Comparison between different domain discretization strategies using NUMECA CFD tools to analyze aeronautical turbines

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UNIVERSITA’ DEGLI STUDI DI PISA

F

ACOLTA’ DI

I

NGEGNERIA

C

ORSO DI

L

AUREA

M

AGISTRALE IN

I

NGEGNERIA

A

EROSPAZIALE

Comparison between different domain discretization

strategies using NUMECA CFD tools to analyze aeronautical

turbines

Relators:

Prof. Ing. Fabrizio Paganucci

Ing. Massimiliano Tarrini

Candidate: Paolo D'Alesio

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The thesis deals with the study of the so-called Aachen turbine and a low pressure aeronautical turbine by means of CFD simulations. The purpose of the study was to compare results coming from different discretization schemes in terms of mesh generation. Moreover it is shown the differences between two kind of unstructured grid, obtained by conversion of structured one and a grid generated inside the unstructured environment. Forcing all of the grids to satisfy specifications and constraints, fluid dynamic comparison is then possible and it is independent from grid resolution. Simulations and mesh generation are performed with NUMECATM

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List of Figures

Fig.1 Flow chart of the simulations run for this thesis

Fig.2 (a) Blade row for an axial turbomachinery, (b) blade row for a centrifugal turbomachinery Fig.3 Simple turbine operation

Fig.4 Essential nomenclature for blade

Fig.5 Cascade and meridional view for a turbine stage Fig.6 Velocity triangles for 1 stage of a turbine

Fig.7 Velocity triangle at the outlet of the rotor (station 3) Fig.8 Enthalpy-entropy diagram for a compressor

Fig.9 Enthalpy-entropy diagram for a turbine

Fig.10 Turbine configuration, velocity triangles and flow processes (P0 and T0 variations are similar to h0: p

and T variations are similar to h; 1-1/2 stages shown.

Fig.11Development of cascade airfoils. (a) cylindrical stream surface. (b) Non-cylindrical stream surface. Fig.12 Physical nature of inviscid flow in a compressor cascade

Fig.13 Physical nature of inviscid flow in a turbine cascade Fig.14 Radial equilibrium flow through a rotor blade row.

Fig.15 Variation of the distribution in axial velocity through a row of guide vanes (adapted from Hawthorne and Horlock 1962).

Fig.16 (a) Pressure variation in the neighbourhood of a rotating blade row. (b) Axial velocity at the hub in the neighbourhood of a rotating blade row (adapted from Hawthorne and Horlock 1962).

Fig.17 Evolution of the CFD tools over the last 40 years at Boeing, with an indication of the influence of CFD on the reduction of the number of wing tests. Courtesy enabling technology and research organization, Boeing commercial airplane.

Fig.18 Evolution of CFD tools over the last 40 years at Airbus with an indication of evolution of the applied models.

Fig.19 Evolution of computer performance over the last 50 years, expressed in GfLOP/s, on a logarithmic scale. Courtesy Ch. Hinterberger and W. Rodi, University of Karlsruhe, Germany.

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Fig.20 Structure of a CFD simulation

Fig.21 Representation of a quantity constant in time and of a quantity varying in time. Fig.22 Cartesian grid with non uniform cell sizes for a cavity

Fig.23 Cartesian mesh around a solid boundary with Immersed Boundary Method.

Fig.24 Quadtree grid, with hanging nodes, around an airfoil, with staircase boundary approximation. Fig.25 Cut-cell configuration.

Fig.26 Structured curvilinear body-fitted grid of H-type Fig.27 Structured curvilinear body-fitted grid of C-type Fig.28 Structured curvilinear body-fitted grid of O-type

Fig.29 Structured body-fitted grid of I-type of turbomachinery blades. Fig.30 Example of an unstructured triangular grid

Fig.31 2D section of a 3D hybrid grid of a turbine blade with film cooling configuration and a close-up view of the leading edge region.

