Experimental Study of the Transport of Solid Particles by an Air Flow
Abstract Generated abstract
This paper investigates the motion of solid spherical particles transported by air flow in a horizontal pipe, focusing on particle velocity along established trajectories and on factors not resolved by earlier mean-velocity studies. Experiments used a rectangular glass-walled pipe, wooden balls of varying diameter, controlled air velocities, and high-speed cinematography to record particle motion after the acceleration section. The results show that mean ball velocity decreases with increasing ratio of ball diameter to pipe hydraulic radius until about 0.65, after which it changes little, and that the dependence is closer to linear only over small diameter ranges. A fitted relation is proposed for relative velocities of balls of the same specific weight as a function of diameter, with comparison to earlier data suggesting possible effects of pipe size and material properties during jumping motion and impacts.
Full Text
Experimental Study of the Process of Transporting Solid Particles by an Air Flow
B. F. Kalugin
(Presented by Honored Worker of Science and Technology Prof. I. N. Butakov)
Although a number of works, both theoretical and experimental, have been devoted to the study of velocities in pneumatic transport in horizontal pipes, there is still no sufficient clarity in this matter. In calculating mean velocities by theoretical formulas, considerable difficulties are encountered. The experimental material available in the literature concerns mean velocities and, in essence, does not touch upon the question of how the velocity changes along the trajectory of motion of a particle. There is also no complete clarity in the mechanism by which particles are suspended in an air stream. The question also remains unclear as to what causes the additional pressure losses in pneumatic transport in comparison with the transportation of clean air through the same pipes.
To obtain a clearer physical picture of the movement of solid particles through pipes by an air flow, investigations using high-speed cinematography were carried out at the Department of Heat-Power Installations of the Tomsk Polytechnic Institute. For this purpose, an experimental installation was assembled, shown in Fig. 1. The arrangement of the illuminators and the camera during filming is also shown there.
The number 1 denotes a high-pressure fan No. 8, providing a head of up to 450 mm of water column. The fan is connected to a wooden pipe of rectangular cross-section, arranged horizontally; two vertical walls of it are made of glass. The pipe length is 20 m, and the hydraulic radius is \(R_h = 0.05\) m (in cross-section—a regular square). The air flow rate was varied by means of damper 2. Behind the damper a straightening grid 3 was installed to reduce the influence on the flow of disturbances at the inlet and to distribute the flow more rapidly over the pipe cross-section.
The mean air velocity was measured with a pneumometric tube 4 according to the general procedure for measuring mean air velocities in pipes of rectangular cross-section. Behind the pneumometric tube there is a loading device 6, consisting of two steel needles between which a ball was clamped and which were quickly and simultaneously pulled apart by means of powerful springs.
At a distance of 11–12 m from the needles is the filming section 5. Preliminary experiments were carried out to determine the length of the acceleration—
of the section where the velocities of motion of the particles were determined by means of photoelectric cells. The experiments showed that already at a distance of 7–8 m from the loading device the motion of the particles may be considered established.
Balls turned from wood, with specific weight \(\gamma = 727\ \mathrm{kg/m^3}\), were passed through the pipe. The diameter of the balls varied within the limits from 10 to 30 mm. The trajectory of the ball was recorded by a high-speed motion-picture camera 9, SKS-1M, providing filming at a rate of up to 4500 frames per second.
Fig. 1. Diagram of the experimental setup.
The ball was clamped by steel needles, the fan was switched on, a specified head was set, then the needles were moved apart, and the ball began its motion in the air stream. Simultaneously with the beginning of the motion of the needles, the circuit of a time relay was closed, which, through an intermediate relay, switched on the motion-picture camera. Illumination of the pipe was provided by 18 photolamps 7, each of 500 W. On the opposite side of the pipe, close against the glass, a screen of white paper 8 was placed. The balls were painted black. On the film, the image of the ball was obtained in the form of a white spot on a black background. The position of the ball along the height and length of the pipe was determined with the aid of special scale rulers fastened to the pipe. Frames from the film were printed with enlargement on photographic paper, and then the image was projected by an epidiascope onto a screen, where the necessary measurements were made. The time was recorded with the aid of a neon lamp connected to an alternating-current circuit and giving a beam of light on the film.
Figure 2 presents a graph of the variation of the mean velocities of the balls as a function of the ratio
\[ \frac{d}{R_h}, \]
where \(d\) is the diameter of the ball. Each curve is constructed at a constant velocity of the air flow for balls of one and the same specific weight. Such a system of coordinates was chosen in order to compare the data of the experiments with experiments published in the work of Zhikharev [1]. In this work [1] there is the relation \(V_{\mathrm{xcp}} = f\left(\frac{d}{D}\right)\), where \(D\) is the diameter of the pipe, but the range of variation of \(\frac{d}{D}\) is small—from 0.05 to 0.12. Zhikharev’s dependence has the form of a straight line. On the graph (Fig. 2), in the small range of variation of \(\frac{d}{R_h}\), the dependence also
close to rectilinear. Over the entire range of \(\dfrac{d}{R_h}\), it is seen that \(V_{\mathrm{avg}}\), with an increase in the ratio \(\dfrac{d}{R_h}\), decreases along a curve asymptotically approaching a straight line parallel to the abscissa axis. At \(\dfrac{d}{R_h} < 0.65\), \(V_{\mathrm{avg}}\) changes with the change in \(\dfrac{d}{R_h}\); at \(\dfrac{d}{R_h} > 0.65\), the change in \(V_{\mathrm{avg}}\) is practically absent.
