2009:107 CIV
M A S T E R ' S T H E S I S
Local and Global Deviations on Outlet Guide Vanes in a
Turbine Rear Frame
Johan Fjällman Thomas Liljerås
Luleå University of Technology MSc Programmes in Engineering
Space Engineering
Local and Global Deviations on Outlet Guide Vanes in a
Turbine Rear Frame
Johan Fjällman and Thomas Liljerås Volvo Aero Corporation Luleå University of Technology
March 25, 2009
Contents
1 Introduction 2
2 Nomenclature 3
3 Problem Statement 5
4 Approach 6
5 Theory 7
5.1 Solver Models . . . 7
5.2 The Y+ Value . . . 9
5.3 Mesh Dependency . . . 10
5.4 Verification of Simulation Results . . . 10
6 Method 11 6.1 Mesh . . . 11
6.1.1 Y+ . . . 11
6.1.2 Mesh Dependency: . . . 12
6.2 Solver . . . 13
7 Geometry 14 8 Model and Boundary Conditions 16 9 Reference Case 17 10 2D 18 10.1 Local Deviations: Bumps . . . 19
10.1.1 Large Bumps . . . 20
10.1.2 Aggressive Bumps . . . 23
10.2 Global Deviations: Angles . . . 24
10.3 Mixed Deviations: Bumps and Angles . . . 25
10.4 Cascade . . . 25
11 3D 26 11.1 Local Deviations: Bumps . . . 27
11.2 Global Deviations: Angles . . . 28
11.3 Global Deviations: Surface Roughness . . . 28
11.4 Global Deviations: Vane Thickness . . . 30
12 Boundary layer 32
12.1 Method . . . 33
12.2 Compare Boundary Layers in 2D and 3D . . . 33
12.3 Boundary Layer Results . . . 34
13 Results 35 13.1 2D Results . . . 36
13.1.1 Local Deviations: Large Bumps . . . 36
13.1.2 Local Deviations: Aggressive Bumps . . . 37
13.1.3 Global Deviations: Angles . . . 38
13.1.4 Mixed Deviations: Bumps and Angles . . . 42
13.1.5 Cascade . . . 46
13.1.6 2D Conclusions . . . 49
13.2 3D Results . . . 50
13.2.1 Local Deviations: Aggressive Bumps . . . 50
13.2.2 Local Deviations: Large Bumps . . . 51
13.2.3 Global Deviations: Angles . . . 54
13.2.4 Global Deviations: Surface Roughness . . . 54
13.2.5 Global Deviations: Vane Thickness . . . 56
13.2.6 Mixed Deviations: Bumps and Angles . . . 58
13.2.7 Cascade . . . 58
13.2.8 3D Conclusions . . . 60
14 Thesis Conclusions 61 15 Future Work 63 15.1 Lower Length Scales and Turbulence Intensity . . . 63
15.2 Deviations with Increased Velocity . . . 63
15.3 The Friction Force Behavior . . . 63
15.4 Realized Pressure Loss . . . 63
15.5 Trailing Edge Pressure Loss . . . 65
Appendices I
A 2D Index Point Locations I
B Simulation Data II
B.1 Local Deviations . . . III B.2 Global Deviations . . . VI B.3 Mixed Deviations . . . XI B.4 Cascade . . . XIV
Abstract
The Turbine Rear Frame is the part made for mounting the engine onto the aircraft wing and to deswirl the airflow. The basic construction of the TRF is inner hub, outer shroud and a number of vanes that connects the hub and shroud.
During production of these items deviations will occur that will affect the per- formance. The purpose of this thesis work was to evaluate these effects and find correlations between disturbances and their effect on performance. The most important parameter is the pressure loss increase. The deviations that were examined included local disturbances, global disturbances and combinations of both. The local deviations consisted of small and large bumps, global ones included change of inlet angle, vane rotation angle, surface roughness, vane thickness and relative offset between vanes. All cases were examined with 2D and/or 3D simulations.
Results:
1. Change of vane rotation angle had a negative effect on the pressure loss and outlet angle.
2. The change in relative offset between vanes show no indications of being a problem for the pressure loss.
3. The Cd values, from the simulations, can be used to estimate arbitrary bumps’ and thickness changes’ effect on the pressure loss.
4. The surface roughness had to reach higher values than normal, for this manufacturing method, for it to induce any noticeable pressure losses.
1 Introduction
The Turbine Rear Frame (TRF), as General Electric calls it (Rolls Royce calls it Tail Bearing Housing and Pratt & Whitney’s name for it is Turbine Exhaust Casing), is the part downstream of the last turbine stage, see figure 1. The TRF is used for mounting the engine onto the aircraft wing and to deswirl (remove the angular component) the outgoing flow. With the increasing demands of fuel efficiency, all parts of the engine has to be optimized with this in mind. In the production of the parts, deviations such as surface roughness, small bumps, offset between adjacent vanes, change in vane thickness and change in vane angle can occur. These deviations will affect the flow properties in different ways.
For example:
Increase the pressure loss.
Increase the air stream turning angle.
Induce separation on the vane.
Etc...
In this thesis work both local (e.g. bumps) and global (e.g. angles) deviations have been studied.
2 Nomenclature
Latin letters
A [m2] Area
C [m] Chord of the vane
Cd [-] Drag coefficient
Cf [-] Friction coefficient
Cp [-] Pressure coeficient
Cp [J/(kg · K)] Specific heat constant
D [m] Diameter
k [m2/s2] Kinetic energy P, Ps, Pstat [Pa] Static pressure
Pdyn [Pa] Dynamic pressure
P0, Ptot [Pa] Total pressure
Re [-] Reynolds number
S [-] Shape Factor
vx [m/s] X-velocity
vy [m/s] Y-velocity
vz [m/s] Z-velocity
v∞ [m/s] Free stream velocity
Greek letters
α [◦] Angle
δ∗ [m] Displacement boundary layer thickness θ [m] Momentum boundary layer thickness τ [Pa] Wall shear force
µ [kg/(m · s)] Dynamic viscosity ρ [kg/m3] Density
² [m2/s3] Turbulent dissipation rate ω [-] Pressure loss coefficient
Abbreviations
BC Boundary Condition
CFD Computational Fluid dynamics FEM Finite Element Method
LE Leading Edge
LHR Length to Height Ratio OGV Outlet Guide Vane SST Shear Stress Transport TBH Tail Bearing Housing TE Trailing Edge
TEC Turbine Exhaust Casing TRF Turbine Rear Frame WLR Width to Length Ratio
Subscripts
design Design plane, 0.8C behind the TE in Inlet plane
max Maximum value min Minimum value
out Outlet plane, 0.9C behind the TE ref Reference case value
t Turning
3 Problem Statement
The problem statement was to investigate the effects of different deviations on an Outlet Guide Vane (OGV).
Local Deviations:
• Find a simple connection between bump height, width, length and the pressure loss.
• Can boundaries be set when a bump no longer can be considered as a local disturbance?
