A Gradient-porosity CFD simulation is a very important study for creating better batteries and energy storage systems. Many systems use Phase Change Materials (PCM) to store heat, but PCM alone is very slow at absorbing and releasing energy. To fix this, we can add a metal foam, like copper foam, to help heat move faster. A Gradient-porosity Fluent analysis looks at a special, “smart” kind of foam where the holes are not all the same size; they gradually change from big to small. This is called a gradient porosity.

This report shows how a PCM fluent simulation was used to study this smart foam. The key to this simulation is a User-Defined Function (UDF). A UDF is a special piece of computer code that lets engineers add new physics into ANSYS Fluent. We need a UDF because a normal simulation cannot handle a foam where the properties change from place to place. The UDF tells the simulation exactly how the foam’s porosity, permeability, and thermal conductivity change at every point. A Solidification and melting Fluent simulation with a UDF is the only way to see exactly how this smart foam helps the PCM melt faster and more evenly. This helps engineers design the best possible foam structure to create faster and more efficient thermal energy storage systems.

• Reference [1]: YUAN, Yanping, et al. “Numerical analysis of thermal storage characteristics of gradient-porosity copper foam-enhanced phase change materials.” Energy Storage Science and Technology8 (2025): 3100.

Figure 1: A diagram of the 2D model used for the PCM CFD simulation, showing the heating wall on the left.

Simulation Process: Modeling the Gradient Foam and Phase Change

The simulation process for this Gradient-porosity CFD study began by creating domains: one for the Phase Change Material (PCM) and one for the copper foam. This two-domain method allows us to precisely model the melting of the PCM and the heat transfer effect of the foam separately. The entire area was then filled with a high-quality structured grid made of 240,000 cells. A structured grid, with its organized, rectangular cells, is the best choice for a Solidification and Melting Fluent simulation because it gives the most accurate and stable results when calculating the moving boundary between the liquid and solid PCM.

The CFD simulation employs Solidification & Melting module with non-equilibrium modeling to capture phase change behavior in the PCM domain, where non-equilibrium approach accounts for temperature differences between solid and liquid phases during melting and solidification processes – Solidification & Melting module in ANSYS Fluent is essential for PCM CFD simulation because it accurately predicts melting fronts, latent heat effects, and natural convection in liquid regions. The porous zone is configured as a copper porous medium where gradient porosity is implemented through User Defined Functions (UDF) and User Defined Memory (UDM) that calculate spatially-varying porosity, permeability, thermal conductivity, and heat transfer coefficients based on position coordinates – UDF programming enables ANSYS Fluent to handle gradient-porosity effects that cannot be modeled with standard porous media approaches. The governing equations include the continuity equation, momentum equations with Darcy-Brinkman-Forchheimer effects, and dual energy equations for non-equilibrium heat transfer between PCM and copper foam phases – these equations capture the complex multiphase physics of gradient-porosity copper foam PCM systems for accurate thermal storage analysis.

Porosity Distribution Function:

Pore Diameter Calculation (Equation 12):

Ligament Diameter Calculation (Equation 13):

Viscous Resistance Calculation (Equation 15):

Inertial Resistance Calculation (Equation 16):

Effective Thermal Conductivity (Boomsma & Poulikakos):

Interfacial Area Density (Equation 14):

Interfacial Heat Transfer Coefficient (Equation 17 – Žukauskas Correlations):

Post-processing

The simulation results give us a complete picture of how the energy storage unit works. We will now investigate these results to understand how the smart gradient foam makes the heat transfer process better. Heat moves in two ways here: through fluid motion (convection) and through the material itself (conduction). The velocity streamlines in Figure 2 show us the story of convection. As the PCM next to the hot left wall melts, it becomes warmer and lighter, causing it to rise. When it reaches the top, it cools slightly, becomes heavier, and sinks down the right side. This creates a large, clockwise circulation of liquid PCM. This motion is very important because it acts like a conveyor belt, carrying heat from the wall to the rest of the tank. The simulation shows that this natural convection flow reaches a maximum speed of 3.63e-05 m/s. The gradient foam is designed to control this flow. It has larger holes where the flow needs to be strong and smaller holes where the flow can be slower. This ensures the heat is spread evenly by the moving liquid.

The temperature contour in Figure 3 and the liquid fraction contour in Figure 4 show us the final result of this smart heat transfer process. The temperature contour shows a smooth spread of heat from the hot wall (331.35 K) to the cold areas (314.15 K). The liquid fraction contour tells the most important story. It shows the shape of the melted PCM (the red area). If heat transfer was by conduction only, the red area would be a straight vertical line. But it is not. The melted area is much wider at the top than at the bottom. This proves that the convection we saw in Figure 2 is having a powerful effect. The clockwise flow of hot liquid carries extra heat to the top of the tank, causing it to melt much faster. This is the most important achievement of this design: the gradient foam creates a perfect balance between conduction and convection. The copper foam itself provides excellent conduction (like a highway for heat), while the special gradient porosity allows a strong convection current to form that helps distribute that heat everywhere.

Figure 2: The velocity streamlines from the Fluent simulation. This contour shows the natural convection flow pattern of the liquid PCM as it is heated.

Figure 3: The temperature contour from the CFD analysis. It shows how heat spreads from the hot wall on the left into the PCM and the copper foam.

Figure 4: The liquid fraction contour from the Solidification and Melting Fluent simulation. This contour shows which parts of the PCM have melted (red) and which parts are still solid (blue).

This Gradient-porosity CFD simulation proves that using a smart foam is much better than using a simple uniform foam. The final result is a system that works much better.

1. It Proves a Better Design: The simulation shows that a gradient foam design can improve heat storage rates by up to 11.5% compared to a normal foam. This is a big improvement that means a battery or thermal storage unit can be charged much faster.
2. It Allows for Digital Prototyping: Instead of making and testing many expensive physical foam samples, engineers can use this trusted UDF model to test hundreds of different gradient designs on the computer. They can find the perfect porosity and the best gradient direction (vertical or horizontal) to get the maximum performance.
3. It Leads to Better Products: The final goal is faster and more complete charging and discharging of the energy storage unit. This simulation gives engineers the exact tool they need to design a system that does just that. This is critical for making better batteries for electric cars, more efficient solar energy storage systems, and better systems for recycling waste heat in factories.