Relationship between surface velocity divergence and gas transfer in open-channel flows with submerged simulated vegetation

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1 IOP Conference Serie: Earth and Environmental Science PAPER OPEN ACCESS Relationhip between urface velocity divergence and ga tranfer in open-channel flow with ubmerged imulated vegetation To cite thi article: M Sanjou et al 016 IOP Conf. Ser.: Earth Environ. Sci Related content - Relationhip between urface velocity divergence and turbulence microcale in open-channel flow with ubmerged trip roughne T Oamoto, M Sanjou and I Nezu - Ga tranfer in a bubbly wae flow A Karn, J S Gulliver, G M Monon et al. - 7th International Sympoium on Ga Tranfer at Water Surface Andrew T. Jeup and William E. Aher View the article online for update and enhancement. Thi content wa downloaded from IP addre on 0/10/018 at :40

2 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 Relationhip between urface velocity divergence and ga tranfer in open-channel flow with ubmerged imulated vegetation M Sanjou, T Oamoto and I Nezu Department of Civil and Earth Reource Engineering, Kyoto Univerity, Kyoto, Japan michio.anjou@water.uciv.yoto-u.ac.jp Abtract. Velocity and ga concentration meaurement were carried out to reveal ga tranfer phenomena in open-channel turbulent flow with flat bottom and ubmerged vegetation bottom condition. A large-cale coherent vortex appear near the vegetation top due to hear intability, and the ubmerged vegetation wa found to promote ga tranfer beneath the airwater interface. Furthermore, we revealed a great dependency of ga tranfer on vegetation denity. The preent meaurement reult propoe a new urface divergence model with wide generality, connecting reaonably the ga tranfer velocity and the urface divergence intenity in open-channel flow, irrepective of bottom roughne condition. 1. Introduction Surface velocity divergence i cloely related to coherent motion induced by bottom turbulence. Intantaneou upward and downward motion occur together with the trong urface divergence, and it reult in periodic renewal of the diolved ga ituation in the free urface. The urface velocity divergence play a ignificant role in the ga tranfer rate a pointed out by McCready et al. (1986), which introduce a theoretical relation, i.e., a urface divergence model (SD model). It i generally well nown that natural river are compoed of variou bottom roughne feature uch a ubmerged vegetation, gravel, and wave, etc. They contribute to produce greater turbulence compared with flat bottom condition. Practical prediction method of the ga tranfer rate are modelled by friction velocity. owever, the friction velocity i hard to evaluate accurately in natural river. With development of video recording device and particle image velocimetry (PIV) technique, the horizontal velocity component could be obtained in the free urface, and it i poible that the SD model will be the mot ueful method to predict the ga tranfer rate in river. The preent tudy focue on the development of an SD-baed model for open-channel flow with ubmerged plant. Surface divergence i found to be affected ignificantly by the free urface velocity. In the vegetated-bed cae, the divergence intenity i greater becaue of the hear vortex produced at the vegetation edge than the flat bottom condition. We propoe a new practical model conidering the turbulence dynamic. A proportionality coefficient of the original SD model depend on the water depth, and thu, a modified SD model wa required that can conider the effect of water depth on ga tranfer. We examined whether the free urface treamwie velocity and turbulent inetic energy can Content from thi wor may be ued under the term of the Creative Common Attribution.0 licence. Any further ditribution of thi wor mut maintain attribution to the author() and the title of the wor, journal citation and DOI. Publihed under licence by IOP Publihing Ltd 1

3 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 be ued a a proper velocity cale. In both cae of mooth and vegetated bed condition, the modified SD model i proved to be ueful without a dependency on the bul mean velocity and depth. (a) Velocity meaurement (b) Ga concentration meaurement high-peed CMOS camera Flow Data logger Flow LLS YAG Laer DO meter B =40cm z W, w U, u x y V, v B =40cm z W, w U, u x y V, v Figure 1. Experimental etup. Experimental procedure Figure 1 how a gla-ided water flume that i 16-m long, 40-cm wide, and 50-cm high, in which water current wa generated by computer control and an electromagnetic flow meter. Streamwie, vertical and panwie coordinate are x, y and z, repectively. The vertical origin, y = 0, wa choen a the free urface. The time-averaged velocity component in each direction are defined a U, V and W, and the correponding turbulent fluctuation are u, v and w, repectively. The meaured region wa located at about 7 m downtream from the channel entrance, at which the turbulent flow wa fully developed. A -W YAG laer (continuou wave) wa ued for the laer light heet (LLS) a hown in figure 1a. The -mm thic LLS wa projected horizontally in the urface elevation. The patial reolution i about 0. mm per pixel. The LLS plane wa illuminated together with tracer particle (diameter of 100 μm and denity of 1.0 g/cm ) and captured by a high-peed CMOS camera. The time variation of the intantaneou velocity vector ( u, w ) wa calculated by PIV algorithm (ee Nezu and Sanjou 011). The PIV analyi wa conducted by direct correlation, in which the interrogation window ize i 5 5 pixel. When the correlation value between the firt and econd image pattern i le than 0.4, a local velocity vector wa judged an invalid vector, and an interpolated velocity value wa given to the correponding poition uing urrounding valid vector. Diolved oxygen (DO) meaurement were alo conducted to evaluate directly the ga tranfer velocity in the ame manner a Moog et al. (1999). After calculation of the reaeration coefficient, the ga tranfer velocity L could be obtained multiplying and. Thee meaured tranfer velocity value were modified to thoe expected at 0 C water temperature. It i well nown that advection effect hould be conidered in the treamwie ditance when we calculate L in unidirectional flow uch a an open-channel tream. In the preent experiment, two DO meter were aligned in the treamwie direction with 7-m pan a hown in figure 1b. Thee meaured ignal were tranferred to the data logger every 1.0.

