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Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
Numerical and Experimental Analyses
of Pump Intakes
Aljaž Škerlavaj
Turboinštitut, Ljubljana, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
25. April 2013, Wien
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 2 / 20
Fluid Flow in Pump Intakes
IMPELLER
Testing:
1.) vortices
2.) swirl angle
3.) axial velocity distr.
PUMP SUMP / INTAKE
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 3 / 20
IMPELLER
PUMP SUMP / INTAKE
Testing:
1.) vortices
2.) swirl angle
3.) axial velocity distr.
Rechannel, model, typical = 8000
Rebell, model, typical = 8E+04
PUMP BELL
Fluid Flow in Pump Intakes
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 4 / 20
Consequences of vortices
• Vibrations and noise
• Extreme consequences:
Case 1: submerged vortices Case 2: Air-entraining vortices
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 5 / 20
(Experimental) Model studies
• Initial geometry design: recommendations, based
on experience
• Properly conducted physical model study is
momentary the only reliable method to prove good
sump design or to identify unacceptable flow
patterns at the pump inlet for a given sump design
• Geometrical similarity, dynamic similarity – Froude
number
• Needs for model studies:
– Improving of existing ("old") pump sumps by introducing
the remedial measures
– Checking of new designs
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 6 / 20
Hydraulic model of pump sump
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 7 / 20
Hydraulic model - details
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 8 / 20
Numerical simulations
• Numerical simulations of pump intakes should be reliable
• Short-term perspective: to assist the physical models
• Long-term perspective: to replace physical model testing
• A prescription of a turbulence model has a large influence on
result of the simulation
• Majority of numerical simulations use k-ε or k-ω turbulence
models (lately some of them use LES)
• The first case of using (quality) LES: Tokyay and
Constantinescu (2005)
– SST steady state simulation vs. LES (unsteady simulation)
– unequal meshes: 1 million el. for SST, 5 million el. for LES
– LES: good agreement with measurement data (velocity, TKE),
measured by Yulin et al. (2000)
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 9 / 20
Governing equations
• Navier-Stokes equations (const. viscosity and density):
• Variable decomposition:
a) Time averaging – RANS equations:
b) Filtering – LES:
0 ,j
j
u
x



2
0
0
1i i i
j
j i j j
u u up
u
t x x x x
  
    
     
A A A 
0 ,j
j
u
x



2
0
0
1 i ji i i
j
j i j j j
u u up
u
t
u
x x x x
u
x
  
     
    
 


2
0
0 0
11
R
ij
j
i i i
j
j i j j
u u up
u
t x xx x x
  
     
    

