Presentation on theme: "PENETRABLE ROUGHNESS FLOWS in NATURE and in ENGINEERING"— Presentation transcript:
1PENETRABLE ROUGHNESS FLOWS in NATURE and in ENGINEERING Yevgeny A. GayevInstitute of Fluid Mechanics of UNASKyiv, May , 2004NATO Advanced Study Institute
2C o n t e n t s Introduction - Examples of canopy (?) flows - Who was the first in the area - Concept of Easily Penetrable Roughness (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 layersTurbulence in the penetrable layers- Wind tunnel measurements of mean characteristics- Theoretical models of the turbulence in EPRs- Spectral appearance of the turbulence in EPRsResults and discussion, prospective problemsConcluding remarks
31. Variety of areas where 'tall roughnesses' may be met River flows invegetated bedsForests and agro- eco- cenosisStorming oceanAfter R.BortkovskyUrban settlementsHeat exchangersSpraying coolersAfter P.Mestayer
41.1. A historical overviewL. Prandtl seemed to be the first in the area… butLudvig Prandtl, Klaus Oswatitsch"Fűrer durch die Strömungslehre"100 yearsof the BL theory…the real achievements, however, should be attributedto meteorologists and (later) river hydraulics experts…
51.2. Important articles in the field 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, ppFor 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.
62.1. 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]Log-like profiles over the forestDistorted shapes of U(z) within the forestData for turbulencewill be provided later…!
72.2. Experimental data: measurements in river flows Two variants of problem formulation:(A) Vertical-plane problem(B) Horizontal-plane problemLog-like profiles outside the vegetated area[Kouwen-1970;]Distorted shapes of U(z) within the vegetated areaData for turbulencewill be provided later…
82.3. What is the 'Spraying System'? Fountains, sprays in every day life1 - Hannover. 2 - Osnabrűck. 3 - Kiev
9Fountains, sprays in every day life 2 – Karlsruhe (De).1 – Guildford (UK)
10Few words about Spraying Cooling Systems (SCS) Panoramic view of the Zaporizhzhya NPP's spraying cooling system (SCS)Specification: 1 – NPP's reactors 61000 MWt; 2 – spraying channel № 1, dimensions 4000100 m;3 – spraying channel № 2; 4 – array of fountains h=6 m; 5 – additional cooling towers.
11anemometers and psychrometers 2.3. Experimental data: in-situ measurements in industrial spraying coolersRemote electricalanemometers and psychrometersat 10 levels of the 15m mast
12Plan view of the Zaporizhzhya's Nuclear Power Plant Spraying Cooling System Conventional "bottle" nozzleZaNPP: cooling water temperatures in January and June 1999
13Typical distributions of wind and air temperature within the SCS Log-portionDistorted portion
142.5.Data generalization: similar to "universal" profiles within forests
15Conclusion 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:Layerwith distributed force[J. Hunt]Too mathematically…CanopyForest canopy, etc.Too narrow…High roughness[Cermak e.a.-1971]Roughness sublayer [Mestayer]Porous mediumIn filtration theories…Penetrable obstructionNot correct…Penetrable roughness[W. Brutsaert]Easily Penetrable Roughness, EPRAn adjective allowing some mathematical operationslike additivity of forces
163.2. Fluid Mechanics' point of view: from 'small' to 'tall' and penetrable roughnesses h<<Hh ~ (0,1 – 0,3)Hh ~ (0,3 – 0,9)H ?Sand roughnessMotion and exchange processes within the roughness are of most interest.Besides, motion of the roughness elementsmay be practically important, too.Height of the roughnessIs neglectedAlmost all Fluid Mechanics case problems may be generalized in order to learn properties of the (Easily) Penetrable Roughnesses
172. 2. What happens within the PR? Kind permission for using this photo given by Prof. J.E.Cermak (Colorado University)is gratefully acknowledgedBulk results of theintensive vorticity:♪ a mean force to each local portion of the fluid♪ intensive mixing to be accounted via exchange coefficients μT etc.