Global Deviations:
• How much can a vane be offset before the flow around the vane start to separate?
• How does the vane angle affect the performance?
• How does the vane angle affect adjacent vanes?
• How does surface roughness affect the performance?
Combined Deviations:
• Does the bump’s effect on pressure loss and flow separation vary with incidence/rotation angles?
• How will the Reynolds number affect the boundary layer thickness?
4 Approach
This thesis study was divided into several parts (which can be seen below), the first two parts builds up the basic knowledge needed (literature and software).
The next two parts was to validate the mesh and solver settings to be used in the parts that followed (2D, 3D simulations). All these parts were then put to use in the last bit where the results and conclusions were made.
Literature studies Comparing theory and boundary conditions with similar cases found in literature and on the Internet.
Software studies (ICEM and Fluent) Learning the software needed for the thesis work according to recommendation and earlier studies.
Mesh dependency investigation The mesh resolution’s effect on the results was investigated and the most time efficient one was chosen.
Solver dependency studies The different solver methods were studied and their effect on the results was deduced.
2D: Simulating 2D models with different bumps, angles, boundary layers and Reynolds numbers.
2D-Cascade: Expanding the 2D simulation for global deviations such as vane rotation angles and vane offset.
3D: Investigating the 3D effects of bumps, angles, boundary layers, Reynolds numbers, vane thickness and surface roughness.
3D-Cascade: 3D correlation for the global deviations considering vane rota- tion angles and vane offset.
Conclusions Results and conclusions drawn from the 2D and 3D simulations.
5 Theory
There is no obvious choice when it comes to turbulence models, no model is superior in all areas. The choice that has to be made comes down to weighing certain key factors, such as available computational resources, time, Reynolds number, separation probability and level of accuracy required. Following infor- mation can be seen unedited at [2].
5.1 Solver Models
To be able to do the simulations a turbulence model had to be chosen, below follows descriptions of the ones that were under consideration.
The k-² realizable (k-²-re) model is a version of the standard k-² model pro- posed by Launder & Spalding. The k-² model is a semi empirical model, and the derivation of the model relies on phenomenological considerations and empiri- cism. It is a well proven and widely used model because of it’s robustness, time efficiency and reasonable accuracy for a wide range of flows. Realizable means that the method satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows. The Realizable version of this model has another formulation for the turbulent viscosity. As well as a new transport equation for the dissipation rate, ², that has been derived from an exact equation for the transport of the mean square vorticity fluctuation.
Pro:
• Improved precision relative to the standard model in predicting the spread- ing of both planar and round jets.
• Likely to perform superiorly for flows involving rotation, boundary layers under strong adverse pressure gradients, separation and recirculation
• Conservative when it comes to predicting pressure losses.
Contra:
• k-²-re is prone to under predict separation.
• It can produce non physical viscosities when the computational domain contains both stationary and rotating fluid zones.
The k-ω Shear Stress Transport (k-ω-SST) model which was developed by Menter, is a variation of the Standard k-ω model. The standard k-ω model was developed by Wilcox and is a two-equation model, meaning it accounts for history effects when calculating the turbulence energy (for example dissipation and convection). It is also modified to handle low-Reynolds-number effects, shear flow spreading and compressibility. It is good at predicting the free shear flow spreading effects (numbers converge with measurements for far wakes, mixing layers and different kinds of jets (plane, round and radial)). All this makes the k-ω model good for wall-bounded and free shear flows. The SST variation of Wilcox k-ω model includes an accurate description of the far fields’
free stream effects derived from the k-² model.
Pro:
• The k-ω-SST model is valid for a great variety of flow cases.
• The definition of the turbulent viscosity is modified to account for the transport of the turbulent shear stress.
• Conservative at predicting separation, which makes it good at simulating off-design separation.
• Predicts separation too early during on-design simulations (Conserva- tive).
Contra:
• Will under predict pressure losses.
• Predicts separation too early during on-design simulations (Too conser- vative?).
The Spalart-Allmaras (S-A) model is a one-equation model that solves the kinematic eddy viscosity transport equation. It is a relatively simple equation that has been designed for use in aerospace applications with wall-bounded flows, the model is good in predicting boundary flows subjected to adverse pressure gradients. The equation is of a new class that removes the necessity to calculate a length scale for the turbulence related to the local shear layer thickness. The S-A model is basically a low Reynolds model that requires a well resolved boundary layer.
Pro:
• In Fluent the S-A model has been complemented by automatically using wall functions when the boundary layer resolution is not fine enough, this makes the model quick when it comes to rough meshes where boundary layer accuracy is not a main concern.
• The S-A model is less prone to be effected by numerical errors when the near-wall mesh is not resolved enough, this is because the transport variable in the S-A model has much smaller near-wall gradients than the transport variable in the k-² model.
Contra:
• The S-A model is a new model and because of this it has not been tested enough to be considered validated for all sorts of complex turbulence cases.
• Being a one-equation model it is missing the ability to compensate for quick changes in length scales, which is a key factor when the flow moves quickly from a near-wall flow to a free-stream flow.
• The model is unreliable in predicting the decay in homogeneous isentropic flows.
5.2 The Y+ Value
Y+ is a value that is used to check how fine the mesh is in the boundary layer region, a low Y+ value (less than 1) means that the mesh is well resolved and can be used in conjunction with a low Reynolds model (e.g. k-²-re with enhanced wall treatment). For a mesh with a high Y+ value (30+) the mesh is well adapted to be used with a high Reynolds model (e.g k-²-re with standard wall functions). Equations (1) and (2) shows how the Y+ is calculated.
Y + = ρuτYP
µ (1)
uτ = rτw
ρw
(2)
YP = Distance from the wall to the point P.
ρ = Fluid density.
ρw = Density at the wall.
τ = Frictional force at the wall.
5.3 Mesh Dependency
Finite element simulations are used to simulate reality with a limited number of values. The best simulation result should then be obtained by using an infinite amount of values giving a result infinitely close to the real case. In reality there has to be some limitations set when an increase in the mesh resolution no longer can be considered justified, simply put ”When the increase in precision between two resolutions is not large enough to be considered important for the results”.
When this level of resolution is reached the simulation can be considered mesh independent.
5.4 Verification of Simulation Results
The results of the simulations are dependent on different factors; the choice of solver, the Y+ value and the mesh resolution. All these factors will affect the results in different ways; the solver will determine which equations Fluent will use and what variables to use in the those equations. The Y+ value will determine how well Fluent calculates in the boundary layers, up to a certain level more calculation points usually means higher precision. The mesh resolu- tion will mainly affect the calculation time, it will also determine how accurate Fluent calculates, as more cells means there are more calculations performed for each path line.
6 Method
In this thesis work the time, stability, precision in pressure loss prediction and ability to handle wall/free stream flow transitions well were of importance.
