a first contact with star-ccm+mdx2.plm.automation.siemens.com/sites/default/files/... · 2018. 5....

Comparing analytical and finite volume solutions

with STAR-CCM+ simulations

A first contact

with STAR-CCM+

Michael Heyer

[email protected]

Analytical Finite volumes STAR-CCM+

2 / 21

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

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3 / 21

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

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4 / 21

Poiseuille flow

→ Analytical solution



Oil film in a bearing

Poiseuille flow : laminar flow in a tube

𝐯𝒛 𝒓 = ∆𝒑

𝟒 𝑳 𝝁 𝑹𝟐 − 𝒓𝟐

vz(r) : fluid velocity at the distance r from the central axis [m/s]

Dp: pressure difference between the inlet and the outlet of the tube: 10 Pa

L: tube length: 50 cm m: dynamical viscosity (water): 8.887110-4 Pas

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 0.141

0.125 0.132

0.25 0.105

0.375 0.062

0.5 0

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Poiseuille flow





Inlet Outlet

50 cm

0.5 cm

Stagnation

inlet

Pressure

outlet

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

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Poiseuille flow





r [cm] Analytical velocity [m/s] STAR-CCM+ velocity [m/s]

0 0.141

0.125 0.132

0.25 0.105

0.375 0.062

0.5 0

0.056

0.055

0.052

0.044

-0.006

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Poiseuille flow





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 0.141 0.056 0.095 0.1

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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 :

𝒑𝒔𝒕𝒂𝒕𝒊𝒄 = 𝒑𝒕𝒐𝒕𝒂𝒍 − 𝝆𝐯𝟐

𝟐= 𝟖. 𝟒 𝑷𝒂

and we use the static pressure in the Poiseuille équation.

Poiseuille flow





Length [m]

Sta

tic

pre

ss

ure

[P

a]

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 )

Velo

cit

y [

m/s

]

0.1

Inlet

Outlet

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Poiseuille flow





Length [m]

Sta

tic

pre

ss

ure

[P

a]

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

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Poiseuille flow





Length [m]

Sta

tic

pre

ss

ure

[P

a]

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 0.1

𝐯𝒛 𝒓 = ∆𝒑

𝟒 𝑳 𝝁 𝑹𝟐 − 𝒓𝟐

0.1025

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Poiseuille flow





Length [m]

Sta

tic

pre

ss

ure

[P

a]

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.

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12 / 21

Poiseuille flow



→ Numerical solution


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

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13 / 21

Poiseuille flow





Principle of mass conservation:

0y

v

x

v yx

Equation of momentum conservation:

y

v

y

vv

x

vv 2

x2

xy

xx

Equation of energy conservation:

yv

xv

y

vx

cya yx

2

p2

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)]

yArbre

Coussinetx

Film

lubrifiant

Lubricating

oil film

Bearing bush

Shaft

shaft = 50 °C

bush = 30 °C

vx

vy = 0 in every point

vx = ay + b

= cy2 + dy + e

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Poiseuille flow





yArbre

Coussinetx

Film

lubrifiant

Lubricating

oil film

Bearing bush

Shaft

shaft = 50 °C

bush = 30 °C

vx

Velocity equation: ys

*1

844,9773vx

vx (Node 3) = 2.199115 m/s

vx (Node 2) = 1.466077 m/s

vx (Node 1) = 0.7330383 m/s

0

1

2

3

4

0 1 2 3

Noeud

vx [m/s]

0.3

mm

vx = ay + b

Vx shaft = 2.9321531 m/s

Vx bush= 0 m/s

N

ode

Shaft

Bearing bush

No

de

0

1

2

3

4

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Poiseuille flow





yArbre

Coussinetx

Film

lubrifiant

Lubricating

oil film

Bearing bush


bush = 30 °C

vx

Noeud

0.3

mm

Node

Shaft

Bearing bush

No

de

1

0

2

3

4

= cy2 + dy + e

𝐜 = −𝜈

2 𝑎𝑐𝑝

𝜕vx𝜕𝑦

2

Temperature equation: C30y*m

K5,145625y*

m

K10*196,263

2

2

6

0

1

2

3

4

25 35 45 [°C]

(Node 3) = 49,44143 °C

(Node 2) = 45,92191 °C

(Node 1) = 39,44144 °C

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yArbre

Coussinetx

Film

lubrifiant

Lubricating

oil film

Bearing bush

Shaft

shaft = 50 °C

bush = 30 °C

vx

0.3

mm

No

de

1

0

2

3

4

Poiseuille flow





Equation of momentum conservation:

y

v

y

vv

x

vv 2

x2

xy

xx

Node y Analytical velocity [m/s] Finite volume velocity [m/s]

4

3

2

1

0

2.932153

2.1991148

1.4660765

0.7330382

0

2.932153

2.1991147

1.4660765

0.7330382

0

uy(t+1) = uy(t) + Dt

Dy2 uy+1(t) - 2 uy(t) + uy-1(t)

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yArbre

Coussinetx

Film

lubrifiant

Lubricating

oil film

Bearing bush

Shaft

shaft = 50 °C

bush = 30 °C

vx

0.3

mm

No

de

1

0

2

3

4

Poiseuille flow





Equation of energy conservation:

Node y Analytical temperature [°C] Finite volume temperature [°C]

4

3

2

1

0

yv

xv

y

vx

cya yx

2

p2

2

50

49.4414354

45.9219139

39.4414454

30

50

49.44142

45.92190

39.44142

30

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Left face

Right face

Front face

Back face Shaft face

Bush face

Meshing models: « Surface Remesher » et « Trimmer »

Poiseuille flow





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

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Poiseuille flow





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

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Poiseuille flow





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


bush = 30 °C

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Questions ?

a first contact with star-ccm+mdx2.plm.automation.siemens.com/sites/default/files/... · 2018. 5....

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