CN1190606A - High-efficiency energy-saving weak wear curvature classifier - Google Patents

Abstract

The invented classifier is a fluid machinery used in the fields of metallurgy, mine, petroleum, chemical industry, building material, electric power and food, etc. for classification, desliming, concentration and dust removal. It is composed of two parts of curvature grading tube and flow divider. It can divide the mixed fluid into two or more grades according to different sizes of particle diameter and density. Compared with the prior cyclone, the fluid machine has the advantages of small volume, light weight, high efficiency, energy conservation, improvement of classification quality and production capacity, reduction of abrasion strength, improvement of service life and the like.

Description

High-efficiency energy-saving weak wear curvature classifier

The present invention is a fluid machine used in the fields of metallurgy, mining, petroleum, chemical industry, electric power, building materials, food, etc. for operations such as classification, desliming, concentration, and dust removal.

1. Research on Existing Cyclone

At present, hydrocyclones are commonly used at home and abroad (Figure 1). It is composed of feed pipe (1), overflow pipe (2), swirl chamber (3), garden cone (4) and sand settling pipe (5). The feed pipe (1) is arranged on the edge of the cylinder wall of the cyclone chamber (3) and is tangent to the cylinder wall. The overflow pipe (2) is arranged on the top of the cyclone chamber (3). The cone (4) is located at the bottom of the cyclone chamber (3). The bottom of the garden cone (4) is connected to the grit chamber (5). Except for the feeding pipe (1), the whole cyclone is a rotating body with ZZ as the central axis. After the fluid enters the swirl chamber (3) from the feeding pipe (1) at the velocity V ₁ along the tangential direction of the wall of the swirl chamber (3), the fluid will spiral downward along the wall due to inertial centrifugal force and gravity. When moving to the garden cone (4), due to the effect of the cone wall, the fluid will also move centripetally, and the radius of motion is getting smaller and smaller. After moving to the sand settling pipe (5), part of the fluid will be drained from the sand settling pipe (5), and the remaining part will spiral upwards from bottom to top under the action of the internal pressure of the fluid, and finally flow from the overflow pipe (2) row away. Therefore, when the cyclone works stably, there are two streams of fluids inside it, "downflow" and "upflow". The velocity V of the fluid at any point in the cyclone can be decomposed into tangential velocity V _t , radial velocity V _r and vertical velocity V _z (Fig. 1), and: ${\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}^2=V_{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="V\; r"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}_r^{}+V_z^2---\left(1\right)$

1. Tangential speed

The fluid in the cyclone is assumed to be continuous and incompressible. When the swirler works stably, the torque sum of all external forces acting on the fluid to the central axis is zero, otherwise the fluid will accelerate or decelerate the swirling motion, which is not attached to the fact of a steady flow. In the cyclone, a regular hexahedral micro-element is randomly selected at the radius r (Fig. 2). The radial cross-sectional area of the microelement is ds, the thickness is dr, the normal pressure on the inner surface is p, the shear stress is τ, the normal pressure on the outer surface is p+dp, and the shear stress is τ+dτ. Apply the momentum moment theorem to get:

(τ+dτ) ds (r+dr)-τ ds r＝0 (2)

Omitting the high-order trace dr·dτ, the above formula can be organized as: $\frac{\mathrm{dr}}{r}+\frac{\mathrm{d\&tau;}}{\mathrm{\&tau;}}=0---\left(3\right)$

Integrate the above formula to get: lnr+lnτ=C ₁ , that is:

rτ=C ₂ (4)

Among them: C ₁ —— integral constant; C ₂ —— constant.

Substituting the boundary conditions at the inlet: r = r ₁ ; τ = τ ₁ (r ₁ - the radius of the swirl chamber; τ ₁ - the shear stress between the fluid layers at the inner wall of the swirl chamber) into formula (4): C ₂ =r ₁ τ ₁ . so:

r·τ＝r ₁ τ ₁ (5) Use Newton's friction formula $\mathrm{\&tau;}=\mathrm{\&mu;}\frac{{\mathrm{dV}}_t}{\mathrm{dr}}$ (μ—viscosity coefficient of the fluid) is substituted into the above formula to get: $r\&CenterDot;(-\mathrm{\&mu;}\frac{{\mathrm{dV}}_t}{\mathrm{dr}})=r_1{\mathrm{\&tau;}}_1$ Right now: ${\mathrm{dV}}_t=-\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\&CenterDot;\frac{\mathrm{dr}}{r}---\left(6\right)$ Points get: $V_t=-\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}1\mathrm{nr}+C_3---\left(7\right)$

C ₃ --integration constant. Using the boundary conditions at the feed inlet, r=r ₁ , V _t =V _t1 =V ₁ (V _t1 - tangential velocity of the fluid at the feed inlet), substituting into the above formula: ${\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">C</figure-callout>}}_3=V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}1{\mathrm{nr}}_1$ so: $V_t=V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-----\left(8\right)$

It can be seen from the above formula that in the swirler, the tangential velocity V _t of the fluid increases as the radius r decreases. The radii of the sand settling pipe and the overflow pipe are relatively small (much smaller than r ₁ ), so after the fluid moves to the sand settling pipe and the overflow pipe, the tangential velocity of the swirling motion is very large. But the radius of fluid swirl movement cannot be zero, because when r=0, V _t is infinite. This is impossible, because the external force is limited, and the limited external force cannot increase the velocity of the fluid to infinity. Therefore, there must be an "air column" near the central axis in the cyclone. This fact has been confirmed by experiments. The shape of the "air column" is roughly as shown by the double-dot dash line in Figure 1.