The simulation time was a factor since there would have to be a large amount of simulations performed in both 2D and 3D. Stability is always sought after because running a large number of simulations for a great amount of iterations it is not desired for the simulations to crash due to instabilities caused by e.g. a poor initial condition setup. This thesis work is based upon calculating the losses (pressure and outlet angle) a TRF encounters when deviations are introduced on the vanes. The pressure loss is an important factor, therefore the precision in predicting it is important in the choice of method. Since the geometry of the simulation and of the actual TRF is requiring the solver to be able to calculate the wall/free stream flow transition properly, the model with the transition equations that gives the smallest error is preferable.
6.1 Mesh
6.1.1 Y+
The different Y+ values for the different groups of simulations can be seen in table 1. For the simulations using k-²-re EhWT, the Y+ should be smaller than 1, although this is mostly true, that limit is exceeded at times (see the right column in table 1). For the cascade setup it would not be practical to use the same resolution, as for the single vanes, for the reason that the computation time would be approximately multiplied by a factor of 5. This goes for both the 2D and 3D cases and therefor the Y+ value is slightly higher for these cases.
The Reynolds simulations are all performed with the same mesh resolution but with different Reynolds number (varied either by speed or viscosity), these variations leads to a change in Y+ when the wall shear stress changes but the grid size remains the same.
The exception (to the single vane mesh setup) is for the surface roughness simu- lations, because of the way Fluent treats surface roughness they are performed by using standard wall functions. These meshes then have a higher Y+.
Table 1: Y+ values measured during post-processing Simulation Solver Recommended Y+ Measured Y+
2D-normal k-²-re EhWT <1 <0.4
2D-cascade k-²-re EhWT <1 <0.7
2D-Reynold’s k-²-re EhWT <1 0.12 - 3.2
3D-normal k-²-re EhWT <1 <0.9 (side 1.4) 3D-cascade k-²-re EhWT <1 <1.4 (side 1.9)
3D-Reynold’s k-²-re EhWT <1 0.22 - 1.9
6.1.2 Mesh Dependency:
To easily be able to modify the mesh size an original mesh resolution was set and then that resolution was multiplied by a factor of 2, 3, 4 and 5. This means that with the factor 2, all cells had their sides split in 2. So the number of cells was multiplied by the factors 4, 9, 16 and 25. The total pressure fraction in the wake (figure 2), Cp on the wing (figure 3) and the pressure losses (see equation 3) for both solver and mesh dependence (table 2) are shown below. The figures below show that already at the factor of 2, the results are sufficiently good to be considered mesh independent.
Ploss= P0,in− P0,design
Pdyn,in · 100 (3)
Figure 2: Mesh dependency wake profiles at 0.8 chord behind the trailing edge.
Table 2: Pressure losses for the different solvers, 0.8 chord behind the trailing edge.
Simulation Pressure loss [%] Simulation Pressure loss [%]
k-²-EhWT (1x) 2.848 k-²-EhWT (2x) 2.839
k-²-EhWT (3x) 2.846 k-²-EhWT (4x) 2.832
k-²-EhWT (5x) 2.862 k-ω-SST 2.422
Spalart-Allmaras 3.333 k-²-StWF 2.834
Figure 3: Mesh dependency Cp profiles.
6.2 Solver
According to the criteria describe in the Method chapter the solver selected for this project was set to k-²-re with enhanced wall treatment (k-²-re EhWT).
It is a good, fast and robust model. It has been validated to give very good results when comparing pressure loss and separation between simulations and wind tunnel tests (as can be seen in figures 4 and 5).
Figure 5: Solver dependency Ps
Pdyn profiles.
7 Geometry
The OGV geometry chosen for the simulations is the same as used by Hjärne [3].
The reason for this is that the vane is tested in a rig and has comparable data.
In the first part of this report the vane will be examined in 2 dimensions while varying different parameters. This will be performed with a single vane with periodic conditions on the top and bottom part and with a 5 vanes cascade, where the top and bottom part has periodic conditions (Geometries can be seen in figures 6 and 7). The single vane setup is mainly used for simulating local deviations and the cascade setup is used for global deviation studies.
To correlate with the 2D results, all of these and a few additional parameters (see sections 10 and 11) will be examined in 3 dimensions as well (where global deviations are being examined in the single vane setup as well as in the cascade setup). The 3D setup will be an extension of the 2D setup along the Z-axis with a given length as the figures 6 and 7 show.
(a)
(b)
Figure 6: 2D (a) and 3D (b) normal setup.
(a) (b)
8 Model and Boundary Conditions
For comparison and correlation of the results with previous simulations and validations the Hjärne [3] boundary conditions were used. The inlet condition was set to ”Velocity Inlet” with constant velocity of 20m/s and a flow angle of 30◦ across the entire inlet. The outlet was set to ”Pressure Outlet”. The top and bottom sides were set to ”Periodic” and the vane (and sides in 3D) was set to no slip ”Wall”. All boundary conditions can be seen in figure 8. The calculations were made with a constant density and incompressible flow.
Figure 8: Boundary conditions.
Figure 9: Design and outlet plane.
9 Reference Case
For all of the different setups a smooth vane reference case is simulated. It will be called the reference case. Not just one case is used because the different setups were calculated with substantial differences, e.g. the 3D case will have sides that will introduce frictional losses when the 2D case have not. The velocity contour plot for the 2D reference case is shown in figure 10.
The important variables being measured and monitored during simulations and post-processing were:
Cp-plots on the vanes.
P0-wake plots on the design plane, 0.8 chord behind the trailing edge (see figure 9).
Cf-plots on the vanes (to monitor separation).
Pressure loss coefficient from the inlet to the design plane (equation (3)).
The airflow angle at the outlet plane.
Figure 10: Velocity magnitude contour plot for the reference case.
10 2D
To make it possible to run more simulations and altering more variables the first step in the simulation process was to start in a 2D environment. 2D also links well to global deviations, since it is the whole width of the vane that is being modified.
The first problem was to find out which variables to variate and to limit the amount of simulations. With the help of Supervisor Sofia, the variables to examine was identified and the list narrowed down to the following:
Local Deviations:
• Bump:
Height (0.5, 1, 2, 3... 9mm, see tables 3, 4 and 5).
Length (0.35 - 203mm, see tables 3, 4 and 5).
Shape (0.18 - 0.81, see tables 3, 4 and 5).
Global Deviations:
• Angle:
Incidence (1, 2, 3 ... 15◦ increase).
Vane Rotation (1, 2, 3 ... 15◦ increase).
• Reynolds Number Multiplier (See chapter 12).
Mixed Deviations:
• Bumps on Rotated Vanes (varying, see table 7).
Access was given to actual deviation data from manufacturing and the aerother- modynamics department, making it possible to find out some of the actual max dimensions for bumps found.
Since the interest was focused on worst case scenarios the dimensions found were increased and tested. This was performed in small steps to see when the flow around the vane started to separate and when pressure losses started to increase dramatically.
Staring with the basics, construction begun with 2D bump geometries.