4 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 Table 1. ydraulic condition for flat bottom flow. (cm) U m (cm/) U (cm/) Re Fr tan θ / / / / / / / / / / / / / /10 4 Table. ydraulic condition for flow with ubmerged vegetation on the bottom. λ (cm) U m (cm/) U (cm/) Re Fr tanθ 1/10 4 Table 1 how hydraulic condition, in which U m i bul-mean velocity and U i time-averaged free-urface treamwie velocity in the centerline of the flume. Subcript mean the free urface. Fr and Re are Froude number and Reynold number defined uing U and, repectively. The DO meaurement tae long duration, from 10 to 40 hour, and thu, we ept contant the water and air temperature by air conditioner. All fifteen hydraulic cae were choen by varying U and ytematically. The apect ratio of the cro-ection, B /, wa 5.0 and larger, to avoid effect of econdary current a pointed out by Nezu and Naagawa (199). Table indicate hydraulic condition for vegetated open-channel cae, in which turbulent meaurement were conducted in the ame way a the mooth-bed open-channel flow. The water depth i three time greater than the vegetation height h, i.e., = h = 15 cm. The preent tudy deal with only ubmerged vegetation flow, and focue on the relation between the vegetation denity and the ga tranfer velocity. A vegetation model i a 5-cm height, 0.8-cm width, 1-mm thic platic plate that cannot warp in the water tream. They are placed vertically on the bae plate with a rectangular grid form. The ubmerged imulated element reduce the treamwie velocity within the canopy, and it reult in hear intability accompanied by coherent vortice at the vegetation top. We conducted not only urface horizontal PIV but alo vertical in the x y plane. The vegetation denity ha been defined in the following way. λ nhb / S (1)

5 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 (1/) β' (cm) U (cm/) Figure. Relationhip between urface velocity and urface divergence intenity. L (cm/) 1.0x10-8.0x10-6.0x10-4.0x10 -.0x10 - preent data =8cm McKenna & McGilli (004), grid tirred tan α = 0. 5 Turney et al. (005), wind-wave α = 0. 4 α = 0.45 =6cm =4cm =cm Tumori & Sugihara (007), grid tirred tan preent data 5.0x10-1.0x10-1.5x10 -.0x10 - D β α = 0. (cm/) Figure. Examination of urface divergence model; comparion with previou meaured data in grid tirred tan and wind wave. S i the horizontal area correponding to the vegetation zone and n i the total number of vegetation element included in the vegetation zone. Grid pan i.4 cm, 4.8 cm and 7 cm, correponding to λ = 0789, 947 and 6, repectively.. Reult in flat-bottom open-channel flow The urface velocity divergence at the air-water interface β could be defined a the following form, in which tilde repreent an intantaneou component. u w v β + = () x z y When β i introduced intead of vertical velocity v, a tranport equation of diolved ga concentration i given by c c + c c c + u w βy = D () t x z y y Thi form implie that β i an important factor when vertical ga tranport i prevalent much more than longitudinal and panwie one. Figure how the relation between urface divergence intenity β and the free-urface velocity or the water depth. β i equal to RMS of the intantaneou urface velocity divergence. β wa calculated from time erie of β during 60. A fluctuation of water urface i negligibly mall in the preent hydraulic cae, and thu, a vertical velocity could be given by zero. When we conider v and i obtained. v' ituated in the free urface with ditance, Δ y, the following relation β' = v' / Δy (4) Turbulence intenitie obey univeral function propoed by Nezu and Naagawa (199) except for near the bottom and free-urface region, and they could be normalized by a bottom friction velocity 4

