Can you tell the direction of flow of a box fan just by looking at the frame?Tweet
Box fans can be used to increase air flow in a room. However, they can also be converted into inexpensive air filters for reducing the transmission of airborne disease.
I asked this question to my students in fluid mechanics in the fall 2020 COVID semester. Below are two photographs of a box fan showing views from the right and from the left. The question is, knowing what you do about angular momentum, which direction does the air flow when the fan is turned on (right to left or left to right)?
View from the left view from the right
As with many of the posts during the COVID semester, there was only a limited response. The responses were generally correct on the direction but occasionally a little off on the explanation.
The only information we have is that there are little feet on the right hand side of the fan and not on the left hand side.
We start by drawing a control volume around the fan blade assuming that the flow is from right to left. We assume that the outflow is a horizontal jet of flow rate UoA where U0 is the velocity out of the control volume and A is the outlet area circle formed by rotating the tip of the fan blades. The flow rate in is the same. The inflow will come in from all directions. However, it is only the horizontal component that contributes to the inflow volume flow rate so the horizontal component of the inflow velocity is the same as that of the outflow (Uin.x=U0). We then write the angular momentum equation (sometimes called moment of momentum) about the bottom right hand corner of the control volume (also where the feet are on the box fan). Taking anti-clockwise as positive we get
On the intake side the only component that creates a moment about (a) is the horizontal component. Therefore, assuming that the inflow and outflow are approximately axisymmetric about the fan blade axis, the right hand side sums to zero. That leaves
Applying Bernoulli’s equation along a horizontal stream line from far upstream to the fan intake we get
For a horizontal streamline and a stationary ambient at zero gauge pressure the elevation terms cancel and the other two terms on the left hand side are both zero. Therefore, the inlet pressure is
Therefore there is a moment about (a) given by
Where R is the radius of the fan blades. This negative moment must be balanced by a moment applied by the fan blade to the flow. The net effect of this is that a positive anti-clockwise (counter-clockwise) moment must be applied to the fan blade by the casing (box). This moment is applied by the two small feet on the right hand side at the base of the fan box. Therefore, our initial assumption of the flow going from right to left is correct.
Box fans are a cheap way to move air in a room. With the advent of COVID-19 there has been increased interest and concern over air quality and improved ventilation. Improving ventilation and and filtration of indoor air can reduce the transmission of airborne pathogens. Improving the quality of the air filter (filter guide) in a ventilation system will reduce the particulate concentration in a room but may reduce the air flow by increasing the pressure drop across the filter. An alternate approach is to add an additional filtration system within a room. There are a broad range of HEPA filters available for purchase but it is also possible to build a cheap air filter using standard HVAC filters and a box fan. The simplest method involves taping a filter to the intake side of a box fan (video). The filter is placed on the intake side so that the air flow pushes the filter against the fan improving the seal whereas putting in on the outflow side would tend to reduce the seal around the edge of the filter. One issue with this design is that the pressure drop across the filter can dramatically reduce the air flow through the system and change the air flow pattern on the outflow side of the fan. An alternate approach is to build a cube of filters and attach that to the box fan (video). This increases the area of the flow through the filter which, in turn, reduces the pressure drop across the filter.
The study of indoor air quality and ventilation is part of the broader field of environmental fluid mechanics. One of the key parameters controlling indoor air quality is the air quality of the surrounding environment. I am currently working on an NSF project to improve our understanding of the dispersion of dense gas pollutants in urban environments. Dense gas pollutants (such as CO2 and Chlorine) can become trapped in the urban canopy as their density inhibits vertical mixing up and out of the canopy. We are running experiments to measure the retention time for pollutants in the wake of a building to understand the relationship between the wind speed, pollutant density, and geometry on the trapping of the pollutant. This work is based upon work supported by the National Science Foundation under Grant No.1703548. Any opinions, findings, and conclusions or recommendations expressed in the material are those of the author and do not necessarily reflect the views of the NSF.
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