2. Radial speed

In the cyclone, a cylindrical imaginary cylinder with a radius of r and a height of h (r is greater than the radius of the overflow pipe and the sand settling pipe) is randomly selected. The side surface area of the imaginary cylinder is S=2πrh. All the fluid in the cyclone needs to enter the imaginary cylinder through the area S. Then it is discharged from the overflow pipe and the sand settling pipe respectively through the top surface and the bottom surface of the imaginary cylinder. Assuming that the volume flow through the cyclone is Q, the radial average velocity of the fluid is: $V_r=\frac{Q}{S}=\frac{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">Q</figure-callout>}}{2\mathrm{\&pi;rh}}---\left(9\right)$

V _r is inversely proportional to the radius r, and the direction points to the central axis. Although the average velocity is not equal to the real velocity at a certain point on the side surface of the imaginary cylinder with radius r, it reflects the trend that the radial velocity V _r increases as the radius r decreases as a whole.

3. Vertical speed

When the cyclone works stably, the outer layer near the edge of the cylinder wall is "downflow", and the inner layer is "upflow". Due to the continuity of the fluid, there must be an interface with a vertical velocity V _z = 0 between the two fluids. If the downward V _z is set as a positive value, then V _z decreases with the decrease of r, and at the interface layer V _z =0, and V _z in the boundary layer is a negative value (direction upward). The boundary layer is a surface of revolution (such as the surface obtained by revolving the AB curve around the ZZ axis in Figure 1). In the cyclone, r is the same, but the vertical velocity of the fluid is different at different positions of Z, and the vertical velocity of the fluid is the largest near the mouth of the sand settling pipe and the overflow pipe. The vertical velocity is more complex, and it is difficult to express it with a functional formula.

4. Analysis of the movement and force of solid materials in the cyclone

Suppose there is a spherical solid material with diameter d and density ρ _s in the cyclone, the distance between the center of the sphere and the central axis is r, and the density of the medium fluid is ρ, ρ _s > ρ. When the cyclone works stably, the solid material will follow the medium fluid for swirling motion at a speed lower than that of the medium fluid under the action of the drag force (traction force) of the medium fluid. Let the tangential velocity of the solid material be V _t '. $V_t^{\&prime;}=V_t-V_{\mathrm{tc}}=V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}}---\left(10\right)$ V _tc ——The tangential relative velocity of medium fluid and solid material. The inertial centrifugal force generated by itself when the solid material is swirling is (Figure 3): $f=m\frac{V_t^{\&prime;2}}{r}=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{(V_l-\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^2---\left(11\right)$ m - mass of spherical solid material.

The inertial centrifugal force will cause the solid material to make a centrifugal motion and stick to the wall, while the centripetal movement of the medium fluid will exert a centripetal thrust (that is, active resistance) on the solid material. According to the general resistance formula of fluid mechanics, the centripetal force on the material is: $R_r={\mathrm{\&psi;\&rho;d}}^2{V}_{\mathrm{rc}}^2---\left(12\right)$

ψ——The resistance coefficient of the medium fluid to the solid material. V _rc ——The radial relative velocity of medium fluid and solid material.

When R _r < F, the solid material will do centrifugal swirling motion and gradually stick to the wall of the cyclone. The material will be in the "downflow" layer and finally discharged from the grit chamber. When R _r >F, the solid material will move in a centripetal swirling flow, and the moving radius will become smaller and smaller. When it enters the "upflow" layer pair, it will be discharged from the overflow pipe with the upflow. When R _r =F, the radial force of the material is balanced, and it will perform swirling motion on a specific radius. At this time, the radial velocity V _r ′ of the material is 0, and the radial relative velocity between the material and the medium fluid is equal to the centripetal velocity of the medium fluid at the location of the material. Right now: $V_{\mathrm{rc}}=V_r=\frac{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">Q</figure-callout>}}{2\mathrm{\&pi;rh}}---\left(13\right)$

For small particle materials with Reynolds number _Re <1 and particle size d<0.5 mm, the radial resistance formula (12) applied by the medium fluid to the solid material becomes the Stokes resistance formula, namely:

R _r ＝3πμd V _rc (14)

μ—viscosity coefficient of the fluid.

From R _r = F: $3\mathrm{\&pi;\&mu;d}{V}_{\mathrm{rc}}=\frac{\mathrm{\&pi;}{\mathrm{\&rho;}}_{\mathrm{the\; s}}{d}^9}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{to}})}^2$ Substituting formula (13) into the above formula, we get: $d=\frac{3}{V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}}}\sqrt{\frac{\mathrm{\&mu;Q}}{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; s}}h}}---\left(15\right)$ ${\mathrm{\&rho;}}_{\mathrm{the\; s}}=\frac{9\mathrm{\&pi;Q}}{{\mathrm{\&pi;hd}}^2(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}---\left(16\right)$

In formula (15), the radius r is regarded as a variable, and d is a function of r. This is the function formula of the particle size distribution of the solid particle material in the cyclone. It shows that the larger the inner radius of the cyclone, the larger the particle size of the distributed solid particle material. Only those fine-grained materials with a small particle size can enter the central area with a small radius.

