Empirical characterization of vertical-tube inlets in hot-water storage tanks

A Flow Rate Dependent 1D Model for Thermally Stratified Hot-Water Energy Storage

“…The Richardson number contains the Archimedes number's information and flow-based information (e.g., velocity gradient). The Richardson number is used extensively throughout tank stratification models, but definitions vary widely for length scale, locations of property evaluation (e.g., thermal diffusivity, temperature), and most importantly, the velocity of inlet or vertical bulk flow [25].…”

“…The equation used in the modeling is the turbulent eddy diffusion/convection equation. The eddy diffusion factors are significantly different between the source heating loop and the draw loop, and both eddy diffusion factors follow exponential allometric relationships based on the Reynolds number divided by the Richardson number [25].…”

“…In total, 9 VTIs were characterized for the CED model. Four were modeled in this paper to show the difference in the turbulent diffusion and accuracy based on tube location [25]. For solving for inlet ε from empirical data [25], a smoothing function was used over 5 points in space for data taken every section to calculate the first and second derivatives.…”

“…Four were modeled in this paper to show the difference in the turbulent diffusion and accuracy based on tube location [25]. For solving for inlet ε from empirical data [25], a smoothing function was used over 5 points in space for data taken every section to calculate the first and second derivatives. For the simulation, the previous temperature solution was used in an explicit method that stepped a Courant number equal to 1 for the ε model that decreases inlet by 1/n to exponent B for heating and 1/(N − n) to the exponent 1/B for draws.…”

“…For the simulation, the previous temperature solution was used in an explicit method that stepped a Courant number equal to 1 for the ε model that decreases inlet by 1/n to exponent B for heating and 1/(N − n) to the exponent 1/B for draws. The ∆t associated with the first step was larger for the first and last space step to match the temperature probe layout of the experimental setup shown in Figure 1 with 0.5 • C instrument error-when all instrument and statistical error was propagated for the setup the uncertainly was less than 4% [1,25]. The temperature measurements were 16 thermocouple probes strung vertically through the center of the tank.…”