Technische Universität MünchenLehrstuhl für Fluidmechanik ● Abteilung Hydraulische Maschineno. Prof. Dr.-Ing. habil. Rudolf Schilling

Content

1. Motivation2. Numerical test rig „IDS“

• Geometric Set, Preprocessing and grid generation

3. Simulation approaches• Level of detail• Fluid flow modeling

Motivation

• FLM develops design, simulation and optimization tools to support the development process of turbo machinery

• Aim of the work performed was to prove the fitness and reliability of these tools as a numerical test rig.– given pump geometry of a specific user– “blind test”

• Introduce CFD simulation tools into the design process.

“classical” design approach

Development Prototype fabrication Mechanical test rig

CAE-based design approach

Development

Numerical test rig

Prototype fabrication Mechanical test rig

IDS

IDS Integrated Design System

Features:

-Geometry tools-“automatic” grid generator-Several solvers -“single click” post processing unit-Automatic run system-Block structured grids are needed

Needed inputs:

-Geometric data from the three main parts-Physical conditions from the fluid-Design point data from the pump

The three main parts

Casing Runner blade Spiral

Content

1. Motivation2. Numerical test rig „IDS“

• Geometric Set, Preprocessing and grid generation

3. Simulation approaches• Level of detail• Fluid flow modeling

Geometric data

CAD – Data (surfaces)

CAD – Data (points)meridiancontour

CAD – Data (surface)spiral

CAD – Data (surface)blade

Meridian contour and stream traces based

on B-Splines

Blade surface cutsbased on linear surfaces

Spiral cutsbased on linear surfaces

Flow channel distribute intogrid blocks

Blade grid based oncubic splines

Transfinite interpolation

Spiral distribute into gridblocks

Single flow channelwithout side space

Single flow channelwith side space

The complete machine

grid rotation

CAD – Data (surfaces)

CAD – Data (points)meridian contour for casing

CAD – Data from the casing (surfaces)

y - Axis

z - axis

Requirements:

-z – axis in flow direction

-rotation symmetric geometries

-absolute coordinates for every part

-rotation axis = z – axis

-measurement is meter

-distribute points along the contour

-right hand system

-CAD – Data file must be an *.igs - file

xx - Axis

CATIA V5 drawing

CAD – Data meridian contour (points)

22 yxr +=

r

z

→every point has an own coordinate (r, z)

The points from CAD - data file will be transformed from (x, y, z) – coordinates into cylinder coordinates with the following rule

z = z

Meridian contour and stream traces based on B-Splines

B-Splines

Uniform B-Spline:

order k = 3Describer points n = 7

support vector elements l = n + k = 10inner knots IK = l – 2k = 4sections p = IK + 1 = 5

Support vector T:

T = T(0, 0, 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.0, 1.0)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 0.2 0.4 0.6 0.8 1

⎩⎨⎧ <≤

= +

sonst:0tttfür:1

(t)N 1iii,1

1iki

1-k1,iki

i1ki

1ki,iki, tt

(t)t)N(ttt

(t))Nt(t(t)N

++

++

−+

−

−−

+−

−=

Recursive Formula

ti: Knot, elements of the support vector Tt: Curve parameter

Flow channel distribute intogrid blocks

Grid – blocks:

-distribute the flow channel into calculation areas

-block boundaries consists of B-Splines and lines

-grid size can be adapted individually to every block

B-Spline

BlockGrid generation with transfinite interpolation

parallelize

processor

CAD – Data (surface)Blade

Requirements:

-positive rotation around the z – axis

-the positioning coordinates must fits into the meridian contour

-CAD – Data file must be a *.stl – file

Blade surface cutsbased on linear surfaces

stream traces consists of B–Splines

blade were cut with stream traces

blade surface cuts based on linear surfaces

blade is cut into slices

B-Spline

Blade surface cutconformal mapping

Blade surface cuts 3-D

Blade grid based oncubic splines

Interpolating the cuts with cubic splines

Cubic parabola

( ) iiiii dxcxbxaxf +++= 23

22

2

21

2

21

21 )()(

kk

kk

kk

dxyd

dxyd

dxdy

dxdy

xfxf

=

=

=

C-Grid

i: Section number

Number of unknown = 4 * number of sections

Number of Nodes = number of sections + 1

Cubic spline

Blade surface cut

CAD – Data (surface)spiral

Requirements:

