An experimental analysis of canopy flows

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1 Jornal of Physics: Conference Series An experimental analysis of canopy flows To cite this article: Antonio Segalini et al 11 J. Phys.: Conf. Ser View the article online for pdates and enhancements. Related content - A new formlation for the streamwise trblence intensity distribtion P Henrik Alfredsson, Ramis Örlü and Antonio Segalini - Negatie streamwise elocities and other rare eents near the wall in trblent flows Peter Lenaers, Qiang Li, Geert Brethower et al. - The effects of a model forest canopy on the otpts of a wind trbine model Yla Odemark and Antonio Segalini Recent citations - Scaling Laws in Canopy Flows: A Wind- Tnnel Analysis Antonio Segalini et al This content was downloaded from IP address on 31//18 at 19:57

2 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 An experimental analysis of canopy flows Antonio Segalini, Jens H. M. Fransson & P. Henrik Alfredsson Linné FLOW Centre, KTH Mechanics, SE- 44 Stockholm, Sweden Abstract. An analysis of forest canopy flows with a wind tnnel model at high Reynolds nmber is presented and discssed. Measred mean elocity and Reynolds stress profiles agree with obserations made in real canopies with no sensible Reynolds nmber dependence, adding confidence to the reslts obtained with the present setp. The analysis of power density spectra of the three elocity components and of the shear stress co-spectra is reported with new coordinate scalings able to improe the collapse of the spectra compared to standard normalizations. This scaling is mostly based on the respectie integral time scale and a simple fit is proposed to estimate sch a qantity in real canopies. From the analysis of joint probability density fnctions, three different regions hae been localized where a change in the coherent strctre behaior is spposed to take place, similarly to what happens in rogh wall trblent bondary layers. 1. Introdction There is a renewed interest in the description of the atmospheric bondary layer oer forest areas de to the strong exploitation of wind energy in Erope bt also elsewhere. From the power prodction point of iew, wind trbine parks located on flat land or at sea are more ideal as compared to locations in forest areas, bt the nmber of sch exploitable areas is limited. Therefore great efforts are spent to characterize the effect of the presence of a forest canopy in order to assess wind trbine performance (in terms of extracted power and fatige loads) and, therefore, the qality of a gien site. Measrements in the atmospheric bondary layer oer a forest canopy are affected by seeral isses, sch as dirnal ariations of both wind elocity, wind direction and stratification (Kaimal & Finnigan, 1994). The non-homogeneity of any forest canopy and the measrement ncertainties add frther complications to the ealation and the qality assessment of the data. While the alidity of the predictions of nmerical methods is still a matter of debate de to modeling isses, wind tnnel experiments, which ensre a better control of the operating conditions, are a good alternatie to field measrements to obtain a physical nderstanding of the most important processes. Howeer the Reynolds nmbers achieable are of the order of one hndred times smaller compared to those of the atmospherical bondary layer, bt may still be sfficiently high to gie a qalitatiely correct description of the flow processes. These considerations jstify the considerable nmber of wind tnnel experiments with simplified canopy models (see Meroney, 1968; Zh et al., 6; Pietri et al., 9, to cite some), with a reasonable agreement of the measred data with the ones acqired oer a real canopy (Zh et al., 6; Noak et al., ). Pblished nder licence by Ltd 1

