Chilled Water Thermal Storage (TES) Stratification Calculator

Chilled Water Stratified Thermal Energy Storage (TES) Principles

Naturally stratified chilled water thermal energy storage utilizes the density difference between cold supply water (40°F / 4.4°C, (\rho \approx 62.43\text{ lb/ft}^3)) and warm return water (56°F / 13.3°C, (\rho \approx 62.38\text{ lb/ft}^3)) to store cooling energy without physical diaphragms or baffles.

1. Storage Volume Formula & Figure of Merit

The net water volume required to store a design ton-hour capacity depends on the chilled water temperature differential (\Delta T = T_{return} - T_{supply}) and the Figure of Merit ((FOM)):

$$V_{\text{gal}} = \frac{\text{Ton-Hours} \times 12,000\ \text{BTU/Ton-hr}}{8.34\ \text{lb/gal} \times c_p \times (T_r - T_s) \times FOM}$$

Figure of Merit (typically 88% to 92%) accounts for thermal conduction across the boundary layer, heat gain through the tank shell, and water volume lost to the thermocline transition zone.

2. Diffuser Design & Inlet Froude Number

To prevent turbulent jet mixing that would destroy thermal stratification, radial octagonal or circular diffusers introduce water at the tank bottom (cold) and tank top (warm) at velocities below 0.5 ft/s. Stratification stability is governed by the densimetric Froude number:

$$Fr = \frac{V_i}{\sqrt{g \cdot D_i \cdot \frac{\Delta \rho}{\rho}}} \le 1.0$$

When (Fr < 1.0) (preferably (Fr < 0.5)), buoyancy forces dominate inertial forces, forming a razor-thin, stable thermocline (typically 2 to 3 feet thick).

3. Peak Demand Shaving Economics

By shifting chiller operation to off-peak nighttime hours, facility owners eliminate hundreds of kilowatts of peak coincident electric demand charges:

$$\text{Avoided kW} = \frac{\text{Ton-Hours}}{\text{Discharge Hours}} \times \text{Chiller kW/Ton}$$