthickness was found to be unstable when the flow over the vane separates. The only cases thatare separation free are the 1 mm bumps, which are located at a height of 32 % of the nominal boundary layer thickness on the regular vane and 30 % on the mount vane. The increase in boundary layer thickness differs from the flat plate results and a detailed analysis on how thethickness is calculated needs to be performed. The correlation was tested on the 1 mm bumpsand the drag coefficient calculated to be 0.285 on the regular vane and 0.275 on the mount vane.This can be compared to a drag coefficient of 0.25 calculated at the department using a similargeometry and another method. However, the correlation needs to be compared with other realgeometry bump sizes to be considered fully validated.

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ContentsPreface.............................................................................................................................................. i

List of figures .................................................................................................................................. ii

List of tables ................................................................................................................................... iv

Nomenclature .................................................................................................................................. v

1 Introduction ............................................................................................................................. 1

1.1 Background ...................................................................................................................... 1

1.1.1 Non-conformance definitions ................................................................................... 2

1.2 Purpose of the project ....................................................................................................... 3

1.3 Limitations ....................................................................................................................... 3

1.4 Problem description.......................................................................................................... 4

2 Theory ...................................................................................................................................... 5 2.1 Computational fluid dynamics ......................................................................................... 5

2.1.1 Turbulence modeling ................................................................................................ 6

2.2 Boundary layers................................................................................................................ 9

3 Method ................................................................................................................................... 12

3.1 Simulation approach ....................................................................................................... 12

3.1.1 Software and simulations settings ........................................................................... 13

3.2 Flat plate ......................................................................................................................... 14 3.2.1 Reference case ........................................................................................................ 14

3.2.2 Bumps ..................................................................................................................... 16

3.2.3 Finding a correlation for Cd .................................................................................... 19

3.3 Real geometry ................................................................................................................ 20

3.3.1 Testing the correlation ............................................................................................ 21

3.4 Boundary layers.............................................................................................................. 22

3.4.1 Flat plate.................................................................................................................. 22

3.4.2 Real geometry ......................................................................................................... 23

4 Results and discussion ........................................................................................................... 24

4.1 Flat plate ......................................................................................................................... 24

4.1.1 Reference case ........................................................................................................ 24

4.1.2 Bumps ..................................................................................................................... 29

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4.1.3 Drag coefficient ...................................................................................................... 35

4.2 Real geometry ................................................................................................................ 40

4.2.1 Nominal................................................................................................................... 40

4.2.2 Bumps ..................................................................................................................... 42

5 Conclusions ........................................................................................................................... 50

5.1 Validation of the defined borders ................................................................................... 50

5.1.1 Flat plate.................................................................................................................. 50

5.1.2 Real geometry ......................................................................................................... 50

5.2 The correlation ............................................................................................................... 52

6 References ............................................................................................................................. 53

7 List of appendices .................................................................................................................. 54

7.1 Reference case ................................................................................................................ 55 7.2 Flat plate with bump ....................................................................................................... 59

7.3 Correlation data .............................................................................................................. 64

7.4 Real geometry ................................................................................................................ 66

7.5 CFX-Scripts .................................................................................................................... 72

7.6 MATLAB code .............................................................................................................. 82

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PrefaceThis thesis is the final project of the Master of Science degree in Space Engineering withspecialization in Aerospace Engineering at the Department of Engineering Sciences and

Mathematics, Division of Fluid and Experimental Mechanics at Lule University of Technology,Sweden. My examiner at the university was PhD Lars-Gran Westerberg and the work has beencarried out at the Department of Aerothermodynamics at Volvo Aero Corporation in Trollhttan,Sweden under the supervision of Cline Souillet and Mats Henstrm.

I would like to express my sincere gratitude to my main supervisor Cline for all the help andguidance you have provided me with and for the large interest you have shown in the project. Iwould also like to thank Hans Mrtensson for your expertise in the subject and Lars Ljungkronafor you extensive knowledge about codes and numerics. To the other thesis students and internsthat lived in Trollhttan during these months, Markus, Franois, Mikael, Visakha and Stijn I send

a big thank you for all the good times outside of office hours and for making my stay here very pleasant. Finally I want to thank Linea for always being there for me and my family for all yoursupport.

Andreas berg

Trollhttan, July 2011

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List of figures Figure 1: Some of the components of a jet engine and also Volvo Aeros commercial component specializations. ..... 1 Figure 2: The two layers in the near-wall region. .......... ........... .......... ........... .......... ........... .......... ........... .......... .......... . 9 Figure 3: Boundary layer along a flat plate. .......... .......... ........... .......... ........... .......... .......... ........... .......... ........... ....... 10

Figure 4: Reference case geometry: flat plate. .......... ........... .......... .......... ........... .......... ........... .......... ........... .......... .... 14 Figure 5: Initial 2D-mesh for the reference case. ......... .......... ........... .......... .......... ........... .......... ........... .......... ........... 15 Figure 6: Standard bump (h/L = 0.318). .......... ........... .......... ........... .......... ........... .......... ........... .......... .......... ........... .. 16 Figure 7: Flat plate with bump. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... .......... ........... ..... 17 Figure 8: Wide bump (h/L = 0.159). ...... .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... .. 17 Figure 9: Aggressive bump (h/L = 0.637). .................. .......... ........... .......... ........... .......... ........... .......... .......... ........... .. 17 Figure 10: Flat plate with a bump. .......... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 18 Figure 11: Close-up on a bump. ........... ........... .......... ........... .......... ........... .......... .......... ........... .......... ........... .......... .... 18 Figure 12: Nominal regular vane. .......... .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... .. 20 Figure 13: Nominal mount vane. .......... ........... .......... ........... .......... ........... .......... .......... ........... .......... ........... .......... .... 20 Figure 14: Regular vane with 5 mm bump on SS. ......... .......... ........... .......... .......... ........... .......... ........... .......... ........... 21 Figure 15: Mount vane with 5 mm bump on PS. ....... ........... .......... .......... ........... .......... ........... .......... ........... .......... .... 21 Figure 16: Boundary layer thickness for the reference case. ........... .......... ........... .......... ........... .......... .......... ........... .. 25 Figure 17: Boundary layer thickness at the four Reynolds numbers a) 10 5 b) 7.5*10 5 c) 2*10 6 d) 10 7 . ..................... 26 Figure 18: Skin-friction drag coefficient for the flat plate. ............ ........... .......... .......... ........... .......... ........... .......... .... 26 Figure 19: Skin-friction drag coefficient for a smooth plane surface depending on Reynolds number. ........ ........... .. 27 Figure 20: Displacement and momentum thickness for three reference cases. .......... .......... ........... .......... ........... ....... 28 Figure 21: Boundary layer thickness for the 10 % case compared to the reference case. .......... ........... .......... ........... 30 Figure 22: Velocity contours for a 10 % bump at Re = 10 6 . ....................................................................................... 30 Figure 23: BLT with bumps at height a) 40 % b) 60 % c) 99 % d) 150 %. ........... .......... ........... .......... ........... .......... .. 31 Figure 24: Velocity contours for standard bumps at a) 40 %, b) 60 %, c) 99 % and d) 150 % of the BLT at Re = 10 6 .

