The application of equivalent disc theory to the optimum design of the feeder of gas centrifuge

Zhang Wei, Tu Guangbei, Wen Baolian (School of environmental engineering, Tianjin University, Tianjin 300072) 1 gas centrifuge principle centrifuge is widely used in national defense and civil industry Figure 1 is the structure diagram of X-type gas centrifuge The outer casing of the centrifuge is stationary, and the inner casing is the rotating casing Driven by the motor, it rotates at high speed, and drives the mixed gas in the casing to rotate together In order to reduce the friction loss between the outer wall of the inner cylinder and the gas, a spiral groove is arranged on the upper part of the inner wall of the outer cylinder When the inner cylinder rotates, it drives the gas in the gap between the two cylinders to rotate together Under the action of the spiral groove, the gas is discharged to the top, and after Zui flows into the center of the rotating cylinder (the pressure in the center of the rotating cylinder is very low), it is pumped along with the material The mixed gas to be separated is supplied to the drum center by the feed pipe Due to the different molecular weight, the distribution of light and heavy components changes along the radial direction in the rotating cylinder The result is: the closer to the rotating cylinder axis, the higher the proportion of light components (relative to the mixed gas for human supply); the closer to the side wall of the rotating cylinder, the higher the proportion of heavy components The separated gas is taken out by the static light and heavy separator In order to comb the flow pattern and improve the separation efficiency, a rectifier plate is added at both ends of the rotary cylinder, and the rectifier plate is bonded with the rotary cylinder When the centrifuge is unloaded, the energy consumption is mainly composed of the friction loss of the outer wall of the drum and the upper and lower covers (close to the vacuum in the drum before feeding) After loading (feeding), the friction loss of two reclaimers and the gas in the drum is produced The share of energy consumption of the feeder in the centrifuge is very high, and it also directly affects the separation effect Therefore, it is necessary to focus on research and analysis 2 The theory of equivalent disk and its application the theory of equivalent disk was first proposed by cenedese and cunsolo, the Italian scholars, to study the energy loss caused by slender obstacles in the strong swirling flow field According to the model, it is assumed that the radial pressure distribution of the gas in the cylinder is in accordance with the same exponential law, and it is extended to the sidewall through the known central pressure For the qualitative research, this assumption greatly simplifies the calculation and does not affect the correctness of the conclusion However, for the quantitative calculation, it is obviously not accurate enough to meet the accuracy required by the research work and the actual project Moreover, it is quite different from the actual centrifuge For this reason, combining with the actual centrifuge structure, this paper deduces again and improves the calculation model With reference to the above model, it is assumed that the structure and speed distribution of the centrifuge reclaiming chamber (the part between the rectifier plate and the upper and lower end covers of the drum) are as shown in Figure 2 and figure 3 In the figure, RA is the radius of the drum, D is the diameter of the reclaimer, and B is the distance from the center line of the reclaimer to the end cover (or the rectifier plate) (the reclaimer is located in the middle of the reclaiming chamber) In the reclaiming chamber, the blocking effect of the reclaimer on the indoor gas is equivalent to a gas disk with β w (velocity coefficient, W is the rotating cylinder angular velocity) angular velocity and the rotating cylinder coaxial as the isothermal rigid body rotation on the plane where the reclaimer is located The radius of the disk is the radial length RP of the reclaimer Within the disk, it is a fixed value, while between the edge of the disk and the side wall, the gas angular velocity coefficient increases linearly to 1 (as shown in Figure 3) However, between the disk and the end cover and the rectifier plate, the speed is linearly distributed, as shown in the left side of Figure 2, and a schematic diagram of axial speed distribution is given Neglecting the suction of the reclaiming port, there is a moment balance in the reclaiming chamber under the stable working condition: according to this balance equation, given the geometric parameters and the working conditions such as rotating speed, medium, temperature and pressure of the drum, the velocity coefficient β can be determined by the iterative method, and then the losses can be obtained by equation (2) 2.1 calculation of the resistance moment of the feeder 2.1.1 calculation of the friction resistance moment of the feeder since the feeder is arc-shaped, the calculation method of the resistance of the yaw cylinder in