3 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 What seems to be clear from theory and experiments is that the presence of the canopy introdces a nonlinear momentm sink term in the Naier-Stokes eqations, with a conseqent change in the flow characteristics inside the canopy and in the neighborhood of the canopy top, phenomena completely absent in smooth wall trblent bondary layers. It has only been recently assessed that the presence of the forest is related to an inflectional point in the mean elocity profile (Rapach et al., 1996) located in the proximity of the canopy top. From the Rayleigh inflectional point criterion it is expected that the canopy flow is nstable to iniscid pertrbations and that a Kelin-Helmholtz instability deelops close to the inflectional point. Conseqently the roll-p and generation of coherent ortices is localized near the canopy interface, while the dynamics of these strctres will be seen across the fll height of the bondary layer. The effect of sch an instability and the dynamics of the generated strctres is still nclear and therefore a wind tnnel experiment has been performed in order to describe the flow from the classical statistical point of iew. The statistical reslts will be discssed in the present work where single-point measrements will be analyzed. The paper is strctred in the following way: first the experimental setp is briefly described in section after which the presentation and discssion of the experimental reslts will be done in section 3. Section 4 concldes the paper by smmarizing the most important reslts achieed.. Experimental setp The experiments hae been performed in the Minimm Trblence Leel wind tnnel (MTL) at the Royal Institte of Technology (KTH) in Stockholm. The facility has a closed-loop configration with a 7 m long test section and a cross section with 1. m width and.8 m height. Figre 1 shows a schematic representation of the model setp in the wind tnnel test section. The atmospheric bondary layer is simlated by means of trianglar spires at the beginning of the test section to artificially increase the bondary layer thickness p to.5 m (Talamelli et al., 4). In order to simlate a forest canopy for pin fin plates with a width of 1. m and a streamwise length of.5 m each hae been sed. The trees of the canopy hae been simlated by 5 mm diameter wooden circlar pins that hae been monted in holes in the plates, where the tip of the pins reaches 5 mm aboe the plate. The pins can be remoed or added in order to create canopies with different densities. The height of the canopy is indeed h c = 5 mm while the length of the total forest model is 4 canopy heights. The high pin density (17 pins/m ) ensres homogeneity in both streamwise and spanwise direction. The reference frame sed in the present paper is schematically shown in figre 1. As a notation, the streamwise elocity will be denoted with, the wall-normal with and the spanwise with w. Also, capital letters will indicate statistically aeraged qantities, while lower case letters will indicate flctations arond the mean ale. Hot-wire anemometry has been sed dring the experimental campaign to determine statistical properties of the flow. The se of crossed-hot-wire sensors has allowed simltaneos measrementsoftwoelocity components. Byrotatingthewiresby9, statistics ofall thethree elocity components hae been determined. Time series hae been acqired for for different free-stream elocities (U, 15, and 5 m/s) at points across the bondary layers with a sampling freqency of khz and a sampling time of s in order to achiee a good statistical conergence and to acqire enogh strctres for the ensemble aerage. 3. Reslts Figre reports the mean elocity profile (a) and the most important Reynolds stress profiles (b) for the different free-stream elocities aailable at the streamwise station x/h c = 3: both qantities, ifappropriatelyscaledwithu, showaweakreynoldsnmberdependence, therefore

4 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 H=8 mm Flow y= y x Probe Probe traersing Canopy model y=-h c Trianglar spires Grid carpet 4 h c Figre 1. Schematic representation of the wind tnnel canopy model setp. y/h c (a) y/h c (b) < > < > <w > <> U/U.1.1. < i j >/U Figre. Statistics of the low density canopy flow for < U < 5 m/s. (a) Mean elocity profiles (b) ariances of the three elocity components and coariance profiles. the flow can be considered as Reynolds nmber independent. Inside the canopy (i.e. for y < ), the mean elocity decays exponentially, in agreement with atmospherical measrements inside forests and with some theoretical models(harman& Finnigan, 7), while the inflectional point is located at the canopy interface (Rapach et al., 1996). Aboe the canopy the logarithmic law is recoered, proided that y is shifted by some displacement height. The normal trblent stresses decay inside the canopy from their maxima achieed close to the canopy top, aboe which a region of approximately constant shear and normal stress is obsered. Spectral analysis has been performed to the elocity time series, calclating both power spectral density of all the three elocity components (P P P w ) and the real part of the crossspectra (S sally called co-spectra). All the spectra hae been normalized in order to ensre a constant area nderneath and a constant ale for zero freqency. This can be accomplished by starting from the definition of cross-correlation between the time series (t) and (t) (the case where = is a special one and follows the same argments): R (τ) = (t)(t+τ). (1) The application of the Wiener-Kinchine theorem (Bendat & Piersol, 1986) relates the cross- 3

5 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 correlation (1) with the cross-spectra as: S (f) = R (τ)e πifτ dτ R (τ) = From eqation () the ale of the spectra in f = is calclated as: S () = R (τ)dτ = Λ with Λ = 1 S (f)e πifτ df. () R (τ)dτ. (3) The introdction of the integral time scale Λ is sally made for the ato-correlations, bt the argment is here generalized proided that. A normalized spectra can be now defined as: Φ (f) = S (f) Λ, (4) that, according to eqation (3), satisfies Φ () = and: 1 S (f)df = Φ ( )d( ) = 1. (5) Eqation (5) sggests that the scaled spectra (4) normalizes the spectra at f = and the integral of the spectra throgh the se of the freqency scaled with the integral time scale, Λ. The adantage of the proposed normalization is einced when the spectra depends on a single length and elocity scale, allowing a niersal description of the spectra, independently from the wall-normal position, y, or free-stream elocity, U. Figres 3 and 4 report normalized spectra of the three elocity components and the real part of the cross-spectra, S, for all the aailable free-stream elocities for < y/h c < 3.6. The pper limit y/h c 3.6 is the edge of the internal canopy bondary layer aboe which the external replicated atmospherical bondary layer starts (this can be appreciated for instance in the skewness profiles in figre 6(a) or by looking at the eoltion of the statistics along the canopy model, not shown here). Therefore below this threshold the flow is expected to be determined by the canopy bondary condition, while aboe it is dominated by the way sed to generate the thick bondary layer, with a different expected spectral distribtion. In the canopy bondarylayer (for < y/h c < 3.6) thecollapse of all thespectraptothedissipatie range(i.e. for 1) is eident. In order to facilitate the qantitatie comparison of the normal stress spectra, they hae been plotted together with a fit of Φ in the inertial range. All the normal spectra show the Kolmogoro 5/3 decay for all the considered y positions inside the internal canopy bondary layer. The spectra reported in figre 3 are plotted together with the spectral distribtion Φ = () 5/3 /18 which is a fit of the streamwise elocity spectrm estimated from the wind tnnel data bt the same fit has been recently fond in real forest data (Segalini et al., 11). The cross-spectra, on the other hand, show a faster decay and some zero crossings in the high freqency range, adding frther scatter in the logarithmic plot in figre 4(a). This qicker decay is howeer consistent with the expected freqency decay of the co-spectra in the inertial range (Kaimal & Finnigan, 1994), namely f 7/3 (shown in figre 4), een if a decay between f 5/3 and f 7/3 seems to fit more appropriately the spectra. It is interesting now to ealate the integral time scales Λ x as fnction of simple parameters. In the preios figres they hae been calclated directly from the definition in eqation (3), since the sampling time in the wind tnnel experiment was sfficiently high, bt real atmospheric measrements hae only a limited time window where the flow can be considered as statistically stationary. It is therefore of se to propose a simple correlation from the present experimental 4