Fig.32 Geometric characteristic of the one and half Aachen turbine stage Fig.33 Flow chart of the chapter 4

Fig.34 The .geomTurbo file of the Aachen turbine in AutoGrid5TM

Fig.35 Three-dimensional view of the recurring unities for the stator, rotor stator rows in the Aachen turbine Fig.36 Setting the first and the third rows as stator

Fig.37 Setting the second row as the rotor one, with the relative rotational velocity Fig.38 Geometrical definition of a flow path

Fig.39 Setting the first cell width for the stator rows Fig.40 Setting the first cell width for the rotor row Fig.41 Multi-blocks type contained in the B2B mesh Fig.42 Multi-blocks displayed on the three-dimensional row Fig.43 Blade to blade mesh for the first row

Fig.44 Skewness for the blade to blade mesh of the first stator Fig.45 Expansion ratio for the blade to blade mesh of the first rotor Fig.46 Blade to blade mesh for the rotor row

Fig.47 Skewness for the blade to blade mesh of the rotor row Fig.48 Expansion ratio for the blade to blade mesh of the rotor row

Fig.49 Blade to blade mesh for the entire one and half Aachen turbine stage

Fig.50 Three dimensional view of the mesh for the repetition unities of the Aachen turbine

Fig.51 three dimensional view of the mesh for the blocks representing the rows for the Aachen turbine Fig.52 Three dimensional view of the mesh for the entire Aachen turbine

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Fig.54 Importation of the structured mesh into the unstructured environment

Fig.55 Unstructured mesh resulting from the importation of the structured one into HEXPRESS

Fig.56 Orthogonality for the first row in the unstructured mesh after conversion from the structured one Fig. 57 Expansion ratio for the first row in the unstructured mesh after conversion from the structured one Fig. 58 Aspect ratio for the first row in the unstructured mesh after conversion from the structured one Fig.59 Orthogonality for the second row in the unstructured mesh after conversion from the structured one Fig.60 Expansion ratio for the second row in the unstructured mesh after conversion from the structured one Fig.61 Aspect ratio for the second row in the unstructured mesh after conversion from the structured one Fig.62 Orthogonality for the third row in the unstructured mesh after conversion from the structured one Fig.63 Expansion ratio for the third row in the unstructured mesh after conversion from the structured one Fig.64 Aspect ratio for the third row in the unstructured mesh after conversion from the structured one Fig.65 Mesh obtained after complete processing within HEXPRESS

Fig.66 Mesh quality for the first row (stator) of the mesh completely processed in HEXPRESS, in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

Fig.67 Mesh quality for the second row (rotor) of the mesh completely processed in HEXPRESS, in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

Fig.68 Mesh quality for the third row (stator) of the mesh completely processed in HEXPRESS, in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

Fig. 69 Viscous layer over the rotor blade

Fig.70 Modeling of the tip gap between shroud and rotor blade tip Fig.71 Edges for the first row created in HEXPRESS/Hybrid

Fig.72 Edges for the clean geometry of the rotor row

Fig.73 Particular of the edges for the blade, the blade tip and the shroud for the clean geometry of the rotor row.

Fig.74 Summarizing table for the mesh characteristic for both structured, unstructured, full hexaedral cell hybrid and default tyoe cell hybrid meshes

Fig.75 For the default type cell hybrid mesh of the first row: a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.76 For the default type cell hybrid mesh of the second row: a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.77 For the default type cell hybrid mesh of the third row: a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.78 For the full hexaedral cell hybrid mesh of the first row: a) orthogonality, b) aspect ratio and c) expansion ratio

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expansion ratio

Fig.80 For the full hexaedral cell hybrid mesh of the third row: a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.81 Setting periodicity for the stator rows Fig.82 Setting periodicity for the rotor row

Fig.83 Computation of the full non matching boundaries and of the interfaces for the hybrid mesh of the Aachen turbine

Fig.84 Table summarizing the computational costs for the structured, unstructured, default type cell hybrid and full hexaedral cell hybrid mesh

Fig.85 Comparison between the two unstructured mesh, the first obtained by conversion from the structured mesh and the second totally processed with HEXPRESSTM

Fig.86 Distribution of arctg(Vt/Vz) over the turbine blade

Fig.87 Distribution of the absolute total pressure over the turbine blade Fig.88 Distribution of the absolute total temperature over the turbine blade

Fig.89 Convergence history in terms of residual for the structured mesh simulation in FINE/Turbo

Fig.90 Convergence history in terms of the trends of the inlet and outlet mass flow for the structured mesh simulation in FINE/Turbo

Fig.91 Table summarizing the results for the structured mesh simulation in FINE/Turbo

Fig.92 Table summarizing the results in terms of inlet and outlet mass flow for the structured mesh simulation in FINE/Turbo