In formula (16), r is regarded as a variable, and ρ _s is a function of r. This is the function formula of the density distribution of the material in the cyclone. It shows that in the cyclone, the greater the density of the material, the larger the radius of its distribution. Where r is small, the density of the material is also small.

In the vertical direction, let G be the gravity of the spherical solid material in the medium fluid. but: $G=\frac{{\mathrm{\&pi;<figure-callout\; id="3"\; label="d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">d</figure-callout>}}^3}{6}({\mathrm{\&rho;}}_{\mathrm{the\; s}}-\mathrm{\&rho;})g---\left(17\right)$

g - acceleration due to gravity.

G will force the solid material to accelerate sedimentation in the medium. The sedimentation movement of the material will be affected by the resistance of the medium fluid. Assuming that the vertical upward resistance of the medium fluid to the solid material is R _z , then: $R_z={\mathrm{\&psi;\&rho;d}}^2{V}_{\mathrm{zc}}^2---\left(18\right)$

V _zc ——The relative velocity of the medium fluid to the solid material in the vertical direction.

When the solid material follows the medium fluid and just enters the swirl chamber from the feed port, the falling speed of the material and the medium fluid is equal. At this time, V _zc =0 and R _z =0. Since ρ _s > ρ, the gravity G of the material in the medium fluid will force the material to accelerate the sedimentation, and then, due to the accelerated sedimentation of the solid material, V _zc and R _z will gradually increase. When R _z =G, the material is balanced in the vertical direction, and the sedimentation velocity of the material is the largest at this time. The maximum settling velocity is:

V _zmax ′=V _z +V _o (19)

V _o ——The terminal velocity of the solid material when it settles freely in the static medium.

Only those solid materials with smaller particle size and lower density, when the radial force _Rr >F they bear, the solid material swirls to the heart and moves to the "upflow" zone, and the medium fluid is applied to it, upward When the resistance R _z >G, the solid material will gradually change from decelerating and settling to ascending swirling motion, and finally discharged from the overflow pipe. It can be seen that the overflow product is a movement that overcomes the dual effects of inertial centrifugal force and gravity.

5. Cyclone wear

For solid materials with larger particle size and higher density, since F>R _r , the solid materials will move close to the wall of the device. Let the horizontal force of the solid material spin on the wall be N. but:

N = FR _r (20)

Substitute (11).(12) into the above formula to get: $N=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^2-{\mathrm{\&psi;\&rho;d}}^2{V}_{\mathrm{rc}}^2---\left(\mathrm{twenty\; one}\right)$ Since the V _rc at the wall is very small, it can be neglected, so: $N=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; s}}{d}^9}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^2---\left(\mathrm{twenty\; two}\right)$

When the solid material moves to the cone (4), the force N can be decomposed into a positive pressure N ₁ perpendicular to the cone surface and a component force N ₂ parallel to the cone surface (Figure 4).

N ₁ =NCosα $=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^2\mathrm{Cos\&alpha;}---\left(\mathrm{twenty\; three}\right)$ N ₂ =NSinα $=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^2\mathrm{Sin\&alpha;}---\left(\mathrm{twenty\; four}\right)$

α—the half cone angle of the cone (4).

The direction of N ₂ is upward along the cone. This has a certain hindering effect on the settlement of coarse-grained and heavy materials. The larger the α angle, the stronger the hindering effect. N ₂ is unfavorable to the classification of the cyclone and the improvement of the processing capacity.

Practice has proved that the wear speed W of a certain position on the wall of the cyclone is mainly proportional to the product of the positive pressure N ₁ generated by the solid particle material on the position and the relative movement speed V _c ' of the solid particle material on the position. It is inversely proportional to the wear resistance e of the worn object. In addition, it is also related to the physical and mechanical properties of solid granular materials. The wear rate can be expressed by the following formula. $W=\frac{{\mathrm{KN}}_1{V}_C^{\&prime;}}{e}$ K - wear coefficient. It takes into account the impact of the size, shape, hardness and other physical and mechanical properties of the external substance (abrasive) on the wear rate. e——The wear resistance (friction resistance) of the object to be worn.

The molecular part of formula (25) is a measure of the abrasiveness of the external substance (abrasive) on the worn object, which is called the abrasion intensity. Denoted by the letter T. Then: T=KN ₁ V _c ′ (26)

Abrasion intensity has nothing to do with the material performance factors of the worn object, it is a physical quantity that characterizes the abrasiveness produced by external substances.

At the wall of the cyclone, since the radial velocity V _r ′ and vertical velocity V _z ′ of the solid particle material are much smaller than the tangential velocity V _t ′, if V _r ′ and V _z ′ are omitted , then V _c ′≈V _t ′. Therefore, the wear intensity of the solid particle material on the cyclone can be expressed as:

T=KN ₁ V _t ' (27)

Substitute (23) and (10) into the above formula to get: $T=K\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r}-V_{\mathrm{tc}})}^3\mathrm{COS\&alpha;}---\left(28\right)$

It can be seen from the above formula that the wear intensity of the same solid particle material in different positions in the cyclone is different. The wear intensity T becomes a function of the position of the swirler radius r. In the cyclone, the smaller the radius r, the greater the wear intensity of the solid particle material. The radii of the overflow pipe, the lower part of the garden cone and the sand settling pipe are all relatively small, so the wear intensity of the solid particle material on them is very large. Equation (28) theoretically explains the reason why the overflow pipe, the lower part of the cone, and especially the sand settling pipe of the existing cyclone wear very fast. Practice has proved that the wear rate of the sand settling tube of the cyclone is tens or even hundreds of times that of the cyclone chamber. For a long time, people have been looking for high-strength wear-resistant materials to make the lower cone of the cyclone and the sand settling tube parts in order to extend their service life. But this doesn't fundamentally solve the problem. The abrasion strength did not decrease. Wear remains a significant problem for cyclones. Although people's efforts have extended the service life of some cyclones, they have increased the cost and usage fee, which is not a desirable way.