 
0 ,j
j
u
x



     , , , d
D
A t G A t x r x x r r
0
0
1 t t
i it
A Adt
t


 
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 10 / 20
Geometry
Rebell = 1.7E+05
Repipe = 2.1E+05
D = 0.1298 m
Dbell = 0,16 m
Wduct = 0.193 m
H = 0.247 m
Ubell = 1.07 m/s
Two inlet channels with
unequal flow rates
Source: (Škerlavaj et al., 2011)
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 11 / 20
Setup of numerical model
• One computational mesh for all turbulence models
tested (block-structured, 35 million el.)
• Ansys CFX
• Steady-state and transient numerical simulations
• Turbulence models: SST, SAS (v. 2005 and 2007),
SSG RSM, BSL EARSM, DES, LES
• Curvature correction (CC): SST, SAS
• Time-step size: equal (i.e, small) in all simulations
Source: (Škerlavaj et al., 2011)
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 12 / 20
Computation time
Source: (Škerlavaj et al., 2011)
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 13 / 20
Results (velocity, TKE)
SST
SST-CC
SAS
SAS-CC
LES
Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE
Velocity TKE
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 14 / 20
SST
SAS
SST-CC
LES
SAS-CC
Results (vortical structures)
DES
Source: (Škerlavaj et al., 2011)
Q=50000 s-2 Q=500000 s-2
Q=50000 s-2 Q=500000 s-2
 1
2
ij ij ij ijQ S S Ω Ω
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 15 / 20
SAS-CC,25mil.el.
Results (SAS-CC)
Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 16 / 20
L2 L1
L3 L4
SAS-CC, 25 mil. el.
Results (SAS-CC model)
Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 17 / 20
Conclusions
• A combination of physical and numerical model (CFD)
seems an optimal combination for quality design of
pump intakes
• Benefits of experiment: easy to perform experiments
with geometry variations, easy to observe free-surface
vortices
• CFD: prediction of floor vortex can be very accurate
(depending on turbulence model):
– SAS-CC: good agreement with LES and with measurements
– DES: (less suitable for industrial cases than SAS), good result
– 2-eq. RANS: usage of CC is necessary
– SST-CC: in the upper part of the vortex the shape is not
predicted well
– RSM in EARSM: slow convergence rate, long computation time
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
www.turboinstitut.si info@turboinstitut.si,
1000 Ljubljana, Rovšnikova 7, Slovenia
ANSYS conference & CADFEM Austria Users’ Meeting
Wien, 25. April 2013 Slide 18 / 20
References
• Geometry and published measurements:
– Tokyay TE, Constantinescu SG (2006). Validation of large-eddy
simulation model to simulate flow in pump intakes of realistic
geometry. Journal of Hydraulic Engineering 132(12),1303-1315.
– Tokyay TE, Constantinescu SG (2005). Large eddy simulation and
Reynolds averaged Navier-Stokes simulations of flow in a realistic
pump intake: a validation study. Proceedings of the World Water and
Environmental Resources Congress. Anchorage, Alaska, USA.
• Measurements:
– Yulin W, Yong L, Xiaoming L (2000). PIV experiments on flow in a
model pump suction sump. Research report, Beijing: Tsinghua
University.
• Our results:
– Škerlavaj A, Škerget L, Ravnik J, Lipej A (2011). Choice of a
turbulence model for pump intakes. Proceedings of the IMechE, Part
A: Journal of Power and Energy 225(6),764-778.
Numerical and Experimental Analyses of Pump Intakes
________________________________________________________________________________________________________________________
________________________________________________________________________________________________________________________
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ANSYS: Numerical and experimental analysis of pump intakes

