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PENETRABLE ROUGHNESS FLOWS in NATURE and in ENGINEERING

PENETRABLE ROUGHNESS FLOWS in NATURE and in ENGINEERING. Yevgeny A. Gayev Institute of Fluid Mechanics of UNAS. Kyiv, May 4 -- 15, 2004. NATO Advanced Study Institute. C o n t e n t s. Introduction - Examples of canopy ( ? ) flows

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PENETRABLE ROUGHNESS FLOWS in NATURE and in ENGINEERING

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  1. PENETRABLE ROUGHNESS FLOWSin NATURE and in ENGINEERING Yevgeny A. Gayev Institute of Fluid Mechanics of UNAS Kyiv, May 4 -- 15, 2004 NATO Advanced Study Institute

  2. C o n t e n t s Introduction- Examples of canopy (?) flows - Who was the first in the area - Concept of Easily PenetrableRoughness (EPR) Experimental data: In forests; in wind tunnels; in vegetated river flows; in spraying systems (SQS) Theoretical considerations - General mathematical model and its particular cases; 1d-simplifications - EPR made up of immobile elements (model of a 'forest' ; EPR in a duct) - EPR made up of mobile particles (model of a 'droplet layer' ) - Heat and mass transfer in the EPRs - Models of a polidisperse and multi- speed droplet layers Turbulence in the penetrable layers - Wind tunnel measurements of mean characteristics - Theoretical models of the turbulence in EPRs - Spectral appearance of the turbulence in EPRs Results and discussion, prospective problems Concluding remarks

  3. 1. Variety of areas where 'tall roughnesses' may be met River flows in vegetated beds Forests and agro- eco- cenosis Storming ocean After R.Bortkovsky Urban settlements Heat exchangers Spraying coolers After P.Mestayer

  4. 1.1. A historical overview L. Prandtl seemed to be the first in the area… but Ludvig Prandtl, Klaus Oswatitsch "Fűrer durch die Strömungslehre" 100 years of the BL theory …the real achievements, however, should be attributed to meteorologists and (later) river hydraulics experts…

  5. 1.2. Important articles in the field For urban ecology: Rotach M. W. Turbulence Within and Above an Urban Canopy. Zuericher Geographische Schriften, H. 45, 1991. Davidson M.J., Belcher S.E., Hunt J.C.R. Atmospheric flow through groups of buildings and dispersion from localized sources. - In: Wind Climate in Cities. NATO ASI, Karlsruhe, 1993. In oceanology: Bortkovsky R.S. Air-see exchange of heat and moisture during storms. D.Reidel, Dortrecht. Wu J. Spray in the atmospheric surface layer: laboratory study. J.Geophysical Research, 1973, 78, N 3. In engineering fluid mechanics: Nickitin I.K. Complex turbulent flows and processes of heat and mass exchange.- Kiev, 1980. Ghosh S., Hunt J.C.R. e.a. Dynamics of turbulent air-flow in droplet driven sprays. Applied Scientific Resarch, 1993, 51. Gayev Ye.A. Aerothermal theory of an Easily Penetrable Roughness. Particular application to the atmospheric flow in and over longscale Spray Cooling System. - Il Nuovo Cimento, C20, 1997. For natural forests: Wright I.L., Lemon E. Photosynthesis under field conditions. Agronomy Journal, 1966, 58, 3. Meroney R.N. Characterictics of wind and turbulence in and above model forests. J. Applied Meteorology, 1968, 7, 5. Konstantinow A.R. e.a. Application experience of gradient masts for determining evaporation and heat exchange in forest. - Proc. GGO, 1969, iss. 81. Plate E.J. Aerodynamic Characteristics of Atmospheric Boundary Layers. - U.S. Atomic Energy Commission, 1971. Menzhulin G.W. On the theory of a stationary meteorological regime of a vegetation canopy. - Proc. GGO, 1973, 297. Shaw R.H. Secondary wind speed maxima inside plant canopy. J. Applied Meteorology, 1977, 16. Dubov A.S., Bickova L.P. e.a. Turbulence in a Vegetation Canopy. - Leningrad: Hydrometeoizdat, 1978. Raupach M.R., Thom A.S. Turbulence in and above plant canopies. Ann. Review Fluid Mech., 13, 1981. Brutsaert W. Evaporation into the Atmosphere, 1982. Finnigan J. Turbulence in Plant Canopies. Ann. Review Fluid Mech., 2000, v. 32. For river hydraulics: Kouwen N., e.a. Flow retardance in vegetated channels. J. of the Irrigation and Drainage Div., Proc. ASCE, 95(IR2), 1969. Knight D.W., Macdonald J.A. Hydraulic resistance of artificial strip roughness. Proc. ASCI, J. Hydraulics Div., HY6, 1979. Nuding A. Fliesswiederstandsverhalten in Gerinnen mit Ufergebuesch. - Technische Hochschule Darmstadt, Institut fuer Wasserbau, Nr. 35, 1991. Nepf H.M. Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resources Research, 1999,35, N 2, pp. 479 - 489.