10.1 Local Deviations: Bumps
The Bump category was divided into two subparts, small aggressive bumps and large bumps. The large bumps had a height between 1 and 9 millimeters and a length between 37 and 203 millimeters. The more aggressive bumps had heights at 0.5 and 1 millimeter and lengths between 0.35 and 20 millimeters (see table 5). The different variables to be examined in 2D were height, length and shape (see figure 11). Height is the bump’s maximum deviation from the reference vane in the surface normal direction. Length is the distance between the bump’s start and end point along the reference vane’s curvature. Shape is the distance from the starting point to the maximum height point (along the reference vane’s curvature) divided by the bump’s total length (equation (4)).
Length to height ratio (LHR) was also a variable of interest, LHR was defined as the length divided by the height of the bump (equation (5)).
A typical large bump geometry can be seen in figure 12, this bump is situated close to the suction peak with a height increase of about 12% of the maximum thickness.
Figure 11: An aggressive bump showing height, length and shape variables.
Figure 12: A 12% bump located close to the suction peak.
S = b
l (4)
LHR = l
h (5)
l = Length h = Height
S = Shape
10.1.1 Large Bumps
Large bumps with heights 1, 2 and 3 mm were first tested, several different lengths and shapes were used.
The vane’s suction side was divided into 12 regions (see figure 13), each point that separates two regions were given an index. This was performed to make it easy to keep track of and index simulations.
Figure 13: Zone reference and bump indexing.
Initially, the starting point of the bump did not change (point 11) and the variations were just applied to the height, shape and length. The first index (in table 3) is the starting point of the bump, the middle index is the location of the highest point and the last index is where the bump ends.
Table 3: Initial bump geometry, all available with heights 1, 2 and 3mm.
Index Length [mm] Shape Index Length [mm] Shape
11-12-13 37 0.46 11-13-21 203 0.18
11-12-14 57 0.30 11-14-15 81 0.70
11-12-15 81 0.21 11-14-17 127 0.45
11-13-14 57 0.65 11-15-17 127 0.64
11-13-15 81 0.46 11-16-21 203 0.50
11-13-17 127 0.29 11-19-21 203 0.81
To get comparable results between the different bumps each bump was con- sidered an obstacle with a projected area and a Cd that corresponds to the difference in pressure loss over the region. The suction side of the vane was divided into 2 zones, one for the area before and around the suction peak and one for the area after the suction peak as can be seen in figure 13. In both these areas, a maximum dynamic pressure was found and this pressure was used to calculate a Cd for the bumps (equation (6) and (7)).
Cd= Ain(∆Pbump− ∆Pref) PdynAproj
(6)
∆P = P0in− P0design (7)
∆Pbump = ∆P for a vane with bump.
∆Pref = ∆P for a smooth reference vane.
P0in = Inlet total pressure.
P0design = Total pressure at design point, 0.8 chord
behind the trailing edge.
Ain = Inlet area perpendicular to the flow.
Pdyn = Max dynamic pressure in the zone where the bump’s maximum height is located.
Aproj = Projected area of the bump.
Based on the results from these initial tests (see chapter 13.1 for detailed re- sults) it was decided that the worst case (regarding increased Ploss) is when the bump’s maximum height is located on the suction peak. This lead to the creation of more geometries where the bump’s starting point could be moved to new locations. This made it possible to keep the shape variations to a minimum while still varying the location of the maximum height point. By increasing the maximum height up to 9 mm the amount of comparable data grew significantly.
The new geometries that were created can be seen in table 4.
Table 4: Extra geometries.
Index Length [mm] Shape Available heights [mm]
11-12-13 37 0.46 4, 5
12-13-14 40 0.50 3, 4, 5
12-14-15 64 0.63 4, 5, 6, 7, 8, 9 13-14-15 44 0.45 3, 4, 5, 6, 7, 8, 9
14-15-16 44 0.55 3
All bumps tested so far had a length greater or equal to 37mm. Considering these bumps and their results (see chapter 13.1) the decision was made to test geometries that affected the flow more.
10.1.2 Aggressive Bumps
The aggressive bumps can be seen to simulate the effect of a thin ridge on the vane suction peak.
These bumps have a length shorter or equal to 20mm. The maximum height position was decided to be point 13 (the suction peak, as seen in figure 13).
The bump was positioned symmetrically around that point. Therefore it was possible to keep the shape of the bumps constant while varying the length and LHR. The aggressive bump geometries tested can be seen in table 5. An aggressive bump geometry can be seen in figure 14.
Table 5: Small bump geometries.
Length [mm] Height [mm] Shape
0.35 0.5, 1 0.50
0.7 0.5, 1 0.50
1.55 0.5, 1 0.50
3.6 0.5, 1 0.50
8 0.5, 1 0.50
20 0.5, 1 0.50
Figure 14: Geometry of an aggressive bump with length (l) 0.35mm and height (h) 1mm.
10.2 Global Deviations: Angles
The next step in the simulation process was to investigate the effect that dif- ferent angles had on the pressure loss. There were two different kinds of angles that were tested, change in incidence angle and change in vane rotation angle (see figure 15).
Changing the incidence angle mean that the inlet vx component was reduced while the vy component was increased as the angle increased. The vane rota- tion angle was changed by rotating the vane geometry. The reference inlet flow angle was 30◦ and the vane rotation angle was 0◦. The angles tested can be seen in table 6.
Figure 15: Rotation and Incidence angle change direction.
Table 6: Off design angles being tested.
Angles [◦] Method 1, 2, 3 ... 15 Incidence 1, 2, 3 ... 15 Vane Rotation
The incidence angle changes were performed by changing the inlet boundary conditions. The vane rotation angle was changed to see the effects of off-design cases and deviations from manufacturing.
10.3 Mixed Deviations: Bumps and Angles
Comparing the results from the bumped and angled simulations the need for testing mixed deviations was confirmed. The choice was made to test the old bump geometries (seen in tables 3 and 4) with different incidence angles. The test cases can be seen in table 7.
Table 7: Testing cases for incidence angles on bumped vanes.
Incidence angle [◦] Bump index Length [mm] Heights [mm]
5, 8, 10, 13 14-15-16 44 3
5, 8, 10, 13 11-12-13 37 3, 4, 5
5, 8, 10, 13 12-13-14 40 3, 4, 5
5, 8, 10, 13 12-14-15 64 4, 5, 6, 7, 8, 9 5, 8, 10, 13 13-14-15 44 3, 4, 5, 6, 7, 8, 9
10.4 Cascade
The simulations so far had had a periodic boundary condition on the top and bottom part of the geometry. This meant that all the vanes had the same deviation in the same place with the same height. This is an unrealistic as- sumption.
A question before these tests were performed was:
Is it possible to find a connection between the results (pressure loss, outlet angle, wake profile etc.) from having one deviated vane (single vane setup) and the results from one or several deviated vane(s) (cascade setup)?
