Effect of Air Pressure on Vortex-Shedding Frequency of Cylinders

Abstract

THE VORTEX-SHEDDING FREQUENCY from circular cylinders is generally considered to be a function of the Reynolds Number (Re), the cylinder diameter (d), and free-stream velocity (u). Previous investigations have correlated the Strouhal Number S = fd/u as a function of the Reynolds Number of cylinders. In the past, several investigators (references 1, 2, and 3 for example) studied the vortex-shedding phenomenon under standard conditions of atmospheric pressure and room temperature. Data from these investigations were grouped into three distinct Reynolds-Number ranges and an empirical Strouhal-Reynolds Number correlation was found by Roshko. In most previous research, the free-stream velocity and cylinder diameter have been common variables and consistently agreed with Roshko's empirical equations. In a more recent investigation, the effect of temperature was found to be not completely accounted for by the Reynolds Number. The major purpose of this investigation was to determine whether Reynolds Number completely accounted for the effect of air pressure on Strouhal Number. Air from the central laboratory system was passed through an electric heater and metered through a standard ASME orifice. The air was then passed through a calming chamber and into a 3by 4/s-in. test section. Pressures from 4 to 40 lbs. psia were controlled by an exhaust system at the downstream end of this test section. A 0.0625-in. diameter rod was placed in a transverse horizontal position at the center of the test section, and shedding frequencies from this rod were sensed by a constanttemperature hot-wire anemometer located at a position 5 diameters downstream. The electrical signal passed through a highpass low-pass filter and an amplifier then fed to the vertical axis of an oscilloscope and to a wave analyzer. Frequenc}^ was determined by connecting an oscillator to the horizontal axis of the oscilloscope so that the vortex-shedding frequency could be determined by the Lissajous-figure method and checked with the wave analyzer. Within the ranges of this investigation, Reynolds Number 175 to 1,000, and pressure 10 in. to 50 in. of mercury absolute, a definite variation in Strouhal Number was observed. At. constant Reynolds Number, the Strouhal Number rose with increasing pressure from lower values and approached the values observed by previous investigators. However, as the pressure was further increased to 50 in. of mercury absolute, the Strouhal Number began to decrease in value. Results of this investigation show a definite dependence of the Strouhal Number of cylinders on pressure and suggest the need for a new correlation including the effects of temperature and pressure in addition to the effect of Reynolds Number.