Flow characteristics of hydrofoil weirs, hydrofoil topped weirs and streamlined triangular profile weir

Abstract

This thesis deals with free and submerged flow characteristics of different shapes of streamlined weirs, which include hydrofoil weirs, hydrofoil topped rectangular weirs, and streamlined triangular profile weirs. In all, 25 weir shapes comprising 4 hydrofoil shapes, 6 hydrofoil topped rectangular shapes, and 15 streamlined triangular shapes have been studied. Half of the symmetric Joukowsky profiles are designated as hydrofoil weirs, and in this study, the L/P ratio of the profile is varied from 2.73 to 6.25 (L is the base length and P is the height of the weir). For the hydrofoil topped rectangular profile weirs, a hydrofoil topping is provided over a rectangular base weir. In this study, 2 hydrofoil shapes are used, with ratios of hydrofoil height to the total height of the weir varying from 0.4 to 0.64. Streamlined triangular profile weirs are composed of two sloping faces connected tangentially on both sides by a circular arc. Fifteen such shapes (7 symmetrical and 8 unsymmetrical) with upstream slope Z1 varying from 0 to 3, and downstream slope Z2 varying from 0.5 to 5 (or horizontal to vertical), are studied. The L/P ratio varies from 1.5 to 7.5, and R/P (R is the crest radius) varies from 0.10 to 2.42. The studies cover a wide range of streamlined triangular profile weirs to suit different field situations. Within this range, there are weirs with very high coefficient of discharge, weirs with good coefficient of discharge and good submergence limit, and weirs with very high submergence limit. Experiments are conducted in a rectangular horizontal flume, 18.6 m long, 0.6 m wide, and 1.2 m deep, with full-width two-dimensional weirs. A total of about 2200 experimental runs are made for 29 weir models. The range of h/P covered is 0.10 to 3.8 for the hydrofoil weir group, 0.03 to 1.9 for the hydrofoil topped weir group, and 0.10 to 1.5 for the streamlined triangular profile weir group. Aspects studied include the variation of free flow coefficient of discharge, submergence limit, reduction of discharge under submerged flow, and flow characteristics such as free surface and pressure profiles. For the hydrofoil weirs, scale effects and effects of minor modification of the profiles on the downstream side are also studied. In the modified profile, a straight downstream slope is used from the point of inflexion on the Joukowsky profile. The non-dimensional crest depth (h or H, where h is the gauged head over the weir and H is the total head including the head due to velocity of approach) increases with increasing h/P and tends to a constant value at high h/P. The depth at the crest is generally lower than the critical depth except for very flat-shaped weirs. Correlations for crest depth as a function of h/P are provided for all weirs studied. Free surface observations show an increase in flow curvature with increasing h/P, with a corresponding decrease in non-dimensional crest pressure and increase in the coefficient of discharge. Correlations for average flow curvature at the crest are provided as a function of h/P (or h/L) for all hydrofoil and streamlined triangular profile weirs. The minimum pressure on the weir surface for all weirs occurs downstream of the crest. As h/P increases, the location approaches the crest. For weirs where subatmospheric pressure is observed within the experimental range, the values of h/P at which subatmospheric pressure starts are provided. Correlations for the pressure at the crest are also provided for all weirs. Except for the flattest hydrofoil weir studied, there are practically no scale effects on the free flow coefficient of discharge and submerged flow correlations for hydrofoil weirs, even when the model sizes are very small (P values down to 10.4 cm). This is because neither separation at the crest, as in the case of a finite-crested weir, nor frictional effects, as in the case of a very elongated weir, play a significant part in flow over hydrofoil weirs. The free and submerged flow characteristics of the modified hydrofoil weir, with a straight slope from the point of inflexion, are practically identical to those of a normal hydrofoil weir, confirming that hydrofoil weirs are not very sensitive to small changes in downstream shape. Correlations for the coefficient of discharge (C_d or C_t, depending on whether total head or gauged head is used) are provided for all 25 weir shapes. Generally, the coefficient increases with increasing h/P, with C_d tending to reach constancy or decreasing at high h/P values. The variation of the coefficient of discharge, as well as its absolute value, is higher for relatively steeper weir profiles. For all hydrofoil weirs, a single