..................................................................................................................................................................................... 32 Figure 25: Aggressive bump at 40 % showing a) BLT for three Re compared with the reference case and the

standard bump b) Velocity contours for Re = 106

. ...................................................................................................... 34 Figure 26: Wide bump at 40 % showing a) BLT for three Re compared with the reference case and the standardbump b) Velocity contours for Re = 10 6 . ..................................................................................................................... 34

Figure 27: Relation between the drag coefficient and the scale factor based on simulation results. .......... ........... ..... 35 Figure 28: Drag coefficient depending on Re for aggressive, wide and standard bumps with height 40 %. .......... .... 36 Figure 29: a as a function of Re. ............... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 37 Figure 30: b as a function of Re. ............... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 38 Figure 31: Relation between the drag coefficient and the scale factor based on the derived correlation. ...... ........... 38 Figure 32: Comparison between correlation and simulation results for three Reynolds numbers. ................. ........... 39 Figure 33: BLT for nominal regular vane, SS. ................... .......... ........... .......... ........... .......... ........... .......... .......... ...... 40 Figure 34: BLT for nominal regular vane, PS. .......... ........... .......... .......... ........... .......... ........... .......... ........... .......... .... 40 Figure 35: BLT for nominal mount vane, SS. ................. ........... .......... ........... .......... ........... .......... ........... .......... ......... 41 Figure 36: BLT for nominal mount vane, PS. .......... ........... .......... ........... .......... ........... .......... ........... .......... .......... ...... 41 Figure 37: Local Mach number around the mid-span of the regular vane. ........... ........... .......... ........... .......... ........... 41 Figure 38: Static pressure contours on the a) regular vane b) mount vane. ................... ........... .......... ........... .......... .. 42 Figure 39: Regular vane, SS, 5 mm. .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 43 Figure 40: Regular vane, SS, 4 mm. .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 43 Figure 41: Regular vane, SS, 3 mm. .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 43 Figure 42: Regular vane, SS, 2 mm. .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 43 Figure 43: Regular vane, SS, 1 mm. .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... ......... 44

http://c/Users/Andreas/Documents/Skolan/Exjobb/volvo/Report_v6.docx%23_Toc300490559http://c/Users/Andreas/Documents/Skolan/Exjobb/volvo/Report_v6.docx%23_Toc300490559http://c/Users/Andreas/Documents/Skolan/Exjobb/volvo/Report_v6.docx%23_Toc300490559

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Figure 44: Regular vane, SS, 5 mm, separation. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 44 Figure 45: Regular vane, SS, 4 mm, separation. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 44 Figure 46: Regular vane, SS, 3 mm, separation. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 44 Figure 47: Regular vane, SS, 2 mm, separation. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 44 Figure 48: Regular vane, SS, 1 mm, separation. ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 44 Figure 49. Mount vane, SS, 3 mm. .......... .......... ........... .......... ........... .......... ........... .......... ........... .......... ........... .......... .. 46 Figure 50: Mount vane, SS, 2 mm. ....... ........... .......... ........... .......... ........... .......... .......... ........... .......... ........... .......... .... 46 Figure 51: Mount vane, SS, 1 mm. ....... ........... .......... ........... .......... ........... .......... .......... ........... .......... ........... .......... .... 46 Figure 52: Mount vane, SS, 3 mm, separation. ...... .......... ........... .......... .......... ........... .......... ........... .......... ........... ....... 46 Figure 53: Mount vane, SS, 2 mm, separation. ...... .......... ........... .......... .......... ........... .......... ........... .......... ........... ....... 46 Figure 54: Mount vane, SS, 1 mm, separation. ...... .......... ........... .......... .......... ........... .......... ........... .......... ........... ....... 47 Figure 55: Mount vane, PS, 5 mm. .......... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 48 Figure 56: Mount vane, PS, 4 mm. .......... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 48 Figure 57: Mount vane, PS, 3 mm. .......... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 48 Figure 58: Mount vane, PS, 2 mm. .......... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 48 Figure 59 Mount vane, PS, 1 mm. ........... ........... ........... .......... ........... .......... .......... ........... .......... ........... .......... ........... 48 Figure 60: Mount vane, SS, 5 mm, separation. ...... .......... ........... .......... .......... ........... .......... ........... .......... ........... ....... 48

Figure 61: BLT for the reference case at Re = a) 2.5*105

, b) 5*105

, c) 106

, d) 4*106

, e) 6*106

and f) 8*106

. ........... 55 Figure 62: DBT for Re a) 10 5 , b) 2.5*10 5 , c) 5*10 5 , d) 10 6 , e) 4*10 6 , f) 6*10 6 and g) 8*10 6 . .................................... 57 Figure 63: MBTfor Re a) 10 5 , b) 2.5*10 5 , c) 5*10 5 , d) 10 6 , e) 4*10 6 , f) 6*10 6 and g) 8*10 6 . ..................................... 58 Figure 64: BLT for the four lowest Reynolds numbers with bump height a) 40 % b) 60 % c) 99 % d) 150 %. .......... 59 Figure 65: Displacement boundary thickness for standard bumps with Re > 10 6 with height 40, 60, 99 and 150 %. 60 Figure 66: Displacement boundary thickness for standard bumps with height 10 %. ............. .......... .......... ........... .... 60 Figure 67: Displacement boundary thickness for aggressive bumps with height 40 %. (Reference included). .......... 61 Figure 68: Displacement boundary thickness for wide bumps with height 40 % (Reference included). .......... ........... 61 Figure 69: Momentum boundary thickness for standard bumps with Re > 10 6 with height 40, 60, 99 and 150 %. ... 62 Figure 70: Momentum boundary thickness for bump height 10 %. .......... ........... .......... ........... .......... ........... .......... .... 62 Figure 71: Momentum boundary thickness for aggressive bumps with height 40 %. (Reference included). .............. 63 Figure 72: Displacement boundary thickness for aggressive bumps with height 40 %. (Reference included). .......... 63 Figure 73: Displacement thickness, Regular vane, SS, bump height 1-5 mm (Nominal included). .......... .......... ......... 66 Figure 74: Displacement thickness, Mount vane, SS, bump height 1-3 mm (Nominal included). .......... .......... ........... 67 Figure 75: Displacement thickness, Mount vane, PS, bump height 1-5 mm (Nominal included). .......... .......... ........... 68 Figure 76: Momentum thickness, Regular vane, SS, bump height 1-5 mm (Nominal included). .......... ........... .......... .. 69 Figure 77: Momentum thickness, Mount vane, SS, bump height 1-3 mm (Nominal included). .......... ........... .......... .... 70 Figure 78: Momentum thickness, Mount vane, PS, bump height 1-5 mm (Nominal included). .......... ........... .......... .... 71

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List of tablesTable 1: Non-conformance definitions for local defects. ........... .......... ........... .......... ........... .......... ........... .......... ........... 3 Table 2: Inlet velocities for different Reynolds numbers. .......... .......... ........... .......... ........... .......... ........... .......... ......... 15 Table 3: Pressure loss and drag coefficients for the grids. .......... ........... .......... ........... .......... ........... .......... ........... ..... 16 Table 4: Pressure loss and drag coefficient for the four grids. .......... .......... ........... .......... .......... ........... .......... ........... 18

Table 5: Flat plate simulation summary. ..................................................................................................................... 24 Table 6: BLT for all Reynolds numbers. ...................................................................................................................... 29 Table 7: The five bump heights (in mm) that were to be created for each Reynolds number. ................... ........... ....... 29 Table 8: Percentile increase in boundary layer thickness due to the bumps. ......... ........... .......... ........... .......... ........... 33 Table 9: Percentile increase in boundary layer thickness for the aggressive and wide bumps. ......... ........... .......... .... 34 Table 10: Percentile difference in C d for aggressive and wide bumps compared to the standard bump, for the sim.data. ............................................................................................................................................................................. 36 Table 11: The a and b coefficients for each Reynolds number. .......... .......... ........... .......... .......... ........... .......... ........... 37 Table 12: Percentile difference between the correlation and the simulation results. .......... .......... ........... .......... ......... 39 Table 13: Boundary layer thickness at the suction peak for the two nominal vanes. ............. ........... .......... .......... ...... 42 Table 14: Summary of all bump analyzed and their location. .......... .......... ........... .......... ........... .......... .......... ........... .. 42 Table 15: Reynolds number for the chord and at the suction peak at 90 % span for both regular and mount vane. .. 49 Table 16: Drag coefficient for the real geometry bumps based on the correlation. Scale factor is included forcomparison. ................................................................................................................................................................. 49 Table 17: Bump height (in mm) at x = 19 m for each Re L depending on the intended position in the reference BL. . 64 Table 18: Drag coefficients calculated from the simulation data. ........... .......... ........... .......... ........... .......... .......... ...... 64 Table 19: Drag coefficients calculated from the correlation.......... ........... .......... .......... ........... .......... .......... ........... .... 65 Table 20: Drag coefficient for 40 % bumps with different shape. ........... .......... ........... .......... ........... .......... .......... ...... 65

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NomenclatureAbbreviationsBL Boundary layerBLT Boundary layer thicknessCFD Computational fluid dynamics

DBT Displacement boundary thicknessDNS Direct numerical simulationLE Leading edgeLES Large eddy simulationMBT Momentum boundary thicknessOGV Outlet guide vanePS Pressure sideRANS Reynolds-averaged Navier-Stokes equationsSP Suction peakSS Suction sideSST Shear stress transportTE Trailing edge

