Measuring dust burning velocity for deflagration vent design

Deflagration vent design should be based on the burning velocity in the pressure range below 3 bara, where vent relief devices normally operate, rather than the K-St deflagration index, which is typically measured at pressures >50% of the maximum deflagration pressure, P-max. Tests using a standardized 1000-L vessel showed that in the pressure range below about 3 bara, niacin and lycopodium burned faster than cornstarch, despite its larger K-St index. We attribute this behavior to the endothermic dehydration of cornstarch during the early stages of deflagration. Deflagration vents for cornstarch and other milled grains may have been oversized while vents for some other dusts may have been undersized. Burning velocities are most relevant in the region of the 2-bara midpoint overpressure and can theoretically be found from the "isothermal pressure rate gradient", or IPRG, which we define as the gradient of (dP/dt) plotted against P (1-1/P)(2/3). However, owing to irregular combustion caused primarily by two 5 kJ igniters, the IPRG is found indirectly from the "pressure rate gradient" or PRG, which we define as the gradient of (dP/dt) plotted against P. The PRG was found to be adequately linear for measurement at 2 bara and the experimental curves passed through the "origin". It was shown mathematically that at 2 bara the PRG is 1.05 times larger than IPRG, permitting the IPRG and turbulent burning velocity to be calculated. Since the calculation of burning velocity from the IPRG requires P-max, a general extrapolation technique was developed for correcting P-max values obtained in vessels smaller than 1000-L. We propose that, owing to the greater turbulence in the 20-L vessel, a calibration be made using methane. This would establish the turbulence factors for each vessel at 2 bara, allowing the underlying "reference" burning velocities to be calculated and compared. However, to measure turbulent dust burning velocities in 20-L vessels a smaller and more efficient igniter must be used. Two 5 kJ igniters not only obscure the pressure history but wastefully expend energy far from the vessel core, depleting the unburned mixture and depressing the subsequent pressure rate. An observed "double sigmoid" dependence of dust deflagration rate on particle diameter suggests that routine explosibility testing of organic dusts is usually carried out in a region where pressure rates are relatively insensitive to particle size.