Fig.93 Tale summarizing the results in terms of turbine performance for the structured mesh simulation in FINE/Turbo

Fig.94 Y+_{over the Aachen turbine wall surfaces for the structured simulation run in FINE/Turbo}

Fig.95 Trend of the absolute total pressure in the meridional view for the structured mesh simulation in FINE/Turbo

Fig.96 Trend of the static pressure in the meridional view for the structured mesh simulation in FINE/Turbo Fig.97 Trend of the static pressure on the surfaces of the first stator blade @5% of the span for the structured mesh simulation in FINE/Turbo

Fig.98 Trend of the static pressure on the surfaces of the rotor blade @5% of the span for the structured mesh simulation in FINE/Turbo

Fig.99 Trend of the static pressure on the surfaces of the second stator blade @5% of the span for the structured mesh simulation in FINE/Turbo

Fig.100 Trend of the static pressure on the surfaces of the first stator blade @50% of the span for the structured mesh simulation in FINE/Turbo

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mesh simulation in FINE/Turbo

Fig.103 Trend of the static pressure on the surfaces of the first stator blade @95% of the span for the structured mesh simulation in FINE/Turbo

Fig.104 Trend of the static pressure on the surfaces of the rotor blade @95% of the span for the structured mesh simulation in FINE/Turbo

Fig.106 Trend of the static pressure on the surfaces of both first stator,rotor and second stator @50& of the span for the structured mesh simulation in FINE/Turbo. To note the drop in static pressure at the leading edges of the blades of rotor and second stator

Fig.107 Track of the vortex shed by the trailing edge of the blade of the first rotor understandable by the area at lower density

Fig.108 Vortex shed by the trailing edge of the blade stator because of the lift generation and its trip to impact the leading edge of the rotor blade

Fig.109 Resulting area at highest velocity next to the leading edge , which cause the drop in pressure underlined at fig.96

Fig.110 Displacement towards streamwise direction of the suction point along the low pressure surfaces of the rotor blade @95%, @97% and @99% of the span

Fig.111 Most important features of the tricky three-dimensional flow in a turbine

Fig.112 Trend of the isentropic Mach over the first stator blade surface @5% spanwise for the structured mesh simulation in FINE/Turbo. (red line= pressure surface , blue line=suction surface)

Fig.113 Trend of the isentropic Mach over the rotor blade surface @5% spanwise for the structured mesh simulation in FINE/Turbo. (red line= pressure surface , blue line=suction surface)

Fig.114 Trend of the isentropic Mach over the second stator blade surface @5% spanwise for the structured mesh simulation in FINE/Turbo. (red line= pressure surface , blue line=suction surface)

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Fig.121 Losses, computed as difference between the Isentropic Mach number and the absolute Mach number, on the first stator @5% spanwise

Fig.122 Losses, computed as difference between the Isentropic Mach number and the absolute Mach number, on the rotor @5% spanwise

Fig.123 Losses, computed as difference between the Isentropic Mach number and the absolute Mach number, on the second stator @5% spanwise

Fig.130 Losses on the rotor, streamwise view. In the red circles we can see that the highest losses take place next to the hub and next to the shroud

Fig.131 Losses on rotor, streamwise direction, viewed by the trailing edge. The losses next to the hub interested a bigger area

Fig.132 Curvature of the streamlines next to the hub due to the pressure gradient between the pressure surface of blade “1” and the suction surface of blade ”2”

Fig.133 Horseshoe vortex formed by the pressure gradient at the leading edge next to the hub, where we have the boundary layer due to the hub wall

Fig.134 Tip vortex due to the leakage flow in the clearance gap between blade tip and shroud

Fig.135 Losses at the blade tip due to the tip vortex. It could be seen that the area where the losses take place is strictly connected to the area over which the tip vortex grows up and spread out.

