Multiphase CFD Modeling of Flow Boiling & Phase Change Dynamics
Numerical prediction of subcooled & saturated flow boiling heat transfer rates, bubble dynamics, and void fraction distribution in internal pipe flows.
Overview of Internal Flow Boiling Regimes
Flow boiling occurs when a liquid flows through a heated tube and undergoes a continuous thermodynamic phase change into vapor along its length. The flow pattern transitions through distinct visual and hydrodynamic regimes—driven by mass flux, heat flux, saturation pressure, and surface orientation.
Sequential Flow Regimes (Inlet to Outlet)
Single-Phase Liquid Flow
Both Horizontal & VerticalSubcooled liquid enters the pipe; heat is transferred strictly via single-phase forced convection prior to local thermodynamic saturation.
Bubbly Flow (Subcooled & Saturated)
Both (Asymmetric in Horizontal)Discrete vapor bubbles nucleate along the heated wall at the Onset of Nucleate Boiling (ONB) and detach into the fluid core.
Plug / Slug Flow
Intermittent / TransitionalAs vapor fraction increases, discrete bubbles coalesce into large vapor plugs. In horizontal tubes, buoyancy forces these plugs to sweep along the upper wall section.
Stratified Flow (Smooth & Wavy)
Horizontal Pipe DominantGravity forces full phase separation: liquid flows along the tube bottom while vapor flows above. As vapor velocity increases, interfacial shear creates stratified waves that roll along the liquid-gas interface, washing up the side walls.
Churn Flow
Highly Transient • Vertical DominantA highly oscillatory, turbulent transitional regime where large vapor slugs break down due to shear forces. Occurs primarily in vertical flows as liquid repeatedly falls back and gets swept upward; in horizontal pipes, it manifests as unsteady wavy-annular flow.
Annular Flow
Both (Thin Film Upper-Wall in Horizontal)A continuous high-velocity vapor core forms in the center of the tube, forcing a liquid film to coat the internal pipe circumference.
Mist Flow / Dryout
Post-Dryout TransitionThe liquid wall film evaporates completely (Dryout), leaving entrained liquid droplets suspended in a continuous vapor stream transitioning to single-phase vapor.
Validation & Benchmark Summary for Flow Boiling Regime
To demonstrate the capability of multiphase CFD in predicting phase-change phenomena, two distinct internal flow boiling benchmark cases were evaluated using R134a and water across subcooled and saturated regimes in a uniformly heated horizontal tube.
The numerical models were validated against the established empirical correlation of Liu & Winterton (1991) and the fundamental heat transfer formulations in Incropera et al.
Key Performance Metrics Evaluated:
- Heat Transfer Coefficients: Agreement with published empirical correlations across varying mass fluxes and heat fluxes.
- Phase Change Dynamics: Accurate prediction of onset of nucleate boiling (ONB) and spatial void fraction evolution along the tube length.
- Thermal Performance: Capturing subcooled fluid heating and saturated boiling transitions under fixed wall heat flux conditions.
Flow Boiling Validation & Analysis
Geometry and Operating Conditions
The validation analysis is performed on straight horizontal circular tubes subjected to uniform outer wall heat fluxes. Fluid enters each domain as a subcooled liquid and undergoes saturated flow boiling along the length. Two distinct working fluids (Refrigerant R134a and Water) are modeled across specific geometric scales and operating parameters:
Case 1: Refrigerant R134a
- Geometry: ID = 10.88 mm, OD = 12.7 mm, L = 1.0 m
- Inlet Condition: Liquid, \(u_{\text{in}} = 0.235 \text{ m/s}\)
- Saturation State: \(5^\circ\text{C}\) at \(349.6 \text{ kPa}\)
- Heat Flux: \(q_{s,o}'' = 8,567 \text{ W/m}^2\) (outer wall)
Case 2: Water
- Geometry: ID = 10.88 mm, OD = 12.7 mm, L = 1.0 m
- Inlet Condition: Liquid, \(u_{\text{in}} = 0.5 \text{ m/s}\)
- Saturation State: \(425 \text{ K}\) at \(500 \text{ kPa}\)
- Heat Flux: \(q_{s,o}'' = 42,835 \text{ W/m}^2\) (outer wall)
Empirical Formulation Framework
To benchmark CFD predictions, the comprehensive Kandlikar correlation (from Incropera) and the Liu & Winterton formulation are paired with core energy balances and slip ratio models to compute two-phase heat transfer coefficients, local wall temperatures, exit vapor quality, and phase distribution dynamics.
Kandlikar Correlation
Calculates saturated flow boiling by taking the maximum value between the convective dominant (\(h_a\)) and nucleate dominant (\(h_b\)) mechanisms.
\(h_b = h_{sp} \left[ 1.136 \left(\frac{\rho_l}{\rho_v}\right)^{0.45} x^{0.72}(1-x)^{0.08}f(Fr) + 667.2 \, Bo^{0.7}(1-x)^{0.8} G_{s,f} \right]\)
Liu & Winterton Model
Asymptotic combination model integrating forced liquid convection and nucleate pool boiling mechanisms.