TEC, TRF Turbine exhaust case, Turbine rear frameLatin letters

Ab [m2] Frontal area, bump A p [m2] Area, plateC d [-] Drag coefficientC f [-] Friction coefficientC p [-] Pressure coefficientc p [-] Specific heat constant, pressurecv [-] Specific heat constant, volumeh [m] Bump heighti [J ] Energyk [m2/s2] Turbulent kinetic energyk t [W/mK] Thermal conductivityL [m2] LengthM [-] Mach numbern [-] Normal direction

P dyn , P d [Pa] Dynamic pressure P stat , P s [Pa] Static pressure P tot , P 0 [Pa] Total pressureRe [-] Reynolds numberV, u , u, v, w [m/s] Velocity

y+ [-] Dimensionless distance from thewall to the first node in thecomputational grid

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Greek letters [m] Displacement boundary thickness [m] Boundary layer thickness ij [-] Kronecker delta

[m2/s3] Turbulent dissipation[-] c p/cv[kg/ms] Dynamics viscosity

t [kg/ms] Turbulent dynamic viscosity[m] Momentum boundary thickness

[kg/m3] Density[Pa] Wall shear force[1/s] Turbulent specific dissipation

Subscriptsin Inletout Outletwall, w Point on the wall Freestreamtan Tangential

per Perpendicular x, y, z Coordinate direction

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1 IntroductionThis chapter presents the reader with an introduction to the thesis, including background,information about non-conformances and the problem description.

1.1 BackgroundVolvo Aero (VAC) develops and manufactures components for commercial and military aircraftengines in co-operation with some of the worlds leading engine manufacturers . These includeGeneral Electric, Pratt & Whitney and Rolls-Royce among others. Because of this, VACscomponents can be found in 90 % of the worlds large commercial aircrafts. The motto, Make ItLight is the core in VACs goal to reduce aircraft emissions by 50 % until 2020, and thecompany focuses heavily on developing lightweight solutions for aircraft engine structures androtors. Within the areas of specialization for commercial components(Figure 1) Volvo hasestablished a number of Centers of Excellence (CoE) and Advanced Technology Areas, whichhave enabled them to focus on developing optimal advanced technology solutions and being able

to provide strong competence in all engineering disciplines.

Figure 1: Some of the components of a jet engine and also Volvo Aeros commercial component specialization s.

This project has been conducted in one of these CoEs, namely the aero-thermodynamicsdepartment, which is the competence centre for method and technology development withinaerodynamics at VAC. This function is part of all the stages of the product development processand provides R&D and specialist competence in a large number of disciplines such as aeroacoustics, aeromechanics, fluid dynamics, CFD/Numerics, combustion, heat-transfer, radiation, performance and experimental verification.

OGV

Fan/compressor structures

Shafts

Vanes

Turbine rear frames

Fan Case

Compressor rotors Combustor structure

LPT-Case

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bumps effect on it. The flat plate is commonly used in boundary layer analysis and it wasassumed that the results would correlate well with those of a vane so that just a few simulationswould have to be done for the real geometries.

1.4 Problem description The project can be divided into two parts, one for the flat plate study and one for the realgeometries. These are presented below.

The first part consists of a flat plate study where the flat plate is simulated at a wide range ofReynolds numbers and the boundary layer thickness is calculated at a certain position along the plate. Bumps are then created with heights based on a percentile part of the undisturbed boundary layer thickness. The bumps effects on the boundary layer in the region behind the bumps are then analyzed. From these simulation results it is possible to determine the addedforce to the plate in the flow direction due to the presence of the bumps so that a correlation forthe drag coefficient can be derived.

The second part consists of boundary layer calculations on a real representative geometry to thevanes in a turbine rear frame. Initially, nominal regular vanes and nominal mount vanes areanalyzed before moving on to the analysis of bumps placed on the suction peak on the suctionside and the region below the suction peak on the pressure side. The idea is to get results that willcorrelate reasonable well with the flat plate results. The correlation derived in the first part isthen to be tested on some of the bumps to see if it is able to predict the drag coefficient for bumps on a vane.

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2 TheoryIn this chapter the reader is given a brief introduction to computational fluid dynamics,turbulence modeling and boundary layer theory. It is however assumed that the reader has someknowledge in the subject.

2.1 Computational fluid dynamicsComputational fluid dynamics (CFD) is a computer-based simulation tool for the analysis ofsystems involving fluid flow, heat transfer and other related processes. These simulation toolsmake use of numerical algorithms to solve the physical process of interest. There are threedistinctive types of numerical solution techniques that can be used, namely, finite difference,finite element and spectral methods. The CFD code chosen in this project, CFX, uses a specialfinite difference formulation called the finite volume method. How this works is that the usercreates a computational grid on the domain consisting of cells (control volumes). The outline ofthe method is then that in each control volume the governing equations of fluid flow are

integrated, discretized into a system of algebraic equations and solved with an iterative method.The iterative method is required because of the complex and non-linear nature of the governingequations (equations (2.1) (2.5)) which can be written in the following form, from Versteeg &Malalasekera (2007).

Continuity: (2.1)

X-momentum: (2.2)Y-momentum:

(2.3)

Z-momentum: (2.4) Energy: (2.5)Where S M and S i are momentum and energy source terms, and the dissipation function(equation (2.6)). Equations (2.2) (2.4) are usually referred to as the Navier-Stokes equations.

(2.6)The governing equations come from applying the three fundamental physical laws ofconservation of mass, momentum and energy to a control volume. For further information aboutthese laws, the derivation of the equations and the numerical approach used by CFX, the readeris referred to standard text books in fluid dynamics and CFD such as Cengel & Cimbala (2006),Versteeg & Malalasekera (2007) and the CFX User-guide (2009).

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2.1.1 Turbulence modelingThe turbulent nature of flows makes them much more difficult to calculate than if they arelaminar. This is because of the random and chaotic behavior of turbulence that gives rise torotational flow structures, so-called eddies, with a wide range of length and time scales. Therecurrently exists three ways to calculate turbulence in CFD, direct numerical simulation (DNS),large eddy simulation (LES) and Reynolds-averaged Navier-Stokes equations (RANS).

The DNS method can use the incompressible form of the turbulent continuity and Navier-Stokesequations to form a set of four equations with four unknowns. These can then be used to find astarting point for the simulations, which then develops a transient solution to resolve all thescales of the motion. This method requires extremely fine computational grids (around 103 grid points in each coordinate direction) and very small time steps, which makes it too computationalheavy to be used in industrial applications and hence it is more commonly used in fundamentalresearch in turbulence.

The LES method uses a filtering method on the Navier-Stokes equations to separate the largerand smaller eddies. The larger eddies are then resolved using unsteady flow simulations whilethe smaller scale eddies are modeled with a so called sub-grid model. This method is much lessdemanding on computational resources than DNS but it still requires a lot more computer powerthan the third method.

The third method, RANS, is the most common way of dealing with turbulence. This methoddoesnt resolve any eddies in the flow but models turbulence by utilizing turbulence models.This makes the method the most practical to use in engineering applications whereits oftenunnecessary to resolve the details of the turbulent fluctuations, and mean and time-averaged

properties of the flow are considered satisfactory enough. The averaging is done by applyingReynolds decomposition on the governing equations so that the flow variables are split up into asteady mean component and a time-varying fluctuating component .

(2.7)

Utilizing this decomposition on the continuity and Navier-Stokes equations (equation (2.1) (2.4)) and using tensor notation yields the set of equations depicted below (the energy equationhas been left out since the case simulated in this project is incompressible).

Continuity: (2.8)

Navier-Stokes: (2.9)

Where ij is the molecular stress tensor andS M the sum of the body forces. The time-averaging process introduces extra terms on the right hand side of the Navier-Stokes equations.

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These terms are usually referred to as the Reynolds stresses and they introduce a new set ofunknowns to the equations. To model these stresses it is possible to use the eddy viscosityhypothesis (ANSYS Inc, Turbulence and Wall Function Theory, 2009) that propose that theReynolds stresses can be related to the mean velocity gradients and the eddy viscosity, analogousto the relationship between the stress and strain tensors in laminar flow.

(2.10)

Where is the Kronecker delta, the eddy viscosity and the turbulence kinetic energy. Anumber of turbulence models have been developed over the years to solve these equations butthe two most commonly used in CFX are thek- and SST k- models, which were the onesunder consideration when choosing turbulence model in this project.

