Numerical Simulation of Three Dimensional Flow in Water Tank of Marine Fish Larvae

Transcription

1 Copyright c 27 ICCES ICCES, vol.4, no.1, pp.19-24, 27 Nmerical Simlation of Three Dimensional Flo in Water Tank of Marine Fish Larvae Shigeaki Shiotani 1, Atsshi Hagiara 2 and Yoshitaka Sakakra 3 Smmary Marine fish larvae are fragile against physical stress. Hoever, fe stdies have been condcted to evalate the flo field in a rearing tank, hich is assmed to provide a high degree of physical stress to marine fish larvae. This paper is a report on the nmerical estimation of stationary flo in the rearing tank of marine fish larvae. The calclated flo in the rearing tank as compared ith the experimental one. The calclation of the stationary flo in the rearing tank shoed good qalitative and qantitative agreement ith the experimental reslts. Introdction Recently, the cltre of marine fish has been developed and groth of many kinds of fish larvae has scceeded by improvements of cltre techniqe. Hoever, marine fish are fragile; physical stress sch as nfavorable flo, light, ater temperatre and etc, may reslt in mass mortality of larvae. Among fish species, groper larvae are highly sensitive to physical stress and mass mortality is cased by floatation in the rearing tank after hatching of eggs. It as thoght that the flo in the rearing tank gave the most effective impact to groper larvae ith small size. In general, the flo in the rearing tank as generated by aerators, hich ere commonly sed to provide oxygen as ell as aid in the even distribtion of live food. Hoever, fe stdies have been condcted on the flo field in the rearing tank [1]. Athors reported the systematic experiments of flo measrement and rearing seven band groper Epinephels Septemfasciats sing 1m 3 polyethylene rearing tank [2]. The estimation of flo in the rearing tank sing a flo meter is very important against the examinations of larvae groth and mass mortality cased by floatation. Hoever, as the comfortable circmstance of flo in the rearing tank is different for each kind of larvae, the measrement of flo each time is not effective for time and economy. This paper deals ith estimation of flo in the rearing tank of marine fish larvae by a nmerical comptation method. The reslts from sch stdies may be very sefl for the prpose of flo estimation in the rearing tank and in the design of larval rearing tanks. 1 Faclty of Maritime Sciences, Kobe University, Japan 2 Faclty of Fisheries, Nagasaki University, Japan 3 Gradate School of Science and Technology, Nagasaki University, Japan

2 2 Copyright c 27 ICCES ICCES, vol.4, no.1, pp.19-24, 27 Nmerical Calclation of Flo For the prpose of estimating the stationary flo in the rearing tank, a nmerical comptation as condcted. The nmerical comptation of three-dimensional flos of the tank as carried ot. The dimensional governing eqations ere the three-dimensional incompressible Navier-Stokes eqations (1, 2 and 3) and the continity eqation (4) as follos: t + x +v y + z = 1 ( p 2 ρ x +ν x y ) z 2 (1) v t + v x +v v y + v z = 1 ( p 2 ρ y +ν v x v y ) v z 2 (2) t + x +v y + z = 1 ( p 2 ρ z +ν x y ) z 2 (3) x + v y + z = (4) here the origin in the Cartesian coordinates system as placed at the center on a free srface of rearing ater tank and (x,y,z) represented the axis in radial and pard directions respectively. The velocity components ere (,v,), p as the pressre in the ater, ρ as the ater density and ν as the kinematic eddy viscosity. The calclation of flo in the rearing ater tank as made by the finite differential method sing MAC scheme. The time differentials in Eqn. (1), (2) and (3) ere expressed by the first forard difference, namely the Eler explicit scheme. The second order central differences ere sed for the spatial differentials in Eqn. (1), (2) and (3). Keeping the nmerical comptation stables, the convection terms ere evalated by the third order pstream difference. The Poisson eqation for obtaining the pressre term as solved by the SOR method. The calclated scheme of flo in the rearing ater tank as made by the crvilinear coordinate systems for the prpose of calclating flo near all and free srface in the ater tank in detail as follos: ξ = ξ ( ) x, y, z η = η ( ) x, y, z ζ = ζ ( ) (5) x, y, z τ = t In general, the calclation of flo in the circlar cylindrical ater tank, is made by the cylindrical coordinate system, it is possible to calclate of flo in an arbitrary ater tank profile.