  • 1. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ Numerical and Experimental Analyses of Pump Intakes Aljaž Škerlavaj Turboinštitut, Ljubljana, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting 25. April 2013, Wien
  • 2. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 2 / 20 Fluid Flow in Pump Intakes IMPELLER Testing: 1.) vortices 2.) swirl angle 3.) axial velocity distr. PUMP SUMP / INTAKE
  • 3. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 3 / 20 IMPELLER PUMP SUMP / INTAKE Testing: 1.) vortices 2.) swirl angle 3.) axial velocity distr. Rechannel, model, typical = 8000 Rebell, model, typical = 8E+04 PUMP BELL Fluid Flow in Pump Intakes
  • 4. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 4 / 20 Consequences of vortices • Vibrations and noise • Extreme consequences: Case 1: submerged vortices Case 2: Air-entraining vortices
  • 5. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 5 / 20 (Experimental) Model studies • Initial geometry design: recommendations, based on experience • Properly conducted physical model study is momentary the only reliable method to prove good sump design or to identify unacceptable flow patterns at the pump inlet for a given sump design • Geometrical similarity, dynamic similarity – Froude number • Needs for model studies: – Improving of existing ("old") pump sumps by introducing the remedial measures – Checking of new designs
  • 6. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 6 / 20 Hydraulic model of pump sump
  • 7. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 7 / 20 Hydraulic model - details
  • 8. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 8 / 20 Numerical simulations • Numerical simulations of pump intakes should be reliable • Short-term perspective: to assist the physical models • Long-term perspective: to replace physical model testing • A prescription of a turbulence model has a large influence on result of the simulation • Majority of numerical simulations use k-ε or k-ω turbulence models (lately some of them use LES) • The first case of using (quality) LES: Tokyay and Constantinescu (2005) – SST steady state simulation vs. LES (unsteady simulation) – unequal meshes: 1 million el. for SST, 5 million el. for LES – LES: good agreement with measurement data (velocity, TKE), measured by Yulin et al. (2000)
  • 9. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 9 / 20 Governing equations • Navier-Stokes equations (const. viscosity and density): • Variable decomposition: a) Time averaging – RANS equations: b) Filtering – LES: 0 ,j j u x    2 0 0 1i i i j j i j j u u up u t x x x x               A A A  0 ,j j u x    2 0 0 1 i ji i i j j i j j j u u up u t u x x x x u x                   2 0 0 0 11 R ij j i i i j j i j j u u up u t x xx x x                  0 ,j j u x         , , , d D A t G A t x r x x r r 0 0 1 t t i it A Adt t    
  • 10. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 10 / 20 Geometry Rebell = 1.7E+05 Repipe = 2.1E+05 D = 0.1298 m Dbell = 0,16 m Wduct = 0.193 m H = 0.247 m Ubell = 1.07 m/s Two inlet channels with unequal flow rates Source: (Škerlavaj et al., 2011)
  • 11. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 11 / 20 Setup of numerical model • One computational mesh for all turbulence models tested (block-structured, 35 million el.) • Ansys CFX • Steady-state and transient numerical simulations • Turbulence models: SST, SAS (v. 2005 and 2007), SSG RSM, BSL EARSM, DES, LES • Curvature correction (CC): SST, SAS • Time-step size: equal (i.e, small) in all simulations Source: (Škerlavaj et al., 2011)
  • 12. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 12 / 20 Computation time Source: (Škerlavaj et al., 2011)
  • 13. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 13 / 20 Results (velocity, TKE) SST SST-CC SAS SAS-CC LES Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE Velocity TKE
  • 14. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 14 / 20 SST SAS SST-CC LES SAS-CC Results (vortical structures) DES Source: (Škerlavaj et al., 2011) Q=50000 s-2 Q=500000 s-2 Q=50000 s-2 Q=500000 s-2  1 2 ij ij ij ijQ S S Ω Ω
  • 15. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 15 / 20 SAS-CC,25mil.el. Results (SAS-CC) Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE
  • 16. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 16 / 20 L2 L1 L3 L4 SAS-CC, 25 mil. el. Results (SAS-CC model) Source: (Škerlavaj et al., 2011); Source of experiment: (Tokyay and Constantinescu, 2006), with permission from ASCE
  • 17. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 17 / 20 Conclusions • A combination of physical and numerical model (CFD) seems an optimal combination for quality design of pump intakes • Benefits of experiment: easy to perform experiments with geometry variations, easy to observe free-surface vortices • CFD: prediction of floor vortex can be very accurate (depending on turbulence model): – SAS-CC: good agreement with LES and with measurements – DES: (less suitable for industrial cases than SAS), good result – 2-eq. RANS: usage of CC is necessary – SST-CC: in the upper part of the vortex the shape is not predicted well – RSM in EARSM: slow convergence rate, long computation time
  • 18. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ www.turboinstitut.si info@turboinstitut.si, 1000 Ljubljana, Rovšnikova 7, Slovenia ANSYS conference & CADFEM Austria Users’ Meeting Wien, 25. April 2013 Slide 18 / 20 References • Geometry and published measurements: – Tokyay TE, Constantinescu SG (2006). Validation of large-eddy simulation model to simulate flow in pump intakes of realistic geometry. Journal of Hydraulic Engineering 132(12),1303-1315. – Tokyay TE, Constantinescu SG (2005). Large eddy simulation and Reynolds averaged Navier-Stokes simulations of flow in a realistic pump intake: a validation study. Proceedings of the World Water and Environmental Resources Congress. Anchorage, Alaska, USA. • Measurements: – Yulin W, Yong L, Xiaoming L (2000). PIV experiments on flow in a model pump suction sump. Research report, Beijing: Tsinghua University. • Our results: – Škerlavaj A, Škerget L, Ravnik J, Lipej A (2011). Choice of a turbulence model for pump intakes. Proceedings of the IMechE, Part A: Journal of Power and Energy 225(6),764-778.
  • 19. Numerical and Experimental Analyses of Pump Intakes ________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________ Thank you for your attention!
  • 20. Kontaktieren Sie uns – wir helfen Ihnen gerne! CADFEM (Austria) GmbH Wagenseilgasse 14 1120 Wien Tel. +43 (0)1 587 70 73 – 0 E-Mail. info@cadfem.at Web. http://www.cadfem.at Immer aktuell informiert – CADFEM Blog, Xing und Youtube-Channel CADFEM Blog - Umfassend informiert – http://blog.cadfem.at • News zur FEM-Simulation - What‘s hot? What‘s new? • Video-Tutorials - ANSYS, LS DYNA & mehr • Hinter den Kulissen: CADFEM intern CADFEM Youtube Channel - Tips & Trick • Video Tutorials - ANSYS Software und CADFEM Applications CADFEM auf Xing - News kompakt • Vorschau auf Events & Seminare • Neue CADFEM Produkte • CADFEM Jobbörse Fragen? Interesse?