-positive rotation around the z – axis

-the positioning coordinates must fit to the exhaust from the pump

-the two connecting edges must be planar, parallel to each other and concentric to the origin

-the measurement is meter

-CAD – Data file must be a *.stl – file

connecting edges

Spiral cutsbased on linear surfaces

define cuts on the spiral

cut spiral with defined cuts

spiral cuts based on linear surfaces

spiral is cut into slices

define spiral cuts

spiral cut

Spiral segmentation into grid blocks

Spiral blocks:

-calculation areas segment the flow channel

-lines in peripheral and radial direction consists of B-Splines

-complete spiral can be meshed with hexahedrons

B-Splines

Content

1. Motivation2. Numerical test rig „IDS“

• Geometric Set, Preprocessing and grid generation

3. Simulation approaches• Level of detail• Fluid flow modeling

Single flow channel without side space

Single flow channel without side space

Quasi Euler calculation

Check the result

RANS calculation with terms of first order discretisation

Check the result

Performance curve

Performance curve

Improve gridfalse

true

RANS calculation with terms of first and second order

discretisation

final blade grid Single flow channel withside space blocks

Inputs:

-Rotation frequency ω-Volume flow-Reference radius rref-Density of fluid ρ-Viscosity ν-Turbulence parameters (k, ε)-Number of blades

Single – flow channel without side space

V&

-Quasi Euler calculation for approximation

-RANS calculation with terms offirst and second order discretisation

-Simplified outlet model

-Blade grid optimization

-Performance curves for operationcharacteristics

-Reference for further simulationsinlet

inlet AVc&

=

Quasi Euler calculation

-grid with large cells low number of nodes

-no wall friction

-no turbulence model

-adjusted viscosity

-fast and simple calculation

-rough result

-first approximation of performance

9522 Nodes

Measurement positions, balancing

Impeller inlet

Impeller outlet

Machine outlet

Machine inlet

Zero pressure level

Result of a quasi Euler calculation

Total pressure profile

RANS calculation with wall friction

-fine grid increased number of nodes

-simplified outlet model

-k, ε – turbulence model

-precise result

-no cavitation effects

-wall friction

-calculation with terms of first and second order discretisation

-final blade grid

about 54000 nodes

Reynolds averaged turbulence model

real stream value ΔtMittelung >> ΔtTurbulenz

p´(t), U´(t)(

<p(t)>, <U(t)>p(t),U(t)

t t

ΔtMittelung >> ΔtTurbulenz

p´(t), U´(t)(

<p(t)>, <U(t)>

ΔtMittelung >> ΔtTurbulenz

p´(t), U´(t)(turbulent variations)

<p(t)>, <U(t)>(averaged on time)p(t),

U(t)

t t

09.0

2

=

⋅=

μ

μ εν

c

kct

Reynolds averaged stream value

{ }23

22

212

1 uuuk ++=

u =velocity [m/s]νt=turbulent viscosity [m³/s²] ε =dissipation rate [m/s²]k =turbulent kinetic energy [m²/s²]

321)( uuutU ++=

Wall friction model

u+

y+

Velocity Wall shearing stress Wall Friction force

Evaluation of wall function

Turbulent kinetic energy

Evaluation of wall function

efficiency

87

87,5

88

88,5

89

89,5

90

90,5

91

0,3 2,7 2,8 3,4 3,9 9,6

y+ value < 30 in %

effic

ienc

y (%

)

efficiency

delivery height

16,6

16,65

16,7

16,75

16,8

16,85

16,9

0,3 2,7 2,8 3,4 3,9 9,6

y+ value < 30 in %

deliv

ery

heig

ht (m

)

delivery height

Power

44,14,24,34,44,54,64,7

0,3 2,7 2,8 3,4 3,9 9,6

y+ value < 30 in %

Pow

er (k

W)

