Correlating the Den Hartog instability criterion to the dynamic response of an oscillating system

The Den Hartog criterion has been used for decades to evaluate the susceptibility of a cross-section to galloping instability. We will present results from our experimental campaign that aims to correlate the Den Hartog stability assessment of altered circular cross-sections and the dynamic response of a 1D oscillator with an identical cross-section. Dynamic tests for the Reynolds number range of 5000 – 35600 with a circular cylinder attached with strips of thickness varying from 0.8% to 8.2% of the cylinder diameter were performed. The results were compared to the static tests with thickness varying from 0 to 12.8% at Reynolds number values of 10000, 20000, and 30000. The maximum angles of attack of the vibrating configuration were projected onto the Den Hartog instability map generated from fixed cylinder lift-drag measurements, and it was found that the maximum angle of attack experienced by the galloping cylinder fell within the Den Hartog instability zones. Increasing the thickness ratio postpones the angle where the lift reaches its maximum and increases the maximum lift and drag values.