What is the liquid jet atomization problem? Will Gerris help us solve it?

Transcription

1 What is the liquid jet atomization problem? Will Gerris help us solve it? Stéphane Zaleski Institut Jean Le Rond d Alembert, Université Pierre et Marie Curie UPMC Paris 6

2 Collaborators past and present on atomization. Jie Li (BPI, Cambride), Phil Yecko (Montclair, NJ), Thomas Boeck (Ilmenau), Jose-Maria Fullana (d Alembert), Ruben Scardovelli (Bolone), Stéphane Popinet (d Alembert), Pascal Ray (d Alembert), Luis Lemoyne (Nevers), Gaurav Tomar (Banalore), Daniel Fuster (d Alembert), Anne Baué (ONERA), Jérôme Hoepffner (d Alembert), Ralph Blumenthal (TUM), Annarazia Orrazo (Naples). Current Student Gilou Abalah

3 coflowin jet atomization (rocket enines, Formula 1 racin cars) 3

4 Interpretation 1: the simulation of liquid jet atomisation requires enormous ressources. It is thus a rand challene similar to the DNS of turbulent flow. The one with the most robust code and the biest computer wins. Interpretation : A series of mechanisms are involved in the breakup of the jet and eneration of the droplets. Explainin these mechanisms and makin quantitative predictions solves the problem. 4

5 Atomization of co-axial jets : experiments with air/water jets Lasheras, Hopfiner,Villermaux, Raynal, Cartellier, (San Dieo, Grenoble and Marseille) 5

6 Problem 1: predict the transverse wavelenth λ or the frequency f 6

7 Photoraph: Cartellier and Matas Problem : predict λ RT. λ RT refers to the theory of Cartellier and Hopfiner but in fact several Rayleih-Taylor mechanisms have been suested in the litterature. 7

8 Kelvin-Helmholtz instability perform simulation of unstable shear flow 8

9 Full DNS and Orr-Sommerfeld aree h Blue : theory Green: computation with harmonic mean Red : computation with arithmetic mean timesteps Boeck & Zaleski PoF 005, Boeck, Li, Lopez-Paes, Yecko & Zaleski TCFD 007, Baué, Fuster, Popinet, Scardovelli and Zaleski, PoF

10 Error level in percentae points : Gerris is much more accurate than Surfer but the error stops decreasin for 56! 10

11 11 Re_ = 4000, We_ = 4000 r = 10 m = 0.05 vorticity.

12 Diesel jet conditions Baué Popinet Yarlaadda It is a Gerris example now! 1

13 13

14 More realistic enineerin: 3D conical jet 14

15 Distribution of droplet sizes (PDF) depends on rid size! Δx = 9 microns Δx = 8 microns 15

16 But arees with experiment at finest resolution dx = 9 microns experiment 16

17 Clearly, we are not world champions in terms of hardware usae. Shinjo and Uemura JAXA supercomputer Δx = 350 nm 5760 cores for 410 hours 6 billion rid points (uniform) We=14000 Re=1470 U = 100 m/s 17

18 - Need for better parallelism. (althouh we et 6 billion rid points equivalent with 40 cores...) - Need for multiscale treatment : combine DNS with some type of subrid modellin, for certain reions and certain physics, such as droplets in dilute reions (far from the core). 18

19 Interpretation : physical analysis of the transverse wavelenth. Analyze the flow as a spatially-developpin mixin layer 19

20 Fully spatial D DNS to simulate setup of Grenoble s planar sheet experiment. Lare-scale structures are D. view from above separator plate super -important Gas Liquid 0

21 A mechanism of Atomization : the Kelvin-Helmholtz Instability Linear stability theory of the Kelvin-Helmholtz instability: (a) Potential flow (except at interface), Inviscid, Piecewise linear profiles (Marmottant, Raynal, Villermaux, Cartellier, Matas, others...) (b) Viscous, Error-function profiles (Yecko, Fullana, Boeck, Zaleski, Gordillo, Perez-Saborid, Ganan-Calvo, Spelt, Valluri, O Naraih... ) 1

22

23 INVISCID LINEAR STABILITY PROBLEM Nondimensional form based on as layer velocity and thickness. Ψ l, = Φ l, ( y) exp(iα(x ct)), u = y Ψ, v = x Ψ ( U, c)(d α ) Φl, D Ul,Φl, l = 0 boundary conditions on interface(s) Φ l = Φ α cwe Φ vertical velocity continuous" = 1 r ( cdφl + ΦlDUl) + cdφ + ΦDU P cont." Analytical solution when U linear function of y; dispersion relation then 4th order polynomial for the broken line profiles in liquid and as phase. General profile: numerical solution with collocation method based on expansion in Chebyshev polynomials in both (finite) layers." 3