correlation independent of the aspect ratio is obtained for C_d vs. h/L, based on the experimentally observed fact that the average flow curvature at the crest is uniquely correlated with h/L. Unique correlations independent of P_g/P (where P_g is the hydrofoil topping height in hydrofoil topped rectangular weirs) are also obtained for the coefficient of discharge of hydrofoil topped weirs using h/L as the independent parameter. Among all weirs studied, the streamlined triangular profile weir with Z1 = 0, Z2 = 0.7, and L/P = 0.9 has the highest coefficient of discharge, which clearly exceeds that of the Ogee weir and several other high-coefficient weirs. The mechanism of submergence is discussed in terms of the location of the hydraulic jump downstream of the crest. At low h/P values, the jump at incipient submergence is closer to the weir crest. As h/P increases, the jump shifts downstream and may lie clearly beyond the weir. For weirs with very high submergence limits, the jump at incipient submergence occurs on the weir face at larger h/P values. Correlations for submergence limits (submergence ratios 1/0 and a) are provided for all weirs. The submergence limit increases with increasing h/P (except for a few very steep profiles) and tends to reach constancy. For most of the 25 weir shapes studied, the submergence limit ranges from moderately high to very high values. orrelations for the discharge reduction factor The discharge reduction factor, f=QsQff = \frac{Q_s}{Q_f}f=QfQs (where QsQ_sQs is the discharge over the weir under submerged flow conditions and QfQ_fQf is the corresponding free flow discharge) for submergence ratios beyond the submergence limit are provided for all the weirs. An important feature is the existence of a unique correlation for f independent of h/P or h/L for most of the weir shapes studied, which is a great advantage in submerged flow operations. In particular, for some of the hydrofoil and streamlined triangular profile weirs with a downstream slope of Z2=5Z_2 = 5Z2=5, the variation of submergence limit with h/P is very small. The streamlined triangular weirs with Z1=1,Z2=2,L/P=6.5Z_1 = 1, Z_2 = 2, L/P = 6.5Z1=1,Z2=2,L/P=6.5 and Z1=2,Z2=5,L/P=7.5Z_1 = 2, Z_2 = 5, L/P = 7.5Z1=2,Z2=5,L/P=7.5 have remarkable submerged flow characteristics, with a 10% reduction from modular discharge occurring at a phenomenally high submergence ratio of just over 0.97. Except for steep profiles, the coefficient of discharge for sharp-crested triangular weirs is slightly higher than that for streamlined triangular profile weirs at low heads. However, the a vs. f correlations show that the streamlined triangular weirs have much better submerged flow characteristics than sharp-crested triangular weirs, which, for submerged flow operations, more than compensates for the small reduction in the free flow coefficient of discharge. The hydrofoil topped rectangular weir is found to give better performance than the rectangular finite-crested weir for both free and submerged flows. At low and moderate heads, the coefficient of discharge is significantly higher than that for the finite-crested rectangular weir. At high heads, which are relevant for submerged flows, the submergence limit is also significantly higher due to the provision of hydrofoil topping. A study is made to determine the increase in storage capacity of irrigation tanks if existing finite-crested rectangular weirs are modified to hydrofoil topped weirs. Correlations are provided for designing the topping, determining the increase in storage capacity, and illustrations of their use are included. An extensive comparative study for all the weirs with Q?h3/2Q \propto h^{3/2}Q?h3/2 is conducted. In total, 56 weir shapes are considered, comprising sharp-crested weirs, rectangular and trapezoidal profile finite-crested weirs, triangular profile weirs, hydrofoil weirs, hydrofoil topped rectangular weirs, and streamlined triangular profile weirs. All these weirs have been classified into 9 groups based on the values of the coefficient of discharge and submergence limit. This classification facilitates proper selection of weirs for specific field applications. The weir with the highest coefficient of discharge as well as the weir with the best submerged flow characteristics are found to be among the streamlined triangular profile weirs developed in this study. Also, the only weir that comes closest to a high coefficient – high submergence limit weir is also found among the streamlined triangular profile weirs studied. Some streamlined triangular profile weirs also rank among the weirs with minimum variation (with head) in the coefficient of discharge and submergence limit. All these factors highlight the wide scope of application of streamlined triangular profile weirs.