ANSYS Fluent Wet Steam Model: Non-Equilibrium Condensation

Kiarash Kord
Reading time: 8 min

In many engineering systems, especially steam turbines, the rapid expansion of steam is a common process. When hot, dry steam expands and cools quickly, it can cross the vapor saturation line. This causes the steam to subcool and form a two-phase mixture of vapor and tiny liquid droplets. This mixture is defined as wet steam, representing a specific two-phase flow regime driven by rapid thermodynamic changes. Modeling wet steam is important for the design and analysis of steam turbines. If too much wetness forms at the exit of a turbine, the small but fast-moving water droplets cause serious impingement wear. For analyzing the mechanical degradation caused by this impact, refer to our guide on Erosion Modeling. However, to predict where those droplets form in the first place, engineers rely on CFD simulation in ANSYS Fluent. While the underlying species transport mathematics can be explored in our Mass Transfer Tutorials, the formation of liquid droplets from a supersaturated vapor requires a specialized solver approach. This guide focuses specifically on how to use the wet steam model in ANSYS Fluent to simulate homogeneous non-equilibrium condensation and predict compressible two-phase phenomena.

Contents

Figure 1: Wet steam formation in the low-pressure stages of a steam turbine. The increase in liquid droplets can impact both efficiency and blade integrity.

Mathematical Framework of the Wet Steam Model

To accurately perform a CFD simulation of wet steam flow, ANSYS Fluent builds upon the standard fluid dynamics equations by adding a specialized mathematical framework for homogeneous non-equilibrium condensation. Unlike equilibrium phase-change approaches such as the Lee model used for standard condensation and evaporation, the wet steam formulation does not rely on a pre-existing secondary phase. Instead, it predicts the spontaneous generation of liquid from a subcooled vapor. This framework relies on classical nucleation theory, corrected for non-isothermal effects, to compute the exact moment droplets appear.

Key Assumptions and Limitations

Before looking at the equations, it is important to understand the model’s assumptions, which define its limitations:

The velocity difference (phase slip) between the tiny liquid droplets and the main steam vapor is considered zero (a homogeneous flow assumption).
The model neglects any interactions, coalescence, or collisions between the droplets.
The liquid mass fraction, also known as the wetness fraction ( $β$ ), is assumed to be small ( $β<0.2$ ), meaning the volume occupied by the liquid droplets is negligible compared to the vapor.

Most Important Governing Equations

The core of the wet steam model involves solving two additional transport equations alongside the main flow equations. These track the local wetness and the concentration of droplets:

Transport Equation for Liquid Mass Fraction ( $β$ ): This equation tracks the wetness fraction, telling us how much of the vapor has converted into liquid.

$\frac{\partial (\rho \beta)}{\partial t} + \nabla \cdot (\rho \vec{v} \beta) = \Gamma$

Here, $Γ$ (Gamma) is the mass generation rate, representing the total source of the liquid.

Transport Equation for Droplet Number Density ( $η$ ): This equation tracks the number of droplets per unit volume, defining the density of the droplet cloud.

$\frac{\partial (\rho \eta)}{\partial t} + \nabla \cdot (\rho \vec{v} \eta) = \rho I$

Here, $I$ is the nucleation rate, representing the rate at which new droplets are born.

Formulation of Source Terms

The source terms $Γ$ and $I$ capture the complex physics of supersaturation and rapid phase change:

Nucleation Rate ( $I$ ) & The Wilson Line: As steam expands rapidly, its temperature drops below the saturation temperature. However, condensation does not happen immediately; the steam becomes subcooled (supersaturated). When the degree of subcooling reaches a critical limit known as the Wilson line or Wilson point ,the vapor collapses, and droplets spontaneously form. This birth rate ( $I$ ) is calculated using classical homogeneous nucleation theory, governed by the critical droplet radius ( $r*$ ) required to overcome surface tension:

$r^* = \frac{2 \sigma}{\rho_l R T \ln(S)}$

(where $σ$ is surface tension, and $S$ is the supersaturation ratio).

Droplet Growth Rate & Condensation Shock: Once droplets form at the Wilson line, they provide surface area for further condensation. As vapor rapidly condenses onto these new droplets, it releases a massive amount of latent heat back into the flow. In high-speed flows, like inside a Laval nozzle, this sudden heat release creates a localized pressure spike known as a condensation shock. The solver calculates this secondary mass generation by computing the droplet growth rate, driven by the temperature difference between the droplet surface and the surrounding vapor.

The total Mass Generation Rate ( $Γ$ ) is simply the sum of the mass from new droplets (nucleation) and the mass added as existing droplets increase in diameter (growth).

ANSYS Fluent Implementation and Post-Processing

Setting up a successful wet steam in ANSYS Fluent is a precise process that involves specific model settings, a careful solution strategy, and knowing which results to analyze.