The two models are so called two-equation models, which means that they introduce two new

transport equations that represents the turbulent properties of the flow. Both models use anequation for the turbulent kinetic energyk but depending on the model they use either a transportequation for turbulent dissipation or turbulent specific dissipation . The transport equationsused by the modelsarent shown here but they can be viewed in a turbulence modeling textbookor in ANSYS Inc. - Turbulence and Wall Function Theory (2009). In the subsequent chapterssome general information about the models and their advantages/disadvantages are presented.

2.1.1.1 The k- mo d elThe model is one of the most widely used in the industry and its proven to show excellent

performance for a large number of industrial flows. Its the simples t model for which only initialand boundary conditions need to be supplied and its also one of the least demanding oncomputational resources. It does however show poor performance in a variety of important casessuch as some unconfined flows, curved boundary layers, swirling flows, rotating flows and fullydeveloped flows in non-circular ducts according to Versteeg & Malalasekera (2007). In curvedmodels thek- model predicts excessive levels of turbulent shear stress, leading to suppression ofseparation, which poses a problem in areas such as aerodynamic flows. Some of the deficienciesof the model can be related to how it calculates in the near-wall region, and hence different walltreatment methods have been developed over the years to try and solve this issue.

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2.1.1.2 The SST k- mo d e l

The standardk- model was developed for solving the -equations problems when modeling theflow in the boundary layer region, close to the wall. This makes the -model much better in predicting adverse pressure gradient boundary layer flows and separation. One of the downsidesof the standard model is its strong sensitivity to freestream conditions, outside the shear layer,which tends to make it difficult to use in aerodynamic flows.

The SSTk- model was designed to deal with this problem by combining the-equation and the-equation by the use of a blending function. This makes it possible for the model to use the

advantages of the -formulation in the freestream region and the-equation in the boundarylayer region. The model is therefore valid for a great number of flow cases and it gives accurate predictions of the onset and the amount of flow separation under adverse pressure gradients.Because of this it is one of the most widely used turbulence models in aerodynamic flows. Someof the deficiencies of the model are that it in some cases can under-predict pressure losses and be

too conservative in predicting separation. The SST model is recommended for high accuracy boundary layers simulation by ANSYS Inc. in the CFX User-guide - Turbulence and WallFunction Theory (2009).

2.1.1.3 The y + valueThe y+ value is the dimensionless distance from the wall to the first node in the computationalgrid. It is used to check how fine the grid is in the boundary layer region and gives informationon what turbulence model and wall treatment can be used. The y+ value can be calculated usingequation (2.11) and (2.12).

(2.11)

(2.12)Where y is the distance from the wall,u the friction velocity at the wall, the local kinematicviscosity, w the wall shear stress and w the density at the wall.

Experiments and mathematical analysis have shown that the near-wall region can be divided intotwo layers, the viscous sub-layer, and the logarithmic layer. In the viscous sub-layer, which is

closest to the wall, the flow is almost laminar and the molecular viscosity is dominant inmomentum and heat transfer while in the logarithmic layer, turbulence is the dominating mixing process. These layers are illustrated in Figure 2. Between these two layers there exists a regioncalled the buffer layer where molecular viscosity and turbulence effects are equally important.

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Figure 2: The two layers in the near-wall region.

There are two approaches that can be used to model the flow in this region, the wall functionmethod and the low-Re method. The wall function method doesnt resolve the inner region(viscous sub-layer and buffer layer) but instead uses empirical formulas to bridge the inner

region between the wall and the logarithmic layer, thus saving a lot of computational resources.This method requires that the first node is in the logarithmic layer with a lower limit on y+ of 30,and an upper limit that can extend up to several thousand depending on the Reynolds number.

The low-Re method fully resolves the details of the boundary layer profile. This does howeverrequire that the grid is refined in the direction normal to the surface so that a y+ < 1 can beachieved. To take full advantage of the capabilities of the method one should try to have between10 and 20 nodes within the boundary layer to fully resolve it. This approach is much morecomputational heavy than using wall functions since is requires a larger number of nodes. If thedetails of the boundary layer are of little interest, a wall function approach might be more

suitable to use.2.2 Boundary layersConsider fluid flow over a flat plate, like in Figure 3. In the vast region of the flow field awayfrom the surface, the velocity gradients are very small and friction has little effect on the flow. Atthe wall however, the velocity gradients are large and friction has a large impact on the flow dueto the frictional forces retarding the motion of the fluid, and hence a thin layer is formed abovethe surface. This thin viscous region is called the boundary layer. At the surface the flow velocityis zero (the no-slip condition) and as we move away from the surface in the y-direction thevelocity increases until it reaches a point where it equals the freestream velocityu. The height

above the wall where this occurs is called the boundary layer thickness and its normallydefined as the point above the wall where the velocity equals 99 % of the freestream velocity(equation (2.13)).

0.99uu (2.13)

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Figure 3: Boundary layer along a flat plate.

Boundary layers (BL) can be either laminar or turbulent, depending on the Reynolds number(Re). In the flow over a flat plate there is a transition between the two at approximately Re =

5*105

. For lower Reynolds numbers the BL is laminar and the velocity changes uniformly as onemove away from the wall, while for higher Re the boundary layer is turbulent and characterized by unsteady swirling flows.

The fluid particles in the BL do not always remain in the thin layer which adheres to the bodyalong the length of the wall (Schlichting, 1979). In some cases when adverse pressure gradientsare present, the flow in the boundary layer can become reversed and the boundary layer increasesits thickness considerably. The consequence of a reversed flow is that the flow separates from thesurface and creates a large wake of recirculating flow downstream of the surface. This will causea pressure drop in the region and will increase the pressure drag on the body.

Two commonly used boundary layer properties are the displacement thickness and themomentum thickness , which can be calculated from equation (2.14) and (2.15).

(2.14)

(2.15)

Where y1 is a point above the boundary layer. The displacement thickness can be thought of asan index proportional to the missing mass flow due to the presence of the BL, but could also be explained as the imaginary increase in wall thickness, as seen by the outer flow, due to theeffect of the growing boundary layer. The momentum thickness in an index that is proportionalto the decrement in momentum flow due to the presence of the BL. In other words, it is theheight of a hypothetical streamtube that contains the missing momentum flow at freestreamconditions (Andersson, 2007; Cengel & Cimbala, 2006).

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Over the years a number of correlations have been derived for and for both laminar andturbulent flows over a flat plate. The most widely used correlations are shown in equations (2.16)

(2.21).

Laminar flow: (2.16) (2.17) (2.18)

Turbulent flow: (2.19)

(2.20)

(2.21)

Where x is a point along the plate and Re x the Reynolds number at that point.

Due to the large uncertainties associated with turbulent flow fields the turbulent flow correlationsare less exact than the correlations used for laminar flow and should therefore be treated as moreapproximate solutions. They do however provide a good measure of comparison when performing boundary layer calculations.

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3 MethodTo validate the local non-conformance definition for the bumps the work was split up intoseveral parts. First an investigation of the flow over a flat plate was conducted (reference case) tovisualize the boundary layers and to find the thickness at a position where the flow was fullydeveloped. This was done for Reynolds numbers ranging from 105 to 107 to see how thethickness changed with Re.

Since the NC definition that VAC use is defined as a percentage of the boundary layer thickness(BLT), bumps were created with a height of 10, 40, 60, 99 and 150 % of the BLTs found in theflat plate simulations. This was done to see how the size and shape of the BL was affected by the bumps. A correlation for the drag coefficient for the bumps was then derived based on the datafrom the bump analysis.

Finally the boundary layers for representative vanes of a TRF were analyzed for both nominalcases and with bumps so that VAC could be provided with recommended values for maximumallowed bump sizes on the vanes. The correlation derived from the flat plate simulations wasthen tested on some of the bump cases to see how well it predicted the drag coefficient.

3.1 Simulation approachA similar approach was used during all the simulations to standardize the work. All the flat platesimulations were very much alike, apart from slight geometry changes and boundary conditions,which made it possible to keep a lot of things constant during the process.

For each case the steps below were followed.

