A first contact with STAR-CCM+ Comparing analytical and finite - - PowerPoint PPT Presentation

Comparing analytical and finite volume solutions with STAR-CCM+ simulations

A first contact with STAR-CCM+

Michael Heyer

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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ParisTech is a consortium of 12 of the most prestigious French institutes of education and research A powerful network that unites and rationalize strength

while bringing international visibility

What is ParisTech?

Best University in France in Production Engineering and Manufacturing Engineering 1000 graduate engineers per year

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Study program of our students : Objectif: to show the relationship between the analytical solution, the finite volume solution and the STAR-CCM+ simulation for the same problem 12 h : 2.5 h Discovering of STAR-CCM+ 2 h Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film of a plain cylindrical journal bearing: 1.5 h → Analytical solution 2 h → Numerical solution : the finite volume equation 2 h → Numerical solution : programming the finite volume equation 2 h → STAR-CCM+ simulation

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

4 / 21

Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Poiseuille flow : laminar flow in a tube 𝐰𝒜 𝒔 = ∆𝒒 𝟓 𝑴 𝝂 𝑺𝟑 − 𝒔𝟑

vz(r) r) : fluid velocity at the distance r from the central axis [m/s] Dp: : pressure difference between the inlet and the

• utlet of the tube: 10 Pa

L: tube length: 50 cm m: dynamical viscosity (water): 8.887110-4 Pas R: tube radius: 0.5 cm r: distance from the central axis: 0 cm, 0.125 cm, 0.25 cm, 0.375 cm, 0.5 cm

r [cm] vz(r) [m/s] 0.141 0.125 0.132 0.25 0.105 0.375 0.062 0.5

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Inlet Outlet

50 cm 0.5 cm

Stagnation inlet Pressure

• utlet

Wall

• Meshing models:

« Surface Remesher », « Polyhedral Mesher » and « Prism Layer Mesher »

• Physics models:

Steady, Liquid, Segregated Flow, Constant Density, Laminar

10 Pa 0 Pa

• STAR-CCM+ version: 7.02.011 and 8.02.011

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing r [cm] Analytical velocity [m/s] STAR-CCM+ velocity [m/s] 0.141 0.125 0.132 0.25 0.105 0.375 0.062 0.5 0.056 0.055 0.052 0.044

• 0.006

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

7 / 21

Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing

• Is it a problem of the Meshing model?
• « Trimmer »
• « Polyhedral Mesher » and « Extruder »

r [cm] Analytical velocity [m/s] STAR-CCM+ Polyhedral Mesher + Prism Layer Mesher [m/s] STAR-CCM+ Trimmer [m/s] STAR-CCM+ Polyhedral Mesher + Extruder [m/s] 0.141 0.056 0.095 0.1

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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But the fluid is moving at the inlet (0 m/s at the wall ; 0.55 m/s at the central axis), so the static pressure is lower then 10 Pa : 𝒒𝒕𝒖𝒃𝒖𝒋𝒅 = 𝒒𝒖𝒑𝒖𝒃𝒎 − 𝝇 𝐰𝟑 𝟑 = 𝟗. 𝟓 𝑸𝒃 and we use the static pressure in the Poiseuille équation. Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing

Length [m] Static pressure [Pa] Static pressure

Why is the static pressure at the inlet 8.4 Pa and not 10 Pa ? The boundary condition « Stagnation inlet » imposes a total pressure of 10 Pa and not a static pressure of 10 Pa at the inlet (Remember: ptotal = pstatic + pdynamic )

Velocity [m/s] 0.1

Inlet Outlet

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

9 / 21

Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing

Length [m] Static pressure [Pa] Static pressure

But the static inlet pressure of 8.4 Pa does not explain all the difference between the analytical solution and the STAR-CCM+ simulation!

2.5 Pa/0.1 m

STAR-CCM+ transforms in the first part of the tube the inlet boundary condition ptotal = 10 Pa = constant over the inlet section into pstatic = constant over the section (with a parabolic velocity profile)

 2 Pa/0.1 m

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

10 / 21

Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing

Length [m] Static pressure [Pa] Static pressure

Is there now comformity between the STAR-CCM+ velocity and the analytical velocity calculated with the Poiseuille equation?

1.45 Pa/0.1 m

r [cm] STAR-CCM+ Polyhedral Mesher + Extruder [m/s] Analytical velocity [m/s] 0.1 𝐰𝒜 𝒔 = ∆𝒒 𝟓 𝑴 𝝂 𝑺𝟑 − 𝒔𝟑 0.1025

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

11 / 21

Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing

Length [m] Static pressure [Pa] Static pressure

Conclusions:  It is difficult to impose a static pressure drop with STAR-CCM+.  We recommand to foresee a run-in length and to calculate the velocity/pressure dependance only in the part where the pressure gradient is constant.  Meshing models have a big influence on the results.

