Fig 1.
Phase diagram of water in temperature and pressure ranges relevant to the current study, as compiled from [11]. Also displayed are experimental results reported in the literature [12] and modeling results developed in the current study for similar conditions.
Fig 2.
Illustration of the geometric models used in the current study.
(A) An MS-1 microreactor (i.e., the isochoric chamber) used in a previous experimental study [12,19] and as a benchmark in the current study. (B) An idealized cylindrical isochoric container used for parametric studies (not drawn to scale).
Table 1.
Thermal response for three representative cases studied in the 3D container shown in Fig 2B, subject to outer surface cooling from an initial temperature of +10°C down to -10°C at a rate of 0.4°C/min, followed by a temperature hold at -10°C thereafter, where ts is the time in minutes to reach s response in percent from the full-scale temperature change (20°C).
Table 2.
Coefficients for thermal expansion of water and ice, Eqs (22) and (23).
Table 3.
Material properties of stainless-steel Type 316 used for modelling the isochoric chamber walls.
Fig 3.
Flow diagram for computation using the proposed model.
The symbol n is a time index.
Fig 4.
Density of water within the range of pressures and temperatures investigated in the current study, as calculated by Eq (26).
Fig 5.
Comparison of experimental data [12] and 1D modeling results.
Comparison of experimental data [12] and 1D modeling results for pressure history during the cooling and rewarming of the isochoric chamber illustrated in Fig 2A. Also overlaid are the equilibrium pressure values according to the phase diagram.
Fig 6.
Temperature-pressure histories in the isochoric chamber illustrated in Fig 2A subject to various temperature rates.
Temperature-pressure histories subject to (A) stepwise cooling of the isochoric chamber; and (B) stepwise rewarming.
Fig 7.
The effect of wall thickness on the temperature-pressure history during isochoric cooling.
The analysis is 1D for a geometric model similar to the experimental setup, where the cooling rate between subsequent temperature steps is 20°C/min while the heat transfer coefficient on the outer surface of the system is 350 W/m2K.
Fig 8.
Temperature and pressure histories at five representative points in the domain shown in Fig 2B.
The representative points are in the radial direction at mid-height of the domain for: (A) a 3 ml chamber having a diameter of 11.7 mm and height of 29.2 mm; and (B) a 500 ml chamber having a diameter of 63.5 mm and height of 158.7 mm.