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| Titel |
Convective instability of sludge storage under evaporation and solar radiation |
| VerfasserIn |
Kirill Tsiberkin, Lyubimova Tatyana |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250086587
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| Publikation (Nr.) |
 EGU/EGU2014-481.pdf |
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| Zusammenfassung |
| The sludge storages are an important part of production cycle at salt manufacturing, water
supply, etc. A quality of water in the storage depends on mixing of pure water and settled
sediment. One of the leading factors is thermal convection. There are two main mechanisms
of the layer instability exist. First, it is instability of water due to evaporation from the free
surface [1]. It cools the water from upside, increases the particles concentration and leads
to the instability in the near-surface layer. Second, the sediment absorbs a solar
radiation and heats the liquid from below making it unstable in the near-bottom
area.
We assume the initial state is the mechanical equilibrium. The water and sediment
particles are motionless, the sediment forms a uniform sludge layer of thickness z0, there are
no evaporation and heating by solar energy, and the temperature has a linear profile is
determined by fixed upper and bottom temperatures of the layer. Taking into account the
evaporation and solar radiation absorption, we obtain a non-stationary solution for the
temperature using Fourier series method. The local temperature gradients increases rapidly
with time, and local Rayleigh number can be estimated by thermal conduction length
Lt:
gβ(-T(z,t)--z)L4t- - –
Raloc(z,t) = νÏ , Lt ~ Ït,
(1)
where g is gravity acceleration, β, ν and Ï are thermal volume expansion coefficient,
kinematic viscosity and thermal conductivity of the liquid, respectively. Raloc* reaches the
critical value at finite time t* and water motion begins.
The maximal power of solar radiation in visible band equals 230 Wt/m2 at the latitude of
"Uralkalii" salt manufacturer (Berezniki, Perm Region, Russian Federation). We neglect IR
and UV radiation because of its huge absorption by water [2]. The evaporation speed is found
using results for shallow water reservoir [3] and meteorological data for Berezniki [4]. We get
the t*~ 6 -
102 s (10 min) for the layer of 1 m depth and t*~ 2 -
103 s (40 min) for the layer
of 10 m depth.
Dynamic of the system is studied by the Galerkin–Kantorovich method. Using the follow
basis along z-axis:
wn = cosqnz - cotqnsinh qnz - cosh qnz + coth qnsinh qnz, tanqn = tanhqn,
(2)
tn = sinpnz, pn = Ï(2n - 1), n = 1,2,3 ...,
2
(3)
we introduce an infinite family of low-mode approximations of the full model. We found the
parameter deviations from initial state grow rapidly with Ra > 0 and oscillate with
Ra < 0 at the lowest order. Here, Ra is defined by temperature difference between
upper and bottom sides of the layer under pure evaporation. The lowest order model
does not describe the system in full, because the unstable areas are localized within
layer.
The study was financially supported by the Russian Foundation for Basic Research (Grant
13-01-96040).
[1] Berg J.C. Acrivos A., Boudart M. Advances in Chemical Engineering. Ed. by Drew
T.B., Hoopes J.W. Vermeulen T. Academic Press, NY, 1966, V.6, pp. 61–124.
[2] ASTM Standard G173-03, 2012, Standard Tables for Reference Solar Spectral
Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface, ASTM International,
2012.
[3] Tanny J. et al. Evaporation from a small water reservoir: direct measurements and
estimates. J. Hydrol., 2008, V.351, pp. 218–229.
[4] Shklyaev V.A., Shklyaeva L.S. Climatic resources of Ural’s Prikamye. Geographical
Bull., Perm State University, 2006, V.2, pp. 76–89. |
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