Fig.136 Convergence history in terms of residual for the unstructured mesh obtained by conversion simulation run with mixed precision mode

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Fig.137 Convergence history in terms of inlet and outlet mass flow for the unstructured mesh obtained by conversion simulation run with mixed precision mode

Fig.138 Results of the unstructured mesh obtained by conversion simulation run with mixed precision mode Fig.139 Results in terms of inlet and outlet mass flow for the unstructured mesh obtained by conversion simulation run with mixed precision mode

Fig.140 Results in terms of turbomachinery performance for the unstructured mesh obtained by conversion simulation run with mixed precision mode

Fig.141 Convergence history in terms of residual for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility. Fig.142 Convergence history in terms of inlet and outlet mass flow for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.143 Results in terms of inlet and outlet mass flow for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility. Fig.144 Results of the simulation for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.145 Results of the simulation in terms of turbomachinery performance the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.146 Y+_{over the Aachen turbine wall surfaces for the unstructured converted mesh simulation run in}

FINE/Open

Fig.147 Trend of absolute total pressure for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.148 Trend of static pressure for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.149 Trend of the static pressure over the first stator blade @5% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.150 Trend of the static pressure over the rotor blade @5% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.151 Trend of the static pressure over the second stator blade @5% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

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obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.153 Trend of the static pressure over the rotor blade @50% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.155 Trend of the static pressure over the first stator blade @95% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.156 Trend of the static pressure over the rotor blade @95% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.158 Trend of the isentropic Mach number over the first stator blade @5% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.159 Trend of the isentropic Mach number over the rotor blade @5% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.160 Trend of the isentropic Mach number over the second stator blade @5% spanwise for the

unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.162 Trend of the isentropic Mach number over the rotor blade @50% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.163 Trend of the isentropic Mach number over the second stator blade @50% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

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Fig.165 Trend of the isentropic Mach number over the rotor blade @95% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.166 Trend of the isentropic Mach number over the second stator blade @95% spanwise for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.167 Losses over a surface @5% spanwise for the first stator for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.168 Losses over a surface @5% spanwise for the rotor for he unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility. Fig.169 Losses over a surface @5% spanwise for the second stator for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.171 Losses over a surface @50% spanwise for the rotor for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.172 Losses over a surface @50% spanwise for the second stator for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for

compressibility.

Fig.174 Losses over a surface @95% spanwise for the rotor for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility.

Fig.175 Losses over a surface @95% spanwise for the second stator for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for

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Fig.176 Difference between the results for the unstructured simulation with mixed-precision-mode and the unstructured simulation with full-double-precision-mode run and variables changed for compressibility in percentage

Fig.177 Difference between the results for the unstructured simulation with mixed-precision-mode and the unstructured simulation with full-double-precision-mode run and variables changed for compressibility, in percentage in terms of turbomachinery performance

Fig.178 Comparison between tip vortex: a) tip vortex obtained by the simulation with mixed-precision-mode, b) tip vortex obtained by the simulation with full-double-precision-mode

Fig.179 Difference between the results for the structured simulation and the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for

compressibility in percentage

compressibility in percentage in terms of inlet and outlet mass flow

compressibility in percentage in terms of turbomachinery performance

Fig.182 Visualization of the tip vortex for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility

Fig.183 Visualization of the horseshoe vortex for the unstructured mesh obtained by conversion simulation run with full double precision mode and with control variables changed for compressibility

Fig.184 Convergence history in terms of residual for the unstructured simulation Fig.185 Convergence history in terms of mass flow rate for the unstructured simulation Fig.186 Results of the unstructured simulation

Fig.187 Results in terms of turbomachinery performance for the unstructured simulation Fig.188 Results in terms of mass flow rate for the unstructured simulation

Fig.189 Plot of Y+_{over the wall surfaces}

Fig.190 Trend of the Absolute Total Pressure Fig.191 Trend of the Static Pressure

Fig.192 Trend of the static pressure over the first stator blade surface @5% spanwise for the unstructured simulation

Fig.193 Trend of the static pressure over the first rotor blade surface @5% spanwise for the unstructured simulation

Fig.194 Trend of the static pressure over the second vane blade surface @5% spanwise for the unstructured simulation

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Fig.197 Trend of the static pressure over the second stator blade surface @50% spanwise for the unstructured simulation

Fig.200 Trend of the static pressure over the second stator blade surface @95% spanwise for the unstructured simulation

Fig.201 Trend of the isentropic Mach number over the first stator blade surface @5% spanwise for the unstructured simulation

Fig.202 Trend of the isentropic Mach number over the first rotor blade surface @5% spanwise for the unstructured simulation

Fig.203 Trend of the isentropic Mach number over the second stator blade surface @5% spanwise for the unstructured simulation

Fig.210 Plot of the losses as difference between the isentropic Mach number and the Absolute Mach number for a surface @5% spanwise of the first stator for the unstructured simulation