1. Create the geometry.2. Create the computational grid. Depending on the inlet boundary condition used in step 3,

modify the distance from the wall to the first node.3. Define the simulation case with appropriate boundary conditions and simulation settings.4. Run the calculations. Monitor convergence of the residuals and domain imbalances until

the monitored parameters can be considered to be low enough and steady.5. Check if the y+ value fulfills the criteria demanded by the turbulence model. If it does,

continue to step 6, otherwise repeat step 2-5.6. Post-process the results.

More details about each step are presented in the subsequent section.

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Figure 5: Initial 2D-mesh for the reference case.

3 .2 .1 .3 Bou ndary condi t ions The leftmost side inFigure 5 was set as an inlet with a velocityV in depending on the

Reynolds number Re L wanted at a location of x = 19 meters(Table 2). VACs applicationsarent restricted to just one Re so it was important to study how the BL changed with anincreasing value, but also to be able to find a correlation that would work for a widerange of Re. The inlet velocity was calculated from equation (3.1).

LV LRe (3.1)

Table 2: Inlet velocities for different Reynolds numbers.

ReL Vin [m/s] 100000 0.081250000 0.203500000 0.407750000 0.610

1000000 0.8132000000 1.6274000000 3.2536000000 4.8808000000 6.506

10000000 8.132

The bottom side of the geometry was given the appearance of a plate by setting it as a

wall with a no-slip boundary condition. The top side of the domain was set as a wall with a free-slip condition. The two walls in the cross-flow direction(Figure 4) were both given a symmetry

boundary condition (ANSYS Inc, Modeling 2D Problems, 2009). For the rightmost side of the domain an outlet boundary condition was set with an

average static pressure of zero Pascal over the whole outlet.

x

y

INLET

WALL

OUTLET

WALL

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3.2.1.4 Mesh depen denc yTo be certain that the simulation results were independent of the grid size a mesh dependencystudy was perfor med on the reference case. An initial resolution of 75000 cells was created andthen multiplied by a factor of 2, 3 and 4 to get four different meshes. Simulations were then runfor all four cases at Re = 106 and variables such as pressure loss P loss (equation (3.2)) and dragcoefficientC d (equation (3.3), where A p is the area of the plate as seen from the y-direction) weremonitored. The results can be seen in Table 3.

100.

,0,0

indyn

out in

loss P

P P P (3.2)

pin

xd

AV

F C

2

2

1

(3.3)

Table 3: Pressure loss and drag coefficients for the grids.

Mesh Cells Measured y + Ploss [%] Cd [10-3]

Initial (x1) 75000

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Figure 7: Flat plate with bump.

The shape of the bumps in the flow direction was also of interest since a larger height to lengthration is more prone to cause separation and increase the amount of pressure drag. Therefore twomore types of bumps were investigated, one with double the length and one with half the lengthof the standard model(Figure 8and Figure 9).

Figure 8: Wide bump (h/L = 0.159).

Figure 9: Aggressive bump (h/L = 0.637).

3.2.2.2 MeshAll the meshes were created in the same way as the reference case with the exception that theywere refined around the bumps. This was done to avoid sharp edges around the bumps andimprove the transition between the cells in this area(Figure 10and Figure 11). Since the y+ valueis dependent on the wall shear and the friction velocity (equation (2.11)), the distance to the firstnode from the plate was adjusted in all cases to ensure a value less than one.

xy

L

h

L

h

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Figure 10: Flat plate with a bump.

Figure 11: Close-up on a bump.

3.2.2.3 Mesh depen denc yFour different grids were created to be certain that the grid size chosen during all simulationswas independent of the resolution. As previously, two variables were monitored and compared( P loss and C d ), and the mesh study was done with a Reynolds number of 106 and a bump height of40 % of the boundary layer thickness. The results can be seen in Table 4.

Table 4: Pressure loss and drag coefficient for the four grids.

Mesh Cells (approx.) Measured y + Ploss [%] Cd Initial (x1) 75000

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3.2.3 Finding a correlation for C d For VAC it is of great interest to find a correlation between the drag coefficient of the bumps, theRe and the bump height in relation to the boundary layer thickness.

For the reference case the drag is almost completely consisting of frictional drag while for the

bumps its mainly due to pressure. By subtracting the force in the x -direction of the referencecase from the bump case it is possible to find the additional force on the plate due to the presenceof the bumps (equation (3.4)).

(3.4)It is then possible to calculate the drag coefficient for all bumps in the whole span of Re usingequation (3.5), taken from Andersson (2007),

(3.5)where the normalization area Ab is the frontal area of the bumps, calculated from hw Ab where w is the width of the bump in the cross-flow direction (1 mm for the flat plate) andh the bump height.

Plotting these values against the bump height in relation to the BLTh/ 99 for each Re yields tenlogarithmically shaped curves. It is then assumed that the correlation for the drag coefficient can be written in the following form,

(3.6)

wherea and b are functions of Re and x of h/ 99. Excel is then used to find values fora and b thatminimize the error between equation (3.6) and the simulations. The results can be seen in chapter4.1.3.

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3.3 Real geometryThe real geometries used for studying the boundary layer thickness were the vanes from arepresentative TRF (both a regular and a mount vane). The simulation results were all supplied by VAC so no simulations were performed.

Two geometries were investigated, and each with a set of non-conformances. Initially the BLT,displacement boundary thickness (DBT) and momentum boundary thickness (MBT) werecalculated at 50 % span (with the method presented in the next chapter) for nominal caseswithout geometry defects, for both the suction and pressure side. The most critical location tohave a non-conformance is on is the suction peak, so by finding the boundary layer thickness inthat position makes it possible to decide where in the boundary layer the investigated bumpswere positioned. Five bumps were studied on the regular vane SS, three on the mount vane SSand finally five bumps on the mount vane PS.

An aerodynamic study of non-conformances on a TRF done by VAC in 2009, where the pressure

losses and the swirl angles had been investigated for the bumps mentioned above, were used foranalyzing the results from the real geometry bump study. Comparisons were done between theresults from the real geometry study and the flat plate study to see if the boundary layer wasaffected in a similar way on the vane as it was on the flat plate.

Figure 12and Figure 13 below shows the nominal vanes and Figure 14and Figure 15two of thegeometry defects studied.

Figure 12: Nominal regular vane. Figure 13: Nominal mount vane.

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Figure 14: Regular vane with 5 mm bump on SS. Figure 15: Mount vane with 5 mm bump on PS.

3.3.1 Testing the correlationThe correlation derived from the flat plate simulations was tested on the bumps of therepresentative geometries to see if the correlation could be used on real geometries.

Hundreds of bump simulations have been conducted at the aerothermodynamics department ongeometries similar to the one analyzed in this project. From these simulations,C d values have been calculated using a method based on force equilibrium for a control volume, resulting in anequation on the following form.

(3.7)

Where )/cos( tan, xin per in vv A A is the domain inlet area perpendicular to the flow, hw Ab is

the front area of the bump, out in P P P ,0,0 is the pressure difference between the inlet andoutlet of the domain and P dyn the maximum dynamic pressure in the zone on the vane where the bump is located.

It was therefore expected that the correlation results would be of similar magnitude as theC d value calculated for bumps at the department, which is 0.25 on the suction side of separation freevanes.

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3.4 Boundary layersCalculating the boundary layer thickness from the simulation data is a quite challenging tasksince there is no built-in function or general method available for doing this in CFX. Because ofthis a method had to be developed for doing the following,

Create lines normal to the surface of interest in CFX. Export the velocity profile along the lines together with position. Use MATLAB to find where 0.99uu and do the integration that yields the

displacement and momentum thicknesses.

3.4.1 Flat plateCreating lines normal to the flat plate is an easy process due to the fact that they are onlydepending on the position along the plate (x-direction) and the normal to the surface (y-direction). However, since a lot of lines had to be created for a wide span of Reynolds numbersthe process was simplified by creating a script for CFX-Post (Appendix 7.5). In addition tocreating the lines the script exports data for position, static pressure and total pressure along eachline to a file, to be used in the post-processing in MATLAB.

To get comparative results between the flat plate and the real geometries the same method forcalculating the velocity was used. Since the stream situation for the real geometries (vanes) lackfree stream conditions the isentropic velocities along the lines had to be calculated for both cases(flat plate and vanes) using equation (3.8).

(3.8)

Where equation (3.8)originates from Bernoullis equation .

