Zhang Wei, Tu Guangbei, Wen Baolian (School of Environmental Engineering, Tianjin University, Tianjin 300072)
1 Principle of gas centrifuge Centrifuge is widely used in national defense and civil industry. Figure 1 is a schematic diagram of the structure of X-type gas centrifuge. The outer sleeve of the centrifuge is stationary, and the inner cylinder is also a rotating drum, which is rotated at a high speed under the driving of the motor, and drives the mixed gas in the cylinder 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 formed in the upper portion of the inner wall of the outer cylinder. When the inner cylinder rotates, the gas in the gap between the two cylinders is rotated together. Under the action of the spiral groove, the gas is discharged to the top, and then flows into the center of the drum (the center pressure of the drum is very low) and is withdrawn along with the material. The mixed gas to be separated is supplied to the center of the drum from the supply pipe. Due to the different molecular weights, the light and heavy components change radially along the drum. As a result, the closer to the axis of the drum, the higher the proportion of light components (relative to the mixed gas for the human being); Near the side wall of the drum, the proportion of heavy components is higher. The separated gas is taken out separately by a stationary light and heavy component extractor. In order to comb the flow pattern to improve the separation efficiency, a rectifying plate is added at both ends of the rotating drum, and the rectifying plate is bonded to the rotating drum.
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When the centrifuge is under no load, the energy consumption is mainly composed of the friction loss of the outer wall of the drum and the upper and lower end caps (close to the vacuum in the cylinder before feeding). After the load (feeding), two reclaimers and cylinders are generated. Friction loss of internal gas. The energy consumption of the reclaimer 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 equivalent disk theory and its application equivalent disk theory
It was first proposed by the Italian scholars cenedese and cunsolo to study the energy loss caused by slender obstacles in the strong cyclonic field. According to the model, it is assumed that the pressure distribution in the radial direction of the gas in the cylinder is distributed according to the same exponential law and is extended to the side wall by the known central pressure. For qualitative research, this assumption greatly simplifies the calculation and does not affect the correctness of the conclusion. However, it is obviously not accurate enough for quantitative calculation, it is difficult to meet the precision required for research work and actual engineering, and it is larger than the actual centrifuge. Therefore, combined with the actual centrifuge structure, the derivation was re-implemented and the calculation model was improved.
Referring to the above model, it is assumed that the structure and velocity distribution of the centrifuge take-up chamber (the portion between the rectifying plate and the upper and lower end caps of the drum) are as shown in Fig. 2 and Fig. 3, where ra is the radius of the drum and d is the reclaimer. Diameter, b is the distance from the centerline of the reclaimer to the end cap (or rectifying plate) (the reclaimer is located in the middle of the reclaiming chamber). In the reclaiming chamber, the blocker's blocking effect on the indoor gas is equivalent to the isothermal rigid body of the drum at the angular velocity of βw (for the speed coefficient, w is the angular velocity of the drum) and the drum. A rotating gas disk with a radius of the retractor radial length rp. Within the disc, a constant value, and between the edge of the disc and the side wall, the gas angular velocity coefficient increases linearly to 1 (as shown in Figure 3). The speed is linearly distributed between the disc and the end cap and the rectifying plate, as shown in the left side of Fig. 2, showing the axial velocity distribution at a certain point.
Ignore the suction of the take-up port. Under steady conditions, there is a torque balance in the take-up chamber:
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According to this equilibrium equation, after the geometric parameters and the working conditions of the rotating speed, medium, temperature, pressure, etc. are given, the speed coefficient β can be determined by an iterative method, and then the loss is obtained by using the formula (2).