6 13th Eropean Trblence Conference (ETC13) Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 (a) (b).1 Φ Φ (c) (d).1 Φ Φ (e) (f).1 w Φ w Φ w w w Figre 3. Normalized power density spectra of the (a b), (c d) and (e f ) w elocity component for < U < 5 m/s and < y/hc < 3.6. (a c e) Non premltiplied form, (b d f ) premltiplied form. For comparison prposes the fnction Φ = (f Λ) 5/3 /18 is plotted (solid red line). 5

7 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 (a).15 (b) Φ 5 Φ.1.5 Figre 4. Normalized co-spectra S for < U < 5 m/s and < y/h c < 3.6. (a) Non premltiplied form, (b) premltiplied form.. For comparison prposes the fnctions Φ = () 5/3 /18 (solid red line) and Φ = () 7/3 /18 (dashed red line) are plotted. reslts able to estimate an approximatie ale of the integral time scales. Dimensional analysis, and some change of ariables, sggests a possible relationship of the form: y Λ x U = A U x +B x, (6) U where, instead of a y-dependent right hand side, a correlation with U/U has been preferred following the idea of the diagnostic plot approach proposed by Alfredsson et al. (11). Figre 5 reports the proposed relationship for Λ, Λ and Λ. The agreement of the linear fit with the measred data can be jdged as good aboe the canopy. It is worth to mention that Λ w has not been plotted becase the data agree with Λ bt they are more scattered and therefore hae been omitted for clarity. It is also interesting to note that for homogeneos isotropic trblence Λ = Λ w = Λ / (Pope, ), while here it seems that Λ Λ /4. Another simple scaling that can be sed is Λ U h /h c 1. with U h = U (y = ). Howeer this scaling seems to work only for the integral time scale of the streamwise elocity component, while the ertical elocity integral scale shows a clear y-dependent trend. A frther statistical description of the flow eents can be obtained by qadrant analysis of the elocity time series. It is known that in smooth wall trblent bondary layers ejections ( < and > ) are the most probable eents. On the other hand, in rogh wall trblent bondary layers sweeps ( > and < ) are the most probable eents close to the roghness (Krogstad et al., 199) while away from it ejections become again the most probable eents. This property is also obsered in canopy flows (Shaw et al., 1995) and in the present model as can be einced from figre 6 where the skewness of the streamwise and wall-normal elocity is reported in part (a) while parts (b), (c) and (d) show the joint probability density fnction at y/h c, y/h c 1 and y/h c 3.6, respectiely. The first location corresponds to the canopy interface where sweeps are expected to be dominant and the joint pdf appears strongly skewed for both axes. At y/h c 1 the skewness of and is approximately zero and the joint probability fnction is centered at the origin and symmetric. In the last station, ejections take place bt the joint pfd appears only slightly asymmetric with a maximm in the forth qadrant, nderlining the complex strctre of the canopy flow and some analogies with rogh wall stdies. Itis worth to note that in each plot reported in figre6statistics with for different 6