To represent this possible interaction a cascade of five vanes was simulated (geometry can be seen in figure 7a on page 15). The cascade simulations will also give a way to simulate other global deviations such as vane offset. The parameters to be tested can be seen in table 8.
Table 8: 2D cascade test parameters.
Offset [%] Vane Rotation Angle 1st 2nd 3rd 4th 5th [◦]
0 0 0 0 0 0
1 0 0 5 0 0
2 0 0 8 0 0
4 0 0 10 0 0
5 0 5 7 5 0
10 0 5 9 5 0
Offset means that the maximum distance between the 3rd and 4th vane was decreased with 1 - 15 %.
After perfmoring the first set of vane rotation angle simulations (just changing the middle vane) it was deduced that it is probably the change in angles be- tween adjacent vanes that is the main reason for the pressure loss increase. This lead to the construction of the 0 5 7 5 0 and 0 5 9 5 0 vane angle geometries, where this theory was confirmed.
11 3D
The largest differences between 2D and 3D geometries is that in 3D the side walls have a no slip boundary condition (see figure 8) and that the bumps cre- ated in 3D are not ”infinitely” wide. The z-direction was increased as much as the y-direction was high, making the inlet (and outlet) cross-section square.
Since 3D simulations need a longer simulation time than 2D, a limited number of cases were to be tested. Testing cases in 3D were chosen with the 2D simu- lations as a base and so that it was possible to observe any 3D effects around bumps with a defined width. The cases in 2D that were on the limit of either passing or failing the pressure loss criteria (2ω0, i.e. two times the reference case pressure loss) were looked at.
The geometries for the 3D tests was chosen to resemble 2D geometries with a few alterations, the only angle change simulated is the vane rotation one (since those represents a deviation in manufacturing). Two new parameters were also introduced to be tested, the full list of testing parameters can be seen below:
Local Deviations:
• Bump:
Height (1 and 6mm).
Length (20, 40, 80 and 120mm).
Width (20, 40, 80, 120, 160 and 200mm).
Global Deviations:
• Angle:
Vane Rotation (5, 8 and 10◦).
• Reynolds Number (see chapter 12).
• Surface Roughness (see table 10).
• Vane Thickness (80, 90, 95, 105, 110 and 120% total thickness).
11.1 Local Deviations: Bumps
The first section to be tested in 3D was the same as in 2D, namely bumps. In 3D it is interesting to test how the 3D effects could help the flow separation to be postponed or to be reconnected. If the flow could reconnect again it would have a great effect on the pressure loss and the outlet angle. This means that the criteria for bump geometries might change to allow for higher bumps and/or larger bumps (length and width) before the flow separates. The bump geometries that were tested in 3D can be seen in table 9.
Table 9: 3D bump geometries.
Width [mm] Length [mm] Height [mm]
1 5 1
2 5 1
5 2, 5 1
20 40, 80 6
40 20, 40, 80, 120 6
80 20, 40, 80, 120 6
120 40 6
160 80 6
200 40, 80 6
The first four simulations were what can be called small aggressive bumps.
They all have their maximum height located just before the suction peak whereas the last 14 simulations have their maximum height located just af- ter the suction peak. An aggressive and a ”normal” bump can be seen in figure 16.
(a) Aggressive bump. (b) ”Normal” bump.
Figure 16: 3D bump geometries.
11.2 Global Deviations: Angles
The angle results from 2D all showed similar results, therefore only four differ- ent angles were tested in 3D. The angles tested were 0◦, 5◦, 8◦ and 10◦ vane rotation angle.
11.3 Global Deviations: Surface Roughness
One of the new parameters to be tested in 3D was surface roughness. During manufacturing the parts will receive a surface roughness, the typical roughness height depends on which manufacturing method is being used. The testing was performed with two assumptions;
1. Only a part of the vane was affected with roughness. This ”patch” of sur- face roughness was about 2% of the total OGV surface area and located on the suction peak, see figure 17.
Figure 17: Geometry for the Surface Roughness Patch cases.
The different cases tested are described in table 10, where:
ksis the equivalent sand roughness height.
Cs is the roughness constant.
Table 10: Surface roughness case setups.
Patch Whole Vane
Cs 25 50 75 25 50 75
ks 1 100 1 100 1 100 1 25 1 25 1 25
2 250 2 250 2 250 2 50 2 50 2 50
5 500 5 500 5 500 5 100 5 100 5 100
10 750 10 750 10 750 10 500 10 500 10 500
25 1000 25 1000 25 1000 50 1500 50 1500 50 1500
To simulate roughness in Fluent the mesh has to be adopted for Standard Wall Functions. The first cell closest to the surface can not have a shorter height than twice the roughness height. With a shortest mesh height of 3mm tests with roughnesses up to 1.5mm could be performed. The equations which Flu- ent uses are equation (8) to (11) from [4]:
u+= 1
κln y++ 5.45 − ∆B (8)
∆B =
0 k+s ≤ 2.25
1 κ ln
hk+s−2.25
87.75 + Csk+s
i sin
½
0.4258(ln ks+− 0.811)
¾
2.25 < ks+≤ 90
1
κ ln(1 + Csks+) k+s > 90
(9)
k+s = ρksu∗
µ (10)
u∗=qp
Cµk (11)
11.4 Global Deviations: Vane Thickness
Another deviation that is likely to occur is that the thickness of the vane can change in both positive and negative directions. To do these changes in the ICEM environment the vane was split into four parts. Leading edge (point 1-2), trailing edge (point 3-4), suction side (point 1-3) and pressure side (point 2-4). The leading and trailing edge were kept constant and the suction and pressure side was scaled according to figure 18.
The different simulation cases during this investigation can be seen in table 11.
Table 11: Thickness simulation cases.
Variable Cases
Top part [%] 80 90 90 95 100 100
Bottom part [%] 100 90 100 100 90 100 Total Thickness[%] 80 80 90 95 90 100 Top part [%] 100 105 110 110 120 Bottom part [%] 110 100 100 110 100 Total Thickness[%] 110 105 110 120 120
Figure 18: Suction and pressure side scaling for the vane thickness variations.
The change was normalized for the model, meaning that a 10% increase or decrease on any side would give a total change of 10% thickness. The choice of modelling it in this way was that the deviations during the manufacturing process is independant of which side it was adding to or reducing from. The absolute thickness increase or decrease would then be the same no matter which side that is modified.
11.5 Mixed Deviations: Bumps on Rotated Vanes
The major difference between 2D and 3D simulations for this part is that in 3D the whole vane was rotated in order to simulate global manufacturing deviations. The conclusions taken from 2D Bumps and Angles (see chapter 13.1.4) guided the simulation case choices in 3D (the cases can be seen in table 12).
Table 12: 3D cases for bumps on rotated vanes, 3mm bumps were angled 10◦ and 6mm bumps were angled 5◦.
