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

Transcription

1 A first contact with STAR-CCM+ Comparing analtical and finite volume solutions with STAR-CCM+ simulations Michael Heer

2 Analtical Finite volumes STAR-CCM+ What is ParisTech? ParisTech is a consortium of 1 of the most prestigious French institutes of education and research Best Universit in France in Production Engineering and Manufacturing Engineering 1 graduate engineers per ear A powerful network that unites and rationalize strength while bringing international visibilit / 1

3 Analtical Finite volumes STAR-CCM+ Stud program of our students : Objectif: to show the relationship between the analtical solution, the finite volume solution and the STAR-CCM+ simulation for the same problem 1 h :.5 h Discovering of STAR-CCM+ h Wh is there a difference? Oil film of a plain clindrical journal bearing: 1.5 h h Numerical solution : the finite volume equation h Numerical solution : programming the finite volume equation h 3 / 1

4 Analtical Finite volumes STAR-CCM+ Wh is there a difference? : laminar flow in a tube v z r = r [cm] p 4 L μ R r v z (r) [m/s] v z (r) : fluid velocit at the distance r from the central ais [m/s] Dp: pressure difference between the inlet and the outlet of the tube: 1 Pa L: tube length: 5 cm m: dnamical viscosit (water): Pas R: tube radius:.5 cm r: distance from the central ais: cm,.15 cm,.5 cm,.375 cm,.5 cm 4 / 1

5 Analtical Finite volumes STAR-CCM+ Wh is there a difference? Inlet Stagnation inlet.5 cm Wall 5 cm Outlet Pressure outlet 1 Pa Pa STAR-CCM+ version: and Meshing models: «Surface Remesher», «Polhedral Mesher» and «Prism Laer Mesher» Phsics models: Stead, Liquid, Segregated Flow, Constant Densit, Laminar 5 / 1

6 Analtical Finite volumes STAR-CCM+ Wh is there a difference? r [cm] Analtical velocit [m/s] STAR-CCM+ velocit [m/s] / 1

7 Analtical Finite volumes STAR-CCM+ Wh is there a difference? Is it a problem of the Meshing model? «Trimmer» «Polhedral Mesher» and «Etruder» r [cm] Analtical velocit [m/s] STAR-CCM+ Polhedral Mesher + Prism Laer Mesher [m/s] STAR-CCM+ Trimmer [m/s] STAR-CCM+ Polhedral Mesher + Etruder [m/s] / 1

8 Velocit [m/s] Static pressure [Pa] Analtical Finite volumes STAR-CCM+ Wh is there a difference? Static pressure Length [m] Wh is the static pressure at the inlet 8.4 Pa and not 1 Pa? The boundar condition «Stagnation inlet» imposes a total pressure of 1 Pa and not a static pressure of 1 Pa at the inlet (Remember: p total = p static + p dnamic ) But the fluid is moving at the inlet ( m/s at the wall ;.55 m/s at the central ais), so the static pressure is lower then 1 Pa :.1 p static = p total ρ v = 8. 4 Pa and we use the static pressure in the Poiseuille équation. Inlet Outlet 8 / 1

9 Static pressure [Pa] Analtical Finite volumes STAR-CCM+ Wh is there a difference? Static pressure Length [m].5 Pa/.1 m Pa/.1 m But the static inlet pressure of 8.4 Pa does not eplain all the difference between the analtical solution and the STAR-CCM+ simulation! STAR-CCM+ transforms in the first part of the tube the inlet boundar condition p total = 1 Pa = constant over the inlet section into p static = constant over the section (with a parabolic velocit profile) 9 / 1

10 Static pressure [Pa] Analtical Finite volumes STAR-CCM+ Wh is there a difference? Static pressure Length [m] 1.45 Pa/.1 m Is there now comformit between the STAR-CCM+ velocit and the analtical velocit calculated with the Poiseuille equation? r [cm] STAR-CCM+ Polhedral Mesher + Etruder [m/s] Analtical velocit [m/s] v z r = p 4 L μ R r / 1