(3.9)

A script was constructed in MATLAB (Appendix 7.6) for post processing all the data from theflat plate simulations. The script calculates the DBT and MBT and gives an approximate valuefor the BLT at each line along the plate and then plots the data to visualize the shape of thelayers. By doing this it was possible to extract the BLT at x = 19 meters for the whole range of

ReL.The same procedure used for the reference case was also used for the case with bumps. InMATLAB it is then easy to compare the differences and see how the shape and size of the boundary layer were affected by the bumps, depending on their height in relation to the referencethickness.

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4 Results and discussionIn this chapter the results from the different phases of the project is presented and discussed. Italso contains a discussion about the methods used, the choice of turbulence model and somerecommendations.

4.1 Flat plateThis section deals with the results from the flat plate and flat plate with bump simulations. For both cases the results were compared to the equations for ideal laminar and ideal turbulent flow presented in the theory chapter. Table 5 summarizes all the simulations done on the flat plate (S= Standard, A = Aggressive, W = Wide, Ref = Reference). The five heights depicted in Table 5were chosen since it was of interest to study the upper and lower limit of the non-conformancedefinition(Table 1) as well as values above the upper limit and values between the two limits.

Table 5: Flat plate simulation summary.

SummaryScale factor

1.5 0.99 0.6 0.4 0.1 -ReL S A W S A W S A W S A W S A W Ref

100000 x - - x - - x - - x x x x - - x250000 x - - x - - x - - x x x - - - x500000 x - - x - - x - - x x x - - - x750000 x - - x - - x - - x x x - - - x

1000000 x - - x - - x - - x x x x - - x2000000 x - - x - - x - - x x x - - - x4000000 x - - x - - x - - x x x - - - x6000000 x - - x - - x - - x x x - - - x8000000 x - - x - - x - - x x x - - - x

10000000 x - - x - - x - - x x x x - - x

As was mentioned in the method chapter it was of great importance to calculate the BLT, DBTand MBT for a flat plate at a wide range of Re. It was believed that by doing so the effect of a bump on the BL could be seen and that the results would correlate well with those for a realgeometry. The reason for choosing a flat plate as reference is because it is good for developing a basic understanding of how the boundary layer develops along a surface and it is known to be afairly good approximation for many applications, such as airfoils. Even though the flow over avane will differ due to increasing/decreasing pressure gradients and depending on if observing

the SS or PS, the flat plate will show a similar behavior and will aid in the understanding of theBL development over the vane.

4.1.1 Reference caseFollowing the method for calculating the BLT for the flat plate yielded the results shown inFigure 16. The line at the top of the graph is the lowest Re (105) and the bottom one the highest(107) and as was mentioned earlier they all correspond to a Re at 19 meters in the flow direction.What is seen is how the boundary layer builds up along the plate and it can be observed that as

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the Re increases the boundary layer thickness decreases. This was of course expected since theBLT is inversely proportional to the Reynolds number. However, what wasnt expected was thatno transition between laminar and turbulent could be seen for either case, since it was anticipatedthat the BLT for the lower Re would correlate quite well with equation (2.16) for laminar flowsand that the higher Re would do the same with the 1/7th power law from Schlichting (1979),equation (2.19). By looking at some of the BLTs individually it can be observed that they deviatefrom these correlations(Figure 17). The exempt is the first portion of the boundary layer for thelowest Re (Figure 17a) which matches quite well with equation (2.16), and the highest Re(Figure 17d) that almost match with the power law. The left-out cases can be seen in Appendix7.1.

Figure 16: Boundary layer thickness for the reference case.

a) Re = 105. b) Re = 7.5*105.

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c) Re = 2*106. d) Re = 107. Figure 17: Boundary layer thickness at the four Reynolds numbers a) 10 5 b) 7.5*10 5 c) 2*10 6 d) 10 7.

A small investigation was done to answer the question as to why the transition from laminar to

turbulent couldnt be seen in the flat plate results. It was expected that by calculating the dragcoefficient C d (equation (3.3)) for each case and plotting it against the respective Reynoldsnumber would yield results(Figure 18) that could be compared to the theory of a flat plate, andthat this would give some insight into the source of the error.

Figure 18: Skin-friction drag coefficient for the flat plate.

Comparing the results with Figure 19from chapter 2-6 in Hoerner (1965) strongly indicated thatthe flow over the flat plate was a forced turbulence flow and not a developing flow. Afterstudying the user manual for CFX in more depth these results could be confirmed, as theturbulence model in CFX models fully turbulent flow, which wasnt realized from the start.Because of this the BLTs for low Re(below 750000) will b e somewhat thicker than what theyshould be. However, since VAC most often deal with Re larger than this the deviation for lowvalues were of less importance.

0.001

0.01

1E+04 1E+05 1E+06 1E+07 1E+08 1E+09 1E+10

C d

Re L

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Figure 19: Skin-friction drag coefficient for a smooth plane surface depending on Reynolds number.

Looking at the DBT and MBT for each case shows that they match very well with the correlationfor an ideal turbulent flat plate (equation (2.20) and (2.21). The reason for this is considered to bethat the method used for calculating both the DBT and MBT is much more robust and accuratethan the approximate method used for finding the BLT. Looking at these thicknesses is thereforea good addition when studying the boundary layer for checking that the simulation results arecorrect. Figure 20 below shows the DBT and MBT for the three Reynolds numbers 7.5*105 (aand b), 2*106 (c and d) and 107 (e and f) and the rest are shown in Appendix 7.1.

a) Re = 7.5*105 b) Re = 7.5*105

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c) Re = 2*106 d) Re = 2*106

e) Re = 107 f) Re = 107

Figure 20: Displacement and momentum thickness for three reference cases.

The boundary layer thickness associated with each Reynolds number at x = 19 meters can beseen in Table 6. This data was the base for determining the height of the bumps for the differentscale factors (h/ 99).

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Table 6: BLT for all Reynolds numbers.

ReL BL thickness [mm] 100 000 471.571 250 000 394.648 500 000 354.515 750 000 331.103

1000 000 317.725 2000 000 287.625 4000 000 260.869 6000 000 250.836 8000 000 240.803

10 000 000 237.458

4.1.2 BumpsAs mentioned earlier three types of bumps were created. Initially a standard cosine shaped bump

was studied for the whole Re range and for all five heights. After this an aggressive and a wide bump was simulated for all Reynolds numbers at a height of 40 % to see how the shape of thenon-conformance in the flow direction would affect the BL. First the results for the standardcosine bumps are presented.

Utilizing the results from Table 6 the five bump heights could be determined for all Re(Table 7).The five heights of interest were 10 %, 40 %, 60 %, 99 % and 150 % of the BLT.

Table 7: The five bump heights (in mm) that were to be created for each Reynolds number.

Scale factor

Re L 1.5 0.99 0.6 0.4 0.1100 000 707.357 466.856 282.943 188.629 47.157250 000 591.973 390.702 236.789 157.860 39.465500 000 531.772 350.970 212.709 141.806 35.452750 000 496.655 327.792 198.662 132.441 33.110

1000 000 476.588 314.548 190.635 127.090 31.7732000 000 431.438 284.749 172.575 115.050 28.7634000 000 391.304 258.261 156.522 104.348 26.0876000 000 376.254 248.328 150.502 100.334 25.0848000 000 361.204 238.394 144.482 96.321 24.080

10 000 000 356.187 235.083 142.475 94.983 23.746

The first height to be tested was 10 %, which was the lower limit of the non-conformancedefinition as was mentioned in the introduction. It was expected that these bumps would havelittle or no effect on the flow and therefore only three Re (105, 106 and 107) were initiallysimulated. If this was proven to be true then it would be unnecessary to do any furthersimulations for that height, which would then save a lot of computational time. Utilizing thescripts (Appendix 7.5 and 7.6) on the simulation data the following results were found.

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The second height simulated was 40 %. An initial simulation for a Reynolds number of 106

indicated that a difference in BLT compared to the reference case existed. That gave a clearindication that all heights larger than this would have an impact on the BLT and hence the wholerange of Re were simulated for each remaining case. In the figures below the four lowestReynolds numbers have been left out to make it easier for the reader to view the results. Theyhave instead been included in Appendix 7.2. The reference cases have been included in thegraphs to visualize the increase in thickness better.

a) 40 %. b) 60 %.

c) 99 %. d) 150 %. Figure 23: BLT with bumps at height a) 40 % b) 60 % c) 99 % d) 150 %.

