A first contact with STAR-CCM+ Comparing analytical and finite volume solutions with STAR-CCM+ simulations Michael Heyer
Analytical Finite volumes STAR-CCM+ What is ParisTech? ParisTech is a consortium of 12 of the most prestigious French institutes of education and research Best University in France in Production Engineering and Manufacturing Engineering 1000 graduate engineers per year A powerful network that unites and rationalize strength while bringing international visibility 2 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ 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+ Poiseuille flow → Analytical solution 2 h → STAR-CCM+ simulation → Why is there a difference? Oil film of a plain cylindrical journal bearing: 1.5 h → Analytical solution → Numerical solution : the finite volume equation 2 h → Numerical solution : programming the finite volume equation 2 h → STAR-CCM+ simulation 2 h 3 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow → Analytical solution → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Poiseuille flow : laminar flow in a tube v z (r) r) : fluid velocity at the distance r from the 𝐰 𝒜 𝒔 = ∆𝒒 𝟓 𝑴 𝝂 𝑺 𝟑 − 𝒔 𝟑 central axis [m/s] D p: : pressure difference between the inlet and the outlet of the tube: 10 Pa r [cm] v z (r) [m/s] L: tube length: 50 cm m: dynamical viscosity (water): 8.8871 10 -4 Pa s 0 0.141 R: tube radius: 0.5 cm 0.125 0.132 r: distance from the central axis: 0 cm, 0.125 cm, 0.25 cm, 0.375 cm, 0.5 cm 0.25 0.105 0.375 0.062 0.5 0 4 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Wall Poiseuille flow → Analytical solution Inlet Outlet → STAR-CCM+ simulation 0.5 cm → Why is there a difference? Pressure Stagnation Oil film in a bearing 50 cm outlet inlet 0 Pa 10 Pa STAR-CCM+ version: 7.02.011 and 8.02.011 Meshing models: « Surface Remesher », « Polyhedral Mesher » and « Prism Layer Mesher » Physics models: Steady, Liquid , Segregated Flow, Constant Density, Laminar 5 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ 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] 0.056 0 0.141 0.055 0.125 0.132 0.25 0.105 0.052 0.375 0.062 0.044 0.5 0 -0.006 6 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow → Analytical solution Is it a problem of the Meshing model? → STAR-CCM+ simulation « Trimmer » → Why is there a difference? « Polyhedral Mesher » and « Extruder » Oil film in a bearing r [cm] Analytical velocity STAR-CCM+ STAR-CCM+ STAR-CCM+ [m/s] Polyhedral Trimmer Polyhedral Mesher + Prism [m/s] Mesher Layer Mesher + Extruder [m/s] [m/s] 0 0.141 0.056 0.095 0.1 7 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Static pressure Poiseuille flow → Analytical solution Static pressure [Pa] → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Length [m] 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: p total = p static + p dynamic ) But the fluid is moving at the inlet (0 m/s at the wall ; 0.55 m/s at the central Velocity [m/s] axis), so the static pressure is lower then 10 Pa : 0.1 Outlet 𝒒 𝒕𝒖𝒃𝒖𝒋𝒅 = 𝒒 𝒖𝒑𝒖𝒃𝒎 − 𝝇 𝐰 𝟑 𝟑 = 𝟗. 𝟓 𝑸𝒃 Inlet and we use the static pressure in the Poiseuille équation. 