6. Energy consumption of cyclone

Z₁分别表示单位重量流体质点处于M₁点时所具有的静压能头、动压能头和位能头。 Z₁分别表示单位重量流体质点运动到旋流器内任意位置M点时所具有的静压能头、动压能头和位能头。h_w-流体质点从M₁点到M点过程中的能头损失。P₁、P分别表示M₁、M点流体的静压力。γ——流体的重度。The energy equation of the cyclone is obtained by applying the Bernoulli equation of the incompressible actual fluid particle in hydrodynamics for stable absolute motion to the cyclone: $h=\frac{P_1}{\mathrm{\&gamma;}}+\frac{V_1^2}{2g}+Z_1=\frac{P}{\mathrm{\&gamma;}}+\frac{{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}^2}{2g}+Z+h_w---\left(29\right)$ H-the total energy head (the total energy consumed when the fluid particle per unit weight enters the cyclone) at the point _M1 of the hydrocyclone inlet.

Z ₁ respectively represent the static pressure energy head, dynamic pressure energy head and potential energy head of the unit weight fluid particle at point M ₁ . Z ₁ respectively represent the static pressure energy head, dynamic pressure energy head and potential energy head that the fluid particle per unit weight moves to any point M in the cyclone. h _w - the energy head loss of the fluid particle from point M ₁ to point M. P ₁ and P represent the static pressure of the fluid at points M ₁ and M respectively. γ - the gravity of the fluid.

Substitute formula (1) into (29) to get: $h=\frac{P}{\mathrm{\&gamma;}}+\frac{1}{2g}({\mathrm{<figure-callout\; id="2"\; label="V\; t"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}_t^{}+{\mathrm{<figure-callout\; id="2"\; label="V\; r"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}_r^{}+V_z^2)+Z+h_W---\left(30\right)$ Substitute (8) and (9) into the above formula to get: $h=\frac{P}{\mathrm{\&gamma;}}+\frac{1}{2g}\&lsqb;{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r})}^2+{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">Q</figure-callout>}}{2\mathrm{\&pi;rh}}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="V\; z"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}_z^{}\&rsqb;+Z+h_w---\left(31\right)$

When the cyclone is working, the sand settling pipe and the overflow pipe are usually directly connected to the atmosphere. Therefore, the static pressure of the boundary layer of the air column in the center of the cyclone is approximately equal to the atmospheric pressure. Assuming that the atmospheric pressure is Pa, and the radius of the central air column at the Z section in the cyclone is r ₃ , then the boundary conditions of the Z section central air column P=Pa, r=r ₃ are substituted into the above formula to obtain: $h=\frac{\mathrm{Pa}}{\mathrm{\&gamma;}}+\frac{1}{2g}\&lsqb;{(V_1+\frac{r_1{\mathrm{\&tau;}}_1}{\mathrm{\&mu;}}\ln \frac{r_1}{r_3})}^2+{\left(\frac{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">Q</figure-callout>}}{2\mathrm{\&pi;}{r}_{3}h}\right)}^2+{\mathrm{<figure-callout\; id="2"\; label="V\; z"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">V</figure-callout>}}_z^{}\&rsqb;+Z+h_w---\left(32\right)$

Consider r ₃ in formula (32) as a variable, and H is a function of r ₃ . Equation (32) shows that the total energy head H possessed (or consumed) per unit weight of fluid particles in the cyclone increases with the decrease of the fluid swirl radius r ₃ . Therefore, the smaller the radius of the sand settling pipe and overflow pipe of the cyclone, the smaller the radius of the central air column, and the higher the energy consumed by the cyclone.

7. Structural analysis of cyclone

The cone angle of the existing hydrocyclone garden cone (4) is generally all relatively small (about 20 °), so the axial dimension of the hydrocyclone is very long and the volume is relatively large. The fluid often has to rotate more than ten or even dozens of times in the cyclone before it can flow out. This not only increases energy consumption, but also aggravates the wear of the material on the cyclone. The root cause of many problems in the existing cyclone is due to its structure. Its inlet radius r ₁ is relatively large, while the radius of the outlet—sand settling pipe and overflow pipe are small (much smaller than r ₁ ), after the fluid enters the cyclone, the external force p (fluid Static pressure) must overcome the inertial centrifugal force produced by the fluid itself to make the fluid swirl from the position with a larger radius to the discharge port with a smaller radius. The result of the work done by the external force increases the kinetic energy of the fluid, that is, increases When the moving speed of the fluid (medium fluid and solid material) is increased, the three sub-velocities of V _t , V _r , and V _z all have larger increments (this fact has been confirmed by experiments). This not only increases the mechanical energy consumed by the _cyclone , but also increases the inertial centrifugal force generated by the fluid itself in a quadratic relationship (see formula (11)), and increases the wear intensity in a cubic relationship (see formula (28)). This is quite harmful. In fact, the grading function of the cyclone is mainly completed in the cyclone chamber. The sand settling pipe and overflow pipe are just to separate the different products after classification and discharge them out of the device. The author thinks that it is a mistake to set the sand settling pipe and overflow pipe of the existing cyclone at the central axis of the cyclone. This is the root cause of many problems in existing cyclones.