Fig. 2. Dependence of the average particle velocity \(V_{\mathrm{avg}}\) on the ratio of its diameter to the hydraulic radius of the pipe \((1—U_{\mathrm{avg}}=35\ \text{m/sec};\ 2—U_{\mathrm{avg}}=32\ \text{m/sec};\ 3—U_{\mathrm{avg}}=25.4\ \text{m/sec})\).
The curvature of the lines shown in the graph decreases as the average velocity of the air flow decreases.
Figure 3 presents a graph of the dependence
\[ \frac{W_{n\mathrm{avg}} d_1}{W_{1\mathrm{avg}} d_n} = \kappa \left( \frac{d_1}{d_n} \right)^{\frac{1}{3}}, \tag{1} \]
where \(W_{n\mathrm{avg}}\) is the average relative velocity of the sphere, i.e., the velocity with which the sphere moves relative to the air flow, m/sec;
\(W_{1\mathrm{avg}}\) is the average relative velocity of the sphere with which the average relative velocities of other spheres are compared, m/sec;
\(d_1\) is the diameter of the reference sphere, m;
\(d_n\) is the diameter of some other sphere having velocity \(W_{n\mathrm{avg}}\), m/sec; m;
\(\kappa\) is a constant.
The diameter of the reference sphere is \(d_1 = 0.0304\). The average relative velocity of the sphere was calculated with respect to the average velocity of the air flow:
\[ W_{\mathrm{avg}} = U_{\mathrm{avg}} - V_{\mathrm{avg}}, \tag{2} \]
where \(U_{\mathrm{avg}}\) is the average flow velocity, m/sec.
Dependence (1) was obtained by fitting. For different air velocities all the points fall on the straight line \(A\). The same graph also shows the straight line \(\Gamma\), constructed by recalculating the experimental data of Gasterstadt [2]. In this case a sphere with a diameter of \(0.0202\ \text{m}\) was taken as the reference.
The balls had specific weights of \(3000\ \mathrm{kg/m^3}\), \(2000\ \mathrm{kg/m^3}\), and \(1000\ \mathrm{kg/m^3}\). The air velocity varied from \(15.5\ \mathrm{m/sec}\) to \(40.3\ \mathrm{m/sec}\). All the experimental points fall on the straight line \(\Gamma\).
The straight lines \(A\) and \(\Gamma\) do not coincide. This may occur because the properties of the materials of the pipe–ball system are manifested here. As motion-picture filming shows, the balls move through the pipe in a jumping manner over the entire range of air velocities at which filming was carried out. Upon impact, the properties of the materials of the ball and the wall may be manifested. It is possible that the position of the straight line is affected by the size of the pipe, the diameter, or the hydraulic radius.
Fig. 3. Dependence
\[ \frac{W_{m\text{avg}} d_1}{W_{1\text{avg}} d_n} = f\left[\left(\frac{d_1}{d_n}\right)^{\frac{1}{3}}\right]. \]
Straight line \(A\): \(+\ U_{\text{avg}}=35\ \mathrm{m/sec}\); \(0\)—\(U_{\text{avg}}=32\ \mathrm{m/sec}\); \(\Delta\)—\(U_{\text{avg}}=25.4\ \mathrm{m/sec}\).
Straight line \(\Gamma\): range of variation of \(U_{\text{avg}}\) from \(15.5\ \mathrm{m/sec}\) to \(40.3\ \mathrm{m/sec}\).
Straight line \(A\) was constructed for a pipe with \(R_h=0.05\ \mathrm{m}\); the pipe and balls were made of wood. Straight line \(\Gamma\) was constructed for a steel pipe with \(D=0.089\ \mathrm{m}\), and the balls were hollow and made of iron.
Conclusions
As a result of the experiments carried out, the change in the mean velocity of a ball was determined over a wide range of variation of the ratio of its diameter to the hydraulic radius of the pipe. By fitting, relation (1) was obtained, characterizing the connection between the relative velocities of balls of one and the same specific weight and their diameters,
Literature
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E. A. Zhikharev. Experimental study of the character of particle motion in pneumatic-transport pipelines. Engineering-Physics Journal, No. 2, 1959.
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Gasterstadt. Pneumatic Transport. VSNKh Publishing House, 1927.