183.1. A main conclusion from the experiments: source terms to be included into equations that govern the processU(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
19General mathematical model ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
20Boundary Layer Approach; Model verification by a sequence of sub-models: EPR made up of immobile elements.Boundary Layer Approach;Is it always valid?Is valid?Boundary conditions:Conjugation conditions:
214.1. Numerical results: general structure of the unrestricted EPR flow Boundary layer over the EPR1 – Initial Region:6 –Main Region,profiles of a final shape:if k=1if k=1Stagnation Zone 7 is possibleif A>A critical ~2,5if k=2
22(E) Pipe lines (heat echangers) of various cross sections with filters 4.2. Pressure driving flows in ducts (fully developed and time dependent flows)(A) Infinite EPRs in an endless plain duct(B) Flow enters a duct with infinite EPRs(D) Flow enters a duct with a finite EPRs(C) Infinite porous insert in a plain duct(E) Pipe lines (heat echangers) of various cross sections with filters
23Navier – Stokes equations become 1d Endless duct with an infinite Easily Penetrable RoughnessNavier – Stokes equations become 1dAnalytical solution for linear EPR, k=1Numerical solution for quadratic EPR, k=2Resistance coefficient via flow&EPR parametersbecause
24(B) Flow enters a duct with infinite EPRs 2d Navier – Stokes equations Dimensionless variables~!
25(B) Some results for flow entering a duct Mean velocity is gradually transformed from an uniform to a final shape (1d) profilePressure distributions in the ductSear stress distributions in the duct
26Length Lx of the initial region ♪ Different curve behavior for small Re♪ For large Rean approach is observedto the limit casealready found fromBoundary Layer Approx[Schlichting]Conclusion: Boundary Layer Approach is valid for large Re
27(D) Flow enters a duct with a finite EPRs (penetrable backward facing steps) 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)♪ 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 …
28Conclusion. Three regimes depending on frequency may be observed: (F) Pulsating flow in a duct with EPRs biological applications are possibleSolution 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)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.
295.1. EPR made up of mobile elements (droplet layer model) The carried medium to be predicted together with the carrying one
306.1.A. Heat transfer in droplet layer 6.1.B. Mass transfer in droplet layer6.2. Mutual action of the heat and mass transfer Profiles of dry and wet air temperature and droplet temperatureHumidity profiles formed by droplet layer
317.1. Model of a polidisperse droplet layer each r-sort of droplets is a separate medium Investigation of the one-dimensional model(model flow in a duct)~~~~~~How to find parameters and of an 'equivalent' monodisperse droplet layer?
327.1. Some results for a polidisperse droplet layer …\0\"Drops_of_2sizes.BMP"Air velocity profiles and velocity profiles of two droplet media ("heavy" and "light") in two cross-sections of the droplet layer
338. Models of multi- speed droplet layers 2 droplet media:♪ rising up♪ falling down4 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
34Conclusions from the 'constant viscosity' models Dimensionless criteriafor the initial EPR regionUniversal coordinatesfor the external BLfor the main EPR region
359. Turbulence in the penetrable layers a number of experiments in various obstruction layers were carried out…[Kouwen; Sherenkov,Bennovitsky]In water flumes…[Raupach,Finnigan e.a.]In forests…In models of urban settlements…[Meroney;Savory; etc][Gayev e.a.]In spraying coolers…[Meroney;Raupach;Gayev,Savory; etc.]In wind tunnels…
369. Some more data for turbulence Geometries of canopy elements studiedDown- and Up-canopies in the wind tunnelof Surrey University [Gayev,Savory](working section dimensions: 1,5 m width, 2 m height; length ~5 mnumber of obstructions up to 500)Canopy element layout and measurement locations*
379.1. Mean velocity profiles over the EPR Contours of normalised mean velocity (U/Uoo) at X=10 rows (D-Canopy)♪ U-profiles are very distinct at the EPR beginning♪ U-profiles become united far away into the EPR
389.2. Turbulence intensity profiles over the EPR Contours of normalised mean velocity (U/Uoo) at X=10 rows (D-Canopy)♪ U'-profiles are very distinct at the EPR beginning♪ U'-profiles become more united far into the EPR
40Bulk properties of the flow Height of external boundary layerabove different canopiesVariation of longitudinal velocity along the EPR's(i.e. D-canopy) and comparison with theory
419.3. Theoretical modeling of the EPR turbulence (a) Algebraic closures: sufficient for most calculations~~~~Within the EPROutside the EPRComparison with Allen's measurementsCalculation for a vegetated channel flow[Gayev,Wenka,Rodi]. More details: Bennovitsky,Gayev
42Well, EPR flows are similar in terms of mean (overaged) properties 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…
439.4. '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.
