Large Eddy Simulation of Impinging Jets with Heat Transfer

1. Large Eddy Simulation of Impinging Jets withHeat Transfer Thomas Hällqvist KTH / Scania CV AB

2. Outline • Background • Project description • Computational method and cases • Results • Summary

3. Background • Project initiated in year 2000 by KTH and Scania CV AB • Industrial goal:Improve the cooling capacity of Scania heavy trucks • Increase of the engine power. • Decrease of available space.

4. Outline • Background • Project description • Computational method and cases • Results • Summary

5. Project description • To capture basic physical features a simplified geometry is studied • The under-hood flow is approximated by an impinging jet • Scientific goal:To enhance the understanding of the flow and dynamics of impinging jets; including • Impinging jet flow and related heat transfer. • Turbulence and its modeling for such flows. • Utilizing modern computational tools.

6. The Impinging Jet (I) Impinging jets are common in engineering applications • Processing of metal, glass and paper. • Cooling applications: electronics, gas-turbine combustion chambers, mechanical devices. Other more indirect application areas • VTOL aircrafts, rockets (when close to the ground). • High pressure washers.

7. The Impinging Jet (II) The impinging jet is characterized by three flow regions • The free jet region. • The stagnation region. • The wall jet region. Geometrical parameters D: Nozzle diameter H: Impingement distance W: Width Nozzle outlet conditions V0: Mean axial velocity C0: Mean concentration k0: Turbulent kinetic energy

8. The Impinging Jet (III) Nozzle condition A Nozzle condition B Impingement wall heat transfer depends on • Nozzle conditions. • Impingement distance (H/D). For small H/D • Minimum of Nu at r/D=0. • Two maximums of Nu. For large H/D • Maximum of Nu at r/D=0. • Monotone decrease with r/D. Maximum in stagnation Nu • Depends on the nozzle conditions. • Within the range: H/D=3-8. • End of the potential core. H/D=2 H/D=4 Nusselt number (Nu) H/D=6 hypothetical impingement wall 0 r/D R

9. Outline • Background • Project description • Computational method and cases • Results • Summary

10. Computational method • Impinging jet simulated by large-eddy simulation (LES). • Space-filtering to reduce the number of degrees of freedom. • The effects from the unresolved scales must be modeled • Dissipation of energy. • Backscatter, structural information. • Despite the filtering LES is computationally highly expensive. • Particularly for wall-bounded flows. • As LES is an unsteady approach • Correct inflow conditions. • Flow development region. • LES must be conducted in a 3-D domain • No symmetry-planes. • Turbulence is three-dimensional. Turbulent velocity spectrum Velocity signal (): Unfiltered signal (): Filtered signal E() large scales, resolved small scales, unresolved ”SGS” cut-off, c  x

11. Main computational cases • Paper 1 & Paper 2: Basics of impinging jets • Basic characters of an impinging circular jet using top-hat inflow velocity profile. Paper 1: flow; Paper 2: heat transfer. • Paper 3 & Paper 4:Swirling impinging jets • Swirl effects on the flow and wall heat transfer for circular and annular impinging jets. • Paper 5: Inflow profile effects • Radial distribution of the axial mean inflow velocity and from periodic forcing. • Paper 6: Parametric studies • Nozzle-to-plate spacing effects. • Reynolds number effects. • Fully developed turbulent inflow condition for circular non-swirling and swirling impinging jets. Data normalized by: Mean inflow velocity (V0), nozzle diameter (D0) and mean inflow temperature (C0). ( Re=V0D0/ )

12. Outline • Background • Project description • Computational method and cases • Results • Summary

13. Dynamical character From Paper 5 Instantaneous vorticity in the xy-plane 2 nozzle outlet, D Inviscid instability Roll-up and shedding of natural vortices, Stn y/D Vortex pairing Shedding of primary vortices, Stn/2 1 shed vortices Convection of primary vortices Formation of secondary vortices Separation and breakdown impingement wall 0 2 1 0 1 2 r/D

14. Dynamical character From Paper 1 & 5 Dominant modes and energy at r/D=0.5 Spectrum at r/D=0.5, y/D=1 y/D PSD • Two dominant modes. • Sharp decrease of PSD for higher St. VP St E St • Natural mode initially dominant. • Delayed amplification of the subharmonic mode. • Vortex pairing (VP) between: E(Stn)=E(Stn/2) and max[E(Stn/2)].

