Effect of a narrow channel inserted in the conventional ice block mold with brine injection on the productivity and ice formation behavior of the low temperature brine bathing ice production process

ABSTRACT

Block ice is cuboid in shape. It is produced by filling water into a mold and bathing it in a brine pool. For 270 × 560 × 1500 mm³ the production batch time is 24 hours. The aim of this work is to improve the conventional mold so that it has a batch time shorter than the low electrical cost duration of 11 hours. A narrow channel having nearly the same width as the mold was installed inside the mold. The brine is injected from the middle of the channel's open end at the mold base by a ½ inch nozzle. A CFD model was developed and validated with the experimental data. It was found that the optimum pool temperature and injection flow rate may be approximated to be −10 and 80 lpm, respectively. Heat transfer can be assumed to be in one dimension in the mold depth direction. As long as the channel height is less than that of the mold, the batch time will be comparable to that of the conventional mold. Regardless of the pool temperature, for a certain channel height, the channel can contribute to the productivity at approximately the same rate. The batch time was 9.73 hours.

KEYWORDS:

• Ice block
• ice formation behavior
• ice block productivity enhancement
• bathe freezing

Nomenclatures

$A_{mush}$	=	the mushy zone constant $\left[kg{m}^{-3}{s}^{-1}\right]$
$c_p$	=	specific heat capacity $\left[Jk{g}^{-1}{K}^{-1}\right]$
$D$	=	the mold depth $\left[mm\right]$
$E$	=	total energy $\left[J\right]$
$f_l$	=	liquid fraction $[-]$
$f_{l,c}$	=	critical liquid fraction $[-]$
$g$	=	acceleration of gravity $\left[m{s}^{-2}\right]$
$G_k$	=	the production of turbulent kinetic energy $\left[kg{s}^{-3}{m}^{-1}\right]$
$h$	=	sensible enthalpy $\left[Jk{g}^{-1}\right]$
$h_{ref}$	=	reference sensible enthalpy $\left[Jk{g}^{-1}\right]$
$H$	=	total enthalpy $\left[Jk{g}^{-1}\right]$
$H$	=	the mold height $\left[mm\right]$
$k$	=	turbulent kinetic energy$\left[Jk{g}^{-1}\right]$
$l$	=	the channel height $\left[mm\right]$
$p$	=	pressure $\left[Pa\right]$
$\underset{t}{Pr}$	=	turbulent Prandtl number $\left[m^2{s}^{-1}\right]$
$Q_i$	=	the brine injection flow rate into the channel $\left[lpm\right]$
$S_M$	=	the momentum sink due to the reduced porosity in the mushy zone or porosity function Equation. 3(3) $S_M=\frac{{\left(1-\beta \right)}^2}{\left({\beta }^3+\epsilon \right)}{A}_{mush}\vec{v}$(3)
$t_{\hspace{0.17em}}$	=	time $[hr]$, $[s]$
$t_b$	=	batch time $[hr]$
$t_{b,1/2}$	=	batch time of the mold with the channel height to the mold height ratio (l/H) of ½ $[hr]$
$t_{b,3/4}$	=	batch time of the mold with the channel height to the mold height ratio (l/H) of ¾ $[hr]$
$t_{b,1}$	=	batch time of the mold with the channel height to the mold height ratio (l/H) of 1 $[hr]$
$T_{b,c}$	=	average brine temperature in the channel $\left[{ }^{\circ }C\right]$
$t_{b,con}$	=	batch time of the conventional mold $[hr]$
$t_{b,i}$	=	ideal batch time $[hr]$
$T$	=	temperature $\left[{ }^{\circ }C\right]$
$T_b$	=	the pool temperature $\left[{ }^{\circ }C\right]$
$T_{liquidus}$	=	liquidus temperature $\left[{ }^{\circ }C\right]$
$T_{ref}$	=	reference temperature $\left[{ }^{\circ }C\right]$
$T_{solidus}$	=	solidus temperature $\left[{ }^{\circ }C\right]$
$t_s$	=	time-step $\left[s\right]$
$T_w$	=	average water temperature $\left[{ }^{\circ }C\right]$
$u$	=	the mean component of the velocity in the $x$ direction $\left[m{s}^{-1}\right]$
$u{ }^{\mathrm{\prime }}$	=	fluctuating component of the velocity in the $x_{\hspace{0.17em}}$ direction $\left[m{s}^{-1}\right]$
$\overrightarrow{v}$	=	velocity vector $\left[m{s}^{-1}\right]$
$W$	=	the mold width $\left[mm\right]$
Greek symbols	=
$\beta$	=	liquid Fraction $\left[-\right]$
${\delta }_{ij}$	=	Kronecker delta $\left[-\right]$
$\mathrm{\Delta }H$	=	latent enthalpy $\left[Jk{g}^{-1}\right]$
$\epsilon$	=	the turbulent dissipation rate $\left[m^2{s}^{-3}\right]$
$\lambda$	=	thermal conductivity $\left[W{m}^{-1}{K}^{-1}\right]$
${\lambda }_{eff}$	=	effective turbulent or eddy thermal conductivity $\left[W{m}^{-1}{K}^{-1}\right]$
${\mu }_{\hspace{0.17em}}$	=	dynamic viscosity $\left[Pas\right]$, $\left[kg{m}^{-1}{s}^{-1}\right]$
${\mu }_{eff}$	=	effective turbulent or eddy viscosity $\left[Pas\right]$, $\left[kg{m}^{-1}{s}^{-1}\right]$
${\mu }_t$	=	turbulent or eddy viscosity $\left[Pas\right]$, $\left[kg{m}^{-1}{s}^{-1}\right]$
$\rho$	=	density $\left[kg{m}^{-3}\right]$
${\left({\tau }_{ij}\right)}_{eff}$	=	the deviatoric stress tensor $\left[N{m}^{-2}\right]$

Acknowledgements

The authors would like to acknowledge Mr. Ian Thomas for kindly making the manuscript more readable.

Disclosure statement

No potential conflict of interest was reported by the author(s).