Experimental study of discharge formulas for rectangular sharp-crested weirs under free flow condition

Laboratory experiments were carried out to investigate the discharge characteristics of rectangular sharp-crested weirs under free flow condition. The performances of available discharge formulas have been evaluated by using the experimental data sets of present and previous studies. Error statistics of our experimental data indicate that the recent stage-discharge relationships show satisfactory performances. Discharge formula in terms of weir Reynolds number proposed by Vatankhah gives the highest accuracy among the existing slit weir equations, with $E_{\pm 4}=100.00\text{\%}$ (i.e. percent error less than or equal to $\pm 4$) and a mean absolute error ${\left|E\right|}_m=0.88\text{\%}$. The full-range discharge equation presented by Bijankhan and Mahdavi Mazdeh shows the highest accuracy among the relationships in terms of weir contraction ratio, with $E_{\pm 4}=100.00\text{\%}$, ${\left|E\right|}_m=0.91\text{\%}$ for slit weirs and, $E_{\pm 4}=94.64\text{\%}$, ${\left|E\right|}_m=1.60\text{\%}$ for partially contracted weirs, respectively. The weir velocity formulae suggested by Gharahjeh et al. exhibit the relatively better performance, with $E_{\pm 4}=98.41\text{\%}$, ${\left|E\right|}_m=1.34\text{\%}$ for slit weirs and, $E_{\pm 4}=91.07\text{\%}$, ${\left|E\right|}_m=1.91\text{\%}$ for contracted weirs, respectively. Statistical results of this study confirm the weir velocity approach presented by Aydin et al. and show that, the weir velocity is a predominant quantity for rectangular sharp-crested weirs, unique characteristics of the weir velocity curves make it more suitable for expressing the discharges. Moreover, it is important to point out that the performance of weir velocity formulae can be further improved.     

Measurements of the flow of supercritical pressure carbon dioxide through Venturi flow meter

The Venturi flow meter exhibits relatively low pressure loss, simple design, and low manufacturing costs. This study describes flow rates measurements for supercritical pressure CO₂ using the Venturi flow meter with pressure ranging 7.379–7.836 MPa and 5.84–7.272 MPa for in supercritical and gaseous regions, respectively. The flow rates of supercritical pressure CO₂ were accurately measured using a Venturi flow meter with a diameter ratio of 0.6468, having large and small diameters of 87.32 mm and 56.48 mm, respectively. The convergent and divergent angles were 21 $°$ ± 1 $°$ and 15 $°$ ± 1 $°$, respectively. The averaged discharge coefficient of 0.9975 was obtained, which was independent of the pressure ratio. Additionally, the expansion factors were also calculated using the experimental results, which ranged from 0.99976 to 0.99987 and 0.99945–0.99995 for the supercritical and gaseous regions, respectively. The experimental results showed that the Venturi flow meter had uncertainties ranging from 0.1 to 2.8%.     

Velocity measurements in developing narrow open-channel flows with high free-stream turbulence: Acoustic Doppler Velocimetry (ADV) vs Laser Doppler Anemometry (LDA)

A developing narrow open-channel flow has been investigated using Acoustic Doppler Velocimetry (ADV) and Laser Doppler Anemometry (LDA). The objectives were to first characterize the flow environment with the LDA system alone, then quantify the intrusion effect of the ADV sensor immersion, and finally compare ADV-LDA measurements. The main features of the flow have been described. The turbulence levels measured in the outer flow region are high and almost isotropic due to the specificities of the flow (3D, narrow, developing). This contributes to a flattening of the mean streamwise velocity profile in this region. The intrusion effect of the ADV sensor is found to be dependent on Froude number ($Fr=U_0/\sqrt{gH}$ with $U_0$ the discharge velocity, $H$ the flow depth, and $g$ the gravity acceleration). Vertical flow below the sensor is amplified while the streamwise component of the flow is enhanced for “low” Fr ($\le 0.6$) and reduced for “high” Fr ($\ge 1.1$). On the other hand, turbulence quantities are not affected by the sensor presence. Compared to the LDA, the ADV is shown to underestimate the mean flow and turbulence intensities, while not affecting Reynolds shear stress measurements. The underestimation of the turbulence intensities can be attributed to the lower sampling rate and larger sampling volume of the ADV, but the underestimations of the mean velocities are more likely linked to a constant bias that the ADV seems to have or to some type of ADV-intrinsic noise. Some implications for practical application are discussed.     