Width [mm] Length [mm] Height [mm] Angle [◦]
20 40 3, 6 10, 5
40 40 3, 6 10, 5
80 40 6 5
80 80 3, 6 10, 5
11.6 Cascade
The 3D cascade setup had the same parameters as the 2D, offset and vane rotation angles were investigated. The 3D cascade simulation setup can be seen in table 13.
Table 13: 3D cascade simulation cases.
Offset [%] Vane Rotation Angle 1st 2nd 3rd 4th 5th [◦]
0 0 0 0 0 0
5 0 0 5 0 0
10 0 0 8 0 0
15 0 0 10 0 0
0 5 7 5 0 0 5 9 5 0
As offset had little to no importance for the pressure loss in 2D (see chapter 13.1.5) it was assumed the same would be true for 3D. Therefore, fewer offset cases were tested in 3D.
The assumption proved to be correct.
12 Boundary layer
To see how the varying Reynolds number affected the size and shape of the boundary layer and how this in turn affected the flow characteristics of differ- ent deviations, the effect of the boundary layer was thoroughly examined. A deviation with a height far less than that of the momentum boundary layer will have little or no effect on the flow, since the velocity that close to the wall is low compared to the free stream and thus cannot be decelerated much further.
This may have the unfortunate effect to under predict the severity of flow when it comes to deviations that are small compared to the momentum boundary layer thickness in the low velocity simulations. In reality the velocities in the structure will be far higher than the ones simulated, probably with a factor of 10 to 20. If the shape of the boundary layer can be assumed to be the same, for an incompressible flow the thickness will decrease with increasing velocity. Ac- cording to the v−1/5 it would be lowered with 35-45%. In reality, the pressure and temperature will also affect the viscosity.
12.1 Method
The stream situation in the simulation lacked real free stream conditions every- where. Therefore the velocity distribution was calculated by using isentropic velocities. The velocity was calculated by using equation (12), the pressure used in the equation was the difference between P0 at every point and P0 at the wall.
The data points where collected along lines perpendicular to the surface. In the 3D case the lines where positioned at the mid span.
v = s
2(P0− P0,wall)
ρ (12)
The boundary layer thickness values were calculated using equations (13) and (14).
δ∗=
Z lv,max
0
1 − v vmax
dl (13)
θ =
Z lv,max
0
v vmax
µ 1 − v
vmax
¶
dl (14)
l = Distance from the wall.
lv,max = Distance from wall at position of maximum velocity.
θ = Momentum boundary layer thickness.
δ∗ = Displacement boundary layer thickness.
12.2 Compare Boundary Layers in 2D and 3D
The thickness of the boundary layer was calculated both in the 2D and 3D case.
The expectation for the thickness was that it would correlate well between 2D and 3D and this was confirmed. It was also compared to the ideal case with a simple flat plate in both 2D and 3D and a simple equation for the thickness.
All this can be seen in figure 19 where the blue and black lines are representing the simulated case, the green and yellow lines being simulated flat plates and the red crosses are the values of the thickness according to equation 15 from [5].
Figure 19: Momentum boundary layer thickness, vin = 20 m/s
As shown in figure 19, Fluent seems to be able to simulate the boundary layer well since the flat plate is close to the equation values. Another positive thing is that the 2D and 3D behavior is similar.
12.3 Boundary Layer Results
For the reference case, around the suction peak, the momentum boundary layer thickness is 0.07 - 0.2mm. All bumps are higher than this, which leads to the conclusion that the bumps should have a similar behavior at higher Reynolds number since the largest part of the bump is above the momentum boundary layer in the ideal case.
The situation where the boundary layer thickness difference between reality and the test case will have a direct effect, is when the deviations are in the same size range as the momentum boundary layer thickness. This is not a problem for the bumps, but it is in the case of surface roughness. A decrease in thickness means that the maximum Ra value that can still be considered hydraulically smooth will be decreased, i.e. the surface roughness height may exceed the boundary layer thickness.
13 Results
To check that all residuals had converged, contour plots of pressure, velocity etc were checked for unexpected behavior. Fluent was then used to write all data that was to be processed into files for further use in Matlab. Typical data were such as pressure and velocity on the OGV’s, pressure and velocities on the inlet, outlet and design cross sections.
Matlab was chosen as post-processing tool since it is easily obtained and con- tains powerful tools for handling large amounts of data and plots. Excel was also used as a compliment to Matlab since the overview when observing a lim- ited number of values is superior in Excel compared to Matlab. The graphical aspects of Excel is also useful when quick plots are of interest.
The investigated parameters and their equations can be seen in table 14.
Parameter Equation/Explanation
Cp P0,in−Pstat,vane
Pdyn,in
Cf τvane
Pdyn,in
Wake P0,design
P0,max,design
Ploss
P0,in−P0,design
Pdyn,in ·100
αout arctan µvy,out
vx,out
¶
Cd
Ain(∆Pbump−∆Pref) PdynAproj
Table 14: Investigated parameters and their equations.
The pressure loss increase that have been induced (in the different simulation cases) is always referred to as an increase from the reference case (i.e. 50%
pressure loss increase equals 50% more losses than in the reference case).
13.1 2D Results
The initial work for this thesis project was performed in a 2 dimensional envi- ronment. The short simulation times were a great help when investigating all the possible case parameters to find the separation and pressure loss (e.g. 2ω0) margins.
13.1.1 Local Deviations: Large Bumps
The large bumps with heights up to 3mm, which are described in table 3 and 4 on page 21 and 22, all had Cd:s below 0.1 with values generally increasing with increasing height for the same bump index (data can be seen in appendix B.1 table 20 and 21a). Only one bump of the 1 and 2mm bumps had any kind of separation and that one reconnected on the vane again. Six of the 3mm bumps had some sort of separation but all flows reconnected. None of the bumps with a height up and equal to 3mm induced a pressure loss increase of 10% or more (compared to the reference case). The bumps from 4mm and up all said the same thing, the higher the bump the larger the pressure loss (as shown in figures 20 and 21). Bumps with a height ≥7mm does not reconnect.
Figure 20: Relationship between ω
and h for different bump indexes, Max is
Figure 21: Relationship between ω
ω0 and h for different bump indexes (zoomed), Max is the index for the maximum height position.
13.1.2 Local Deviations: Aggressive Bumps
The aggressive bumps generated heavy disturbances caused by their extreme shape. The two bumps with the longest lengths (8 and 20mm) were the only aggressive ones that did not separate at all. The remaining aggressive bumps all induced separation directly after the bump, but for many of the cases the flow reconnected. The cases with no reconnection was the 1mm bumps with a length between 0.35 - 1.55mm. The pressure loss for the aggressive bumps is shown in figure 22. Simulation data can be seen in appendix B.1 table 21b.
Figure 22: Relationship between ω
ω0 and h for different bump indexes.
13.1.3 Global Deviations: Angles
The incidence angle and the vane rotation angle simulate different situations therefore, they give different results. Changing the incidence angle is the same as if the flow into the TRF is changed, while changing the vane rotation angle is equal to having a deviation on the TRF where the vane is turned slightly out of alignment. Changing the incidence and vane rotation angle effects the outlet flow angle first and the pressure loss second. When the incidence angle is changed (i.e. the angle the air flow has when it enters the TRF) the out- let angle is not affected as much as when the vane rotation angle is changed.
