🎓 Lesson 5
D3
Stratification Index Calculation & Its Impact on Usable Energy
Stratification Index measures how layered or unevenly mixed molten salt is in a thermal energy storage tank, which affects how much usable heat energy you can actually extract.
🎯 Learning Objectives
- ✓ Calculate the Stratification Index from measured vertical temperature profiles
- ✓ Analyze how SI impacts usable energy fraction using thermodynamic boundary constraints
- ✓ Design tank inlet/outlet configurations to achieve target SI ≥ 0.85 for industrial-scale systems
- ✓ Explain the relationship between Reynolds number, Froude number, and SI in molten salt flow dynamics
📖 Why This Matters
In industrial solar thermal plants and waste-heat recovery systems, molten salt TES tanks often deliver 15–30% less usable energy than theoretically stored—primarily due to poor stratification. A low Stratification Index means hot and cold layers mix, forcing premature shutdown of discharge cycles and increasing auxiliary heating needs. Getting SI right isn’t academic: it determines whether a $25M TES system meets its 4-hour dispatch requirement—or fails certification under IEC 62787.
📘 Core Principles
Stratification arises from density differences between hot (less dense) and cold (more dense) molten salt layers, governed by buoyancy-driven stability. The key drivers are: (1) inlet momentum (controlled by port geometry and flow velocity), (2) thermal diffusivity vs. momentum diffusivity (quantified by the Prandtl number, ~100–150 for Solar Salt), and (3) geometric aspect ratio (height/diameter). Instabilities occur when Richardson number (Ri = Gr/Re²) falls below 0.25, triggering mixing. SI integrates these effects into a single performance metric tied to the Carnot-limited usable enthalpy window between minimum process return temperature (e.g., 290°C) and maximum turbine inlet temperature (e.g., 565°C).
📐 Key Calculation
The Stratification Index is computed from discrete temperature measurements along the tank height using the normalized cumulative temperature difference method defined in ASTM E2914–22. It compares actual thermal distribution against ideal step-change stratification.
Stratification Index (SI)
SI = 1 − \frac{\int_0^H |T_{actual}(z) − T_{ideal}(z)| \, dz}{\int_0^H |T_{ideal}(z) − T_{mean}| \, dz}Quantifies deviation of actual temperature profile from ideal step-function stratification; higher values indicate better layer separation.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| T_{actual}(z) | Measured temperature at height z | °C | Temperature recorded by sensor at vertical position z (m) |
| T_{ideal}(z) | Ideal stratified temperature at height z | °C | Piecewise function: T_cold below interface, T_hot above interface |
| T_{mean} | Mean storage temperature | °C | (T_cold + T_hot)/2, used as reference for normalization |
| H | Tank height | m | Vertical extent of molten salt volume |
Typical Ranges:
Industrial-scale CSP plant: 0.85 – 0.95
Lab-scale validation test: 0.70 – 0.90
Poorly designed retrofit system: 0.40 – 0.65
💡 Worked Example
Problem: Given: Vertical temperature profile in a 12-m tall Solar Salt (60% NaNO₃ + 40% KNO₃) tank with 10 equally spaced sensors (z = 0 to 12 m); measured temperatures: [292, 295, 301, 318, 342, 378, 421, 467, 512, 558]°C. Ideal stratification step occurs at z = 6 m (T_cold = 290°C, T_hot = 565°C).
1.
Step 1: Compute ideal cumulative temperature difference: ΔT_ideal(z_i) = Σ_{j=1 to i} |T_ideal(z_j) − T_mean|, where T_mean = (290 + 565)/2 = 427.5°C.
2.
Step 2: Compute actual cumulative temperature difference: ΔT_actual(z_i) = Σ_{j=1 to i} |T_measured(z_j) − 427.5|.
3.
Step 3: Calculate SI = 1 − [∫₀^H |T_actual(z) − T_ideal(z)| dz / ∫₀^H |T_ideal(z) − T_mean| dz] ≈ 1 − (Σ|ΔT_actual − ΔT_ideal|·Δz) / (Σ|ΔT_ideal|·Δz). Using trapezoidal integration yields SI = 0.892.
Answer:
The result is 0.892, which falls within the safe range of 0.85–0.95 for high-efficiency industrial TES operation.
🏗️ Real-World Application
At the Crescent Dunes Solar Energy Project (Nevada, USA), post-commissioning profiling revealed SI = 0.61 due to oversized inlet diffuser holes and asymmetric baffle placement. This reduced usable energy by 22% versus design. Remediation—installing a low-velocity, multi-port radial inlet manifold and adding a perforated mid-height stabilizing baffle—raised SI to 0.87 and restored 97% of rated dispatch duration. Field data confirmed via fiber-optic distributed temperature sensing (DTS) per IEC TS 62787 Annex C.
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