  6. Log-like profiles over the forest Distorted shapes of U(z) within the forest Data for turbulence will be provided later… 2.1. Experimental data:measurements in forests and in agricultural crops[Rauner-1958; Inoue-1963; Lemon&Wright-1965; Allen-1968; Dubov&Marunich-1971] [Thom&Raupach-1970; Oliver-1971; Cionco-1972; Shaw-1974] !

  7. (A) Vertical-plane problem (B) Horizontal-plane problem Log-like profiles outside the vegetated area Distorted shapes of U(z) within the vegetated area 2.2. Experimental data:measurements in river flows Two variants of problem formulation: [Kouwen-1970;] Data for turbulence will be provided later…

  8. 2.3. What is the 'Spraying System'? Fountains, sprays in every day life 1 - Hannover. 2 - Osnabrűck. 3 - Kiev

  9. Fountains, sprays in every day life 2 – Karlsruhe (De). 1 – Guildford (UK)

  10. Few words about Spraying Cooling Systems (SCS) Panoramic view of the Zaporizhzhya NPP's spraying cooling system (SCS) Specification: 1 – NPP's reactors 61000 MWt; 2 – spraying channel № 1, dimensions 4000100 m; 3 – spraying channel № 2; 4 – array of fountainsh=6 m; 5 – additional cooling towers.

  11. 2.3. Experimental data:in-situ measurements in industrial spraying coolers Remote electrical anemometers and psychrometers at 10 levels of the 15m mast

  12. ZaNPP: cooling water temperatures in January and June 1999 Plan view of the Zaporizhzhya's Nuclear Power Plant Spraying Cooling System Conventional "bottle" nozzle

  13. Typical distributions of wind and air temperature within the SCS Log-portion Distorted portion

  14. 2.5.Data generalization: similar to "universal" profiles within forests

  15. Conclusion 1: there are many similar features for (at least mean quantities of) flows within differing obstruction layers. A uniform theory may be possible. 3.1. The terms in use: Layer with distributed force [J. Hunt] Too mathematically… High roughness [Cermak e.a.-1971] Canopy Forest canopy, etc. Too narrow… Roughness sublayer[Mestayer] Porous medium In filtration theories… Penetrable roughness [W. Brutsaert] Penetrable obstruction Not correct… Easily Penetrable Roughness, EPR An adjective allowing some mathematical operations like additivity of forces

  16. h ~ (0,1 – 0,3)H h ~ (0,3 – 0,9)H ? h<<H 3.2. Fluid Mechanics' point of view: from 'small' to 'tall' and penetrable roughnesses Sand roughness Motion and exchange processes within the roughness are of most interest. Besides, motion of the roughness elements may be practically important, too. Height of the roughness Is neglected Almost all Fluid Mechanics case problems may be generalized in order to learn properties of the (Easily) Penetrable Roughnesses

  17. Kind permission for using this photo given by Prof. J.E.Cermak (Colorado University) is gratefully acknowledged 2. 2. What happens within the PR? Bulk results of the intensive vorticity: ♪a mean force to each local portion of the fluid ♪intensive mixing to be accounted via exchange coefficients μT etc.