3 Nmerical Simlation of Three Dimensional Flo 21 Calclated Reslts Fig. 1 shos a 1m 3 polyethylene tank for investigating the effects of flo in a rearing tank on mass mortality in the initial stage after hatching of seven band groper, experiments of rearing larvae. The rearing tank as cylindrical ith a 154cm diameter at the top and a height of 82cm. The flo in the rearing tank as generated ith a typical spherical aerator ith a diameter of 5cm placed at the bottom center of the rearing tank. Figre 1: Rearing tank for experiments of rearing larvae In the experiments of rearing larvae, for aeration rates ere proposed. The nmbers of dead larvae on the ater srface in the tank ere conted everyday. The reslts of rearing experiments ere compared nder each set of different aerating rate, in addition, the effects of the varios aeration rates on srvival and larva deaths, according to the nmber dead and floating, ere investigated. From the measred reslts of the experiments of rearing tank larvae, the srvival of larvae as very high in the initial stage after the hatching of eggs in tanks ith an aeration rate at 2ml/min. The measrements of stationary flo by aerating in the rearing tank generated by an aeration ere carried nder the condition of the rearing rate at 2ml/min. The flo in the rearing tank as measred at each positions in the half plane of vertical section inclded the center of ater tank. The mean velocities of three components (, v, ) of flo in the rearing tank ere obtained from sampling data. From the reslts of the experiments of rearing, the estimation of flo in the tank for an aerating rate of 2ml/min as carried ot by nmerical calclation. The calclated flo in the rearing tank as compared ith the experimental one. Fig.2 shos the grid topology of the calclated region in the rearing ater tank. The nmber of grid points as 3 3 in the (x, z) vertical plane and 3 7 in the (x, y) horizontal plane. The grid spacing as clstered to all, ater srface plane and the center of the rearing tank.

4 22 Copyright c 27 ICCES ICCES, vol.4, no.1, pp.19-24, 27 Y.5.2 X.4 X Z Free Srface Half vertical section Figre 2: Grid topology of a rearing tank Bondary conditions in the comptational domain ere as follos. On the bottom and sideall bondaries, the no-slip condition as implemented. At the center of the rearing tank bondary, the mean flo obtained from the measred flo as implemented becase the relation beteen the aeration rate and the distribtion of the flo velocity as not flly knon. On the free ater srface condition, it as assmed that the free srface elevation as fixed and the velocity component of as zero, becase the eak aerating rate as not almost cased the variation of the free srface elevation. The Reynolds nmber based on the diameter of rearing tank and the strongest mean velocity generated by aerating on the center line in the rearing tank as abot order. M=2ml/min 1cm/s B/2=69.5cm, d=68cm (1cm/s) (1cm/s) z (cm) 2 4 z ( cm ) x (cm) x ( cm ) Figre 3: comparison of the calclated and experimental velocity distribtions Fig.3 shos comparison of the calclated and experimental velocity distribtions on the vertical section inclding the center of the tank in the rearing tank

5 Nmerical Simlation of Three Dimensional Flo 23 flo velocity distribtion. The figre on the left shos - velocity distribtion on the measred vertical section (x, z). and the remarkable vertical circlation as observed. The figre on the right shos calclated - velocity distribtion. A comparison of the experimental and calclated reslts indicates that the comptational method herein presented can be sed to satisfactorily represent the stationary vertical circlating flo. Fig.4 shos the comparison of calclated and experimental velocity distribtions on the vertical and horizontal lines inclding the center of vertical circlation. Both velocity distribtion ere very similar qantitatively. The calclation of the stationary flo in the rearing tank shoed good qalitative and qantitative agreement ith the experimental reslts. The nmerical estimation of the flo in a rearing tank of marine fish larvae as confirmed to be effective and satisfactory for the design of a tank that old provide optimm performance X=center of circlation elocity (cm/s) Exp. Cal. z (cm) elocity (cm/s) 8 4 Center of circlation Exp. Cal. 2 x (cm) 4 6 Figre 4: comparison of calclated and experimental velocity distribtions Conclsion Three dimensional calclations can be sed to estimate the flo in the vertical section of the rearing tank, inclding the center of the tank. Comparing the experimental and calclated reslts, the stationary vertical circlating flo as satisfactorily represented by nmerical comptation method of three dimensional crvilinear coordinates system proposed in present paper. Both velocity distribtions are in good agreement. Also, both locations of the center of the vertical circlating flo ere very similar. This stdy as spported by a grant from the Prefectral Collaboration of Regional Entities for the Advancement of Technological Excellence, JST. Athors

6 24 Copyright c 27 ICCES ICCES, vol.4, no.1, pp.19-24, 27 express thanks to Lena H. Asano for revieing the manscript. References 1. Shiotani S., Akazaa A., et al. (23): Measrements of Flo Field in Rearing Tank of Marine Fish Larvae, A Case Stdy of the Seven Band Groper Epinephels Septemfasciats, Fisheries Engineering,ol. 39, No. 3, pp Shigeaki Shiotani, Atsshi Hagiara, Yoshitaka Sakakra, (25): Estimation of Flo in Rearing Tank of Marine Fish Larvae by Simplified Nmerical Comptation -Case of To Dimensional Flo, Aqacltral Engineering, ol.32/3-4, Elsevier, pp