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2.1 Retractor torque calculation
2.1.1 Calculation of Frictional Resistance Torque of Reclaimer Since the reclaimer is curved, the method of calculating the resistance of the yaw cylinder in aerodynamics is used to solve the frictional resistance of the reclaimer. At this time, the normal force and the tangential force acting on the d-micro-element are:
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2.1.2 Calculation of shock resistance torque In the high-speed gas centrifuge, the end of the reclaimer is close to the inner wall of the drum, and the airflow speed is very high, which can reach several times the speed of sound (different media, the sound speed varies greatly at normal temperature) Through the smear photograph of the model in the wind tunnel of the x-type gas centrifuge reclaimer, a de-shock shock wave can be clearly seen, and according to the gas dynamics, the energy loss is calculated according to the positive shock wave:
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2.2 Calculation of the acceleration torque of the take-up chamber
2.2.1 Calculation of the acceleration torque of the side wall of the drum According to the model, it can be approximated that the side wall is in a gas flow with a relative velocity of (1-β)νω, and the flow is laminar, so that the frictional moment of the side wall for:
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3 Calculation of energy consumption of different reclaimers Under the premise of knowing the geometric parameters of the reclaimer and the pressure of the reclaiming port. Through iteration, the speed coefficient can be calculated. First set the interval, let β ∈ [O, 1], take the interval median β 1/2 with human (1), compare the two sides of the equation, if the resistance torque is less than the acceleration torque, it indicates that β 1/2 is small, β should If it is greater than the median, change the lower limit of the interval to β1/2/ (otherwise, change the upper limit to island?), and then take the median value of the interval. Continue the comparison according to the above method until the accuracy is satisfied. Then calculate the energy consumption of the reclaimer. In the calculation, the pressure at the take-up port is used as the post-wave stagnation pressure, and then the wave front is reversed according to the shock theory to obtain the pressure distribution. As mentioned above, the proportion of the reclaimer in the total energy consumption of the centrifuge is very large, so it is of great significance to optimize its design.
The design of the actual reclaimer should consider many factors, and the energy consumption should be small. If it is to ensure stable reclaiming and high-efficiency separation, it must withstand the strong impact of high-speed airflow without vibration. That is to meet the stiffness requirements.
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Figure 4 is a development view of three different reclaimers. The A reclaimer has an equal section, B is an equal taper variable section, and C is a variable section from the middle. The energy consumption calculation is performed according to the equivalent model. difference.
Calculation parameter selection:
The medium has a temperature of 320 K for C1F14 and a semi-circular shape for the reclaimer. The line speed of the simple side wall is 475 m/s, r is 125, rp is 1 20, and b is 35. The calculation results are shown in Table 1.
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It can be seen from Table 1 that the A reclaimer consumes a large amount of energy at the same pressure, and B and C are similar. This is because the energy consumption of the reclaimer mainly comes from the head. In the loss caused by the reclaimer, the shock loss is In most working conditions, a large proportion is occupied. Under the premise of ensuring the amount of material to be taken, the head area should be minimized. In the friction loss, the tangential friction loss is mainly used, and the normal friction loss is smaller. According to the analysis, the tangential wear is mainly caused by the vicinity of the mouth of the reclaimer, because the tangential velocity component of this area is large and the pressure is also large, while the normal wear is mainly generated by the middle and rear parts of the reclaimer. In the strong swirl field, under the action of centrifugal force, the material is smashed to the side wall, the middle of the drum is close to the vacuum, the density is extremely low, and the loss is also low. The lower the pressure in the centrifuge take-up chamber, the greater the speed coefficient, because the lower the pressure, the thinner the gas in the drum, and the smaller the disturbance of the forward airflow from the reclaimer.
For this reason, the C retractor is preferred in terms of the preparation of the reclaimer, the installation process, and the rigidity and energy consumption of the root.
4 Conclusions This model is mainly proposed for high-speed gas centrifuges. It has great guiding significance for the optimization design of centrifuges, and its ideas have certain reference value for other types of centrifuges. It can be seen from the calculation results that in the high-speed gas centrifuge, the shock loss of the head of the reclaimer accounts for the majority of the total energy consumption of the reclaimer. This is followed by tangential wear near the ends. Therefore, the key to reducing the energy consumption of the reclaimer is the end portion. The method of reducing the diameter of the head and cutting the angle to reduce the shock intensity is an effective measure, but this is only from the perspective of energy consumption. Considering that in the actual centrifuge, it is necessary to comprehensively consider the stability of the flow field, separation efficiency, economy and many other factors.