As can be seen in Figure 23a c, the boundary layer stabilizes before reaching the outlet for allcases and it is quite straightforward to see how much the boundary layers have been affected by

the bumps. For the 150 % case(Figure 23d) it nearly stabilizes for the highest Reynolds number but for the remainder the domain is too short to make this possible. This indicates that the BLwould need a substantial distance behind the bumps to stabilize themselves. If the domain was to be extended around 10 meters or so it would probably be enough to solve this problem. It shouldtherefore be noted that the BLT values at the outlet for this height is somewhat larger than whatthey should be.

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In Figure 24the velocity contours can be seen for the four bump heights at a fixed Re. The dark blue color in the figures represents negative velocity, i.e. separated flow and its easy to see thatthe two largest bump heights (99 % and 150 %) induce a large separated region behind them.

a) 40 %. b) 60 %.

c) 99 %. d) 150 %. Figure 24: Velocity contours for standard bumps at a) 40 %, b) 60 %, c) 99 % and d) 150 % of the BLT at Re = 10 6.

By comparing the BLT for each bump with the corresponding reference case it was possible tocalculate the increased thickness due to the presence of the bumps. The results presented in Table8 are shown as an increase from the reference case (i.e. a 20 % increase is the same as a 20 %thicker boundary layer than the reference case) and values at the domain outlet are used.

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Table 8: Percentile increase in boundary layer thickness due to the bumps.

BLT increase Scale factor ReL 0.4 0.6 0.99 1.5

100000 5.8 18.0 48.0 129.5250000 8.3 19.3 54.8 125.1500000 9.0 21.2 57.2 124.4750000 8.1 20.0 55.6 118.1

1000000 9.8 20.2 50.6 109.12000000 12.8 25.4 61.1 114.14000000 15.2 29.2 62.1 112.86000000 13.6 28.0 60.6 108.98000000 13.4 28.2 60.6 107.8

10000000 12.4 26.2 54.0 92.8Average increase [%] 10.8 23.6 56.5 114.3

From the results presented in the table it can be seen that for the lowest scale factor the averageincrease in boundary layer thickness is only about 11 %, which indicates that the bump has asmall impact on the BL but not small enough to be considered unimportant. Its in teresting to seethat the increase rises about 50 % between each scale factor, which could indicate that it followssome sort of power law and that a correlation might be possible to derive from the results. Thelarge increase in thickness due to the bumps with a size close to or above the BLT tells us thatthey will have a large effect on the aero parameters. A large increase of the thicknesses (BLT,DBT and MBT) will have the unfortunate effect of changing thegeometrys effective shape andhence reduce the circulation and lift. It will also be highly prone to cause separation on the vaneand give rise to a high pressure drag, consequently increasing the total drag on the vane.

The aggressive and the wide bumps were studied at a height of 40 % and for the full range of Re.The reason for not analyzing the rest of the bump sizes was because it was assumed that theywould follow the same trend as the standard cosine bumps. In Figure 25and Figure 26the BLTfor three Reynolds numbers (105, 106 and 107) are shown for the two bump types and thedisplacement and momentum boundary thicknesses in Appendix 7.2.

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a) Boundary layer thickness for aggressive bumps at 40 %. b) Velocity contours, Re = 106. Figure 25: Aggressive bump at 40 % showing a) BLT for three Re compared with the reference case and the standard

bump b) Velocity contours for Re = 10 6.

a) Boundary layer thickness for wide bumps at 40 %. b) Velocity contours, Re = 106. Figure 26: Wide bump at 40 % showing a) BLT for three Re compared with the reference case and the standard bump

b) Velocity contours for Re = 10 6.

Comparing the figures shows that the wide bump affects the shape and size on the boundarylayer less than the aggressive one does, and in Table 9 we can see that the wide bump has a verysmall increase in BLT compared to the reference case. The aggressive bump however showstendencies towards the 60 % case for the standard bumps. The velocity contours tells us that theseparated region behind the bumps is noticeably larger for the aggressive bump. We cantherefore assume that the wide bumps will have a smaller impact on the aero parameterscompared to the standard case and that the aggressive one will have a larger impact.

Table 9: Percentile increase in boundary layer thickness for the aggressive and wide bumps.

BLT increase Scale factor = 0.4Re L Aggressive Standard Wide

100000 9.4 5.8 5.11000000 11.9 9.8 4.6

10000000 17.9 12.4 5.4

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4.1.3 Drag coefficientBelow follows the results from the derivation of the correlation for the drag coefficient. First theresults from the simulation data is presented and then the corresponding correlation. Thecorrelation has been derived from the simulation data for the standard cosine bump.

4.1.3.1 Simu lat ions

4.1.3.1.1 Standard bumpUsing equation (3.4) from the method chapter it was possible to calculate the force induced bythe bumps in the flow direction. This data was then used in equation (3.5) and normalized withthe height of the bumps to find a corresponding drag coefficient for each bump height and Re.The tables containing the calculated drag coefficients are shown in Appendix 7.3. By plotting theC d for each Re against the scale factorh/ 99 it was possible to see the correlation between thevariables(Figure 27).

Figure 27: Relation between the drag coefficient and the scale factor based on simulation results.

It is clear that the curves in the figure follow a logarithmic shape and that a logarithmic functioncan be derived from the data, as was mentioned in the method chapter. More about this inchapter 4.1.3.2.

0.20.250.3

0.350.4

0.450.5

0.550.6

0 0.5 1 1.5 2

C d

h/ 99

10^52,5*10^55*10^57,5*10^510^62*10^64*10^66*10^68*10^610^7

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4.1.3.1.2 Aggressive and wide bumpsSince the aggressive and wide bumps were only evaluated at 40 % of the BLT they werecompared the 40 % case for the standard bump and plotted against the Re.

Figure 28: Drag coefficient depending on Re for aggressive, wide and standard bumps with height 40 %.

In Figure 28we can see that the aggressive bump follows the same trend as the standard bumpwith the exception that the drag coefficient is higher due to the increase in pressure drag. TheC d for the wide bump on the other hand starts to decline somewhat for Re higher than 106. Theshape and magnitude of the curves can be related to the height to length ratio of the bumpsh/L,where a higherh/L value will increase the amount of pressure drag and hence increase the dragcoefficient, while a lower value will decrease the drag coefficient.

The results from comparing the increase/decrease inC d for the aggressive and wide bumps withthe standard bump can be seen in Table 10.

Table 10: Percentile difference in C d for aggressive and wide bumps compared to the standard bump, for the sim. data.

Difference Scale factor = 0.4ReL Aggressive bump Wide bump

100000 18.82 -27.84250000 22.85 -31.86500000 25.54 -33.81750000 25.99 -35.15

1000000 23.42 -37.072000000 26.62 -41.504000000 28.81 -47.206000000 30.78 -50.858000000 30.95 -52.95

10000000 31.68 -56.07

0.00

0.10

0.20

0.30

0.40

0.50

0 5000000 10000000

C d

Re

Standard

Aggressive

Wide

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Clearly, there are large differences between the bumps, with an average increase inC d of 27 %for the aggressive and a 41 % decrease for the wide compared to the standard bump.

4.1.3.2 Correlation

Following the results inFigure 27 it was assumed that the correlation would have the form presented in the method chapter (equation (3.6)). By using the simulation results from thestandard cosine bump study it was possible to find values for the coefficientsa and b in equation(3.6). The solver in Excel was used for guessing values ofa and b that minimized the error between the correlation and the simulation results. The results are presented in Table 11.

Table 11: The a and b coefficients for each Reynolds number.

CoefficientsReL a b

100000 0.455424553 0.252791285250000 0.454860716 0.221292917500000 0.461813834 0.195293037750000 0.462009399 0.179833327

1000000 0.471259180 0.1637461982000000 0.460685200 0.1378724494000000 0.452094966 0.1212801896000000 0.444300587 0.1120799768000000 0.436480399 0.106156106

10000000 0.435992571 0.089439931

It was sought after to find coefficients depending on the Reynolds number, hence a and b were plotted against the Reynolds number to find suitable values(Figure 29and Figure 30).

Figure 29: a as a function of Re.

y = -3E-09x + 0.4628

0.430.440.450.460.470.48

0 5000000 10000000

f(Re)

Re

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Figure 32: Comparison between correlation and simulation results for three Reynolds numbers.