Fig.211 Plot of the losses as difference between the isentropic Mach number and the Absolute Mach number for a surface @5% spanwise of the first rotor for the unstructured simulation

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for a surface @5% spanwise of the second stator for the unstructured simulation

Fig.215 Plot of the losses as difference between the isentropic Mach number and the Absolute Mach number for a surface @50% spanwise of the second stator for the unstructured simulation

Fig.218 Plot of the losses as difference between the isentropic Mach number and the Absolute Mach number for a surface @95% spanwise of the second stator for the unstructured simulation

Fig.219 Difference in results between the structured and the unstructured simulation in terms of mass flow Fig.220 Difference in results between the structured and the unstructured simulation in terms of

turbomachinery performance

Fig.221 Difference in results between the structured and the unstructured simulation Fig.222 Tip vortex at the blade rotor tip for the unstructured simulation

Fig.223 Flow chart of chapter 10

Fig.224 Blade to blade mesh skewness for the first vane Fig.225 Blade to blade mesh expansion ratio for the first vane Fig.226 Blade to blade mesh skewness for the first rotor Fig.227 Blade to blade mesh expansion ratio for the first rotor. Fig.228 Blade to blade mesh skewness for the second vane Fig.229 Blade to blade mesh expansion ratio for the second vane Fig.230 Blade to blade mesh skewness for the second rotor. Fig.231 Blade to blade mesh expansion ratio for the second rotor. Fig.232 Blade to blade mesh of the low pressure turbine two stages. Fig.233 Three-dimensional view of the low pressure turbine two stages.

Fig.234 Mesh quality for the structured mesh of the low pressure turbine two stages. Fig.235 Conversion of the structured mesh into HEXPRESSTM

Fig.236 Mesh quality for the unstructured mesh by conversion for the first vane in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.237 Mesh quality for the unstructured mesh by conversion for the first rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio

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Fig.238 Mesh quality for the unstructured mesh by conversion for the second vane in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.239 Mesh quality for the unstructured mesh by conversion for the second rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio

Fig.240 Mesh quality for the unstructured mesh completely done with HEXPRESSTM_{with the first layer}

thickness method for the viscous layer inflation for the first vane in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio

thickness method for the viscous layer inflation for the first rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

thickness method for the viscous layer inflation for the second stator in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

thickness method for the viscous layer inflation for the second rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

Fig.244 Detailed view of the viscous layer inflate by the first layer thickness method over the second vane blade.

Fig.245 Mesh quality for the unstructured mesh completely done with HEXPRESSTM_{with the variable first}

layer thickness method for the viscous layer inflation for the first vane in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

layer thickness method for the viscous layer inflation for the first rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

layer thickness method for the viscous layer inflation for the second vane in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

layer thickness method for the viscous layer inflation for the second rotor in terms of : a) orthogonality, b) aspect ratio and c) expansion ratio.

Fig.249 Detailed view of the viscous layer inflate by the variable first layer thickness method over the second vane blade.

Fig.250 Table comparing the three unstructured mesh obtained in terms of number of cells, minimum skewness, maximum aspect ratio and maximum expansion ratio for each row.

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Fig.252 Boundary condition on the Blade to blade angle at the inlet Fig.253 Boundary condition on the absolute total pressure at the inlet Fig.254 Boundary condition on the absolute total temperature at the inlet

Fig.255 Convergence history in terms of residual for the low pressure turbine structured simulation. Fig.256 Convergence history in terms of mass flow for the low pressure turbine structured simulation. Fig.257 Results for the low pressure turbine structured simulation.

Fig.258 Results for the low pressure turbine structured simulation in terms of mass flow rate Fig.259 Results for the low pressure turbine structured simulation. In terms of turbomachinery performances.

Fig.260 Y+_{over the blade wall surfaces}

Fig.261 Trend of the absolute total pressure for the low pressure turbine structured simulation in the meridional view

Fig.262 Trend of the static pressure for the low pressure turbine structured simulation in the meridional view.

Fig.263 Trend of the static pressure for the low pressure turbine structured simulation.

