Session K.pdf - Clarkson University

dtdient along the flow , the concentration of surface frazildx, intensity of frazil formationS , frazil discharge Q and its gradient along the flowffβ fdQ fdx(table 1) (Pekhovich,Tregub, 1980; Tregub, 1997). The detailed method of estimation of the mentionedsection positions was given in (Tregub, 1977).Table 1. Ice Thermal Conditions for Typical Sections along River Flow№ Sectiont,oCdtdxoC,mParameters of ice thermal stateβ fWtS f ,s3mQ f ,sdQ 2 f m,dx s1 Zero isotherm 0 03 Beginning of frazilflowing up 04 Maximum of watersupercooling 0 >00< β f 0 >0 >06 Ice edge ∼ 0 ≥0 ∼ 1 ≥0 ≥0 ∼ 0The position of the maximum supercooling section is calculated with the formulawhereP x.maxxmax2 h=bLv.fα1⋅V⋅ P( − ϑ )ex.max, (1)dimensionless parameter taken from the following relations:Px.maxβ f .maxP−β f .max − ln( − β )= 1 , (2)f max( P +1) 2 −1= −P max + max , (3)maxα1b=2 Lv.f( − ϑ )⋅Vehb, (4)α1,ϑ e– heat transfer coefficient and equivalent air temperature (Recommendations,1986); b – width of the flow: V – flow speed; – initial ice thickness (Recommendations,1986);L v. fh b– volumetric latent frazil formation heat.336