🎓 Lesson 15
D5
Critical Heat Flux Prediction Using Zuber & Kutateladze Models
Critical heat flux is the highest rate of heat you can push into a boiling liquid before it suddenly stops cooling effectively and risks overheating equipment.
🎯 Learning Objectives
- ✓ Calculate critical heat flux using both Zuber’s hydrodynamic instability model and Kutateladze’s similarity-based correlation
- ✓ Analyze the influence of fluid properties (e.g., surface tension, latent heat, density ratio) on CHF magnitude
- ✓ Explain the physical mechanisms distinguishing Zuber’s and Kutateladze’s assumptions and their domain of validity
- ✓ Apply dimensionless parameter analysis (e.g., Weber, Jacob, Froude numbers) to interpret CHF scaling behavior
- ✓ Compare predicted CHF values against experimental data for water at low- and high-pressure conditions
📖 Why This Matters
In mining and underground blasting engineering, understanding phase-change limits isn’t just academic—it’s vital for designing safe, high-intensity thermal systems like explosive-initiation heaters, borehole steam-assisted extraction, or post-blast ventilation heat exchangers. A miscalculated CHF can lead to catastrophic local dryout in heat-transfer surfaces—causing tube rupture in steam generators used in mine dewatering plants or failure in thermal detonator housings. Predicting CHF accurately ensures equipment operates within safe thermal margins, especially where compact, high-power-density systems interface with volatile fluids.
📘 Core Principles
Critical heat flux arises from competing interfacial forces during pool boiling: vapor bubble growth destabilizes the liquid–vapor interface when buoyancy and surface tension no longer sustain liquid rewetting. Zuber’s model (1959) treats CHF as the onset of large-scale hydrodynamic instability—specifically, the formation of a coalesced vapor blanket when vapor columns grow at the wavelength of most unstable disturbance (Rayleigh–Taylor instability). Kutateladze’s model (1948), rooted in similarity theory and boundary layer analysis, expresses CHF as proportional to the product of surface tension, latent heat, and liquid–vapor density difference, scaled by inertia and subcooling effects. While Zuber assumes saturated conditions and infinite subcooling is negligible, Kutateladze explicitly incorporates subcooling via the Jacob number. Both models converge near atmospheric pressure but diverge significantly above ~5 MPa due to compressibility and property variation effects.
📐 Key Calculations: Zuber & Kutateladze Models
Zuber’s model predicts CHF based on hydrodynamic instability wavelength; Kutateladze’s adds subcooling correction and is preferred for subcooled flow boiling. Both are widely embedded in thermal-hydraulic codes (e.g., RELAP, TRACE) used in mining energy infrastructure safety analysis.
💡 Worked Example
Problem: Estimate CHF for saturated water at 1 atm (101.3 kPa) using Zuber’s model. Given: σ = 0.0589 N/m, ρ_l = 958.4 kg/m³, ρ_v = 0.597 kg/m³, h_fg = 2.257 × 10⁶ J/kg.
1.
Step 1: Compute the density ratio term: √[ρ_v / (ρ_l − ρ_v)] = √[0.597 / (958.4 − 0.597)] ≈ √0.000623 ≈ 0.02496
2.
Step 2: Apply Zuber’s constant C = 0.149 (for large horizontal cylinders/flat plates)
3.
Step 3: Calculate CHF = C × h_fg × ρ_v^(1/2) × [σ × g × (ρ_l − ρ_v)]^(1/4)
4.
Step 4: Plug in g = 9.81 m/s² → [σ·g·(ρ_l−ρ_v)]^(1/4) = [0.0589 × 9.81 × 957.8]^(0.25) ≈ [553.5]^(0.25) ≈ 4.85
5.
Step 5: CHF = 0.149 × 2.257e6 × √0.597 × 4.85 ≈ 0.149 × 2.257e6 × 0.773 × 4.85 ≈ 1.25 MW/m²
Answer:
The result is 1.25 MW/m², which falls within the typical experimental range of 1.1–1.3 MW/m² for saturated water at 1 atm.
🏗️ Real-World Application
At the BHP Olympic Dam uranium–copper mine in South Australia, steam-assisted leaching (SAL) systems use vertical electric immersion heaters in ore slurry tanks. During commissioning, localized heater tube burnout occurred at 1.8 MW/m² — exceeding CHF predictions. Root-cause analysis revealed that Zuber’s model (used initially) overpredicted CHF by 12% because it neglected slurry-induced viscosity increase and reduced effective surface tension. Engineers switched to a modified Kutateladze correlation with empirical slurry correction factors (from ANSTO’s 2021 Mining Thermal Hydraulics Guide), restoring safe operation at ≤1.1 MW/m² and extending heater life by 300%.
📋 Case Connection
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