Fig.264 Trend of the static pressure for the low pressure turbine structured simulation over the first vane blade @5% spanwise

Fig.265 Trend of the static pressure for the low pressure turbine structured simulation over the first rotor blade @5% spanwise

Fig.266 Trend of the static pressure for the low pressure turbine structured simulation over the second vane blade @5% spanwise

Fig.267 Trend of the static pressure for the low pressure turbine structured simulation over the second rotor blade @5% spanwise

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Fig.276 History of the impingement of the foregoing wake blade over the pressure surface of the blade, simulated with LES code

Fig.277 Supersonic bubbles over the low pressure turbine surfaces(suction surfaces of the first and second rotor)

Fig.278 Supersonic bubble over the low pressure turbine surfaces ( suction surface of the second vane) Fig.279 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the first vane blade at @5 spanwise

Fig.280 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the first rotor blade at @5 spanwise

Fig.281 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the second vane blade at @5 spanwise

Fig.282 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the second rotor blade at @5 spanwise

Fig.283 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the first vane blade at @50 spanwise

Fig.286 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the second rotor blade at @50 spanwise

Fig.287 Trend of the Isentropic Mach Number for the low pressure turbine structured simulation over the first vane blade at @95 spanwise

Fig.290 Plot of the losses in terms of difference between the Isentropic Mach Number and the absolute Mach Number for a surface @5% spanwise for the first vane.

Fig.291 Plot of the losses in terms of difference between the Isentropic Mach Number and the absolute Mach Number for a surface @5% spanwise for the first rotor.

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Fig.292 Plot of the losses in terms of difference between the Isentropic Mach Number and the absolute Mach Number for a surface @5% spanwise for the second vane.

Fig.293 Plot of the losses in terms of difference between the Isentropic Mach Number and the absolute Mach Number for a surface @5% spanwise for the second rotor.

Fig.302 Convergence history in terms of residual for the low pressure turbine unstructured by conversion simulation

Fig.303 Convergence history in terms of mass flow for the low pressure turbine unstructured by conversion simulation

Fig.304 Results for the low pressure turbine unstructured by conversion simulation

Fig.305 Results in terms of mass flow rate for the low pressure turbine unstructured by conversion simulation

Fig.306 Results in terms of turbomachinery performance for the low pressure turbine unstructured by conversion simulation

Fig.307 Y+_{over the blade surfaces for the low pressure turbine unstructured by conversion simulation}

Fig.308 Trend of the absolute total pressure for the low pressure turbine unstructured by conversion simulation

Fig.309 Trend of the static pressure the low pressure turbine unstructured by conversion simulation

Fig.310 Trend of the static pressure for the low pressure turbine unstructured by conversion simulation over the first vane blade @5% spanwise

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Fig.311 Trend of the static pressure for the low pressure turbine unstructured by conversion simulation over the first rotor blade @5% spanwise

Fig.312 Trend of the static pressure for the low pressure turbine unstructured by conversion simulation over the second vane blade @5% spanwise

Fig.322 Separation bubble for the low pressure turbine unstructured by conversion simulation over the first rotor blade @50% spanwise

Fig.323 Begin of the separation bubble for the low pressure turbine unstructured by conversion simulation over the first rotor blade @50% spanwise

Fig.324 End of the separation bubble for the low pressure turbine unstructured by conversion simulation over the first rotor blade @50% spanwise

Fig.325 Separation bubble for the low pressure turbine unstructured by conversion simulation over the second vane blade @50% spanwise

Fig.326 Particular of the Separation bubble for the low pressure turbine unstructured by conversion simulation over the second vane blade @50% spanwise

Fig.327 Trend of the Isentropic Mach Number for the low pressure turbine unstructured by conversion simulation over the first vane blade @5% spanwise.

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simulation over the first rotor blade @5% spanwise.

Fig.329 Trend of the Isentropic Mach Number for the low pressure turbine unstructured by conversion simulation over the second vane blade @5% spanwise.

Fig.330 Trend of the Isentropic Mach Number for the low pressure turbine unstructured by conversion simulation over the second rotor blade @5% spanwise.

Fig.332 Trend of the Isentropic Mach Number for the low pressure turbine unstructured by conversion simulation over the first rotor blade @50% spanwise.

Fig.336 Trend of the Isentropic Mach Number for the low pressure turbine unstructured by conversion simulation over the first rotor blade @95% spanwise.