aerodynamics is used here to solve the friction resistance of the feeder At this time, the normal and tangential forces acting on the d-element are: 2.1.2 calculation of shock resistance moment In the high-speed gas centrifuge, the end of the feeder is close to the inner wall of the drum, and the air flow speed is very high, which can reach several times of the speed of sound (different media, the speed of sound varies greatly at room temperature) Through the schlieren photos of the model in the X-type gas centrifuge feeder wind tunnel, we can clearly see a detached shock wave According to the aerodynamics, we can calculate the energy loss according to the positive shock wave: 2.2 calculation of the acceleration moment of the reclaiming chamber The velocity coefficient can be calculated by iteration on the premise that the geometric parameters of the reclaimer and the pressure of the reclaimer are known First set the interval, make β ∈ [O, 1], take the median β 1 / 2 of the interval with formula (1), compare the two sides of the equation, if the resistance moment is less than the acceleration moment, it indicates that β 1 / 2 is smaller, β should be greater than the median, then change the lower limit of the interval to β 1 / 2 / (otherwise, change the upper limit to island?), then take the median of the interval, and continue to compare according to the above method until the accuracy is met Then, the energy consumption of the reclaimer is calculated In the calculation, the pressure at the reclaimer port is used as the stagnation pressure behind the wave, and then the wave front is pushed back according to the shock theory to obtain the pressure distribution As mentioned before, the proportion of the feeder in the total energy consumption of the centrifuge is very large, so it is of great significance to optimize its design Many factors should be considered in the design of the actual feeder, and the energy consumption should be small For example, to ensure the stable reclaiming, the separation of rate, to withstand the strong impact of high-speed airflow without vibration, that is to say, to meet the rigidity requirements V Fig 4 is the unfolded drawing of three different kinds of feeders A is the constant cross section, B is the constant taper variable cross section, and C is the variable cross section starting from the middle Next, the energy consumption will be calculated according to the equivalent model, and the differences will be compared Selection of calculation parameters: the medium is c1f14, the temperature is 320 K, the shape line of the feeder is semicircle, the linear speed of the simplified side wall is 475 M / s, R is 125, RP is 120, B is 35, and the calculation results are shown in Table 1   It can be seen from table 1 that the energy consumption of a feeder is large under the same pressure, and B and C are similar, because the energy consumption of the feeder mainly comes from the head In the loss caused by the feeder, the shock loss accounts for a large proportion in most working conditions On the premise of guaranteeing the quantity of material taken, the head area should be reduced as much as possible; in the friction loss, the tangential friction loss is the main factor, and the normal friction loss Smaller The analysis shows that the tangential wear is mainly caused by the part near the mouth of the feeder, because the tangential velocity component Zui in this area is large and the pressure Zui is large, while the normal wear is mainly caused by the middle and rear part of the feeder In the strong swirling flow field, under the action of centrifugal force, the material is thrown near the side wall, the middle part of the rotary cylinder is close to the vacuum, the density is very low, and the resulting loss is also low The lower the pressure and the larger the velocity coefficient are in the reclaiming chamber of the centrifuge, because the lower the pressure is, the thinner the gas in the drum is, and the smaller the disturbance of the reclaimer to the air flow in front is Therefore, from the aspects of the production and installation process of the feeder, as well as the protection of its root stiffness and energy consumption, C feeder is considered comprehensively 4 Conclusion this model is mainly proposed for high-speed gas centrifuge, which has great guiding significance for the optimal design of centrifuge, and its idea has certain reference value for other forms of centrifuge It can be seen from the calculation results that in the high-speed gas centrifuge, the shock loss at the head of the feeder accounts for the majority of the total energy consumption of the feeder, followed by the tangential wear near the end Therefore, the key to reduce the energy consumption of the reclaimer lies in its end It is an effective measure to reduce the shock wave strength by means of head reducing, angle cutting, etc., but this is only considered from the perspective of energy consumption In the actual centrifuge, many factors such as the stability of the flow field, separation efficiency, economy and so on should be considered comprehensively.