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17th International Symposium on IceSaint Petersburg, Russia, 21-25 June 2004International Association of Hydraulic Engineering and ResearchMODELING OF ICE COVER IN EXPERIMENTAL BASINSValery Zuev 1 , Eugene Gramuzov 1 , Marina Balakshina 1ABSTRACTPhysical modeling of ships and hydraulic structures interaction with ice is impeded,mainly, by the difficulties of creation of adequate ice cover model. Practical and theoreticalaspects of modeling are reviewed. It is shown that under impossibility of the fullsatisfaction of the similarity theory requirements, partial modelling can bring useful resultsif similarity criteria set, ice cover model and methods of data expantion were chosenrationally. Similarity criteria, allowing widening of model ice cover search area, areformulated. Effective ice cover models, allowing modeling of resistance to ice destructionand methods of data expantion are suggested. Research results are verified by numerousexperiments in ice experimental basin.Complexity of processes of interaction of ships and constructions with ice not alwaysallows to make authentic mathematical model of such interaction. At the same time necessityof reception of the information about ships ice qualities during their designingmakes address to modeling experiment.At known criteria of modeling [6] the most natural way is selection of the materialsimulating an ice cover and satisfying these criteria. However, until now the model ofan ice cover completely satisfying much figurative conditions of modeling is not createdyet. Therefore, search of new materials satisfying conditions of similarity and developmentof techniques of recalculation of tests results at partial similarity are of great interest.At the decision of task on modeling, interaction of the vessel and hydraulic engineeringconstructions with ice in ice pool, the big degree of detailed elaboration of this componentis necessary since this component has the greatest densities in balance of full iceresistance and in the most sensitive way depends on "quality" of lab ice.On the basis of extensive experience of natural supervision, we shall present process ofdestruction of ice as follows. Stem of the ice breaker, contacting the ice rumples an edgeof an ice cover and bends it. In process of vessel stem movement , normal pressure ofstem on ice grows. It occurs until bending pressure in ice cover do not achieve breakingpoint and there will be first radial crack before stem. At its occurrence there is a redistributionof pressure in an ice plate then one more or several radial cracks are formed1 RFNC–VNIIEF, bal@niik.vniief.ru; balac@rol.ru370
from each board, going from stem to periphery. The further bend of an ice field resultsin occurrence of a concentric crack with the center on stem and radiusr = 1/α; α = 4ρ g ,D3Ehwhere α – parameter of a bend of an ice plate on the elastic basis, D = –212(1 −ν )cylindrical rigidity of an ice plate, ρ – density of water, g – gravitational acceleration,α – the module of normal ice elasticity, h – thickness of an ice plate, ν – Poisson factorof ice.Formation of a concentric crack does not result in loss of carrying ability of an icecover. First, it is because at big radial sizes ice plates (at the further load) continue bending,and second, with occurrence on coast of a crack of the significant contact pressureinterfering ice breach. Therefore character of connection between loading and a deflectionat kinematic load has a step kind. To each step of the curve loading-deflection correspondsoccurrence of the next concentric crack, and new cracks are formed from peripheryto the center (stem). The bend occurs until there will come a breach of ice on thenearest to stem concentric crack.Because of nonlinearity of the ice cover destruction diagram it is necessary to knowbreaking force value, but it is insufficient information for the description of interactionof the vessel with ice, and it is also necessary to have information on the work necessaryfor ice cover destruction.At modeling of a vessel movement in a continuous ice field, using division of full resistanceinto components we shall consider resistance of destruction of ice R p . Necessarycondition of ice destruction modeling is geometrical similarity of destruction picture inthe plan at which performance the number and an arrangement of ice contact points withthe case at model movement will be identical with natural. Similarity of destruction picturesis determined by similarity of tensely deformed conditions (TDC) of ice plates forwhich definition we shall use differential equation of plates bend, on the elastic basisresulted in a dimensionless form.where wDρgL4∇ w + w =40 , (1)= w L – a dimensionless deflection; L – characteristic linear size in the plan.From the equation (1) follows, that the TDC of an ice cover for a nature and models willbe similar ifAsρn = ρ mandDidem4 =ρgLg = const expression it is possible to transform to(2)DDnmL=L4n4mwhere λ – the module of geometrical similarity.371= λ4, (3)
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Page 3 and 4: 57.00056.000Elevation (m)55.00054.0
Page 5 and 6: (m 3 /s)50004000300020001000Hour 24
Page 7 and 8: Tailwater Elevation vs. DischargeOb
Page 9 and 10: REFERENCESBerger, R.C. and Stocksti
Page 11 and 12: consequences of the blocked up turb
Page 15 and 16: The position of the section of maxi
Page 17 and 18: The purpose of the tests was to def
Page 19 and 20: size of the flowing up particle is
Page 21 and 22: The combined usage of the umbrella-
Page 23 and 24: hτιj⎡∂(hu∂ ⎤i ) (hu j )=
Page 25 and 26: length was ≈800 m, its average wi
Page 27 and 28: Fig. 5. The ice thickness distribut
Page 31 and 32: the most appropriate automatic spil
Page 33 and 34: HPP turbines were not operating dur
Page 35 and 36: shown (Figure 4). Along the front c
Page 39 and 40: constant inclination. The channel s
Page 41 and 42: All temperatures are compared with
Page 43 and 44: Differance [ o C]5.004.003.002.001.
Page 47: Fig. 2. Grounded hummock by drying
Page 51 and 52: consist in indemnification of the i
Page 53: REFERENCE1. Goldshtejn R.V., Osipen

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