An anomalous method of using a camera in determining the velocity distribution within a boundary layer

The current study proposes a cost-effective technique wherein a camera can be used anomalously in tandem with the working of a pitot tube in determining the velocity distribution within a boundary layer. The technique involves the traversal of a pitot tube at a uniform velocity inside the width of boundary layer and simultaneously imaging the change in meniscus location of liquid column in the corresponding manometer, inside a wind tunnel set-up. The study aims in establishing a relation between the traversal velocity and the free stream velocity. The proposed approach holds the advantage of providing velocity values at equally spaced locations within the boundary layer, with the number of values depending on the velocity of retraction (traversal away from the surface) as well as the frame rate of recording. Experiments were performed at different combinations of retraction velocity ($V_r$) and Fan Speed for establishing the method. An optimum velocity at which the pitot tube should be retracted was determined based on convergence of trend of the variation in instantaneous meniscus locations to a standard reference trend. Results show that dimensionless optimum velocity (${\overline{V}}_o$) defined as the optimum ratio between tunnel velocity ($U_t$) and $V_r$ is related to the Fan Speed (FS) by ${\overline{V}}_o\propto$ FS${}^{0.6}$. Additionally, with regard to the manual traversing performed, the probability density function plots show that traversing manually at $\overline{V}\gg {\overline{V}}_o$ introduces higher non-uniformity in the results, thereby preferable to perform the traversal closer to values of ${\overline{V}}_o$. Using the results obtained from the developed imaging technique, the velocity variation within the boundary layer was studied. The technique was successful in precisely locating the prominent points inside a boundary layer for a particular flow condition. Finally as a case study, the imaging approach was also utilized in determining the effect of roughness change across the seam of a cricket ball on its aerodynamics. This case study also shows that the technique is successful in obtaining the flow characteristics of a general boundary layer as well as a flow separation case.     

Measurements of suspended ashes concentration in turbulent flow with acoustic doppler velocimeter

Measuring and estimating dispersion coefficients for ash particles released in watercourses is required for a broad understanding of their transport and behaviour in aquatic ecosystems. Calibration of a high-frequency acoustic backscattering system and estimates of its sensitivity to particulates of known size distribution and concentration are presented. Laboratory experiments were conducted to derive the relationship between suspended sediment concentration (SSC) of biomass ashes and the signal-to-noise ratio (SNR) measured by a 10 MHz ADV. Small portions of ashes were added in steps (0.006–20 gl⁻¹) into a stirred water tank while ADV was recording changes in SNR, with various combinations of ADV settings, which included power (LOW, LOW${}^{+}$), transmit length (TL = 0.3 mm, 0.6 mm) and frequencies of data acquisition (25 Hz, 100 Hz). Samples were collected for gravimetric and particle size distribution (PSD) analysis. As expected, the salinity and pH of the collected samples increased with SSC. Different backscatter responses were detected depending on the ADV settings and SSC. To maximize the calibration range, the ADV settings power LOW${}^{+}$, TL = 0.3 mm and sample frequency 25 Hz were combined, resulting in a calibrated SSC range of 10–500 mgl⁻¹, where a linear relationship was obtained. The results suggest that it may be possible to apply a single-frequency acoustic technique to the detection of suspended ashes. The particle type and size distribution changed with a concentration above 0.5 gl⁻¹, which may lead to errors in the acoustic estimates of SSC in ash-laden flows.