Energy Balance Discrepancies

Issue

After completing a heat transfer analysis, the amount of heat added to the air is computed by hand using the equation: q = M * Cp * deltaT. This value is compared against the amount of heat applied as boundary conditions, and found to be significantly higher. The discrepancy appears worse at higher flow rates.

Solution

A typical cause of energy balance discrepancies is when the distance between the applied heat boundary conditions and the outlet is not long enough to allow the temperature profile to flatten out. The energy balance will not be very accurate for such situations because the bulk temperature is still changing a lot at the outlet, especially with higher mass flow rates.

A similar situation occurs when the outlet is placed too close to a sharp bend: the mass balance may be off by 20-30% if the flow is forced to turn and then immediately exit. The solution is to extend the outlet to ensure an accurate mass balance.

An alternative way to deal with a mass flow imbalance is to use the inlet mass flow rate to compute the energy change in the fluid using this equation: q = Min * Cp * deltaT. A discrepancy in the mass flow rate will cause the resultant energy from this equation: q = (M Cp T)in - (M Cp T)out, to be very different from the energy actually added to or removed from the system.

Autodesk® Simulation CFD minimizes the energy equation residual at the nodes, as opposed to forcing fluxes to balance. This helps to ensure an accurate prediction of component temperatures. This often means that the temperature on the object is independent of whether an energy balance is achieved (M * Cp * deltaT = applied heat).

For example, if you extend the outlet, you probably will not get a very different temperature distribution on the object, but you will get a better energy balance inlet to outlet.

It is important to balance the cost of an improved energy balance (in terms of model size and computation time) with the small (or negligible) improvement in predicted component temperatures.