8. Conclusion

From the above analysis, it can be seen that the structure of the existing hydrocyclone is unreasonable, the fluid moves in the cyclone for a long time, and the moving speed and route are very complicated. It has the defects of high energy consumption, low efficiency, high wear intensity of solid particle materials in the cyclone, very fast wear, short life, and high cost.

2. High-efficiency energy-saving and weak-wear curvature polarizer

The "high-efficiency energy-saving weak wear curvature classifier" of the present invention provides a new type of fluid machinery with simple structure, small size, light weight, high efficiency and energy saving, which can improve the classification quality, reduce the wear intensity and prolong the service life.

1. Structure and working principle

The "high-efficiency energy-saving weak wear curvature classifier" of the present invention is realized in this way (Fig. 5). It is made up of two parts, the curvature grading pipe (2) and the flow divider (9), which are connected as a body by bolts (5) through flanges (4) and (14). Point 0 is the center of curvature of the curvature grading pipe (2). The arc AB is the axis of the curvature grading pipe (2). Take the Cartesian coordinate system XOY, the X axis is horizontal and the Y axis is vertical. After the fluid enters the curvature grading tube from the inlet (A) of the curvature polarizing tube (2), the fluid will move in a curved line along the pipeline AB. Assume that the tangential velocity of the medium fluid with density ρ moving along the pipeline is V _t , and there are spherical solid materials with particle diameter d and density ρ _s (ρ _s > ρ) in the medium fluid. The tangential velocity of spherical solid material is V _t '. The inertial centrifugal force generated by the spherical solid material when it moves in a curve is: $f=m\frac{V_t^{\&prime;2}}{r}=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{V}_t^{\&prime;2}---\left(33\right)$

m - mass of spherical solid material. r—the distance from the center of the sphere to the center of curvature (that is, the radius of curvature).

Let the angle between the spherical solid material and the horizontal plane be β. The gravity of the spherical solid material in the medium is G, then the radial and tangential component forces of G are (Figure 5): $G_1=\mathrm{GSin\&beta;}=\frac{{\mathrm{\&pi;<figure-callout\; id="3"\; label="d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">d</figure-callout>}}^3}{6}({\mathrm{\&rho;}}_{\mathrm{the\; s}}-\mathrm{\&rho;})\mathrm{gSin\&beta;}---\left(34\right)$ ${\mathrm{<figure-callout\; id="2"\; label="G"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">G</figure-callout>}}_2=\mathrm{GCos\&beta;}=\frac{{\mathrm{\&pi;<figure-callout\; id="3"\; label="d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">d</figure-callout>}}^3}{6}({\mathrm{\&rho;}}_{\mathrm{the\; s}}-\mathrm{\&rho;})\mathrm{gCos\&beta;}---\left(35\right)$ In the radial direction, the resultant force of the centrifugal force on the solid material is: $f^{\&prime;}=f+G_1=\frac{{\mathrm{\&pi;\&rho;}}_{\mathrm{the\; <figure-callout\; id="3"\; label="s\; d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">s</figure-callout>}}{d}^{}{}^3}{6r}{V}_t^{\&prime;2}+\frac{{\mathrm{\&pi;<figure-callout\; id="3"\; label="d"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">d</figure-callout>}}^3}{6}({\mathrm{\&rho;}}_{\mathrm{the\; s}}-\mathrm{\&rho;})\mathrm{gSin\&beta;}---\left(36\right)$

The resultant centrifugal force F' will force the solid particle material to perform centrifugal movement (away from the center of curvature), and gradually stick to the outer tube wall (15) with a larger radius of curvature. When the medium fluid is an incompressible fluid, while the solid material is moving centrifugally, the medium fluid with the same volume outside will be excited to move centripetally. Let the radial centrifugal velocity of solid material be V _r ′. The centripetal velocity of the medium fluid at the location of the solid material is V _r . Then the radial relative movement speed of medium fluid and solid material is: V _rc =V _r -V _r '. The medium fluid can produce a resistance effect on the radial movement of the solid material. The resistance size is: $R_r={\mathrm{\&psi;\&rho;d}}^2{V}_{\mathrm{rc}}^2---\left(37\right)$

ψ——The resistance coefficient of the medium fluid to the solid material.