8 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 (Λ U/y) Linear fit U/U Figre 5. Distribtion of (ΛU/y) 1 as a fnction of U/U. free-stream elocities hae been plotted confirming that Reynolds nmber effects are negligible aboe the canopy layer. 4. Conclsions An experimental analysis of canopy flows has been performed and discssed. The canopy flow has been artificially reprodced in a wind tnnel in order to achiee a similar description of what is happening in a real forest. Most of the experimental reslts of the present work are in agreement with the ones obsered by other researchers in both field experiments and nmerical simlations (Rapach et al., 1996; Finnigan, ) nderlining the fact that the present simplified canopy model is able to replicate realistically what happens in a real forest. An analysis of the statistics measred at x/h c = 3 shows no Reynolds nmber dependence (despite the change of U of a factor three). The flow can be sbdiided in three regions, namely the one below the canopy interface (where a decay of the trblence with y is obsered), the region jst aboe the canopy interface (where a constant stress layer is sally assmed to be present) and the region aboe the internal canopy bondary layer (where the present flow is affected by the spires sed to artificially increase the thickness of the incoming bondary layer). The new scaling of the elocity spectra with the integral time scale has shown a remarkable collapse of the spectra oer the ertical extension of the canopy bondary layer, demonstrating scale separation by two freqency decades. All the power density spectra of the three elocity components agree with the Kolmogoro f 5/3 law, with some small discrepancy in the and w spectra. The co-spectra relatie to the coariance show a trblence decay between f 5/3 and the theoretically predicted f 7/3. A linear relationship between the normalized integral time scale and the mean elocity has been proposed in order to facilitate the estimation of the integral time scales in real canopies where the ealation of sch qantities is complicated by the lack of a sfficient statistical conergence. The analysis of the skewness profiles and of the joint probability density fnctions at some key points hae highlighted the changes in the strctre behaior across the canopy bondary layer. Namely, close to the canopy interface sweeps are likely to occr, with patches of high speed flid 7

9 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/ Sk Sk (a) 3 1 (b) y/h c 4 /σ Sk Sk /σ 3 (c) 3 (d) 1 1 /σ /σ /σ /σ Figre 6. (a) Skewness profile of and for < U < 5 m/s. Normalized joint pdf for < U < 5 m/s at (b) y/h c, (c) y/h c 1 and (d) y/h c 3.6. The iso-leels starts from. with steps of.. going inside the canopy region from aboe, while far from the canopy classical ejections take place, with patches of low speed flid going towards the oter region of the bondarylayer. This behaior is analogos to rogh wall trblent bondary layers, where this strctre dynamics change has also been obsered with qadrant analysis methods. This work is part of Vindforsk III, a research program sponsored by the Swedish Energy Agency. The athors wish to thank Dr. Ebba Dellwik for the sefl comments dring the preparation of the present manscript. References Alfredsson, P. H., Segalini, A. & Örlü, R. 11 A new scaling for the streamwise trblence intensity in wall-bonded trblent flows and what it tells s abot the oter peak. Phys. Flids 3,

10 Jornal of Physics: Conference Series 318 (11) 718 doi:.88/ /318/7/718 Bendat, J. S. & Piersol, A. G Random data, nd edn. USA: John Wiley & Sons. Finnigan, J. J. Trblence in plant canopies. Ann. Re. Flid Mech. 3, Harman, I. N. & Finnigan, J. J. 7 A simple nified theory for flow in the canopy and roghness sblayer. Bond. Lay. Meteorol. 13, Kaimal, J. C. & Finnigan, J. J Atmospheric bondary layer flows. Their strctre and measrement. Oxford Uniersity press. Krogstad, P. Å., Antonia, R. A. & Browne, L. W. B. 199 Comparison between roghand smooth-wall trblent bondary layers. J. Flid Mech. 45, Meroney, R. N Characteristics of wind and trblence in and aboe model forests. J. Applied Meteorology 7, Noak, M. D., Warland, J. S., Orchansky, A. L., Ketler, R. & Green, S. Wind tnnel and field measrements of trblent flow in forests. part 1: Uniformly thinned stands. Bond. Lay. Meteorol. 45, Pietri, L., Petroff, A., Amielh, M. & Anselmet, F. 9 Trblence characteristics within sparse and dense canopies. Eniron. Flid Mech. 9, Pope, S. B. Trblent flows. Cambridge niersity press, UK. Rapach, M. R., Finnigan, J. J. & Brnet, Y Coherent eddies and trblence in egetation canopies: the mixing-layer analogy. Bond. Lay. Meteorol. 78, Segalini, A., Arnqist, J. & Dellwik, E. 11 Uniersality isses in forest canopies. Bond. Lay. Meteorol. (manscript in preparation). Shaw, R. H., Brnet, Y., Finnigan, J. J. & Rapach, M. R A wind tnnel stdy of air flow in waing wheat: two-point elocity statistics. Bond.-Lay. Meteorol. 76, Talamelli, A., Riparbelli, L. & Westin, K. J. A. 4 An actie grid for the simlation of atmospheric bondary layers in a wind tnnel. Wind Strct. 7, Zh, W., an Hot, R., Lznik, L., Kang, H. S., Katz, J. & Meneea, C. 6 A comparison of pi measrements of canopy trblence performed in the field and in a wind tnnel model. Exp. Flids 41,