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What are porous resistance coefficients?
What are porous resistance coefficients?
Porous resistance coefficients are a constant, dependent on a material's characteristics and geometry, that directly relate the pressure drop across a porous material to the mass flow rate.
Analytical methods can be used to obtain porous resistance coefficients by starting with the 1D theory of basic flow through an orifice followed by sudden expansion. The equations and values used to obtain these coefficients are shown below.
These coefficients can be used to determine the inertial and viscous resistances of the material. Additionally, ATA used computational fluid dynamic analysis on a single honeycomb cell to numerically obtain these coefficients, with great similarity to theoretical values. The results of which can be seen to the right, with standard honeycomb dimensions.
Effect of Vent Hole Diameters
Effect of Vent Hole Diameters
The equation for the porous resistance coefficients, seen in blue, relies heavily on the area of the orifice (Ao).
Due to the very small size, these vent holes are difficult to measure accurately. Initially, the team used a microscope and a calibration slide to measure the holes to be between 0.003"-0.004".
This measurement was revisited later in the project to more accurately calculate and compare the theoretical pressure drops to our experimental values. The team reached out to the MRSEC Materials Characterization Facility (MCF) at UC San Diego, and we were able to use their scanning electron microscope (SEM) to more accurately size the diameters of the holes.
The SEM machine at the MRSEC MCF on the right with an magnified vent hole seen on the monitor.
One vent hole seen with the SEM.
Another vent hole seen with the SEM.
Results of these SEM images were quite shocking. As seen here, the holes are not circular, but instead have a more oval shape. The CFD model used by ATA and subsequent equations used for the previously calculated theoretical values assume a perfectly circular hole, which was found to be very idealized through this high resolution imaging.
Four vent holes were measured, with the largest width of the vent holes measured was around 0.0049 inches and the lowest was around 0.003 inches. This confirmed that the estimate of 0.004 inch hole diameter made for the theoretical values of the final honeycomb test was not an unreasonable number.
With the addition of this newfound honeycomb vent hole geometry information, it is advised that for more accurate results, ATA’s CFD model would most likely have to be adjusted to accommodate for this hole geometry. Or, possibly an equivalent diameter could be obtained from SEM images that could be put into the theoretical calculations directly to reduce assumptions and improve accuracy. However, it should be noted that to obtain an equivalent diameter, a much larger sample size of SEM images with many more vent hole diameter measurements should be used compared to the initial measurement of only four vent holes shown here.
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