  18. 3.1. A main conclusion from the experiments:source terms to be included into equations that govern the process U(x,z) and u(x,z) account for motion of the carrying media (air or water) and the carried media (elements of the EPR) n(x,z) or s(x,z) account for density of the resistant elements, i.e. elements of the EPR; they thus represent an architectonics of the penetrable roughness

  19. General mathematical model ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~

  20. Is valid? Is valid? Is valid? Model verification by a sequence of sub-models:4.1. EPR made up of immobile elements. Boundary Layer Approach; Is it always valid? Boundary conditions: Conjugation conditions:

  21. if k=1 Stagnation Zone 7 is possible if A>A critical ~2,5 4.1. Numerical results:general structure of theunrestricted EPR flow Boundary layer over the EPR 1 – Initial Region: 6 –Main Region, profiles of a final shape: if k=1 if k=2

  22. (A) Infinite EPRs in an endless plain duct (B) Flow enters a duct with infinite EPRs (C) Infinite porous insert in a plain duct (D) Flow enters a duct with a finite EPRs (E) Pipe lines (heat echangers) of various cross sections with filters 4.2. Pressure driving flows in ducts(fully developed and time dependent flows)

  23. Analytical solution for linear EPR, k=1 Resistance coefficient via flow&EPR parameters because • Endless duct with an infinite Easily Penetrable Roughness • Navier – Stokes equations become 1d Numerical solution for quadratic EPR, k=2

  24. Dimensionless variables ~ ~ (B) Flow enters a duct with infinite EPRs2d Navier – Stokes equations !

  25. (B) Some results for flow entering a duct Mean velocity is gradually transformed from an uniform to a final shape (1d) profile Pressure distributions in the duct Sear stress distributions in the duct

  26. Length Lx of the initial region ♪ Different curve behavior for small Re ♪ For large Re an approach is observed to the limit case already found from Boundary Layer Approx [Schlichting] Conclusion: Boundary Layer Approach is valid for large Re

  27. Vortical motion behind "penetrable steps" h=0,3, l=1 in a duct flow Re=100 depending on A=100 (above) or A=10 (below) (D) Flow enters a duct with a finite EPRs (penetrable backward facing steps) ♪ there is no vorticity for easily penetrable EPR (small A); ♪ the vorticity is only appearing for A~10; ♪ there is an intensive vorticity for A~100; ♪ another calculation method is required if one needs precise knowledge within the PR with large A. More details: Gayev, Shikhaliev …

  28. Solution has been obtained in an analytical form using complex numbers. There is an animation graphical program… (a) Smooth walls in the duct(Richardson' phenomenon) (b) EPRs near walls in the duct (opposite currents are larger) (F) Pulsating flow in a duct with EPRsbiological applications are possible Conclusion. Three regimes depending on frequency may be observed: ♪ at slow pulsations, ω<5, the flow resembles the Puaseule flow at each time moment; ♪ at frequent pulsations, ω>50, a phase shift occur, and the opposite currents become larger.

  29. 5.1. EPR made up of mobile elements (droplet layer model) The carried medium to be predicted together with the carrying one

  30. 6.1.B. Mass transfer in droplet layer 6.1.A. Heat transfer in droplet layer 6.2. Mutual action of the heat and mass transfer  Profiles of dry and wet air temperature and droplet temperature Humidity profiles  formed by droplet layer

  31. How to find parameters and of an 'equivalent' monodisperse droplet layer? 7.1. Model of a polidisperse droplet layereach r-sort of droplets is a separate medium 7.1.1. Investigation of the one-dimensional model (model flow in a duct) ~~~ ~~~

  32. 7.1. Some results for a polidisperse droplet layer Air velocity profiles and velocity profiles of two droplet media ("heavy" and "light") in two cross-sections of the droplet layer