When the radial force F'>R _r on the solid material, the material will perform centrifugal motion and gradually stick to the outer pipe wall (15). When F'<R _r , the solid material will move centripetally, gradually moving from the outside to the inside. When F'=R _r , the radial force of the solid material is balanced, and the material will move around a certain radius at this time. Let F′=R _r , and use equations (36) and (37) to substitute into the solution: $d=\frac{6\mathrm{\&psi;\&rho;<figure-callout\; id="2"\; label="r\; V\; rc"\; filenames="A9611128000231.png,A9611128000251.png"\; state="\{\{state\}\}">r</figure-callout>}{V}_{\mathrm{rc}}^{}{}_2^{}}{\mathrm{\&pi;}\&lsqb;{\mathrm{\&rho;}}_{\mathrm{the\; s}}{V}_t^{\&prime;2}-\mathrm{r\; g}({\mathrm{\&rho;}}_{\mathrm{the\; s}}-\mathrm{\&rho;})\mathrm{Sin\&beta;}\&rsqb;}$ $\left(38\right)$ ${\mathrm{\&rho;}}_{\mathrm{the\; s}}=\frac{\mathrm{\&rho;r}(6\mathrm{\&psi;}{V}_{\mathrm{rc}}^2-\mathrm{\&pi;dSin\&beta;})}{\mathrm{\&pi;d}(V_t^{\&prime;2}+\mathrm{Sin\&beta;})}\text{---}\left(39\right)$

In formula (38), r is regarded as a variable, and d is a function of r. Equation (38) is the functional expression of the distribution of solid particle materials along the direction of the curvature radius in the curvature classification tube according to the size of the particle size. It shows that in the curvature grading pipe, the larger the radius of curvature, the coarser the particle size of the solid material distributed, and vice versa.

Equation (39) is a functional formula for classifying materials according to density in the curvature classifying pipe. It shows that in the curvature graded pipe, the greater the curvature radius, the greater the density of the material distributed. On the contrary, the smaller it is.

When the fluid enters the curvature grading tube from the inlet (A) of the curvature grading tube (2) at a speed of V ₁ , the large particles and high-density materials will quickly migrate to the outer tube wall and gradually stick to the outer tube wall ( 15), while the medium fluid detours in the opposite direction, driven by the centripetal medium fluid (resistance effect), some light and small particle materials will also migrate to the inner side of the curvature grading tube. Therefore, the first half of the curvature grading pipe (the A side of the double-dashed line CD in FIG. 5 ) is the material grading stage. The radial movement of material and medium fluid in this section is relatively intense, and the movement of fluid is in a state of turbulent flow. In the second half of the curvature grading tube (side B of the double-dot dash line CD), the grading process of the material has basically ended, and the movement of the fluid is in a laminar flow state. The closer to the outlet, the better the laminar flow of the fluid. At the feed port (B), coarse-grained and heavy (larger ρ _s ) materials have completely adhered to the outer pipe wall (15) of the curvature grading pipe and formed a material layer with a certain thickness (δ ₁ ). Near the inner side of the curvature grading pipe, there are mostly medium fluids and fine-grained, light material fluids.

The direction of the tangential component G ₂ (see formula 35) of the gravity G of the solid material in the medium fluid is consistent with the direction of the velocity of the fluid. It can speed up the movement speed of materials, is beneficial to discharge, and can improve the production capacity of equipment.

The flow divider (9) is fixed on the discharge port (B) of the curvature grading pipe (2) by bolts (5) through flanges (4) and (14). A splitter consists of two flow tubes. The flow tube near the inner side of the curvature grading tube is called the inner tube (13), and the flow tube near the outer side of the curvature grading tube is called the outer tube (10). A dividing plate (12) is arranged between the inner pipe and the outer pipe to separate the two pipes. The material inlet of the outer pipe (10) is connected with the coarse-grained, heavy and high-concentration material flow layer (δ ₁ ) at the outer pipe wall (15) of the curvature graded pipe (2) outlet (B). The material inlet of the inner pipe (13) communicates with the medium fluid and the flow layer (δ ₂ ) of the medium fluid and fine-grained, light-weight and low-concentration material at the inner pipe wall (3) of the curvature grading pipe outlet (B). The partition plate (12) divides the laminar flow fluid classified by the curvature grader pipe (2) into two grades with different particle sizes, densities and concentrations. After classification, the coarse-grained, heavy-weight and high-concentration material fluid is discharged from the outlet _J1 through the outer pipe (10), and the medium fluid and fine-grained, light-weight and low-concentration material fluid are discharged from the outlet J through the inner pipe (13). ₂ row away. Therefore, the "high-efficiency energy-saving and weak wear curvature classifier" of the present invention can meet the requirements of metallurgy, mining, petroleum, chemical industry, building materials, electric power, food and other fields for classification, desliming, concentration, dust removal and other operations.

2. Wear problem

Compared with the existing cyclone, the curvature grading pipe (2) of the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention is equivalent to intercepting (or producing) a section of arc bend in the swirl chamber along the fluid movement direction. If the flow section of the curvature grading pipe is equal to the flow section of the cyclone inlet, and the curvature radius r ₁ of the outer pipe wall (15) of the curvature grading pipe is equal to the radius r ₁ of the cyclone chamber, then when they When the passing fluid flows are equal, the fluid velocity at the outer pipe wall (15) of the curvature grading pipe and the fluid velocity at the wall of the swirl chamber of the cyclone should be equal. If the influence of gravity is not considered, the same fluid should have the same abrasion intensity on the curvature grading pipe and the abrasion intensity on the cyclone chamber. The wear intensity produced by the tube is much weaker. If the radius of curvature from the inner pipe (13) and outer pipe (10) of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention to the discharge port _J2 , _J1 is designed to be larger than _r1 , the material fluid will be split If the wear intensity produced by the device is less than that of the curvature classifying pipe, the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention fundamentally solves the wear problem as a whole. This is not to reduce wear and increase service life from the perspective of improving the material properties of the equipment and increasing the wear resistance, but to reduce wear and improve service life from the perspective of reducing the wear intensity produced by the material fluid. This is an important feature of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention.

