# Solution Dependent Expressions for Fan Cooling Simulation with ANSYS AIM 18

In ANSYS AIM 18, design engineers have reason to be excited about increased functionality for fluids, structural, thermal and electromagnetics. While the foundational problem-solving functionality has existed since AIM 16, new functionality is being added in every release so AIM can better address niche applications. One such enhancement I’d like to bring to your attention is solution-dependent expressions for applications like fan cooling simulation. While this isn’t something I guarantee you’ll use in your everyday simulations, it is a powerful feature needed for certain calculations.

In most fluids studies, the general starting point in calculating flow through a pipe, for example, are the known quantities of inlet velocity and outlet static gauge pressure, or inlet and outlet pressure. These values are generally assumed and solver iterations will converge on an outlet velocity (or mass flow rate) among other calculated values.

Assigning inlet velocity and outlet static gauge pressure

However, these values are not known when considering things like fan cooling. In this case the mass flow rate and inlet pressure are dependent on a manufacturer’s fan curve (or “P-Q curve”) from testing. These fan curves show the relationship between the air volume and the static pressure resulting from loss due to the pressure applied to the inlet and the outlet of the fan.

ANSYS AIM can be used to determine the system resistance of fan cooling applications.

In previous releases of AIM this problem simply could not be solved. Design engineers were faced with two choices: either make faulty assumptions, or throw your hands in the air and rely upon a more experienced analyst to use more complex software, like ANSYS Fluent.

AIM’s Solution for Fan Cooling Optimization

But AIM 18 has a solution for this type of problem, and without sacrificing the ease of use for design engineers! It’s called “solution dependent expressions”. This new functionality essentially allows for an expression as a boundary condition, where the expression contains an output value.

Solution dependent expressions use an output variable to determine a boundary condition.

In this case, the outlet mass flow rate is used to determine the inlet pressure. In the previous example of fan cooled applications, the goal in the solution is to determine if the fan produces a mass flow rate that adequately cools the system. While the mass flow rate and pressure drop are unknown, the known values are supplier given test data points, typically shown through a graphical curve.

Static pressure curve data is usually supplied by fan manufacturers.

Using various data points along this curve and simple curve generation software like a spreadsheet, an equation can be generated that represents the P-Q curve. Once the resistance of a system is known — which AIM will intrinsically solve, then the operating pressure and flow rate are also known. Matching the data from AIM to the supplier’s curve, you’ll quickly know if a given fan will provide adequate cooling or will unnecessarily consume too much energy in cooling.

Velocity color map of a fan-cooled fuse box

Another example where solution dependent expressions are useful are in fluid storage tanks. Pressure increases with depth in the tank due to the weight of the fluid above. Thus, for a given tank, an expression for fluid pressure as a function of depth more accurately defines the boundary condition than a constant pressure on all interior walls.

To learn more about this functionality and other enhancements in ANSYS AIM 18, I invite you to take a look at the highlight page, watch this on-demand webinar, and try AIM in the cloud right now.

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