Energy Balance & Zivi Slip Model
Global energy conservation defines exit vapor quality (\(\bar{X}_{\text{exit}}\)), while Zivi's slip ratio accounts for phase velocity differences to compute accurate exit void fractions (\(\alpha\)).
Validation and Results
The performance metrics below benchmark numerical CFD results against established empirical models, including the Liu & Winterton model, the Kandlikar correlation, and global energy balances coupled with the Zivi Slip Ratio model for both R134a and Water flow boiling test cases.
| Parameter / Metric | Liu & Winterton Model | Kandlikar Model | Global Energy Balance & Zivi Slip Model | CFD Results | Deviations |
|---|---|---|---|---|---|
| HTC – R134a (\(\text{W}/\text{m}^2\cdot\text{K}\)) | 2,000 | 2,800 | — | 1,800 | 10% |
| Wall Superheat – R134a (\(\text{K}\)) | 5 | 8.5 | — | 5.5 | — |
| HTC – Water (\(\text{W}/\text{m}^2\cdot\text{K}\)) | 12,900 | 9,400 | — | 8,600 | 9% |
| Wall Superheat – Water (\(\text{K}\)) | 3.9 | 5.7 | — | 7.6 | — |
| Vapor Quality (\(x\)) – R134a | — | — | 6.1% | 3.5% | — |
| Vapor Quality (\(x\)) – Water | — | — | 1.9% | 1.5% | — |
| Vapor Void Fraction – R134a | — | — | 54% | 55% | 2% |
| Vapor Void Fraction – Water | — | — | 50% | 65% | 30% |
Transient Visualization: Void Fraction and Heat Transfer Coefficient Evolution
Transient Evolution of Void Fraction and Heat Transfer Coefficient Contours
The following animations illustrate the time-dependent phase behavior and thermal performance inside the heated tube. The top contours demonstrate the spatial development of vapor volume fraction (α), capturing the transition from single-phase liquid to slug and annular regimes over time. Below, the corresponding heat transfer coefficient (h) contours show local thermal spikes driven by micro-layer evaporation and bubble agitation. Comparisons between R134a and Water highlight significant differences in transient phase distribution and local cooling capacity due to their distinct latent heat, density ratios, and surface wetting characteristics.
Conclusion: Due to the complex physics of flow boiling and the absence of a single, unified CFD model, every project requires case-by-case validation against established empirical correlations before applying the methodology to complex target geometries.
Advanced CFD Case Study: Non-Equilibrium Boiling & Conjugate Heat Transfer in a Concentric U-Tube
Case Study: Transient Flow Boiling & Conjugate Heat Transfer in a U-Tube Heat Exchanger
This numerical study investigates the thermal-hydraulic performance and subcooled flow boiling characteristics of R134a refrigerant inside a concentric U-tube heat exchanger. The geometry features a 46 mm inner pipe ID with a 3 mm wall thickness, enclosed by a shell transitioning from an inner diameter of 52 mm to 88 mm, spanning a total straight length of 1,800 mm plus a full 180-degree U-bend. Operating conditions comprise saturated liquid R134a at 5°C entering the inner tube at 0.235 m/s (0.50 kg/s), counter-flowed against shell-side cooling water introduced via a top nozzle (56 mm inner diameter) at 12°C and 1.23 kg/s. The simulation captures complex multi-physics interactions by coupling an advanced Eulerian multiphase framework and the Non-equilibrium wall boiling model on the tube side with single-phase turbulent convection on the shell side through full Conjugate Heat Transfer (CHT).
Flow Regimes & Inlet Reynolds Numbers: Flow characterization at the inlets confirms fully turbulent conditions for both fluids. The R134a inner pipe flow yields a Reynolds number of approximately Re = 64,100 (based on a 46 mm ID and 0.235 m/s inlet velocity), establishing robust forced convection prior to nucleation. On the shell side, the cooling water entering through the 56 mm top nozzle at 0.5 m/s yields an inlet Reynolds number of approximately Re = 22,760, ensuring stable turbulent injection and heat transfer across the conjugate solid boundary.
Key Analysis Highlights & Visualizations:
Mesh Convergence & Stability: A comparative spatial discretization study evaluating coarse versus fine mesh performance. The fine mesh successfully resolves steep thermal gradients and local vapor formation, ensuring stable solver convergence where coarser grids struggle.
Transient Void Fraction & Velocity Fields: Time-resolved 3D tracking of phase change dynamics, capturing the evolution of gas void fraction as subcooled liquid R134a absorbs thermal energy from the shell-side water inlet.
U-Bend Phase Separation Mechanics: High-resolution iso-surface tracking of the vapor core at the U-turn section, illustrating centrifugal and inertial phase separation where denser liquid lags behind while vapor accumulates along the inner radius and top pipe surface.
Performance Summary: The table below outlines the primary operating parameters, thermal-hydraulic metrics, and wall boiling flux components extracted from the converged CFD solution.
Conclusion: This simulation represents an advanced class of computational fluid dynamics that goes far beyond standard single-phase conjugate heat transfer. By coupling multi-species Eulerian multiphase formulations, non-equilibrium wall boiling frameworks, transient phase-change mechanics, and turbulent boundary layer closures across complex U-bend geometries, the analysis captures highly non-linear thermo-fluid interactions that demand specialized multiphase modeling expertise.