24 Broken line profile 4

25 Continuous profile 5

26 Viscous linear stability problem (U (U Nondimensional form based on as layer velocity and thickness. " Ψ l l, = Φ c)(d c)(d l, ( y) exp(iα(x ct)), α α ) Φ ) Φ l D D U U l Φ Φ l = u = r m = y Ψ 1 iα Re, 1 iα Re v (D = (D x α Ψ α ) ) Φ Φ l boundary conditions on interface(s)" Φ l DΦ = Φ l + DU l Φ c l = DΦ + DU Φ c vertical velocity continuous" horizontal velocity continuous" 6

27 Viscous linear stability problem II m(d boundary conditions on interface(s)" α cwe + cdφ + α Φ + + Φ 1 c = D 1 r DU ( cdφ + Φ DU ) U ) Φ l = 1 + iα Re (D l (D 3 + α l 3α + r m 1 c D D) Φ 1 iα Re U ) Φ l (D l 3 continuity of" tanential stress " 3α D) Φ continuity of " normal stress" l 7

28 viscous case 8

29 Reynolds number influence 9

30 Air-water case Re = We = infinity" I : connects to inviscid KH at very hih Re II : H-mode (zero Re mode) III : similar to Tollmien-Schlichtin It is the interaction of the H mode (mode I) and the inviscid mode (mode II) that explains the difference between the Orr-Sommerfeld and inviscid results. 30

31 What is the new H mode? - named after Hooper and Boyd (198) and Hinch (1984). - a mode at Re=0 - zoom in on vicinity of the interface zoom ives Couette flow 31

32 - The H mode is an instability of Couette flow at zero Re. The scalin of the H mode can be explained as follows: - the only time scale in the shear layer is 1 / ω = δ /U thus the only lenth scale is l = ν ω = δ Re implies that the (dimensionless) most unstable wavenumber rows like Re 3

33 H-mode branch is shifted in lo diaram when Re is increased Air-water case Re = 10 3, 10 4, , , We = infinity 33

34 Numerical solutions of the Orr-Sommerfeld equations in the rane of the experiments show that dimensional wavelenth decreases like λ U 1 But experimental results show rather λ U 1/ which is the result expected for the inviscid mode! 34

35 But the theory fails. -1/ slope from inviscid theory. H-mode obtained from Orr-Sommerfeld Computations. -1 slope!!! 35

36 36 Inviscid theory also «fails». Its prediction are here.. but with the correct scalin.

37 We aere convinced that the real world is viscous... but the experiment can be interpreted only usin inviscid scalin theories! Simple explanations: - the experiment is wron (after all, it took «them» ten years to fix the errors in the initial measurements ). - the Gaster transformation does not apply (but would this chane the scalin?) Gerris will at least allow us to verify the experiment 37

38 Back to the «Grenoble» D setup. Gas Liquid 38

39 Elementary multiscale treatment: Navier-Stokes with variable minimum rid size accordin to a subdivision of the computational domain. lare minimum Δx Gas Liquid small minimum Δx medium minimum Δx 39

40 More refined multiscale modellin? E and Enquist (Comm. Math. Sci, 003) introduce the followin typoloy : Type A problems : problems that require a localised effort to capture explicitly the smallest scales. Typically a boundary layer. Type B problems: lare reions containin a homoeneous distributions of smaller sales for which an effective larer-scale model must be found. Typically the derivation of Navier-Stokes from kinetic theory, or an averaed multiphase-flow model. 40

41 Dense spray convoluted interfaces : Type A reion. Intermediate reion: Type A reions with proressive coarsenin downstream. Type B reion: dilute spray. 41

42 Simulation methodoloy Dense spray convoluted interfaces : need DNS. No subrid scale model will work. Intermediate reion: requires work and subtelty. Dilute spray: droplets may be accurately modelled as Laranian particles. 4

43 Turn to full, spatially developpin DNS Fuster et al IJMF 43

44 Viscous, Orr-Sommerfeld theory is verified!! near nozzle all stations Not the real experimental parameters however (not air-water properties) 44

45 Simulation with a separator plate at larer density ratio (1/r) m r Re Re l We We l M , ,4 45

46 Conclusion We are not solvin the problems that we think we are solvin 46

47 The End 47