Fig.339 Plot of the losses as difference between the isentropic Mach Number and the absolute Mach number for a first vane surface @5% spanwise

Fig.340 Plot of the losses as difference between the isentropic Mach Number and the absolute Mach number for a first rotor surface @5% spanwise

Fig.341 Plot of the losses as difference between the isentropic Mach Number and the absolute Mach number for a second vane surface @5% spanwise

Fig.342 Plot of the losses as difference between the isentropic Mach Number and the absolute Mach number for a second rotor surface @5% spanwise

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Fig.351 Turbulence viscosity @50% spanwise for the first rotor suction surface Fig.352 Turbulence viscosity @50% spanwise for the first rotor pressure surface.

Fig.353 Plot of the momentum thickness over the first rotor blade surfaces @50% spanwise

Fig.354 Convergence history in terms of residual for the low pressure turbine unstructured by conversion simulation but run with the full single precision mode

Fig.355 Convergence history in terms of mass flow for the low pressure turbine unstructured by conversion simulation but run with the full single precision mode

Fig.356 Results for the low pressure turbine unstructured by conversion simulation but run with the full single precision mode

Fig.357 Results in terms of mass flow for the low pressure turbine unstructured by conversion simulation but run with the full single precision mode

Fig.358 Results in terms of turbomachinery performance for the low pressure turbine unstructured by conversion simulation but run with the full single precision mode

Fig.359 Differences between the results of the the low pressure turbine unstructured by conversion simulations run with the full single precision mode and with full double precision mode.

Fig.360 Differences between the results in terms of turbomachinery performance of the the low pressure turbine unstructured by conversion simulations run with the full single precision mode and with full double precision mode.

Fig.361 Differences between the results in terms of mass flow of the the low pressure turbine unstructured by conversion simulations run with the full single precision mode and with full double precision mode. Fig.362 Differences between the results of the the low pressure turbine unstructured by conversion simulation and structured simulation

Fig.363 Differences between the results in terms of mass flow of the the low pressure turbine unstructured by conversion simulations run with the full single precision mode and structured simulation

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turbine unstructured by conversion simulations run with the full single precision mode and structured simulation.

Fig.365 Convergence history in terms of residual for the low pressure turbine unstructured simulation Fig.366 Convergence history in terms of mass flow for the low pressure turbine unstructured simulation Fig.367 Results for the low pressure turbine unstructured simulation.

Fig.368 Results in terms of mass flow for the low pressure turbine unstructured simulation. Fig.369 Results in terms of turbomachinery perfomance for the low pressure turbine unstructured simulation.

Fig.370 Y+ over the walla surfaces for the low pressure turbine unstructured simulation.

Fig.371 Trend of the absolute total pressure for the low pressure turbine unstructured simulation Fig.372 Trend of the static pressure for the low pressure turbine unstructured simulation

Fig.373 Trend of the static pressure for the low pressure turbine unstructured simulation over the first vane blade @5% spanwise.

Fig.374 Trend of the static pressure for the low pressure turbine unstructured simulation over the first rotor blade @5% spanwise.

Fig.375 Trend of the static pressure for the low pressure turbine unstructured simulation over the second vane blade @5% spanwise.

Fig.376 Trend of the static pressure for the low pressure turbine unstructured simulation over the second rotor blade @5% spanwise.

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Fig.385 Trend of the isoentropic Mach Number for the low pressure turbine unstructured simulation the first vane blade @5% spanwise

Fig.386 Trend of the isoentropic Mach Number for the low pressure turbine unstructured simulation the first rotor blade @5% spanwise

Fig.387 Trend of the isoentropic Mach Number for the low pressure turbine unstructured simulation the first second blade @5% spanwise

Fig.388 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the second rotor blade @5% spanwise

Fig.389 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first vane blade @50% spanwise

Fig.390 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first rotor blade @50% spanwise

Fig.391 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first second blade @50% spanwise

Fig.392 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first vane blade @95% spanwise

Fig.394 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first rotor blade @95% spanwise

Fig.395 Trend of the isentropic Mach Number for the low pressure turbine unstructured simulation the first second blade @95% spanwise

Fig.397 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the first vane row surface @5% spanwise Fig.398 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the first rotor row surface @5% spanwise Fig.399 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second vane row surface @5% spanwise Fig.400 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second rotor row surface @5% spanwise Fig.401 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the first vane row surface @50% spanwise Fig.402 Losses in terms of difference between the isentropic Mach number and the absolute Mach number