Initial Setup and Model Limitations

Before you begin, you must be aware of the model’s primary limitations, which dictate your setup choices:

Solver Requirement: The wet steam model is only compatible with the density-based solver. You cannot use the pressure-based solver.
Boundary Conditions: You are restricted to using specific boundary conditions. For inlets, you must use either a Pressure Inlet or Mass Flow Inlet. For outlets, you must use a Pressure Outlet.
Material Properties: When the model is active, Fluent uses built-in steam property functions. If you need custom properties, you must load them using a special text command for user-defined wet steam functions.

Figure 2: Wet steam multiphase model activated in ANSYS Fluent

The Recommended Two-Step Solution Strategy

The most critical part of achieving a stable simulation is the two-step solution strategy. First, solve the flow field with the condensation process turned off to establish a converged dry-steam solution. Do this by deselecting the “Wetsteam equations” in the solution control panel. Once the compressible aerodynamics (shock waves and expansion fans) are stable, switch on the condensation process by re-enabling the equations.

Convergence and Troubleshooting: When the wet steam equations activate, the sudden release of latent heat often disrupts the solver. To prevent divergence:

Temperature Limits: Set the minimum temperature limit to at least 273 K in the solver limits panel to prevent unphysical freezing errors (“temperature limited to 1.000e+00”).
Under-Relaxation: If you encounter “turbulent viscosity ratio exceeded” warnings when condensation begins, aggressively drop the Courant number and the Under-Relaxation Factors (URFs) for the wetness fraction.
Wetness Limits: The model is physically designed for a wetness fraction below 20% ( $β<0.2$ ). However, the density-based solver often becomes numerically unstable if the wetness factor rapidly spikes beyond 10% ( $β>0.1$ ). Ensure your mesh is highly refined through the nozzle throat or turbine blade trailing edge to resolve the steep gradients smoothly.

Figure 3: Wet steam equation in Solution Controls panel

Special Output Parameters for Wet Steam Analysis

After your CFD calculation is complete, standard pressure and velocity plots are not enough. The wet steam model provides special output variables essential for understanding the phase transition. During post-processing, generate contours and centerline XY-plots for:

Liquid Mass Fraction ( $β$ ): The most important result. It shows the wetness fraction of the steam, identifying where condensation happens and how much liquid forms.
Saturation Temperature: This contour shows the temperature at which steam should start to condense at the local pressure. It acts as a reference line to compare against the actual degree of subcooling.
Nucleation Rate: Crucial for locating the Wilson line. It shows the birth rate of new droplets and highlights the precise boundary where condensation initiates, often visualized as a very thin shock region.
Liquid Mass Generation Rate: Shows the overall rate of mass transfer from vapor to liquid, combining both nucleation and droplet growth.
Droplet Growth Rate: Shows where existing droplets are increasing in diameter as they travel downstream.

A practical example of applying these setup rules and analyzing these specific outputs against experimental benchmark data (like the Moore or Barschdorff nozzle) is demonstrated in our Wet Steam Multiphase Fluent Analysis in a Convergent Nozzle tutorial, which provides a guided workflow from setup to post-processing.

Figure 4: Key outputs from a wet steam simulation showing liquid mass generation

Conclusion

The wet steam model in ANSYS Fluent is a powerful tool for analyzing high-velocity, compressible condensing flows. Its accuracy comes from a mathematical framework based on transport equations for liquid mass fraction and droplet number density, allowing it to predict the onset of non-equilibrium condensation. To achieve reliable results, you need to follow a rigorous implementation process: utilizing the density-based solver, applying compressible boundary conditions, and securing convergence through the two-step dry-to-wet solution strategy. By analyzing key outputs like the nucleation rate and wetness fraction, engineers gain the insights needed to mitigate blade erosion and optimize turbine efficiency. If you are developing a turbine, ejector, or supersonic nozzle and need an expert to configure these complex thermodynamics, our team is ready to help. We handle complex CFD setups from geometry preparation to validation. Submit your requirements through our ordering CFD project service portal to get accurate, professional results for your engineering assets.

Frequently Asked Questions (FAQ)

What is the Wilson line in a wet steam simulation? The Wilson line (or Wilson point) is the thermodynamic boundary where subcooled (supersaturated) steam abruptly condenses into a two-phase mixture. In a CFD simulation, it represents the exact spatial location where the nucleation rate ( $I$ ) spikes and droplets spontaneously form.
Why does the wet steam model require the density-based solver? Wet steam applications, such as steam turbines and convergent-divergent nozzles, involve rapid expansion, high-speed compressible aerodynamics, and sudden latent heat release (condensation shock). The pressure-based solver struggles with these extreme density variations and coupled thermodynamic shocks, making the density-based solver mandatory.
How do I fix divergence when turning on the wet steam equations? Divergence typically occurs because the sudden release of latent heat destabilizes the flow field. To fix this, ensure you first run a fully converged dry-steam solution. When enabling wet steam, drop your Courant number, reduce the wetness fraction under-relaxation factors, and set a minimum temperature limit of 273 K. If your geometry continues to diverge due to complex shockwave interactions, our CFD Consultation team can diagnose the solver setup and stabilize your mesh.

ANSYS Fluent Wet Steam Model: Non-Equilibrium Condensation