# Analyzing the Venturi Effect in CFD Simulations and Testing

July 27, 2020

### Key Takeaways

• The Venturi effect refers to a change in fluid velocity when it encounters a discontinuity in the cross-section of the flow region.
• This change in fluid velocity affects heat transfer during laminar flow past a boundary.
• This relationship between fluid flow rate and heat transfer can be examined in a multiphysics field solver program.

CFD simulation results. Follow the streamlines between components in constriction regions to examine the Venturi effect in CFD simulations.

Computational fluid dynamics (CFD) simulations are great for treating complex geometries with varied boundary conditions. In addition, these simulations can treat any source you can envision and define in your system. However, they aren’t so great at helping you discern specific effects that may occur when fluid flows through a system. One example is the Venturi effect in CFD simulations, where the flow field becomes modified by changes in the geometry in the system.

How can you ensure you account for these types of effects in simulations of your new electronics? The best simulation tools will build a finite element model or network model directly from your PCB layout and will use this model for numerical simulations. Here’s how you can spot the Venturi effect in CFD simulations for your PCB and how you can analyze its effect on heat transfer away from hot components.

## What is the Venturi Effect?

Although it may not be obvious, the Venturi effect occurs due to a combination of conservation of mass and conservation of momentum. When a fluid flows through an enclosure, such as a pipe, the fluid pressure and velocity will increase, and the pipe is gradually made smaller along the direction of flow. Because the axial pressure gradient has not changed in the pipe, the body forces on the fluid are constant, but the cross-sectional pressure on the fluid is smaller in the section of the pipe with smaller diameter. The result is an increase in the fluid velocity as it flows through the narrower section of a pipe.

Just like many physical processes, the Venturi effect is reversible; if the diameter of a pipe expands from small to large diameter, the fluid will slow down. This idealized system, where a fluid constriction along a sudden discontinuity in a pipe, is called a Venturi tube. The illustration below shows how this would occur for water flowing through a constriction region in a pipe.

The Venturi effect in CFD arises due to constriction along the length of a tube.

If you’re the mathematical type, the Venturi effect can be quantified for an incompressible fluid like water using the Bernoulli equation. Assuming there is no change in elevation along the length of the pipe, the pressure p and mass flow rate Q in two regions can be related as follows:

The Venturi effect for an incompressible fluid.

There is also a method for treating compressible fluids (e.g., gases), although the equations involved are more complicated. In general, this expression will depend on the specific heat ratio of the gas and will be a complex function of fluid velocity in each region. As a result, you have a pair of equations that need to be solved numerically for the pressure in each section of the pipe.

Due to the difficulty in treating compressible fluids in the laminar regime, full 2D or 3D field methods are needed to examine the Venturi effect in complex systems. The Venturi effect can be examined using fluid flow models with standard CFD techniques (FEM, FEA, FDTD, and others).

## The Venturi Effect in CFD Simulations for Electronics

When working with electronics systems, CFD simulations can help you examine how heat flows away from hot components and spreads around a board. By formulating heat transfer and fluid flow as a multiphysics problem, you can examine how airflow helps carry heat away from hot portions of a system. Electronics systems, and especially PCBs, have complex geometries that cannot be solved analytically, thus a numerical simulation is required to fully understand transient and steady-state fluid flow and heat transfer.

In a real PCB, we have all the forces of mathematics conspiring against us to make CFD simulations and analysis more difficult. Here are the effects that need to be considered in CFD simulations for heat transfer in a PCB:

• Complex geometry. The geometry in a real PCB cannot is very complicated due to the passives and ICs on the surface layer, as well as mechanical components. As a result, the geometry cannot be easily approximated beyond a set of small boxes.

• Air is a compressible fluid. If you’re using a fan to provide airflow to cool your board, you need to consider that air is compressible. This means we cannot use a simple analytical expression like that shown above to determine how the Venturi effect in CFD simulations aids heat transfer.

• Feedback between the Navier-Stokes equation and heat equation. This feedback between these equations describes how heat transfers into a flowing fluid, which is then carried away along the flow direction.

This last point is the crux of examining the Venturi effect in CFD simulations. As you vary the geometry in your board, such as with different component arrangements, you can examine how the steady-state temperature varies near areas where air flow is constricted in your board. Similarly, you can examine how the Venturi effect influences the transient temperature rise in your board.

For the steady-state case, you can easily plot the steady-state temperature in constriction regions vs. average distance between components and identify the component spacing that produces the lowest temperature. This is quite important in smaller boards that use multiple processors, which need to be placed farther apart on the board to ensure heat is produced evenly throughout the system.

Once you create your electronic system with a powerful PCB design and analysis software package, you can examine how the Venturi effect in CFD simulations affects heat flow and the steady-state temperature in your system. The Celsius Thermal Solver from Cadence takes your PCB layout and creates a 3D mesh model for use in CFD simulations with standard numerical algorithms. This platform gives you everything you need for electrical and thermal analysis in your PCB.