Pow er input

Pow er output

better better

better

Single Flow Performance Curve

0,700

0,750

0,800

0,850

0,900

0,950

1,000

1,050

1,100

1,150

1,200

0,014

50,0

158

0,017

10,0

184

0,019

70,0

210

0,022

40,0

237

0,025

00,0

263

0,027

60,0

289

0,030

20,0

315

0,032

9

PHI

PSI,

ETA

ETA Euler 9 STdelta PSI total Euler 9 STETA RANS 15 STdelta PSI total RANS 15 ST

Comparison of results

refref urQ⋅⋅

=π

ϕ 2

2

2

ref

tt u

p⋅Δ⋅

=Ψρ

Single flow channel with side space

Single flow channel withside space blocks

Optimized pump grid(single channel)NPSH - Characteristic Performance curve

Only positive pressure on Blade

The complete machine

Single run with cavitation model

NPSH – Curve with lowresolution

NPSH – Curve with highresolution

Single flow channel withside space blocks

-fine grid large number of nodes

-simple outlet

-k, ε – turbulence model

-precise result

-no cavitation

-wall friction

-calculation with terms of first and second order discretisation

-optimized side space grid

-reference for NPSH curve

237500 nodes

Total pressure meridian contour

Pressure gradient

Pressure profile on blade

Pressure profile on blade without side space

Pressure profile on blade with side space

Turbulent kinetic energy meridian contour

Sealing side spaceHigh turbulence

Comparison of results

Dimesionless total pressure

0,000,200,400,600,801,001,201,40

0,013

90,0

165

0,019

00,0

216

0,024

10,0

266

0,029

20,0

317

PHI

PSI t

otal

delta PSI total withoutbypassdelta PSI total with bypass

delta PSI total machine

refref urQ⋅⋅

=π

ϕ 2

2

2

ref

tt u

p⋅Δ⋅

=Ψρ

NPSH - Characteristic

NPSH Net Positive Suction Head

-Single flow channel with side space-Cavitation model (volume fraction based)-Back pressure on exhaust

Cavitation on place with lowest pressure

Reduce back pressure one exhaust

No „negative“ pressurein the pump

Cross section decreases

Turbulence increases

Delivery head decreases 3%

gpp

NPSHref

vaporinlett

⋅

−=

ρ,

NPSH-Value [m]pt,inlet = total pressure inlet [Pa]pvapor = vaporizing pressure [Pa]ρref = density of fluid [kg/m³]g = gravity [m/s²]

NPSH Curve

NPSH value for design point

Pressure profile on blade

lowest pressure

cavitate at first

Cavitation on blade

Areas with cavitation

Pressure profile on blade

Complete machine

The complete machine

Optimized pump grid(complete machine)

Frozen rotor calculation withterms of first order

discretisation

Frozen rotor calculation withterms of first and second

order discretisation

The complete machine

-rotate grid with side space

-very resource intensive calculation

-connect spiral with rotated grid

-pump characteristic at design point

-frozen rotor calculation

-rotor change position in steps of 9 degree

-characteristic through different rotor settings

727000 Nodes

Pressure profile 0°

Sections of high pressure

Sections of low pressure

Outlet Stagnation point

Blades

Hub

Rotation direction Connection between pump and spiral

Pressure profile 45°

Comparison of results

Total pressure and efficiency depend on rotor position

Total pressure

115000

120000

125000

130000

135000

140000

145000

150000

155000

0° 9° 18° 27° 36° 45° 54° 63° 72°

Impeller position

Pa

p total pump p total impeller p total overall

Efficiency

0,60

0,65

0,70

0,75

0,80

0,85

0,90

0,95

0° 9° 18° 27° 36° 45° 54° 63° 72°

Impeller positioneta pump eta impeller eta overall

Conclusions

• It is possible to mesh pump geometry with the given mashing tools.

• An iterative procedure is the best procedure to get the results.

• It is possible to get results only with the given inputs.

• The results of the IDS-Suite matching with the results of the industrial test rig.

• It is possible to design a centrifugal pump with CAE

Discussion

Thank youDiscussion