Quantitative supersonic flow visualization by hydraulic analogy

Abstract

The hydraulic analogy, which forms the basis for the phics. current investigation, can be used to study supersonic gas flows with great ease by means of a water table. As a result of the analogy, water heights in free surface water flow correspond to certain properties (density, pressure, temperature, etc.) in gas flow. Many of the existing techniques for measuring water heights on a water table are intrusive in nature, thus reducing the accuracy and the reliability of the height measurements. The primary goal of the current work is to develop a reliable and accurate technique for measuring water heights on a water table. As a result, a new non-intrusive optical technique for measuring water heights has been developed. In the current work the optical technique has been employed to obtain water heights along the hydraulic jumps formed for flow past a wedge and a cylinder. The technique involves optically superimposing a series of alternating dark and clear mechanical fringes on the flow. The fringes appear deviated when viewed through a hydraulic jump. It is proposed that the fringe deviations seen under a hydraulic jump can be simulated using a series of flat-topped optical prisms, both isosceles and scalene, where the prisms are oriented along the direction of the hydraulic jump. The height of each such prism (one per fringe) gives the maximum local water height along the hydraulic jump. Images of the fringe deviation patterns formed due to the hydraulic jumps are obtained and analyzed to determine certain geometrical properties of the fringe deviations. The variation of water heights along a hydraulic jump for wedges, obtained from the optical technique, has been compared with that obtained using the conventional intrusive depth-gauge technique. The optical technique has been tested for a range of Froude numbers (Fr = 1.93, 2.27 and 2.46) and for water heights ranging from5smm to 7mm. The depth gauge results have also been compared with those obtained using a rounded-top prism model.