SURFACE DRAG MODELING FOR MILLED SURFACES Division of Fluid Mechanics, KTH Author: Lars Johansson Supervisor at KTH: Jens Fransson Supervisor at GKN: Hans Mårtensson and Fredrik Wallin Summary One of the governing sources of energy loss in a modern day jet engine is attributed to surface drag. This energy loss can be divided into friction loss and to surface geometry loss. The friction loss is the shear stress the fluid experience due to a no slip condition at the wall, while the surface geometry loss is due to pressure drop when the fuel passes an obstacle. The objective of this work is to study the drag coefficient of a plate for different types of milled tracks and for different kinds of flow conditions. The theories used to calculate the drag coefficient are based on the momentum thickness theory including shear stress- and pressure integration. The computations were carried out with ANSYS CFX assuming a Shear Stress Transport � − � turbulence model. The steady state flow conditions tested are varying boundary layer thicknesses, milled track heights, milled track widths, Reynolds numbers over the milled track height, Reynolds numbers over the plate length and free-stream angle of attack. By knowing what affects the drag coefficient for different types of milled tracks, more practical models can be developed making the prediction of surface drag inside the jet engine more accurate. This report has resulted in a formula that predicts the drag coefficient for different types of milled surfaces. The formula is derived from the assumption that the CFD results on ANSYS CFX are correct. A physical test has not been made to verify those results, however this has to be done to prove that this formula is valid. Preface This master thesis in the field of fluid mechanics is done with the help of GKN Aerospace. I would like to thank the people involved in my master thesis and to thank all people around me at GKN for all the help I have received. I would specially thank my two supervisors Hans Mårtensson and Fredrik Wallin at GKN who have given me the support and knowledge to make this thesis possible and for the help they have offered me during this project. I would also like to give my gratitude and appreciation to my supervisor Jens Fransson at KTH for all the help and support I have received throughout this project. Trollhättan, June 2015 Lars Johansson Nomenclature U = Free stream velocity [m/s] ν = Kinematic viscosity [m2/s] �= Shear stress by the wall [Pa] y = Height of plate [m] � = Density [kg/m3] � = Length of plate [m] h = Boundary layer thickness [m] u = Velocity distribution along the stream line [m/s] �!= Profile height (cusp height) [m] �! = Distance between the milled tracks [m] � = Radius of the miller tool [m] �!= Total pressure [Pa] � = Static pressure [Pa] � = Boundary layer thickness [m] �! = Displacement thickness [m] �! = Momentum thickness [m] ∆�!= First layer thickness of the mesh �!"#$= Velocity at the disturbance body [m/s] � = Cusp angle on the milled tracks [˚] �!"!#$%= Momentum loss [kg*m/s] � = width of test plate [m] � = Total length of plate [m] � = Cusp angle [˚] � = Free stream angle of attack [˚] Contents Summary ................................................................................................................................................. 8 Preface .................................................................................................................................................... 9 Nomenclature ........................................................................................................................................ 10 1. Introduction ......................................................................................................................................... 1 1.1 Background ................................................................................................................................... 1 1.2 Purpose .......................................................................................................................................... 1 1.2 Thesis question .............................................................................................................................. 1 1.3 Limitations .................................................................................................................................... 2 2. Theory ................................................................................................................................................. 3 2.1Milled tracks .................................................................................................................................. 3 2.2 Momentum thickness �2 ............................................................................................................... 4 2.3 y+ determination ........................................................................................................................... 6 2.4 SST k-� turbulence model ............................................................................................................ 8 2.5 Effect of pressure gradient ............................................................................................................ 8 2.6 Effect of flow separation ............................................................................................................... 9 2.7 Drag coefficient ........................................................................................................................... 11 2.7.1 Momentum thickness �2 ...................................................................................................... 11 2.7.2 Force integration .................................................................................................................. 12 2.8 Effective dynamic pressure ......................................................................................................... 13 3 Method ............................................................................................................................................... 15 3.1 Geometry ..................................................................................................................................... 15 3.2 Mesh ............................................................................................................................................ 16 3.3 Pre-process .................................................................................................................................. 18 3.3 Post process ................................................................................................................................. 19 4. Result ................................................................................................................................................ 19 4.1 Varying � .................................................................................................................................... 19 4.2 Varying ��� ................................................................................................................................ 20 4.2 ��� dependence .......................................................................................................................... 22 4.3 Varying free stream angle of attack � ......................................................................................... 25 5. Conclusion ........................................................................................................................................ 29 6. Future work ....................................................................................................................................... 33 7. Reference .......................................................................................................................................... 34 8. Appendix ........................................................................................................................................... 35 8.1 Theory ......................................................................................................................................... 35 8.1.1 k-� model ............................................................................................................................ 35 8.2 Method ........................................................................................................................................ 37 8.2.1 Boundary conditions ............................................................................................................ 37 8.3 Results ......................................................................................................................................... 42 8.3.1 Varying inlet boundary thickness � ...................................................................................... 42 8.3.2 Varying � and ��� .............................................................................................................. 42 8.3.3 Varying ��� and ��� .......................................................................................................... 47 1. Introduction 1.1 Background One of the fundamental loss sources in a modern day jet engine is loss due to surface drag. Surface drag loss can be divided into friction loss and loss due to surface geometries. The friction loss is the shear stress the fluid experience due to a no-slip condition at the wall, while the surface geometry loss is