Unsteady Inherent Convective Mixing in Thermal-Energy-Storage Systems during Standby Periods

Recent studies on the flow phenomena in stratified thermal-energy-storage (TES) systems have shown that heat conduction from the hot upper fluid layer through the vertical tank sidewall into the lower cold fluid layer leads to counterdirected wall jets adjacent to the vertical sidewalls. It was shown that these phenomena destroyed half of the total exergy content in less than a tenth of the storage time constant of a $2$-${\mathrm{m}}^3$ stratified TES system. This paper investigates short-term fluctuations of the wall jets since these fluctuations can potentially mix the hot and cold zones of the thermal stratification that are separated by the thermocline region. Using particle-image velocimetry measurements in two regions of a TES model experiment (near-wall region and far-field region) and analyzing the frequency content of the velocity fields revealed characteristic oscillations for different regions. In the near-wall region, observed fluctuations agreed well with an adjusted boundary layer frequency from the literature, showing that the wall jet is transitioning from laminar to turbulent flow. In the far-field region, the oscillations are related to the Brunt-Väisälä frequency. It is shown that the fluctuations from the boundaries of the thermocline region are most dominant and propagate into deeper regions of the thermocline. A comparison to data from the large-scale test facility for thermal energy storage in molten salt at the German Aerospace Center in Cologne showed good agreement. The consensus between the two experiments proves firstly that a small-scale model experiment with water as a storage liquid can be used to analyze the physical phenomena of large-scale molten salt storage facilities and secondly that these fluctuations are relevant for exergy destruction in real-scale TES.

Popular Summary

The efficiency of a sensible-heat thermal-energy-storage system relies on minimizing the mixing between the hot and cold fluid regions. Here, the authors show that in a stratified thermal-energy-storage tank an unsteady inherent flow develops and promotes mixing of the hot and cold regions. They studied this mixing behavior using laser-based measurements in a model system, and frequency analysis showed that flow near the walls of the thermal storage tank fluctuates periodically. This wall-jet phenomenon was assigned to a transition from laminar to turbulent flow, and it triggers additional fluctuations in the tank that further mix the hot and cold layers. The authors complemented their study by additional measurements on an industrially-relevant, large-scale thermal-energy-storage system using molten salt as the thermal-storage fluid and found similar fluctuations. They suggest that this detrimental mixing behavior could be limited by modifying the tank walls with additional insulation or structures to reduce flow. These findings will contribute to improving the efficiency of future thermal-energy-storage systems.

Figure 1

Depiction of the overall flow structures inside the model experiment of stratified TES due to the influence of a vertical, highly heat-conducting sidewall.

Figure 2

Model experiment including the PIV system for flow measurements in the near-wall region and in the far field of the wall. The shown camera setup corresponds to the far-field measurement consisting of two adjacent cameras, while in the wall measurement, only one camera in combination with an objective lens with higher magnification is used. The differently colored rectangles show the corresponding fields of view (FOVs) of the two measurements.

Figure 3

(a) Snapshot of the far-field PIV result showing the near-wall measurement’s vertical velocity component $v$. (b) Space-time plot of $v$ along the vertical line at $x=3\mathrm{mm}$ [indicated by a dashed line in (a)]. (c) Space-time plot along the horizontal line at $y=500\mathrm{mm}$ [also indicated by a dashed line in (a)]. (d) Power spectral densities (PSDs) of two time series of $v$ at two different distances to the vertical sidewall for a height of $y=500\mathrm{mm}$. The time series are indicated as star markers or solid lines by their colors in the other subfigures.

Figure 4

(a) Snapshot of the far-field PIV result showing the horizontal velocity component u. The left and right borders of the field of view are masked in gray since velocities in those regions were too high to be properly resolved. (b) Space-time plot of $u$ along the vertical line at $x=100\mathrm{mm}$ [indicated by a dashed line in (a)]. (c) Space-time plot along the horizontal line at $y=500\mathrm{mm}$ [also indicated by a dashed line in (a)]. (d) PSDs of two time series of $u$ at two different distances to the vertical sidewall for a height of $y=500\mathrm{mm}$. The time series are indicated by their colors in the other subfigures.

Figure 5

Subfigures (a) and (b) show the PSD calculated for all time series at a wall distance of $x=3\mathrm{mm}$ for the vertical and the horizontal velocity components, respectively. Subfigure (c) shows the temperature profile measured at the beginning of the wall measurement in the water (black line) and the space-averaged and local temperature difference (red solid line and red dashed line) used to calculate the corresponding characteristic wall-jet frequencies $\widehat{f_{\mathrm{wj}}}$ and $f_{\mathrm{wj}}$, respectively. Subfigures (d) and (e) show the PSD at a wall distance of $x=100\mathrm{mm}$ taken from the far-field measurement and again for the vertical and horizontal velocity components, respectively. Subfigure (f) shows the temperature profile (black line) at the beginning of the far-field measurement and the corresponding vertical density gradient of the water (red line) used to calculate the local BVF $\widehat{f_{\mathrm{BV}}}$. The dashed lines in (c) and (f) show the lower and upper boundaries of the wall and far-field PIV measurements, respectively.

Figure 6

Space-frequency illustration of the 15 thermocouples’ PSD spectra during the additional temperature measurement. The red solid and dashed lines show the development of the BVF from the beginning ($t=150\mathrm{s}$) to the end ($t=3750\mathrm{s}$) of the investigated time series and the red dots show the frequency of maximum PSD for all spectra.

Figure 7

(a) Schematic depiction of the TESIS:store TES test facility as part of the TESIS facility at the German Aerospace Center (DLR) in Cologne, Germany. The sketch shows the relative dimensions, the origin of the cylindrical coordinate system, and the positions of the used sensors. (b) Vertical temperature distribution ${\vartheta }_{\mathrm{s}}(z)$ (black lines) inside the TES facility at the beginning (solid line) and the end (dashed line) of the measuring period. The red lines show the corresponding vertical density gradient $\mathrm{\partial }{\rho }_{\mathrm{s}}/\mathrm{\partial }z(z)$ of the temperature distribution. (c) Space-frequency plot of the PSD of the vertically aligned temperature sensors [see (a)] with red dots indicating their maxima. The red solid and dashed lines show the theoretical BVFs at the beginning and the end of the measuring period, respectively. (d) Standard deviation of all utilized temperature sensors where the black line (and the corresponding black axis) shows the standard deviation of the horizontally aligned sensors at a height of $z=0.75\mathrm{m}$, and the red line (and the red axis) shows the standard deviation of the vertically aligned sensors at the radius $r=0.69\mathrm{m}$.

Figure 8

The subfigures (a)–(j) show a series of consecutive temporal snapshots of the flow field in the near-wall region with a time difference of one second between the snapshots. The colored background shows the vertical velocity component $v$ with the corresponding color bar on the right. The arrows show every 15th vector in both the horizontal and the vertical direction, respectively. Subfigure (e) shows the same snapshot as Fig. 3.

Figure 9

Partial spectra of the black spectrum in Fig. 3 ($x=3\mathrm{mm}$, $y=500\mathrm{mm}$) as a result of splitting the corresponding time series into four equally long parts of $10\min$ each. The vertical gray line indicates the peak frequency of $f=1.1\times {10}^{-1}\mathrm{Hz}$.