  33. 8. Models of multi- speed droplet layers 2 droplet media: ♪ rising up ♪ falling down 4 droplet media: ♪ starting with u0=+1, initially rising up and then falling down; ♪ starting with u0= -1, initially rising up and then falling down. Conclusion: various structures of the 'obstruction medium' may be represented in the EPR concept

  34. Conclusions from the 'constant viscosity' models Dimensionless criteria for the initial EPR region Universal coordinates for the external BL for the main EPR region

  35. In water flumes… In forests… [Raupach,Finnigan e.a.] [Meroney;Savory; etc] [Kouwen; Sherenkov,Bennovitsky] In wind tunnels… In spraying coolers… [Gayev e.a.] [Meroney;Raupach;Gayev,Savory; etc.] 9. Turbulence in the penetrable layersa number of experiments in various obstruction layers were carried out… In models of urban settlements…

  36. Geometries of canopy elements studied Canopy element layout and measurement locations 9. Some more data for turbulence Down- and Up-canopies in the wind tunnel of Surrey University [Gayev,Savory] (working section dimensions: 1,5 m width, 2 m height; length ~5 m number of obstructions up to 500) *

  37. Contours of normalised mean velocity (U/Uoo) at X=10 rows (D-Canopy) 9.1. Mean velocity profiles over the EPR ♪U-profiles are very distinct at the EPR beginning ♪U-profiles become united far away into the EPR

  38. Contours of normalised mean velocity (U/Uoo) at X=10 rows (D-Canopy) 9.2. Turbulence intensity profiles over the EPR ♪U'-profiles are very distinct at the EPR beginning ♪U'-profiles become more united far into the EPR

  39. Height of external boundary layer above different canopies Variation of longitudinal velocity along the EPR's (i.e. D-canopy) and comparison with theory Bulk properties of the flow

  40. 9.3. Theoretical modeling of the EPR turbulence(a) Algebraic closures: sufficient for most calculations ~~~~ Within the EPR Outside the EPR Comparison with Allen's measurements Calculation for a vegetated channel flow [Gayev,Wenka,Rodi]. More details: Bennovitsky,Gayev

  41. Well, EPR flows are similar in terms of mean (overaged) properties.Are they so similar, i.e. have common features in term of the turbulence? Bulge (i.e. sec. max.) problem in forest flows…

  42. 9.4. 'Fine structure' of the turbulence It might have been expected that (1) vortices are proportional to the 'grid size' within the EPR, and (2) dissipate to small scales over the EPR… It is suggested to examine this expectation by a spectrum measurements.

  43. Spectra over a smooth surface Spectra in some points within D-wake Measurements in Surrey university WT [Gayev,Savory] Features are known: 1. Energy containing vortices 1<f<200 Hz; 2. Inertial sub-layer E~f^(-5/3) for 20<f<500 Hz; 3. Dissipation E~f^(-4) for 700<f<3 000 Hz; 4. Vortices calm down with the height z. 1. Energy of the vortices is much larger; 2. Peaks on spectrum curves are present for some points in the wake. 3. Again, vortices calm down with the height.

  44. Spectra within an extended easily penetrable roughness array Measurements in Surrey university WT [Gayev,Savory] (2) Behind 20 rows (1) Behind 5 rows

  45. Spectral appearance of the EPR turbulence Spectrum curves almost over the surface with the 'tall trees' h=70 mm, on the elevation z=2 mm taken as a reference level

  46. Spectrum measurements within the EPR Spectrum curves almost coincide for all the elevations 0 < z <1h: here z=40 mm

  47. z=100 mm z=60 mm Spectrum curves almost coincide for all the elevations 0 < z <1h Conclusion: turbulence is rather homogeneous within the EPR although the EPR is significantly inhomogeneous.

  48. Spectrum measurements over the EPR fetch z=160 mm z=140 mm Spectrum curves began rise up over the EPR, z > h =70 mm … contrary to the case of a smooth surface. ! ! ! ???

  49. Spectrum measurements over the EPR z=230 mm z=180 mm Spectrum curves rise up till the elevation z ~1,5h – 3h

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