International Journal of Chemical Engineering

Volume 2019, Article ID 6454958, 9 pages

https://doi.org/10.1155/2019/6454958

## Experimental Quantification of Local Pressure Loss at a 90° Bend in Low-Pressure Dilute-Phase Pneumatic Conveying of Coarse Particles

^{1}School of Environmental and Chemical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China^{2}School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Correspondence should be addressed to Fei Yan; moc.361@617nayf

Received 9 January 2019; Accepted 6 March 2019; Published 1 April 2019

Academic Editor: Doraiswami Ramkrishna

Copyright © 2019 Rui Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Focusing on the insufficient estimation of the local pressure loss at a 90° horizontal-vertical bend in low-pressure pneumatic conveying of coarse particles, experiments are conducted in a 80 mm inner diameter test bend by using polyethylene particles having an equivalent spherical diameter of 4.00 mm. The influences of the local pressure loss versus the gas flow Reynolds number, the solid-gas ratio, and the bending radius ratio are investigated. Based on the additional pressure theory of Barth, an empirical formula estimating the local pressure loss is obtained using dimensional and nonlinear regression analysis. Summarizing the experiments and literature, the results expound on the local gas flow pressure loss coefficient decreases with increasing Reynolds number, and first decreases and then increases with increasing bending radius ratios from 0.5 to 7. The additional solid flow pressure loss coefficient decreases with the increasing Reynolds number and bending radius ratio in the dilute phase, and linearly increases with increasing solid-gas ratio. Compared with the estimated values with the experimental values, the calculated standard deviation is below 4.11%, indicating that the empirical formula can be used to predict local pressure loss at the bend in the low-pressure dilute-phase pneumatic conveying.

#### 1. Introduction

To improve the flexibility of the pneumatic conveying system, a bend is usually regarded as an important component in the process route. However, a bend makes the flow situation complicated and causes a sharp pressure loss. Especially in engineering, pressure loss is typically used as a key parameter to guide and design pneumatic conveying systems. Hence, to reasonably estimate the local pressure loss through a bend is very significant for pneumatic conveying systems.

Considering the universality of the 90° bend of a circular cross section, it has been applied and studied by numerous researchers. Cornish and Charity [1] listed all the important parameters (e.g., gas density and viscosity, particle density and size, bend curvature radius and diameter, the conveying velocity, and mass flow rate) of the local pressure loss at a 90° bend for a given pneumatic conveying system and found that the local pressure loss is higher for a short bend curvature radius and linearly increases with the increasing solid-gas ratio (i.e., the mass flow rate of solids to gas). Ghosh and Kalyanaraman [2] studied the local pressure loss in dilute-phase (solid-gas ratio <5.3) pneumatic conveyance of coarse particles (e.g., wheat) for a horizontal-horizontal bend. The results show that the additional pressure loss coefficient is constant for all conveying velocities and is a linear function of the solid-gas ratio. Singh and Wolfe [3] considered the angle of bend deflection (i.e., change in flow direction), the changes of local pressure loss versus the conveying velocity, the mass flow rate of solids, and the bend curvature radius were investigated in the pneumatic conveying. An empirical formula for local pressure loss was deduced, but the impact of gravity was neglected. Mason and Smith [4] and Rossetti [5] reported that the local pressure loss includes gas flow and additional pressure loss of solids. They took the local pressure loss of gas-only flow for a constant, and the additional pressure loss of solids is closely correlated with the particle terminal velocity. Westman et al. [6], based on the additional pressure theory of Barth [7], found that larger curvature radius bends produce lower pressure loss in vacuum pneumatic conveying systems. An empirical formula for local pressure loss was derived from the gas-velocity at the bend exit. Yu and Wang [8] fully considered the bend pressure loss upstream and downstream, where the gas-solid flow was impacted by the bend. They found that the local pressure loss increases with increasing solid-gas ratio in dense-phase conveying of powder and derived an empirical formula for estimating local pressure loss. However, its applicability is limited due to only one bending radius ratio (i.e., the bend curvature radius to diameter). Pan and Chi [9] investigated the effects of local pressure loss for different angles and short curvature radius bends. The results show that the local pressure loss (gas only) decreases with the increasing bend angle and curvature radius, and it proportionally increases with the increasing solid-gas ratio. Moreover, the gas-solid flow was difficult to fully develop in the short straight pipe after the bend. Pan [10] proposed an accurate way of estimating the local pressure loss at a bend (here, the straight pipe and bend are separately dealt with) in high-pressure conveying of fly ash. Based on numerous experiments, a semiempirical formula was set up to predict additional pressure loss using mathematical and dimensional analyses and starting from the bend exit conditions. After that, Pan and Wypych [11] also considered the compressibility of gas flow due to conveying pressure and mixed particles. On the basis of Barth’s [7] and Ito’s [12] researches, the semiempirical formula [10] of local additional pressure loss was corrected by the bend exit conditions (e.g., average gas density, velocity, and solid-gas ratio). Furthermore, Das and Meloy [13] found that the local pressure loss through a double-coupled bend conveying solid material is not equivalent to the cumulative effect of two separated bends. The local pressure loss in a double-coupled double bend is less than twice of that in a single bend. Liang et al. [14] considered the influences of the different materials, bend curvature radii, and locations (i.e., horizontal-horizontal, horizontal-vertical, and vertical-horizontal bends) in high-pressure dense-phase of pulverized coal conveying. They found that the pressure loss of a horizontal-vertical bend is the largest than the horizontal-horizontal and vertical-horizontal bends, and the local pressure loss increases with increasing coal size. Accordingly, the corresponding empirical formulas of different bend locations were obtained to estimate the additional pressure loss using Barth’s theory [7] and multivariate regression analysis.

