Session K.pdf - Clarkson University

size of the flowing up particle is d f =7,5 mm. The time needed for the particle to reach thesize d f =7,5 mm can be found by the empiric formula of D.N.Bibikov (Tregub, 1997)τf=0,345( 0,5 d )1,5f0,47( 0,96⋅V+ 0,32 ( − t )At the maximum possible supercooling t w = –0.04 °C,) w. (12)τ f = 381 sec. For example, if thelength of the pipe is 120 m water passes it in τ t = 100 sec. In this time the particles offrazil formed in the supercooled water according to formula (12) grow to diameterd t = 3 mm. In the delivering pipe as frazil forms supercooling reduces. As a result thewater temperature coming into the collector well can be estimated by the followingformula:⎛ d ⎞3t t 1t⎛ ⎞= в ⋅ ⎜ − ⎟ = ( − 0,04) ⋅ ⎜1− ⎟ = −0,024 °С.d⎝ f ⎠ ⎝ 7,5 ⎠When water gets into the collector well the flow widens, supercooling disappears andintensive inside water ice formation starts. To prevent blocking of the collector wellsMO-2 with frazil it is necessary to give the water as much heat as needed to get rid ofthe supercooling. For carrying out of the listed tasks both the power and the type of theheater for operation of the collector well is necessary to determine. The necessary powerof the heater is found on the basis of the thermal balance equation, according to whichthe heating power is used for both increasing the water temperature up to t 0 = 0 °C andthe thermal output into the air:c Wτ( t − t ) + α F ( t − ϑ)( t − t )v s0 w=0e01 0+ λe⋅ F Nδ, (13)Wwhere W – the water collector well volume; τ 0= – the time of water exchange in theQ2πd well; t w – water temperature at the well exit (t w ~0,5° C); F = w– the area of the well4water-air contact; ϑ – air temperature; concrete thermal conductivity; λ e – heat concluctivityof concrete; ts – average long term soil temperature of the river floor; δ e –concrete well wall thickness. For the collector well with the diameter 4 m , the height9 m, the wall thickness 0,5 m and the temperatures ts = 4 o C, ϑ = –26 o C the necessarypower of the well heating is N = 127 kWt. The heating zone is to be located on the wellfloor close to both water delivering and withdrawing holes. Free convection developedin the water because of the heat coming up from the heater situated in the lower part ofthe well is favourable to the water temperature increase and the frazil melting. Forsteady-state heating of the collector wells the system consisted of flat heaters with activeelements made of compositional resistive materials (CRM) is worthwhile using.With the power of the well heating equal 127 kWt, 64 kWt are necessary for the heatingof the side well walls in the zone of water delivering and withdrawing and 63 kWt areneeded for the floor heating. Active heating elements developed by the authors andmade up of different CRM are proposed to be used. As one of the possible solution aspecial material with positive coefficient of resistance-temperature dependence is sug-341