1 Principle of gas centrifuge Centrifuge is widely used in national defense and civil industry. Figure 1 is a schematic diagram of the structure of X-type gas centrifuge. The outer sleeve of the centrifuge is stationary, and the inner cylinder is also a rotating drum, which is rotated at a high speed under the driving of the motor, and drives the mixed gas in the cylinder 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 formed in the upper portion of the inner wall of the outer cylinder. When the inner cylinder rotates, the gas in the gap between the two cylinders is rotated together. Under the action of the spiral groove, the gas is discharged to the top, and then flows into the center of the drum (the center pressure of the drum is very low) and is withdrawn along with the material. The mixed gas to be separated is supplied to the center of the drum from the supply pipe. Due to the different molecular weights, the light and heavy components change radially along the drum. As a result, the closer to the axis of the drum, the higher the proportion of light components (relative to the mixed gas for the human being); Near the side wall of the drum, the proportion of heavy components is higher. The separated gas is taken out separately by a stationary light and heavy component extractor. In order to comb the flow pattern to improve the separation efficiency, a rectifying plate is added at both ends of the rotating drum, and the rectifying plate is bonded to the rotating drum.
When the centrifuge is under no load, the energy consumption is mainly composed of the friction loss of the outer wall of the drum and the upper and lower end caps (close to the vacuum in the cylinder before feeding). After the load (feeding), two reclaimers and cylinders are generated. Friction loss of internal gas. The energy consumption of the reclaimer 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 equivalent disk theory and its application equivalent disk theory
It was first proposed by the Italian scholars cenedese and cunsolo to study the energy loss caused by slender obstacles in the strong cyclonic field. According to the model, it is assumed that the pressure distribution in the radial direction of the gas in the cylinder is distributed according to the same exponential law and is extended to the side wall by the known central pressure. For qualitative research, this assumption greatly simplifies the calculation and does not affect the correctness of the conclusion. However, it is obviously not accurate enough for quantitative calculation, it is difficult to meet the precision required for research work and actual engineering, and it is larger than the actual centrifuge. Therefore, combined with the actual centrifuge structure, the derivation was re-implemented and the calculation model was improved.
Referring to the above model, it is assumed that the structure and velocity distribution of the centrifuge take-up chamber (the portion between the rectifying plate and the upper and lower end caps of the drum) are as shown in Fig. 2 and Fig. 3, where ra is the radius of the drum and d is the reclaimer. Diameter, b is the distance from the centerline of the reclaimer to the end cap (or rectifying plate) (the reclaimer is located in the middle of the reclaiming chamber). In the reclaiming chamber, the blocker's blocking effect on the indoor gas is equivalent to the isothermal rigid body of the drum at the angular velocity of βw (for the speed coefficient, w is the angular velocity of the drum) and the drum. A rotating gas disk with a radius of the retractor radial length rp. Within the disc, a constant value, and between the edge of the disc and the side wall, the gas angular velocity coefficient increases linearly to 1 (as shown in Figure 3). The speed is linearly distributed between the disc and the end cap and the rectifying plate, as shown in the left side of Fig. 2, showing the axial velocity distribution at a certain point.
Ignore the suction of the take-up port. Under steady conditions, there is a torque balance in the take-up chamber:
According to this equilibrium equation, after the geometric parameters and the working conditions of the rotating speed, medium, temperature, pressure, etc. are given, the speed coefficient β can be determined by an iterative method, and then the loss is obtained by using the formula (2).