44Spectra 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.
45Spectra within an extended easily penetrable roughness array Measurements in Surrey university WT [Gayev,Savory](2) Behind 20 rows(1) Behind 5 rows
46Spectral 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
47Spectrum measurements within the EPR Spectrum curves almost coincide for all the elevations 0 < z <1h:here z=40 mm
48Spectrum curves almost coincide for all the elevations 0 < z <1h z=100 mmz=60 mmSpectrum curves almost coincide for all the elevations 0 < z <1hConclusion: turbulence is rather homogeneous within the EPRalthough the EPR is significantly inhomogeneous.
49Spectrum measurements over the EPR fetch z=160 mmz=140 mmSpectrum curves began rise up over the EPR, z > h =70 mm …contrary to the case of a smooth surface.! ! ! ???
50Spectrum measurements over the EPR z=230 mmz=180 mmSpectrum curves rise up till the elevation z ~1,5h – 3h
51Then, spectrum curves fall down like it were over the smooth surface… z=260 mmz=200 mmThen, spectrum curves fall down like it were over the smooth surface…
52For more high elevations, spectrum curves continue to fall down… z=280 mmz=220 mmFor more high elevations, spectrum curves continue to fall down…
53For more highest elevations, a spike appears on spectrum curves … z=320 mmz=240 mmFor more highest elevations, a spike appears on spectrum curves …
54…and the peaks continue rising for next elevations. z=480 mmz=300 mm…and the peaks continue rising for next elevations.
55What the reason of such behavior of the vortices? z=540 mmz=480 mmVortices dissipate for only elevations z=6h (5 rows) and z=8h (20 rows) .What the reason of such behavior of the vortices?
56Finnigan’s e. a. image of coherent vortices over the PR [Ann. Rev Finnigan’s e.a. image of coherent vortices over the PR [Ann. Rev. Fluid Mech., 2000, v.32]Vorticity within and over the EPRs is an interesting subjectfor further investigations.
57Source/sink terms as a mean for capturing PR features In momentum equations:… there is only one possibility given by dimensional analysis, that is the force term.
58For the turbulent kinetic energy For the dissipation rate
59How should these terms look like? Dimensional analysisfor the turbulent kinetic energy – two variantsDimensional analysisfor the dissipation rate – four variants… it might be worth to examine all of these termsto express peculiarity of various possible PR structures…
60Main conclusionsA variety of problems that look out from the first glance as different ones may be treated, in fact, as problems of a penetrable roughness (i.e. canopy, porous layer etc) flows.The EPR model given here allows investigation of PRs differing in nature and in structure, e.g. constructed from immovable, movable, multi speed and, may be, waving, flexible etc. elements.An approach for distinguishing the “initial” and “main” regions of the canopy (=EPR) flow was suggested along with some analytical estimation formulas.Approaches based on continuous media models capture important averaged flow features but more sophisticated models are required for predicting EPR flow turbulence characteristics.The latter may be done by including source/sink terms into corresponding equations.PR flows should be, because of their novelty, investigated further and deeper.It should be thought over how the 'useful features' of the PR flows discovered by meteorologists and hydrologists may be utilized in engineering science and technology.
61Prospective problems EPR models for "waving" and flexible elements EPR models for shallow water flowswith the water surface affected by the EPRModels for SQS constructed with 're-freshen' gapsAnd much moreto give job for many meteorologists, hydraulics, wind engineers, engineering people and those of other expertise area…
62AcknowledgmentDeutsche Forschungsgemeinschaft: Institute of Hydromechanics, University of Karlsruhe, Germany (Prof. G. Ernst, Prof. W. Rodi)Royal Society: University of Surrey, United Kingdom (Prof. E. Savory, Prof. N. Toy)Colorado University, USA (Prof. R. Meroney)University of California, Davis, USA (Prof. R.Shaw)My native Institute of Hydromechanics Ukr. Nat. Academy of Sci.NATO Scientific Affairs Divisionfor such a unique possibility to carry out this Institute
63Thank you very for your patient attention! NATO ASIFlows in Obstructed geometries+=