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

12 / 21

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

• Simplified study of the bearing

Arbre Film lubrifiant Coussinet 0,3 mm x y v

x



arbre = 50 °C



coussinet = 47 °C

• Plain cylindrical journal bearing

Lubricating oil film Bush Shaft

shaft = 50 °C bush = 30 °C

Hub

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

• Principle of mass conservation:

y v x v

y x

     

• Equation of momentum conservation:

y v y v v x v v

2 x 2 x y x x

        

• Equation of energy conservation:

y v x v y vx c y a

y x 2 p 2 2

                      

vx: : fluid velocity in the x axis direction [m/s] : : kinematical viscosity [m2/s] a: : thermal diffusivity [m2/s] : temperature [°C] cp: : specific heat [J/(kg K)]

y Arbre Coussinet x Film lubrifiant Lubricating

• il film

Bearing bush Shaft

shaft = 50 °C bush = 30 °C

vx

 vy = 0 in every point  vx = ay + b   = cy2 + dy + e

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

14 / 21

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

y Arbre Coussinet x Film lubrifiant Lubricating

• il film

Bearing bush Shaft

shaft = 50 °C bush = 30 °C

vx

• Velocity equation:

y s * 1 844 , 9773 vx 

vx (Node 3) = 2.199115 m/s vx (Node 2) = 1.466077 m/s vx (Node 1) = 0.7330383 m/s

1 2 3 4 1 2 3

Noeud

vx [m/s]

0.3 mm

 vx = ay + b

Vx

x sha haft =

= 2. 2.9321531 m/s /s Vx

x bus ush= 0

0 m/s /s Node

Shaft Bearing bush

Node

1 2 3 4

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

15 / 21

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

y Arbre Coussinet x Film lubrifiant Lubricating

• il film

Bearing bush Shaft

shaft = 50 °C bush = 30 °C vx Noeud

0.3 mm

Node

Shaft Bearing bush

Node

1 2 3 4

  = cy2 + dy + e 𝐝 = − 𝜉 2 𝑏𝑑𝑞 𝜖vx 𝜖𝑧

2

• Temperature equation:

C 30 y * m K 5 , 145625 y * m K 10 * 196 , 263

2 2 6

     

1 2 3 4 25 35 45

 [°C]  (Node 3) = 49,44143 °C  (Node 2) = 45,92191 °C  (Node 1) = 39,44144 °C

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

16 / 21 y Arbre Coussinet x Film lubrifiant Lubricating

• il film

Bearing bush Shaft

shaft = 50 °C bush = 30 °C

vx

0.3 mm

Node

1 2 3 4

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

• Equation of momentum conservation:

y v y v v x v v

2 x 2 x y x x

        

Node y Analytical velocity [m/s] Finite volume velocity [m/s] 4 3 2 1 2.932153 2.1991148 1.4660765 0.7330382 2.932153 2.1991147 1.4660765 0.7330382 uy(t+1) = uy(t) +  Dt Dy

2 uy+1(t) - 2 uy(t) + uy-1(t)

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

17 / 21 y Arbre Coussinet x Film lubrifiant Lubricating

• il film

Bearing bush Shaft

shaft = 50 °C bush = 30 °C

vx

0.3 mm

Node

1 2 3 4

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

• Equation of energy conservation:

Node y Analytical temperature [°C] Finite volume temperature [°C] 4 3 2 1

y v x v y vx c y a

y x 2 p 2 2

                      

50 49.4414354 45.9219139 39.4414454 30 50 49.44142 45.92190 39.44142 30

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

18 / 21 Left face Right face Front face Back face Shaft face Bush face

• Meshing models: « Surface Remesher » et « Trimmer »

Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

• Physics models:

Steady, Liquid, Segregated Flow, Constant Density, Laminar, Segregated Fluid Temperature

• STAR-CCM+ version: 7.02.011 and 8.02.011

Wall 2.93 m/s Wall Symmetry plane Symmetry plane Translational periodic Translational periodic 0 m/s 50 °C 30 °C

0.3 mm

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation 3 2 1 2,1991148 1,4660765 0,7330382 2,1991147 1,4660765 0,7330382 STAR-CCM+ velocity

Left face Right face Front face Back face Shaft face Bush face

Node y Analytical velocity Fin volume velocity 2,1958 → 2,1962 1,4650 → 1,4879 0,7315 → 0,7354

2.93 m/s 0 m/s

michael.heyer@metz.ensam.fr

Analytical  Finite volumes  STAR-CCM+

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Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation

Conclusion :

Students learn the application of the fondamental heat transfer equations a simple version of programming code of STAR-CCM+  a (mistrustful) use of STAR-CCM+

Arbre Film lubrifiant Coussinet 0,3 mm x y v

x



arbre = 50 °C



coussinet = 47 °C

Lubricating oil film Bush Shaft

shaft = 50 °C bush = 30 °C

michael.heyer@metz.ensam.fr

Questions ?