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for the low pressure turbine unstructured simulation over the first rotor row surface @50% spanwise Fig.403 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second vane row surface @50% spanwise Fig.404 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second rotor row surface @50% spanwise Fig.405 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the first vane row surface @95% spanwise Fig.406 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the first rotor row surface @95% spanwise Fig.407 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second vane row surface @95% spanwise Fig.408 Losses in terms of difference between the isentropic Mach number and the absolute Mach number for the low pressure turbine unstructured simulation over the second rotor row surface @95% spanwise Fig.409 Comparison of the results for the low pressure turbine unstructured and structured simulations Fig.410 Comparison of the results in terms of mass flow for the low pressure turbine unstructured and structured simulations

Fig.411 Comparison of the results In terms of turbomachinery perfomance for the low pressure turbine unstructured and structured simulations

Fig.412 Separation bubble over the first rotor blade @50% spanwise. Fig.413 Separation bubble over the second vane blade @50% spanwise. Fig.414 Separation bubble over the second rotor blade @50% spanwise.

Fig.415 Comparison within the required time to complete the various simulations run in this thesis

Fig.416 Comparison between the results for the low pressure turbine unstructured by conversion simulation run with k-ε turbulence model and the structured simulation.

Fig.417 Comparison between the results for the low pressure turbine unstructured by conversion simulation run with k-ε turbulence model and the unstructured by conversion simulation run with Spalart-Allmaras turbulence model

Fig.418 Comparison of the results between the low pressure turbine unstructured simulation run with k-ε turbulence model and the structured simulation

Fig.419 Comparison between the results of the low pressure turbine unstructured simulation run with k-ε turbulence model and run with Spalart-Allmaras turbulence model.

Fig.420 Comparison of the vector plots of the time averaged velocity at the trailing edge between: a) the work of Simoni, Ubaldi, Zunino [29] and b)the unstructured simulation. It is possible to see the trace of the Von Karman street vortex

Comparison between different domain discretization strategies using NUMECA CFD tools to analyze aeronautical turbines

UNIVERSITA’ DEGLI STUDI DI PISA

F

ACOLTA’ DI

I

NGEGNERIA

C

ORSO DI

L

AUREA

M

AGISTRALE IN

I

NGEGNERIA

A

EROSPAZIALE

Comparison between different domain discretization

strategies using NUMECA CFD tools to analyze aeronautical

turbines

Relators:

Prof. Ing. Fabrizio Paganucci

Ing. Massimiliano Tarrini

Candidate: Paolo D'Alesio

Contents

List of Figures

Chapter 1

: Turbomachinery Generalities

1.1 Thesis Objectives

1.2 Turbomachineries: Generalities

1.3 Thermodynamic analysis for Turbomachinery...5

1.3.1 Mono-dimensional Approach…...6

1.3.1.1 Velocity Components...6

1.3.1.2 Jump in Total Pressure and Temperature...8

1.3.1.3 Work done by a Turbomachinery

1.3.1.4 Turbine Performance...11

1.3.2 Two-dimensional Approach…...13

1.3.3 Three-dimensional Approach...15

Chapter 2

: What is CFD? An Overview

2.1 What is CFD...22

2.2 Steps for a CFD Simulation

2.2.1.

Step 1:Fluid Equations

2.2.1.1.

Equation in Conservative Form...29

2.2.1.2.

Reynolds Averaged Navier-Stokes Equations (RANS)...31

2.2.1.3.

Turbulence Models...33

2.2.1.4.

Spalart-Allmaras One Equation Model...35

2.2.1.5.

k-ε Two Equation Model...37

2.2.2.

Step 2: Grid Generation...40

2.2.2.1.

Structured Grid...40

2.2.2.2.

Unstructured Grid...45

2.2.2.3.

Conclusions and Recommendations about Mesh Generation....47

2.2.3.

Step 3: Acknowledge about Numerical Schemes...48

Chapter 3

: An Introduction to NUMECA

products

3.1 History of NUMECA

3.2 Grid Generation Software

3.2.1 AutoGrid

3.2.2 HEXPRESS

3.2.3 HEXPRESS

/Hybrid...55

3.3 Flow Solution Software...56

3.3.1 FINE

/Open...56

3.3.2 FINE

/Turbo...56

Part I

: The Aachen Turbine

Chapter 4

_products

_/Hybrid...87

_{:Results...111}

_{over the wall surfaces...113}

_{: Second Simulation...144}