15. Unsteady heat transfer From Paper 2 Instantaneous vorticity in the xy-plane, Nu and Cf plots nozzle outlet, D Attached vortices PV A: mean flow convection B: coherent heat transfer C:incoherent heat transfer V0 PV:Primary vortex SV :Secondary vortex Conv. vel. Uc V0 / 2 (—): Cf (—): Nu impingement wall C B A B C Stagnation point SV, separation

16. Unsteady heat transfer From Paper 2 Instantaneous vorticity in the xy-plane, Nu and Cf plots (—): Cf (—): Nu separation point reattachment point

17. Unsteady heat transfer From Paper 2 Vorticity, z Velocity vectors PV hot fluid SV Separation point Reattachment point PV: counter-clockwise rotating SV: clockwise rotating (---): Cf

18. Unsteady wall heat transfer From Paper 2 Wall friction Wall heat transfer convective wave convective spot Red color: high wall friction Blue color: low wall friction, separation Red color: high wall heat transfer Blue color: low wall heat transfer

19. Mean inflow profile effects From Paper 6 Instantaneous temperature distribution in the xy-plane (H/D=4) • Top-hat: irregular flow character, coherent structures only close to the nozzle outlet. Qualitatively similar to the reference case. • Mollified: distinct axisymmetric ring vortices  large-scale mixing, delayed transition. top-hat ”fully turbulent” (ref. case) mollified

20. Mean flow character From Paper 1 & 6 Inflow: ”Fully developed ” turb. pipe flow. Top-hat mean velocity profile. Fully developed turb. pipe flow. Mean axial velocity decay Radial velocity at r/D=1 (): LES (pipe) (): LES (top-hat) (О): Cooper et al. (): Geers et al. • Potential core extends to y/D≈1. • Top-hat: earlier decay. • Pipe: later decay  high correlation with Geers et al. y/D V/VCL U • Top-hat: low axial momentum  low peak velocity. • Pipe: stronger wall shear-layer, high peak velocity. • High correlation with Cooper et al. • Experimental discrepancy: • Measurement technique. • Nozzle conditions.

21. Turbulence statistics From Paper 1 & 6 urms(vrms) at r/D=0 Production of k at r/D=0 urms at r/D=1 (): LES (pipe) (): LES (top-hat) (О): Cooper et al. (): Geers et al. (vrms) y/D • Pk=0 for y/D>1. • Pipe: as the gradient increases so does Pk. • Close to the wall Pk<0 as Pk (vrms2 - urms2). • Top-hat: overall zero production. urms urms Pk • As r/D increases: inflow conditions less important. • Pipe: clear near-wall peak of Urms. • Overall good agreement with experiments (within tolerance for the two exp. setups). • Top-hat: weaker wall-shear  no distinct near-wall peak. • Top-hat: negligible level of fluctuations. • Pipe: Urms≈0.04, sharp increase close to the wall. • High correlation with Geers et al.

22. Effect from swirl From Paper 3 & 6 Mean axial velocity decay k at y/D=0.15 Nusselt number S=Ut/V0 k y/D Nu V/VCL r/D r/D • Pipe: high level of k high Nu. • Top-hat:Nu is low, despite high level of k. • Negligible rate of mean flow convection. • Jet spreading increases with swirl. • Top-hat: significant increase  recirculation bubble. • The bubble reaches downstream to r/D≈1. • At small r/D k is strongly influenced by swirl. • Less influence at larger radius. (  ): LES S=0 (pipe) (- - -): LES S=1(pipe) (  ): LES S=0 (top-hat) (- - -): LES S=1(top-hat) (): Geers et al. top-hat case, S=1 (  ): LES S=0 (pipe) (- - -): LES S=1(pipe) (  ): LES S=0 (top-hat) (- - -): LES S=1(top-hat) (): Geers et al. • Significant influence from the character of the inflow • Radial distribution of the axial and azimuthal velocity components. • Swirl generator structures.

23. Outline • Background • Project description • Computational method and cases • Results • Summary

24. Summary • The inflow boundary conditions is of significant importance for the development of the flow and scalar fields. • The underlying mechanisms of impinging jet heat transfer have been identified, discussed and visualized. • The dynamics of non-swirling and swirling impinging jets have been studied in some detail. Swirl has large effect on the wall heat transfer. The swirl generating method is crucial. • The LES approach provides accurate results in an efficient manner. The simulation method is not problem dependent.

25. Possible extensions • Study and explore (new) SGS models for the near-wall region. • Determine quantitatively the sensitivity of the Nusselt number from inflow condition uncertainties. • Study the effects of blade generated flow. • Determine the flow due to wall porosity. • Flow induces acoustics. Acoustics source distribution Instantaneous velocity field

26. Thank you!

28. Summary: wall heat transfer From Paper 2 & 5 Correlation between Nu and Cf Trends of: mean Nu, Cf , k,  III I IV Ruc • Nu: Local peak at r/D≈0.6. • Cf: Strong accelerating wall jet, local peak at r/D≈0.7. • k: Zero in the core region, local peak at r/D≈1.75. • : Indicates formation of counter rotating secondary vortices  high k and local increase of Nu. Nu,Cf ,k, (): Nu (): Cf (): k ():  II r/D r/D • I: Low level of k, laminar-like wall jet  high Ruc. • II: Vortical structures penetrates the wall boundary layer  low Ruc. • III:Convective structured primary vortices  high Ruc. • IV: Influence from secondary vortices and increasing level of irregular structures, i.e. eddies  low Ruc.