3. Energy consumption and efficiency

Assume that the velocity of the fluid passing through the inlet (A) of the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention is V ₁ , and the velocity of the outlet J ₁ and J ₂ is also V ₁ (the speed does not increase). The outlet J ₁ and J ₂ are connected to the atmosphere, so the static pressure inside the fluid at the outlet is equal to the atmospheric pressure Pa. The Bernoulli equation of fluid passing through the inlet and outlet of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention is: $h^{\&prime;}=\frac{P_1}{\mathrm{\&gamma;}}+\frac{V_1^2}{2g}+Z_1=\frac{\mathrm{Pa}}{\mathrm{\&gamma;}}+\frac{V_1^2}{2g}\text{+Z+}{h}_w---\left(40\right)$ When the speed of the fluid through the swirler inlet is also V ₁ , the comparison formula (40), (32) can know: the total energy head consumed by the unit weight fluid particle through the "high-efficiency energy-saving weak wear curvature classifier" of the present invention H' is considerably less than the total energy head H consumed by the cyclone. Therefore, the "high-efficiency, energy-saving and weak-wear curvature classifier" of the present invention is energy-saving and has high mechanical efficiency compared with a cyclone. The main characteristic of its energy saving is that the static pressure at the feed port will be less than that of the cyclone feed port.

Because the curvature classification pipe (2) of the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention is equivalent to intercepting a section of garden arc elbow pipe along the direction of fluid movement in the swirl chamber of the cyclone, it has the advantages of simple structure, small volume and low weight. light. The movement path and time of the fluid in the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention are much shorter than those in the cyclone, so the energy loss h _w of the "high-efficiency energy-saving and weak-wear curvature classifier" of the present invention is also shorter than that of the cyclone The device is small, so it is energy efficient.

4 Conclusion

In summary: Compared with the existing cyclone, the "high-efficiency, energy-saving and weak-wear curvature classifier" of the present invention has the following advantages: simple structure, small volume, light weight, high efficiency and energy saving, and can improve the classification quality and production capacity, and reduce the wear intensity , Improve the service life and other advantages.

5. Other

Fig. 6 is a structural schematic diagram of a three-product flow divider, which divides the flow divider (9) into inner pipe (1), Middle pipe (2), outer pipe (3) three flow pipes and obtain. J ₁ , J ₂ , and J ₃ are the three outlets of the three-product splitter. If the flow divider shown in Figure 6 is combined with the curvature classifying pipe (2) in Figure 5, a three-product "high-efficiency, energy-saving and weak-wear curvature classifier" is obtained. Coarse, heavy and high-concentration material fluid is diverted through the outer pipe (3) and discharged from the outlet _J1 . The medium fluid and some fine-grained and light material fluids are diverted through the inner pipe (1) and discharged from the outlet _J3 . What the middle pipe (2) divides will be the intermediate product between the outer pipe and the inner pipe. If the flow divider (9) is divided into three or more flow tubes along the radius of curvature direction at the outlet (B) of the curvature grading tube (2), an "high-efficiency energy-saving and weak-wear curvature classifier" with more than three products can be obtained.

The curvature grading pipe (2) of the "high-efficiency energy-saving and weak wear curvature classifier" of the present invention is characterized in that: 1. the arc angle θ can be any value, preferably 90°-180°; 2. the radius of curvature can be a constant or It varies with the θ angle; ③The cross-sectional shape of the flow can be arbitrary, and the rectangular cross-section is the best; ④The installation position of the inlet (A) plane in the space can be arbitrary, but it is better to arrange it horizontally or vertically . The characteristics of the flow divider (9) are: ① The shape of the inlet must be adapted to the outlet (B) of the curvature grading pipe (2), so that the classified fluid can be smoothly separated and discharged; ② The outlet The directions of ports J ₁ and J ₂ can be arranged arbitrarily.

3. Description of drawings

Accompanying drawing 1 is the schematic diagram of the structure of the existing hydrocyclone commonly used at home and abroad and the velocity decomposition diagram of the fluid in the hydrocyclone.

Accompanying drawing 2 is the force analysis diagram of the regular hexahedral microelement taken at any section z in the cyclone and the radius is r.

Accompanying drawing 3 is the force analysis diagram of solid particle material in the cyclone.

Accompanying drawing 4 is the decomposition diagram of the force that solid particle material acts on the cylinder wall of the cyclone.

Accompanying drawing 5 is the schematic structural diagram and working principle diagram of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention.

Accompanying drawing 6 is the structural diagram of the shunt of the three products "high-efficiency energy-saving weak wear curvature classifier".

In accompanying drawing 1: 1-feeding pipe; 2-overflow pipe; 3 _- swirl chamber; 4 _- cone; 5-settling pipe; 6-air _column ; speed.

In accompanying drawing 5: 1-flange; 2-curvature grading pipe (part); 3-inside pipe wall; 4-flange pipe; 11-flange; 12-partition plate; 13-inner pipe; 14-flange ; 15 - outer tube wall. J ₁ is the outlet for coarse-grained, heavy-weight and high-concentration material fluids; J ₂ is the outlet for medium fluids and some fine-grained, light-weight and low-concentration material fluids.

