On the Thermal Regime of the Protective Granular Bed of a Gas Distributor
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 4, July, 2020
HEAT AND MASS TRANSFER IN DISPERSED AND POROUS MEDIA ON THE THERMAL REGIME OF THE PROTECTIVE GRANULAR BED OF A GAS DISTRIBUTOR Yu. S. Teplitskii, E. A. Pitsukha, and A. R. Roslik
UDC 532.529
A numerical solution of a two-temperature problem on the thermal state of an aerated granular bed, constituting the thermal protection of the gas distributor of a high-temperature bubbling bed, is carried out. An equation is obtained for the coefficient of the efficiency of cooling the gas distributor. It is shown that on the side of the bubbling bed the surface temperature of the granular bed is independent of its thermal conductivity and thickness. Keywords: bubbling bed, thermal protection, granular bed, gas distributor, cooling efficiency. Introduction. As is known [1], at high temperatures of the upper surface of the gas distributing grating of fluidizedbed plants the problem of warping of a gas distributing grating and reducing its strength often arises. One of the methods of protecting the grating is covering it by a fixed bed of rather large and heavy particles. The nonlinear character of the distribution of temperature over the height of such an aerated bed provides a rather low temperature of the gas distributor even at a small height of the protective granular bed. Thus, it is reported in [1] that at the temperature of the bubbling bed of coal dust particles of diameter 0.15–0.18 mm Tb = 1300oC the grating temperature did not exceed 300oC if there was a fixed 50-mm-high bed of heavy Alundum particles under the fluidized bed. The goal of the present work was to model the thermal regime of the protective granular bed, which can be conveniently considered as a part of a not entirely fluidized bidisperse bed costing of a fixed layer of heavy (large) particles and of a bubbling high-temperature layer of light (fine) particles. The hydrodynamics of such a system was investigated in detail in [2]. Formulation of the Problem. Fixed protective bed. We used a two-temperature nonlinear model of heat transfer
Cf J f
dTf d ⎛ dTf ⎞ 6(1 − ε)α = ε (Ts − Tf ) , ⎜λf ⎟+ dx dx ⎝ dx ⎠ ds
0 = (1 − ε)
d dx
⎛ dTs ⎞ 6(1 − ε)α (Ts − Tf ) ⎜λs ⎟− dx ⎠ ds ⎝
(1)
(2)
with the boundary conditions x = 0:
Cf J f (Tf − T0 ) = ε λ f
(1 − ε) λ s
x = H :
(1 − ε) λ s
dTf dTs + (1 − ε) λ s , dx dx
dTs = α 0 (Ts − T0 ) , dx
dTs = α b (Tb − Ts ) + σ r (T b4 − T s4 ) = Cf J f (Tf − T0 ) , dx
(3)
(4)
(5)
A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., Minsk, 220072, Belarus; email: [email protected]. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 4, pp. 793–799, July– August, 2020. Original article submitted July 16, 2019. 766
0062-0125/20/9304-0766 ©2020 Springer Science+Business Media, LLC
dTf = 0. dx
(6)
The parameters entering into Eqs. (1)–(6) are calculated by the formulas
⎛ ds 3 ds ⎞ α = 1 ⎜⎜ 0 + 1/3 2 ⎟⎟ ⎝ λ f (2 + 1.8 Pr Res ) 2 π λ s0 ⎠
St 0 =
λs =
α0 = 0.5 Re s −0.5 Pr −0.6
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