6 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 U *. There remain uncertainty about turbulence tructure near the urface; when we aume v U *, a proportional relation β U * i obtained. In the open-channel flow, U i proportional to U *, and it i then expected that β i proportional to U. Thi tendency i oberved in figure. A variation of β i relatively mall againt the water depth. In a urface renewal model (SR model), L i given by L Dr (5) in which D i molecular diffuivity of diolved oxygen in water and r i a urface renewal rate. Phyical ga tranfer modeling ha been generally conducted on the bai of equation (5). In contrat, McCready et al. (1986) propoed a urface divergence model (SD model) by connecting the ga tranfer velocity and the urface velocity divergence. L = α Dβʹ (6) in which α i a proportional coefficient. The validity of the SD model wa examined mainly for the grid-tirred tan experiment. owever, not much i nown about open-channel flow. Figure how the relation between L and β ', in which meaured data in the grid-tirred tan and wind-induced water wave are indicated for the comparion. When the water depth i fixed, there i a linear relation in the preent data a well a previou tudie. α varie in a range of 0. to 0.5 in previou tudie, and it i 0.45 in the preent tudy of = 8 cm. Therefore, the preent proportional coefficient agree well with thoe oberved in other ind of flow field. The linear relation i not oberved among different water depth cae. Thu, a more practical SD model hould be propoed for the open-channel cae uch a natural river. (cm/) 6.0 L 4.0 (cm) α = (cm/) 6.0 L 4.0 (cm) α = Figure 4. Relationhip between ga tranfer velocity and D β / U D β U (cm/) (cm/) D 1 / β Figure 5. Relationhip between ga tranfer velocity and 1/ D β / The proportional coefficient α in the original SD depend on the water depth. In a new propoed model, the water depth i choen a characteritic length cale. It i further important in modeling of urface renewal rate to elect only hydrodynamic value obtained by horizontal PIV meaurement in field meaurement in term of practical ue. When the urface treamwie velocity U i choen a characteritic velocity, the new tranfer model i indicated in the following way. L D β (7) U Figure 4 how variation of the ga tranfer velocity againt D β / U. The linear relation could not be obtained with little diperion, irrepective of the water depth. 5

7 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 The urface renewal proce i correlated to the coherence turbulence, and thu, the turbulence tatitic uch a turbulent inetic energy, turbulence intenity, and eddy advection velocity, etc., may be better for the characteritic velocity cale than the time-averaged velocity uch a U. When we aume that vertical turbulence intenity at the free urface i ignorably mall compared to treamwie and panwie one, the turbulent inetic energy of the free urface could be indicated by 1 1/ ( u' + w' ) (8) When i ued for U, the following relation could be introduced. L D 1/ β (9) Figure 5 how variation of the ga tranfer velocity againt 1 /, in which a linear relation i recognized. The tandard deviation of / Dβ / U L D β / i greater than 1/. Thi ugget that L / Dβ / equation (9) i more reliable than equation (7). Then, equation (10) could be propoed for an experimental formula about ga tranfer velocity in open-channel flow. L / D βʹ = (10) 1 / In the near future, we will examine equation (10) in a larger cale laboratory flume and natural river. 4. Ga tranfer in vegetated-bottom condition Figure 6 how the relation between the urface divergence intenity and the vegetation denity. Thi reult ugget that the divergence intenity increae with increaed vegetation denity. Thi may be becaue the large-cale coherent vortex play a more ignificant role on the urface renewal in the dener vegetation cae. Some previou tudie offered that more remarable hear intability could be oberved in the dener vegetation, and correponding integral cale of coherent tructure increae ignificantly. Figure 7 and figure 8 how ignificant relation of L and D β / U, and L and 1/ D β /, repectively. In figure 7, the reult of the non-vegetation cae, i.e., only a bae plate over the flume bed, agree with the linear relation of equation 6, while thoe in the vegetation cae hift below mooth bed reult. Thi implie that U cannot be ued a the velocity cale to conider large-cale turbulence induced by the coherent vortice near the vegetation top. In figure 8, the reult of vegetation cae are conitent with equation 10, irrepective of the vegetation denity. Thi ugget that the prediction model uing turbulent inetic energy a the velocity cale ha a wide generality. (1/).0 β' Figure 6. Relation of urface divergence intenity and vegetation denity. λ 6

8 7th International Sympoium on Ga Tranfer at Water Surface IOP Conf. Serie: Earth and Environmental Science 5 (016) IOP Publihing doi: / /5/1/01016 (cm/) 6.0 L 4.0 mooth bed vegetation α = (cm/) 6.0 L 4.0 mooth bed vegetation α = (cm/) Figure 7. Relation between ga tranfer velocity and for both bottom type. D β / U D U β (cm/) D Figure 8. Relation between tranfer velocity and 1/ D β / for both bottom type. 1 / β 5. Concluion It wa found that a proportionality coefficient of the original SD model depend on the water depth. The preent tudy developed a modified SD model that conider the effect of water depth on ga tranfer. We examined whether the free-urface treamwie velocity and turbulent inetic energy are ued a a proper velocity cale, and then, in both cae, the modified SD model i ueful without a dependency on the bul-mean velocity and the water depth in flat bottom condition. When the modified SD model uing the free-urface velocity i applied to the vegetated openchannel flow, there i a large gap between the mooth bed cae and the vegetated. In contrat, the modified model uing the turbulent inetic energy ha a contant proportionality coefficient, irrepective of bottom roughne condition. It i therefore indicated that the modified SD model, which give the urface renewal rate uing the turbulent inetic energy and urface divergence, ha the ame proportionality coefficient for mooth and vegetated bottom. Reference [1] McCready M J et al 1986 AIChE J [] Nezu I and Sanjou M 011 J. ydro-environment Re [] Moog D B and Jira G 1999 J. ydraulic Eng. 15 [4] Nezu I and Naagawa 199 Turbulence in Open-Channel Flow (CRC Pre) [5] Komori S et al 1989 J. Fluid Mech