8 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Static pressure Poiseuille flow → Analytical solution Static pressure [Pa] → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Length [m] 2 Pa/0.1 m 2.5 Pa/0.1 m But the static inlet pressure of 8.4 Pa does not explain all the difference between the analytical solution and the STAR-CCM+ simulation! STAR-CCM+ transforms in the first part of the tube the inlet boundary condition p total = 10 Pa = constant over the inlet section into p static = constant over the section (with a parabolic velocity profile) 9 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Static pressure Poiseuille flow → Analytical solution Static pressure [Pa] → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Length [m] 1.45 Pa/0.1 m Is there now comformity between the STAR-CCM+ velocity and the analytical velocity calculated with the Poiseuille equation? r [cm] STAR-CCM+ Analytical velocity 𝐰 𝒜 𝒔 = ∆𝒒 𝟓 𝑴 𝝂 𝑺 𝟑 − 𝒔 𝟑 Polyhedral Mesher [m/s] + Extruder [m/s] 0 0.1 0.1025 10 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Static pressure Poiseuille flow → Analytical solution Static pressure [Pa] → STAR-CCM+ simulation → Why is there a difference? Oil film in a bearing Length [m] 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. 11 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow Oil film in a bearing → Analytical solution → Numerical solution → STAR-CCM+ simulation Plain cylindrical journal bearing Simplified study of the bearing Hub Lubricating oil film Film lubrifiant Coussinet Bush shaft = 50 ° C arbre = 50 °C Shaft Arbre v y x 0,3 mm x bush = 30 ° C coussinet = 47 °C 12 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow shaft = 50 ° C v x y Oil film in a bearing Shaft Arbre → Analytical solution → Numerical solution Film Lubricating → STAR-CCM+ simulation oil film lubrifiant Principle of mass conservation: x Coussinet Bearing bush v v y v y = 0 in every point bush = 30 ° C x 0 x y Equation of momentum conservation: 2 v v v v x = a y + b x x x v v x y 2 x y y v x : : fluid velocity in the x axis direction [m/s] Equation of energy conservation: : : kinematical viscosity [m 2 /s] 2 a: : thermal diffusivity [m 2 /s] 2 vx = c y 2 + d y + e a : temperature [ ° C ] v v x y 2 y x y y c c p : : specific heat [ J/(kg K) ] p 13 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow v x = a y + b shaft = 50 ° C v x y Oil film in a bearing V x haft = = 2. 2.9321531 m/s /s Shaft x sha Arbre → Analytical solution 4 Node → Numerical solution 3 0.3 mm Film Lubricating → STAR-CCM+ simulation 2 oil film lubrifiant 1 0 x V x ush = 0 0 m/s /s x bus Coussinet 1 Bearing bush v x Velocity equation: 9773 , 844 s * y bush = 30 ° C Shaft 4 Node v x ( Node 3 ) = 2.199115 m/s 3 v x ( Node 2 ) = 1.466077 m/s Noeud 2 v x ( Node 1 ) = 0.7330383 m/s 1 0 0 1 2 3 Bearing bush v x [m/s] 14 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Poiseuille flow = c y 2 + d y + e v x y Oil film in a bearing shaft = 50 ° C Shaft Arbre → Analytical solution 4 Node 2 → Numerical solution 3 𝜉 𝜖v x 0.3 mm 𝐝 = − Film Lubricating → STAR-CCM+ simulation 2 2 𝑏 𝑑 𝑞 𝜖𝑧 oil film lubrifiant 1 0 x bush = 30 ° C Coussinet Bearing bush K K Temperature equation: 2 6 263 , 196 * * 145625 , 5 * y 30 C y 10 2 m m Shaft 4 ( Node 3 ) = 49,44143 ° C Node 3 Noeud ( Node 2 ) = 45,92191 ° C 2 ( Node 1 ) = 39,44144 ° C 1 0 25 35 45 [ ° C] Bearing bush 15 / 21 michael.heyer@metz.ensam.fr
Analytical Finite volumes STAR-CCM+ Equation of momentum conservation: Poiseuille flow shaft = 50 ° C Oil film in a bearing v x 2 y → Analytical solution v v v x x x Shaft Arbre v v 4 x y → Numerical solution 2 x y y Node 3 → STAR-CCM+ simulation 0.3 mm Film Lubricating 2 oil film lubrifiant 1 u y (t+1) = u y (t) + D t 2 u y+1 (t) - 2 u y (t) + u y-1 (t) 0 x D y Coussinet Bearing bush bush = 30 ° C Node y Analytical velocity [m/s] Finite volume velocity [m/s] 4 2.932153 2.932153 3 2.1991148 2.1991147 2 1.4660765 1.4660765 1 0.7330382 0.7330382 0 0 0 16 / 21 michael.heyer@metz.ensam.fr
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