Though separation is induced at lower angles. For changes up to 10◦ none of the angle change methods predicts separation. Separation occurs at 11◦ for incidence angle change, where for the vane rotation method separation does not occur at all for angles up to 15◦.
Looking at the air flow turning angles, in figure 23, the difference between incidence and vane rotation can be seen. For the vane rotation 1◦ change in rotation angle equals around 1◦in out angle, all the way up to 12◦. For 13◦the change is less than 13◦ (i.e. the change in out angle per rotation angle is now less than 1◦). The incidence angle curve has a maximum turning angle when the incidence angle has been changed 13◦ after that the outlet angle decreases as the incidence angle increases. This can be explained by the fact that the flow separates around the vane (starting at 11◦ where the curve starts to dampen).
Separation causes the vane to have less effect on the flow and therefore the outlet angle is less affected.
Figure 23: Turning for incidence and rotation angle changes in 2D.
Both angle changing methods start to induce pressure loss increases above 10%
when the changes are above 5◦. For both methods the pressure losses are sim- ilar until the angle changes over 10◦(i.e. when the incidence angle simulations starts to separate, see figure 24).
Figure 24: Relationship between ω
ω0 and angle.
For the vane rotation cases the highest pressure loss increase was 49% (for 14◦, the 15◦ case does not have good enough residuals). The indidence simulations pressure loss increases were measured at up to 165% for 15◦. Pressure losses just before separation was 33% for 10◦ incidence angle. For the vane rotation angles there are no cases that separates. Cf plots for 10◦, 11◦ and 12◦ inci- dence angle is shown in figures 25 to 27. Cf is calculated using equation (16), a negative Cf means that separation has occured.
Simulation data can be seen in appendix B.2 table 23 and 24.
Cf = τ · τx
|τx|
Pdyn,in (16)
τ = Wall shear force.
τx = Wall shear force, in x-direction.
Figure 25: Cf plot for 10◦ off design incidence angle. Case has not separated.
Figure 26: Cf plot for 11◦ off design incidence angle. Case has separated.
Figure 27: Cf plot for 12◦ off design incidence angle. Case has separated.
13.1.4 Mixed Deviations: Bumps and Angles
Combining incidence angles with bumped vanes increases the vane’s tendencies to separate. Comparing incidence angles with vane rotation angles the differ- ences are small for small angles. Therefore the assumption that the behavior for both vane rotation and incidence angles should be the same is drawn. The
ω
ω0 relationship would mainly be scaled differently, since the turning angle is larger for vane rotation. In figure 28 the relationship between incidence angles and bumps, considering pressure loss and separation at small angles, is shown.
To get the same behavior as the figure shows it is appropriate to multiply the pressure losses according to equation (17).
When considering the outlet angle no easy connection can be seen, the outlet angle does not change much from the unbumped vane to the bumped vane as long as the flow has not separated. Just increasing the incidence angle gives a positive turning angle change whereas adding a bump to a vane usually induces a negative change in turning angle. Considering this it can be appropriate to subtract the 0◦bumped vane angle change from the unbumped incidence vane (equation (18) and figure 29).
ωa
ω0 ≈ωab
ωb ⇔ ωab≈ ωaωb
ω0 (17)
ω0 = Pressure loss for smooth vane (reference case).
ωa = Pressure loss for vane with incidence angle change.
ωb = Pressure loss for bumped vane, no incidence angle change.
ωab = Pressure loss for bumped and angled vane (incidence).
Figure 28: Relationship between incidence angles and bumps, black line is the reference case.
αt,ab≈ αt,a− (αt,0− αt,b) (18)
αt,0 = Turning angle for smooth vane (reference case).
αt,a = Turning angle for vane with incidence angle change.
αt,b = Turning angle for bumped vane, no incidence angle change.
αt,ab = Turning angle for bumped and angled vane (incidence).
Figure 29: Relationship between incidence angle and turning angle, black lien is the reference case.
Equation (17) and (18) are only valid when the flow reconnects, if it separates.
Although these equations are not 100% correct they do come very close.
The Cp curves for a bump with the same index (12-13-14) as the one shown in figure 12 can be seen for different incidence angles together with the reference case in figure 30. The wake plots for the same bump and the same incidence angles can be seen together with the reference case in figure 31.
As shown in the figures, the reference case and the bump with no incidence angle only have local differences in the Cp curve around the bump’s position.
They coincide with each other well along the vane except for the area around the bump. The airflow around the vane does not separate at low incidence angles but when the angles increases the difference between the reference case and the bumped and angled vane increases. Separation occurs at angles 10◦and 13◦, therefore their Cp curve differences are larger, compared to the reference case.
In the wake plots the increase of incidence angles will move the wake to the left in the figure (towards the top part in the geometry) and also cause the wake to deepen. This is caused by a local reduction in P0(which means that the energy has been lost due to turbulence). The deepening of the wake also means that the outlet angle has been increased as an effect of the flow separating around the vane. Simulation data can be seen in appendix B.2 table 28 and 29.
Figure 30: CP curve for the 12-13-14 4mm bump with different incidence angle and the reference case (black dotted line is the reference case).
Figure 31: Wake profile plot for the 12-13-14 4mm bump and the reference case with different incidence angles, 0% height is at the top of the geometry (see figure 12) (black dotted line is the reference case).
13.1.5 Cascade
When changing the offset for the 2D cascade case the difference in pressure loss and outlet angle are small, Cp curves for all the five vanes is shown for offset in figures 32 - 36.
Figure 32: Cp for vane 5 with vane 3 having an offset of 0, 5, 10, 15%.
Figure 33: Cp for vane 4 with vane 3 having an offset of 0, 5, 10, 15%.
Figure 34: Cp for vane 3 with vane 3 having an offset of 0, 5, 10, 15%.
Figure 35: Cp for vane 2 with vane 3 having an offset of 0, 5, 10, 15%.
The Cp curves for all the vanes proves the assumption that the effects of offset deviations are local. It only affects the vane itself (vane 3 in this case) and the two closest ones (vanes 2 and 4). The rest of the TRF will remain unaffected.
The Cp differences are small and according to the pressure loss (table 15) the increase is in the range of parts per mille.
Table 15: Pressure loss for the 2D cascade offset simulations.
Offset ω ω0
0 1
5 1.001
10 1.002 15 1.003
The other part of the cascade simulations was to change the vane angles for the middle vane and for the two vanes closest to the middle vane. The results from the simulations when only changing the middle vane’s rotation angle (table 16) gave a theory that it is not the individual vane’s angle that is of importance for the separation and pressure loss, it is the relative vane angle change between two adjacent vanes.
