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Fast solution of cases with difficult fan curves

Courtesy of NTS Ltd and Daat Research Corp.

Most electronic devices involve fans, which are used to remove hot air from the system in order to keep temperature under control. Fan specifications are provided by the manufacturers with the most important characteristic for cooling being the fan (or performance) curve that specifies the pressure drop across the fan as a function of flow rate. A typical curve, Fig. 1, shows this dependence between pressure drop and flow rate, where each flow rate has a unique value of pressure drop, as one would expect.

The one-to-one nature of pressure-flow rate dependence is very important for CFD codes modeling electronic devices with fans. This is because CFD calculates a solution by solving a quasi-time-dependent problem, usually starting from no-flow and gradually building up from specified flow and heat sources until steady state flow is reached. As the solution (and hence the flow) evolves, the flow rate through the fan changes, too. With a one-to-one pressure-flow curve, such as Fig. 1, most CFD codes will have no problem finding a solution because for each iteratively evolving flow rate there is only one pressure drop.

Another, still rather common, fan curve is shown in Fig. 2. The problem with such a curve is immediately obvious: there are sections of the curve where a single pressure drop corresponds to more than one flow rate. Such fan curves are discussed in the Fan Physics section below. If you are lucky and the operating point for your system is to the right of [3] on Fig. 2, you may get a solution. However, between 1-2-3 most CFD codes will either fail to converge or converge to a wrong solution, with the operating point often off the fan curve.

Some CFD codes recognize the problem up front and tell the user to modify the fan curve, so that the multi-value section 1-2-3 is replaced with a one-to-one curve connecting 1-3 (dashed line). This should help with convergence, but you might be converging to a solution of a different problem, as the modified fan curve is not the curve that was specified for your fan. Thus if your system is such that the fan actually does operate to the left of [3] on Fig. 2, your solution will be wrong. In systems with multiple fans, this will not even point out what is amiss, as you cannot know which particular fan is at fault as they all affect each other's performance and, hence, the operating point.

Daat engineers discovered that this apparently intractable problem has a unique solution, despite the multivalue-ness of the fan curve. Their discovery not only permits the solution of problems with complex and multivalue fan curves, it also drastically speeds up the convergence rate. The advantage is especially noticeable for problems with multi-value fan curves, even in cases where standard algorithms manage to converge. An order of magnitude speed increases for such cases is not uncommon. Even with one-to-one curves, the new algorithm converges 30%-100% faster.

Fan Curve Physics

Consider the case of a fan in a wind tunnel. The fan starts operating with a fully unobstructed flow - point 1 on Fig. 3. As the flow resistance increases, the flow rate diminishes and the pressure drop rises along the curve 1-2-3. As the resistance further increases, the corresponding flow rate decreases beyond point [2], and the fan goes into an unstable regime. There could be different reasons for this, such as flow separation and stall. At this point the flow rate drops sharply together with dP until it reaches point [5]. During the unstable regime the fan may possibly vibrate and generally display signs of "distress". Once the system resistance increases further, the flow rates drops below point [5] and the fan regains the stable operation, so that dP rises along 5-6.

One can conduct a different experiment by starting with a fully obstructed wind tunnel to the left of point [6]. As the wind tunnel is gradually opened, flow resistance is decreased, and the flow rate is increased along 6-5-4. At [4], the fan becomes unstable until it regains stability at [2]. It then moves along 2-1 as the flow resistance is further reduced.

The fan operation inside the 2-3-5-4 gray box is unstable and generally unknown. Fan manufacturers show only a single line on their performance curve, rather than the uncertainty box and an explanation of its origin.

Figure 1. A typical fan curve.
Figure 2. A typical, but difficult for CFD fan curve, with up to 3 different pressures corresponding to a single flow rate.
Figure 3. Fan curve hysteresis.

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