Recently, in order to study the applicability of the present empirical formulas, Naveen et al. [15] compared the values calculated by the formulas [3, 5, 6, 10, 11, 13] with experimental values in conveying fly ash, and the results indicate that only the empirical formulas of Pan [10] and Pan and Wypych [11] could be applied to estimate the local pressure loss at bends in a dilute-phase regime. However, the formulas in [10, 11] were only verified in the pneumatic conveying of powders (e.g., fly ash and pulverized coal), and the flow parameters (e.g., gas density, gas velocity, and mass flow rate) of gas-solid flow at the bend exit are difficult to obtain, causing the inconvenience in the design of dilute-phase pneumatic conveying systems in the beginning. In addition, previous literature is almost aimed at the powders [3–5, 7–10, 12–14] or high-pressure pneumatic conveying [9, 10, 13–15]. From the above, the local pressure loss estimates for a bend in low-pressure dilute-phase pneumatic conveying (e.g., air supply from roots blower) of coarse particles are very insufficient.

In this study, based on a low-pressure dilute-phase pneumatic conveying system, the influences of local pressure loss arising from the change of superficial conveying gas velocity, particle mass flow rate, and bending radius ratio are investigated in a horizontal-vertical 90° bend. Meanwhile, to provide theoretical support for designing the low-pressure dilute-phase pneumatic conveying systems as conveying the coarse particles, an empirical formula of the local pressure loss is derived using dimensional and nonlinear regression analysis.

#### 2. Experimental Apparatus

The experimental apparatus of the low-pressure pneumatic conveying system is shown in Figure 1. The system consists of a fan, feed bin, rotary value, separator, bag filter, and several section pipes. The test pipeline frame has a horizontal length *L* = 4.0 m and a vertical height *H* = 2.5 m, connected by two 90° bends and a short straight pipe. The pipes are made of organic glass and have the same inner diameter *D* = 80 mm ± 5.85%. When conveying, air from the fan blows away the particles fed by the rotary value into the test pipeline, and then, the gas-solid mixture is separated by the separator at the pipeline exit. Meanwhile, the gas flow rate and pressure are measured by the orifice meter and four pressure sensors (*P*_{1}, *P*_{2}, *P*_{3}, and *P*_{4}), and the particle mass flow rate is controlled by the rotation speed of the rotary value.