Numerical study of fluid flow through double bell‐shaped constrictions in a tube

The effects of steady fluid flow through double bell‐shaped constrictions in tubes were investigated numerically for the Reynolds number range of 5 to 400. The double constrictions studied were for similar first and second constrictions of 1/3, 1/2 and 2/3. A dimensionless constriction spacing of 1.0 was considered. Study showed that the major part of the mean dimensionless pressure drop in the constricted tube occurs predominantly across the first constriction when flow moves towards the valley region formed by the two constrictions. Minimum pressures along the constricted tubes occurs downstream of each constrictions. When the constriction magnitudes increased, the pressure drop across the same length of the tube increases exponentially. The effect of increasing the Reynolds number for all the constriction values considered here is to increase the spreading of the recirculation region between the valley region of the constrictions. The recirculation region formed between the two constrictions has a deminishing effect on the generation of wall vorticity near the second constriction. The effects are more pronounce when the recirculatory flow from the first constriction has spread over the second constriction. In general, a peak wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity increases and its location moved upstream. It is noted for the cases considered here that the peak wall vorticity generated by the first constriction is always greater than the peak wall vorticity generated by the second constriction.