11 Static pressure [Pa] Analtical Finite volumes STAR-CCM+ Wh is there a difference? Static pressure 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 velocit/pressure dependance onl in the part where the pressure gradient is constant. Meshing models have a big influence on the results. 11 / 1

12 Analtical Finite volumes STAR-CCM+ Numerical solution Plain clindrical journal bearing Hub Simplified stud of the bearing Lubricating Film lubrifiant oil film Coussinet Bush Arbre Shaft arbre shaft = 5 5 C C v,3 mm coussinet bush = 3 = 47 C C 1 / 1

13 Analtical Finite volumes STAR-CCM+ shaft = 5 C Numerical solution Shaft Arbre Lubricating Film oil lubrifiant film v Principle of mass conservation: v v Equation of momentum conservation: v v v v v Equation of energ conservation: a c p v v v = in ever point v v = a + b = c + d + e Bearing Coussinet bush bush = 3 C v : fluid velocit in the ais direction [m/s] : kinematical viscosit [m /s] a: thermal diffusivit [m /s] : temperature [ C] c p : specific heat [J/(kg K)] 13 / 1

14 Noeud Node Node.3 mm Analtical Finite volumes STAR-CCM+ v = a + b shaft = 5 C Numerical solution V shaft = m/s Shaft Arbre Lubricating Film oil lubrifiant film v Velocit equation: v ,844 s * V bush = m/s Bearing Coussinet bush bush = 3 C Shaft 1 3 Bearing bush v [m/s] v (Node 3) = m/s v (Node ) = m/s v (Node 1) = m/s 14 / 1

15 Noeud Node Node.3 mm Analtical Finite volumes STAR-CCM+ = c + d + e Numerical solution c = ν v ac p shaft = 5 C Shaft Arbre Lubricating Film oil lubrifiant film v bush = 3 C Bearing Coussinet bush Temperature equation: Shaft Bearing bush K K 63,196*1 6 * 14565,5 * 3 C m m [ C] (Node 3) = 49,44143 C (Node ) = 45,9191 C (Node 1) = 39,44144 C 15 / 1

16 Node.3 mm Analtical Finite volumes STAR-CCM+ Numerical solution u (t+1) = u (t) + Dt D Equation of momentum conservation: v v v v v u +1 (t) - u (t) + u -1 (t) Shaft Arbre Lubricating Film oil lubrifiant film Bearing Coussinet bush Node Analtical velocit [m/s] Finite volume velocit [m/s] shaft = 5 C v bush = 3 C / 1

17 Node.3 mm Analtical Finite volumes STAR-CCM+ Equation of energ conservation: shaft = 5 C Numerical solution a c p v v v Shaft Arbre Lubricating Film oil lubrifiant film v Bearing Coussinet bush bush = 3 C Node Analtical temperature [ C] Finite volume temperature [ C] / 1

18 Analtical Finite volumes STAR-CCM+ Numerical solution Translational periodic Left face.3 mm Wall Shaft face.93 m/s Front face Smmetr plane STAR-CCM+ version: and C Smmetr plane m/s 3 C Bush face Wall Back face Right face Translational periodic Meshing models: «Surface Remesher» et «Trimmer» Phsics models: Stead, Liquid, Segregated Flow, Constant Densit, Laminar, Segregated Fluid Temperature 18 / 1

19 Analtical Finite volumes STAR-CCM+ Numerical solution Left face Shaft face.93 m/s Back face Right face m/s Front face Bush face Node Analtical velocit Fin volume velocit STAR-CCM+ velocit 3, , ,1958,196 1, , ,465 1,4879 1,73338,73338,7315, / 1

20 Analtical Finite volumes STAR-CCM+ Numerical solution Lubricating Film lubrifiant oil film Coussinet Bush Arbre Shaft shaft = 5 C arbre = 5 C v,3 mm coussinet = 47 C bush = 3 C 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+ / 1

21 Questions?