Flow characteristics of sharp-edged orifices,quadrant-edged orifices and nozzles

Abstract

This thesis presents an integrated study of flow past sharp-edged orifices, quadrant-edged orifices and long radius nozzles, covering different aspects such as metering characteristics, loss characteristics and flow development characteristics, for a range of pipe Reynolds numbers R, from 1 to 10,000. Where available, results from literature are used to extend the studies up to a Reynolds number of 100,000. In all, 22 orifices and nozzles are studied with p ratio (ratio of orifice or nozzle diameter to pipe diameter) varying from 0.2 to 0.8. For the quadrant-edged orifice, r'/d ratio (ratio of edge radius to orifice diameter) is varied from 0.08 to 0.25. The studies are conducted in an oil recirculation system with four oils as fluid media. Besides measurements for the discharge coefficient, for each run the pressure field is measured for a distance of 30D (D = pipe diameter) upstream of the orifice or nozzle and 240D downstream. For a few identified Reynolds numbers the development of velocity distribution is also obtained over the test reach. All the velocity measurements are confined to the region where no return flow exists. In all, 975 runs are made. These studies facilitate a detailed discussion of the variation of the coefficient of discharge, coefficient of contraction, sensitivity of the discharge coefficient to pressure tap location, loss coefficient, excess loss as a percentage of the pressure differential across the meter, critical Reynolds number at which turbulence originates downstream of the orifice or nozzle, settling length, and nature of development of pressure and velocity fields. Flow past orifices and nozzles may be classified into three regimes, namely, purely laminar flow regime, relaminarisation regime and turbulent flow regime. At a critical Reynolds number, the value of which depends on the orifice geometry and p ratio, the laminar approach flow becomes turbulent immediately downstream of the orifice or nozzle and if R < 2,000, the flow relaminarises over a distance. The effects of each flow regime on different parameters are studied in detail. The nature of variation of coefficient of discharge C with Reynolds number is discussed in detail for all the orifices and nozzles. Results show that for quadrant-edged orifices, a range of r'/d values, rather than a single r'/d value, is equally satisfactory from the viewpoint of constancy of the discharge coefficient. This broadens the scope of the applicability of quadrant-edged orifices. For p = 0.4, the tolerances on r'/d ratio for 0.5% and 1.5% change in C value are obtained and these results are very encouraging. Studies show that among the three devices, the nozzles are least affected by a small shift of the downstream metering tap location. Both the sharp-edged and quadrant-edged orifices are found to be very susceptible to such minor shifts at high p ratios. Computations of contraction coefficient values show that the influence of Reynolds number is much more pronounced for sharp-edged orifices than for quadrant-edged orifices. A detailed comparative study is made of the variation of the loss coefficient K (K u²/2g gives the excess loss due to the orifice or nozzle where u is the mean velocity) with Reynolds number for the sharp-edged and quadrant-edged orifices and the nozzles. The shape of K vs. R curves are discussed for the different cases. The results show that the nozzles cause only about 40% of the sharp-edged orifice loss at high Reynolds numbers while at low Reynolds numbers they cause 1.6 to 3.2 times the sharp-edged orifice loss. The quadrant-edged orifices give a loss which is closer to that of nozzles at high Reynolds numbers and to that of sharp-edged orifices at low Reynolds numbers. The variation of the parameter G giving the excess loss as a percentage of the pressure differential across the meter is studied for all the cases. It is seen that G generally reaches constancy at a lower Reynolds number than K or C. The variation of G also reveals several interesting features. Based on momentum and energy considerations, the loss coefficient is obtained in terms of the discharge and contraction coefficients for Reynolds numbers greater than the critical. The theoretical and experimental results compare well for all the orifices and nozzles. The critical Reynolds number at which turbulence originates downstream of the orifice or nozzle is determined by two methods. In the first approach, the variation of C, K or G with Reynolds number is used to identify the critical Reynolds number. It is shown that while all the three parameters yield the critical Reynolds number for sharp-edged orifices, only C indicates the critical Reynolds number for all the orifices and nozzles. The second method for determination of critical Reynolds number is based on a study of the variation of pressure recovery length downstream of the orifice or nozzle. This approach is more rational and direct besides being more generally valid. A detailed comparison of the relative magnitudes of the critical Reynolds numbers for all the cases is given. It is shown that the critical orifice Reynolds number tends to a constant value for low p ratios. A detailed study is made of the development of pressure and velocity fields downstream of the orifice or nozzle. The variation of settling length with Reynolds number is studied for all the cases. It is shown that settling length increases linearly with Reynolds number in the relaminarisation regime. A universal equation for the settling length is obtained which is expected to hold good for several cases besides concentric orifices and nozzles. Detailed discussions are presented regarding the development of velocity profiles downstream of the orifice or nozzle. The influences of p ratio and edge conditions are discussed.