2.1 Retractor torque calculation
2.1.1 Calculation of Frictional Resistance Torque of Reclaimer Since the reclaimer is curved, the method of calculating the resistance of the yaw cylinder in aerodynamics is used to solve the frictional resistance of the reclaimer. At this time, the normal force and the tangential force acting on the d-micro-element are:
2.1.2 Calculation of shock resistance torque In the high-speed gas centrifuge, the end of the reclaimer is close to the inner wall of the drum, and the airflow speed is very high, which can reach several times the speed of sound (different media, the sound speed varies greatly at normal temperature) Through the smear photograph of the model in the wind tunnel of the x-type gas centrifuge reclaimer, a de-shock shock wave can be clearly seen, and according to the gas dynamics, the energy loss is calculated according to the positive shock wave:
2.2 Calculation of the acceleration torque of the take-up chamber
2.2.1 Calculation of the acceleration torque of the side wall of the drum According to the model, it can be approximated that the side wall is in a gas flow with a relative velocity of (1-β)νω, and the flow is laminar, so that the frictional moment of the side wall for:
3 Calculation of energy consumption of different reclaimers Under the premise of knowing the geometric parameters of the reclaimer and the pressure of the reclaiming port. Through iteration, the speed coefficient can be calculated. First set the interval, let β ∈ [O, 1], take the interval median β 1/2 with human (1), compare the two sides of the equation, if the resistance torque is less than the acceleration torque, it indicates that β 1/2 is small, β should If it is greater than the median, change the lower limit of the interval to β1/2/ (otherwise, change the upper limit to island?), and then take the median value of the interval. Continue the comparison according to the above method until the accuracy is satisfied. Then calculate the energy consumption of the reclaimer. In the calculation, the pressure at the take-up port is used as the post-wave stagnation pressure, and then the wave front is reversed according to the shock theory to obtain the pressure distribution. As mentioned above, the proportion of the reclaimer in the total energy consumption of the centrifuge is very large, so it is of great significance to optimize its design.
The design of the actual reclaimer should consider many factors, and the energy consumption should be small. If it is to ensure stable reclaiming and high-efficiency separation, it must withstand the strong impact of high-speed airflow without vibration. That is to meet the stiffness requirements.
v
Figure 4 is a development view of three different reclaimers. The A reclaimer has an equal section, B is an equal taper variable section, and C is a variable section from the middle. The energy consumption calculation is performed according to the equivalent model. difference.
Calculation parameter selection:
The medium has a temperature of 320 K for C1F14 and a semi-circular shape for the reclaimer. The line speed of the simple side wall is 475 m/s, r is 125, rp is 1 20, and b is 35. The calculation results are shown in Table 1.
It can be seen from Table 1 that the A reclaimer consumes a large amount of energy at the same pressure, and B and C are similar. This is because the energy consumption of the reclaimer mainly comes from the head. In the loss caused by the reclaimer, the shock loss is In most working conditions, a large proportion is occupied. Under the premise of ensuring the amount of material to be taken, the head area should be minimized. In the friction loss, the tangential friction loss is mainly used, and the normal friction loss is smaller. According to the analysis, the tangential wear is mainly caused by the vicinity of the mouth of the reclaimer, because the tangential velocity component of this area is large and the pressure is also large, while the normal wear is mainly generated by the middle and rear parts of the reclaimer. In the strong swirl field, under the action of centrifugal force, the material is smashed to the side wall, the middle of the drum is close to the vacuum, the density is extremely low, and the loss is also low. The lower the pressure in the centrifuge take-up chamber, the greater the speed coefficient, because the lower the pressure, the thinner the gas in the drum, and the smaller the disturbance of the forward airflow from the reclaimer.
For this reason, the C retractor is preferred in terms of the preparation of the reclaimer, the installation process, and the rigidity and energy consumption of the root.
4 Conclusions This model is mainly proposed for high-speed gas centrifuges. It has great guiding significance for the optimization design of centrifuges, and its ideas have certain reference value for other types of centrifuges. It can be seen from the calculation results that in the high-speed gas centrifuge, the shock loss of the head of the reclaimer accounts for the majority of the total energy consumption of the reclaimer. This is followed by tangential wear near the ends. Therefore, the key to reducing the energy consumption of the reclaimer is the end portion. The method of reducing the diameter of the head and cutting the angle to reduce the shock intensity is an effective measure, but this is only from the perspective of energy consumption. Considering that in the actual centrifuge, it is necessary to comprehensively consider the stability of the flow field, separation efficiency, economy and many other factors.
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