In accompanying drawing 6: 1-inner pipe; 2-middle pipe; 3-outer pipe; 4-buffer chamber; 5-buffer chamber. J ₁ , J ₂ , and J ₃ are the outlets communicating with the outer tube, the middle tube, and the inner tube respectively.

Four, the best embodiment of the present invention

Accompanying drawing 5 is a best embodiment of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention. It consists of two parts, a curvature graded pipe (2) and a flow divider (9). Through flange (4), (14), connect as a whole by bolt (5) between them. The curvature grading pipe (2) is a section of garden arc elbow, the curvature radius is constant, the garden arc angle θ=90°, and the flow cross section is rectangular. The shape of the feed port of the flow divider (9) is compatible with the shape of the discharge port (B) of the curvature grading pipe (2), which is also rectangular. The flow divider (9) divides the curvature grading pipe (2) into two flow pipes, the outer pipe (10) and the inner pipe (13), along the direction of the radius of curvature (Y axis) at the discharge port (B). The outer pipe (10) is connected with the coarse-grained, heavy and high-concentration material flow layer at the outer pipe wall (15) of the curvature grading pipe (2), and the inner pipe (13) and the curvature grading pipe (2) are discharged The medium fluid at the pipe wall (3) inside the mouth is in contact with the fine-grained, light-weight and low-concentration material fluid. Therefore, what the outer pipe (10) of the "high-efficiency energy-saving weak wear curvature classifier" diverter of the present invention diverts will be the high-concentration material fluid with a coarser particle size and higher density, and what the inner pipe (13) diverts will be medium fluid and particle size. A finer, less dense material fluid with low concentration. The buffer chamber (8) is used to reduce the velocity of the fluid in the outer pipe (10), so as to reduce the impact and wear of the material on the pipe. The bolt holes on the flanges (4), (14) are made into long waist-shaped holes along the curvature radius direction (Y axis) at the outlet (B) of the curvature graded pipe (2), and the connecting bolts (5) can be loosened according to actual needs. ) Adjust the flow divider (9) up and down along the length direction of the waist-shaped hole to change the openings δ ₁ and δ ₂ of the outer tube (10) and inner tube (13) to obtain a more satisfactory grading effect.

Claims (3)

1. "High-efficiency energy-saving weak wear curvature classifier" is a fluid machine used for classification, desliming, concentration, dust removal and other operations in metallurgy, mining, petroleum, chemical industry, building materials, electric power, food and other fields. It consists of two parts, the curvature grading pipe (2) and the flow divider (9). Through flange (4), (14) link as one (also can be made into one) by bolt (5) between them. It is characterized in that: the curvature grading pipe (2) is a section of curved pipe. It uses the characteristics of inertial centrifugal force and radial resistance produced when materials with different particle sizes and densities move in a curve, so that the mixed fluid passing through the curvature grading tube can be classified according to the different particle sizes and densities along the direction of the radius of curvature (stratification) ), so that coarse-grained and heavy materials stick to the outer tube wall (15) with a larger radius of curvature and form a material layer with a certain thickness (δ1) at the outlet (B); medium fluid and some fine-grained, light The material is on the inner side with the smaller radius of curvature. The material inlet of the flow divider (9) is connected with the material outlet (B) of the curvature grading pipe (2). The flow divider (9) divides the curvature grading pipe (2) into two flow pipes—the outer pipe (10) and the inner pipe (13)—along the direction of the radius of curvature at the outlet (B) of the curvature grading pipe (2). The outer pipe (10) is connected with the coarse-grained, heavy and high-concentration material flow layer (δ ₁ ) at the outer pipe wall (15) of the curvature grading pipe (2), and the inner pipe (13) and the curvature grading pipe ( 2) The medium fluid at the inner pipe wall (3) of the discharge port is connected with the flow layer (δ ₂ ) of fine-grained, light-weight and low-concentration material. Therefore, what the outer tube (10) of the "high-efficiency energy-saving weak wear curvature classifier" of the present invention diverts will be the high-concentration material fluid with coarser particle size and higher density, and what the inner tube (13) divides will be the medium. Fluid and some low-concentration material fluids with fine particle size and low density. The bolt holes on the coupling flanges (4) and (14) between the curvature grading pipe (2) and the flow divider (9) are made into a long waist shape along the curvature radius direction at the outlet (B) of the curvature grading pipe (2) hole, loosening the connecting bolt (5) can translate the whole diverter (9) along the length direction of the waist hole to change the opening δ ₁ and δ ₂ of the outer tube (10) and inner tube (13), so that A more satisfactory grading effect can be obtained to meet the requirements of the production process. 2. According to claim 1, the feature of "high-efficiency, energy-saving and weak-wear curvature classifier" is: the arc angle θ of the curvature grading pipe (2) can be any value; the radius of curvature can be a constant, or vary with the angle θ The cross-sectional shape of the flow can be arbitrary. 3. The "high-efficiency energy-saving weak wear curvature classifier" according to claim 1 is characterized in that: the flow divider (9) can divide the flow divider into two or more along the radius of curvature direction at the outlet (B) of the curvature classification pipe (2) The flow tube is used to make a multi-product "high-efficiency energy-saving weak wear curvature classifier". The direction of the outlet of the splitter can be arranged arbitrarily.

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