Looking at these results even further we can see that the percentile difference between Figure 27and Figure 31is within 5 %(Table 12), which can be considered to be a quite good match.

Table 12: Percentile difference between the correlation and the simulation results.

Difference Scale factor ReL 0.4 0.6 0.99 1.5

100000 -5.58 3.46 2.52 -0.06250000 1.49 3.42 3.51 0.65500000 1.49 0.86 0.90 -0.64750000 1.30 -0.10 -0.22 -0.75

1000000 -3.63 -2.86 -2.93 -2.122000000

0.20 -1.24 -1.58 -0.614000000 3.42 0.37 -0.60 -0.736000000 4.37 1.51 -0.12 -0.808000000 5.13 2.30 0.08 -0.78

10000000 0.67 -0.37 1.92 -1.20

The correlation is based on the simulation results from the standard cosine bump study. It willtherefore miss-predict the drag coefficient if used with aggressive or wide bumps since thecorrelation is independent of the length in the flow direction. A more detailed analysis needs to be carried out by e.g. finding a coefficient that the correlation can be multiplied with so that the

correlation can be used with bumps of differenth/L.

0.20.250.30.35

0.40.450.5

0.550.6

0 0.5 1 1.5 2

C d

h/ 99

Sim. Re = 10^5Sim. Re = 10^6Sim. Re = 10^7Corr. Re = 10^5Corr. Re = 10^6Corr. Re= 10^7

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4.2 Real geometryTo see how the size and shape of the boundary layer was for a real geometry, the vanes of arepresentative Turbine Rear Frame was investigated. As was mentioned in the method chapter,two models were initially looked at, a nominal regular vane and nominal mount vane. Themodified scripts for CFX-Post and MATLAB were used on the simulation results to calculate theBLT, DBT and MBT for both the SS and PS of the vanes, and also at different spans.

After this the results from a bump investigation on the suction side of the regular vane andsuction and pressure side on the mount vane are presented and discussed.

4.2.1 NominalThe BL results for the regular and the mount vane on both the SS and PS can be seen in thefigures below (DBT and MBT in Appendix 7.4). It was assumed that the SS would have asimilar appearance as the flat plate, with the exception that the boundary layers would be thinner before the suction peak due the increase in velocity and wider after the suction peak due to the

decrease in velocity. For the PS the BL were assumed to show a similar tendency, with theexception of being thinner near the TE due to the shape of the geometry. It was also suspectedthat the stagnation point at the LE would cause problem in the BL calculations, which laterturned out to be correct for some of the cases.

Figure 33: BLT for nominal regular vane, SS. Figure 34: BLT for nominal regular vane, PS.

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Table 13: Boundary layer thickness at the suction peak for the two nominal vanes.

BLT[mm] Case Span Regular vane Mount vane50 % 3.4 4.090 % 3.1 3.3

The reason that the boundary layer thickness is lower at 90 % span was assumed to be due todifferent velocities at the suction peak along the vane. This could be confirmed by looking at thestatic pressure contours(Figure 38) on both the regular and the mount vane, which also explainswhy the boundary layer is somewhat thicker on the mount vane.

a) Regular vane, SS. b) Mount vane, SS. Figure 38: Static pressure contours on the a) regular vane b) mount vane.

4.2.2 Bumps

Table 14 shows a summary of the range of bump sizes that were part of the validation work forthe real geometries and also their location.

Table 14: Summary of all bump analyzed and their location.

Regular vane Mount vaneHeight [mm] SS PS SS PS

1 x - x x2 x - x x3 x - x x4 x - - x

5 x - - x

The graphs for the DBT and MBT from all cases are presented in Appendix 7.4 and shown nextare the results for the BLT, starting with the regular vane.

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4.2.2.1 Regu lar van eIf we look at Figure 39- Figure 42we can see that the boundary layer calculations collapse inthe region behind the bump. Comparing these results with the pressure losses in VAC (2009) andwith the negative axial velocities in Figure 44 Figure 47, we can see large regions of separationfor all four heights. The code used in the boundary layer calculations therefore has large problems with determining the thicknesses for highly separated regions. However, for the 3 mmcase there is a separation free region about halfway between the bump and the trailing edge ofthe vane and for the 2 mm case the flow barely manages to reattach near the trailing edge, whichexplains the spikes in Figure 41and Figure 42and gives some information of how much the boundary layer thickness has increased due to the bumps.

Figure 39: Regular vane, SS, 5 mm. Figure 40: Regular vane, SS, 4 mm.

Figure 41: Regular vane, SS, 3 mm. Figure 42: Regular vane, SS, 2 mm.

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Figure 43: Regular vane, SS, 1 mm.

Figure 44: Regular vane, SS, 5 mm, separation. Figure 45: Regular vane, SS, 4 mm, separation.

Figure 46: Regular vane, SS, 3 mm, separation. Figure 47: Regular vane, SS, 2 mm, separation.

Figure 48: Regular vane, SS, 1 mm, separation.

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The 1 mm case experiences a small separation behind the bump, but the effect in negligible onthe calculation method. The BLT is however affected at the end of the vane, with an increase ofabout 80 % compared to the nominal case. For the 2 mm bump the increase is about 250 %compared to the nominal case but the second result is unreliable due to the separated flow alongthe vane. The 1 mm bump height is approximately 32 % of the BLT at the suction peak for thenominal case, while for the 2 mm bump it is roughly 65 %. Since the 2 mm bump causesseparation that barely manages to reattach there seems to be a limit of what height can beallowed on the regular vane of roughly 30 %, to be conservative. It is likely that bumps in therange 30-60 % of the BLT can be allowed but this needs to be studied in more detail.

As can be noted from the results the percentile increase in boundary layer thickness in the region behind the 1 and 2 mm bumps compared to nominal is much larger than for bumps located at thesame h/ 99 on the flat plate. The cause of this can be due to the shape of the vane being curvedand the adverse pressure gradients causing a more rapid increase in boundary layer thickness inthe region behind the bumps.Its possible that the boundary layer thicknesses from the flat platesimulations are somewhat underestimated, seeing as the boundary layer thicknesses werecalculated to be thinner than the ideal turbulent boundary layer thicknesses calculated from thetheory. The impact would be that the bumps created and simulated on the flat plate would be in asmaller percentile part of the BLT, which would imply that the real geometry bumps should becompared to flat plate bumps located at a higher percentile part of the BLT rather than at thesame percentile part.

It is unlikely that the boundary layer would be affected by the 1 mm bump on the regular vane tosuch a large extent compared to the mount vane (presented in the next chapter). Looking at theincrease in displacement boundary thickness(Figure 73e and Figure 74c in Appendix 7.4) andmomentum boundary thickness(Figure 76e and Figure 77c) compared to nominal for both 1 mm bumps gives some insight into this problem. It can be seen in the figures that the thicknessincrease is about the same for both bumps. This tells us that there must be some error in thecalculation method when used on the regular vane since there is such a large difference betweenthe increases in boundary layer thickness for the two cases. The code used when analyzing theBLT on the vanes as well as the method in chapter 3.4.2 therefore needs to be investigatedfurther.

4.2.2.2 Mo un t van eIt was found that the mount sector is more sensitive to NC since the 3 mm bump(Figure 52) shows a separated region that is larger than the separation observed for the 5 mm bump on theregular vane. It was therefore decided not to analyze 4 and 5 mm bump heights. The analysis onthe simulations results from the mount vanes suction side was therefore done for three bumpheights (1, 2 and 3 mm).

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Figure 49. Mount vane, SS, 3 mm. Figure 50: Mount vane, SS, 2 mm.

Figure 51: Mount vane, SS, 1 mm.

Clearly the boundary layer calculation falters for the 3 and 2 mm defects while its just slightlyaffected by the 1 mm bump. Again, comparing the results with the negative axial velocities(Figure 52and Figure 53) gives a clearer image as to what happens in the flow.

Figure 52: Mount vane, SS, 3 mm, separation. Figure 53: Mount vane, SS, 2 mm, separation.

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Figure 54: Mount vane, SS, 1 mm, separation.

There is a large difference in separated flow between the 2 and 3 mm cases and thecorresponding results for the same bump heights on the regular vane(Figure 46and Figure 47).This further strengthens the conclusions from VAC (2009) that the mount vanes are much more