Simulating this condition as well proved the theory correct. Changing the two closest vanes 5◦ did make the pressure loss go down and separation did not occur, however the outlet angle increased as an effect of this. Simulation data can be seen in appendix B.4 table 31a
Table 16: Pressure loss and outlet angles for the 2D cascade angle changes cases.
Angle [◦] ω
ω0 Outlet Angle [◦]
0 0 0 0 0 1.000 -0.31
0 0 5 0 0 1.058 -1.24
0 0 8 0 0 1.168 -1.52
0 0 10 0 0 1.327 -1.40
0 5 7 5 0 1.120 -3.68
0 5 9 5 0 1.173 -3.98
13.1.6 2D Conclusions
From the 2D simulations the following conclusions are drawn.
1. An axial shorter bump is more crucial and has larger tendencies to sepa- rate, the aggressive bumps can be compared to welding lines which should then be avoided at all costs at the suction peak.
2. For this design, the flow around bumps with heights ≤3mm always re- connects (if it separate) and have pressure loss increases below 10%.
3. For this vane’s outlet region, a change in incidence or vane rotation angle
≤5◦ gives a pressure loss increase of less than 10%, but increases the outlet angle with the same value as the incidence/vane rotation angle has been changed.
4. When considering a combination of bumped vanes and incidence/vane rotation angles the pressure losses can be multiplied to get the combined pressure loss as long as the flow does reconnect (equation (17)).
5. For values of offset up to 15% the changes in pressure loss and outlet angles are insignificant, on the order of parts per mille for pressure losses and up to 12% in outlet angle for the worst 15% offset case (equals an ab- solute outlet angle change of 0.03◦). Only the deviated vane and adjacent ones are affected.
13.2 3D Results
Continuing from 2D to 3D gives the possibility to investigate more parameters, such as the width of bumps and the various 3D effects that occur when the side walls introduce additional friction forces due to the no slip wall boundary condition.
13.2.1 Local Deviations: Aggressive Bumps
The small aggressive bumps (the first four geometries shown in table 9) that were tested induced separation. In figure 37, the Wall shear stress in the x direction is shown on a bump (with width 5mm height 1mm and length 2mm).
The same bump is shown in figure 16a. In the plot the lower limit was set to zero so that back flow could be observed. The uncolored areas indicates a negative shear stress. As the zoomed out view to the right shows, the flow reconnects but there is a small change in the shear stress behind the bump (relative to the unaffected part of the vane). The shear pattern show that a disturbance of this kind can be considered local. A similar behavior was observed for all four aggressive bumps. The Cp for the same case can be seen in figure 38 and it is clear that the flow stabilizes quickly after the disturbance.
Figure 37: X-wall shear stress for a 2x5x1mm bump, the bump is positioned on the middle of the vane.
A thing to note is that all of these four small aggressive bump cases had a lower pressure loss than the reference case (at the most 0.5% lower, see appendix B.1).
This can be explained by assuming that the small aggressive bumps are acting
Figure 38: Cp plot for the 2x5x1mm bump (orange), black is the reference case.
13.2.2 Local Deviations: Large Bumps
The large bump simulations (the geometries shown in table 9 with 6mm height) showed a consistent but varying behavior. The geometry with the lowest length to height ratio caused the largest pressure losses and highest Cd’s (as seen in figures 39 and 40). This is because a bump that has a low LHR can be modeled as a single step causing a momentum pressure loss.
Separation, or back flow, is an important behavior to investigate for deviations.
If the bump simulation separates, with no reconnection, the Cdequation (6) is not valid. A vane with such a deviation is unusable without extra treatment.
Figure 41a displays the negative portion of vx on a 40x40x6mm bump, it is apparent that the back flow caused by that bump is small. The figures 41b, 41c and 41d (with more aggressive bumps) displays back flow in the same way, but here it is apparent that the flow situation is more crucial than for the bump with 40mm width and length.
Figure 39: Cd for bumps with constant LHR.
(a) Width:40mm, Length:40mm (b) Width:40mm, Length:20mm
(c) Width:80mm, Length:20mm (d) Width:200mm, Length:40mm
Figure 41: Negative vxplots for four different bumps, all with height 6mm.
The worst cases (figures 41d and 41c) caused more than double the pressure loss relative to the reference case. The separated flow of the smaller bump (figure 41b) had just under 10% increase in pressure loss compared to the reference case. The rest of the large bump geometries all had pressure loss increases below 5%. To be conservative the Cd for all large bumps without separation can be set to 0.1 (see also figures 40 and 39).
The wider a bump gets the more difficult it becomes for the flow to pass on the sides, to make the separated flow reconnect. Simulation data can be seen in appendix B.1 table 22. The important factor seems to be the bump’s width to length ratio (WLR), a WLR above 4 (for this design) always induces separation without reconnection.
13.2.3 Global Deviations: Angles
The angle simulations performed in 3D was for three different off design vane rotation cases (5◦, 8◦ and 10◦). In figure 23 the comparison between the turn- ing angles for 3D vane rotation, 2D vane rotation and 2D incidence angles can be seen.
The only difference observable is a small offset (between 2D and 3D vane ro- tation angles) and it is assumed to be caused by the 3D side effects. In figure 24 the normalized pressure loss coefficients can be seen as a function of angle deviation. Since the ω0 is different for the 3D and the 2D case there is a dif- ference in the scale of them but the behavior is similar, they are both linear.
Simulation data can be seen in appendix B.2 table 24b.
13.2.4 Global Deviations: Surface Roughness
The surface roughness only affected the pressure loss when the ks was over a certain level. For ks at 10µm and below no effect can be seen on the flow. In figure 42 the normalized pressure loss is plotted against the roughness height, both with roughness on the entire vane and roughness limited to the patch (figure 17). The 3 roughness regions observed in the figure 42 are;
1. At 10µm and below it can be considered hydraulically smooth.
2. The transition region extends from 25µm to 500µm.
3. At 1000µm it is considered completely rough since the increase in height no longer increases the pressure loss.
Completely rough is however valid only on the patch since the boundary layer thickness on the rest of the surface is higher, thus enabling the pressure loss to increase with increasing ksvalues. The reason for this not being investigated is that at ks= 500µm the roughness is already higher than any expected rough- ness levels from manufacturing.
The curve is expected to ”slide” to the left (in figure 42) at realistic conditions since the airstream velocity is expected to decrease the boundary layer thick- ness.
Simulation data can be seen in appendix B.2 table 25 and 26.
Figure 42: Relationship between ω
ω0 and ks.
13.2.5 Global Deviations: Vane Thickness
The thickness was changed in different ways (see chapter 11.4). The pressure loss and outlet angle results can be seen in figures 43 and 44. As the figures show, the normalized pressure loss is behaving linearly and does not display any tendencies to separate. The expected behavior was that a thinner vane would have a lower pressure loss and less flow turning and that a thicker vane would do opposite (higher pressure loss and higher turning angle). This was proved to be correct.
Figure 43: Relationship between ω
ω0 and total thickness fraction.
