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A new volute design method for the turbo air classifier
Powder Technology 348 (2019) 65–69
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Short communication
A new volute design method for the turbo air classifier Yuan Yu a, Wenjing Ren b, Jiaxiang Liu c,⁎ a b c
College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaan'xi, China Beijing Key Laboratory of Electrochemical Process and Technology for Materials, Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 10 December 2018 Received in revised form 5 March 2019 Accepted 8 March 2019 Available online 12 March 2019 Keywords: Turbo air classifier Volute profile Logarithmic spiral Volute design method
a b s t r a c t Volute profile plays an important role in guiding the airflow for a turbo air classifier. The traditional volute design is based on the method of analogue and there is a lack of uniform theoretical design basis and guidance. To meet the needs of guiding the airflow better, a logarithmic spiral volute design method is put forward based on the analyses of airflow motion in the volute and classification characteristics of the turbo air classifier. The numerical simulations on flow field distribution in the turbo air classifier show that the logarithmic spiral volute has a good effect on guiding the airflow and can form a well-distributed flow field in the classifier, which is conducive to improve the classification performance. The single particle trajectory verifies that the logarithmic spiral volute makes the airflow flow along the guide vanes circumferentially uniformly, forming a well-distributed flow field in the annular region of the classifier. So the classification results for the particles with the same size are in correspondence when the logarithmic spiral volute is applied. The numerical simulations of both gas phase and discrete phase indicate that the logarithmic spiral volute can provide a well-distributed flow field for the classification and this volute deign method for turbo air classifier is feasible. © 2019 Published by Elsevier B.V.
1. Introduction The turbo air classifier is widely used in the fields of fine chemical industry, ceramic and composite material manufacturing due to its simple structure and adjustable operating parameters [1–4]. In recent years, with the development of powder technology, the performance of the classifier has been continuously improved, especially in the refinement and narrow distribution fields. The separation of coarse and fine particles is implemented in the turbo air classifier under the influence of the airflow field which influences classification performance of the classifiers directly. When the operating parameters are constant, the classifier structure determines the flow field distribution, even the classification performance. Comparing to the airflow distribution using positive bending, reverse bending and straight guide vanes, Huang Qiang concluded that the positive bending blades can reduce the swirl in the blade passages of the rotor cage, making the flow field welldistributed, improving classification accuracy, as well as reducing the cut size [5]. Liu Rongrong pointed out that the axial guide vanes with 2.5° are favorable to keep the flow field well-distributed and the ⁎ Corresponding author. E-mail address: [email protected] (J. Liu).
https://doi.org/10.1016/j.powtec.2019.03.015 0032-5910/© 2019 Published by Elsevier B.V.
classification force field is enhanced to improve the dispersion of the powders, which leads to an improved classification performance [6]. Sun Zhanpeng compared and analyzed the effect of air-inlet direction on the performance of classifier through powder classification experiments [7]. Zhao Dongmei did some researches on the influences of material feeding types on the classification performance [8]. Hideto Yoshida improved the air inlet structure of the cyclone separator and the new inlet provided a smaller cut size and a higher classification accuracy [9]. At present, the structure improvement of classifier is mainly focused on the rotor cage, guide vanes and spreading plate. However, there are few reports on the volute of the turbo air classifier. Before the air flows into the annular classification region, it will pass through the volute firstly. The structure of the volute determines the distribution of the airflow, the stability of the flow field and the classification performance. Since there is a lack of clear design method for the volute, the analogy method is often used to determine the volute profile of a turbo air classifier. The common volute profile types include involute, multi-arcs and approximate logarithmic spiral. However, in the turbine machinery such as centrifugal blower and gas turbine compressor, there is a set of complete volute design theory to standardize industrial applications [10]. In this paper, the volute design theory of turbine is
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Y. Yu et al. / Powder Technology 348 (2019) 65–69
Nomenclature a b θ ∅0 φ Q q'φ qφ R Rh Vt Vht V0 Vhr′ δ n1 Vht′
width of the volute (mm) height of the volute (mm) setting angle of the guide vanes (°) tongue angle (°) direction angle (°) inlet air volumetric flow rate (m3/s) air volumetric flow rate passing through the section of AB (m3/s) air volumetric flow rate passing through the section AC (m3/s) radius of the located fluid element (m) radius of the outer edge of the guide vanes (m) tangential velocity of the fluid element with radius R (m/s) tangential velocity of the fluid element with radius Rh (m/s) air inlet velocity (m/s) air radial velocity at the outer edge of guide vanes (m/s) thickness of the guide vanes(m) number of the guide vanes air tangential velocity at the outer edge of guide vanes (m/s)
introduced and applied to the turbo air classifier, combining its classification characteristics. A logarithmic spiral volute design method for the turbo air classifier is proposed. The well-distributed flow field of the air turbo classifier with the logarithmic spiral volute is feasible to improve the classification performance. 2. Theoretical design of volute 2.1. The formula derivation of volute profile The structural scheme of the turbo air classifier used in the present study is shown in Fig. 1. Under central negative pressure, the airflow enters the annular classification region through the guide vanes from two horizontally symmetrical airflow inlets, forming a rotating velocity field. At the same time, the powder materials to be classified are fed onto the feeding plate, which is rapidly rotating together with the rotor cage. The particles are thrown outward into the annular region, which is a cylindrical space between the outer edge of the rotor cage and the inner edge of the guide vanes. The powder materials are separated into coarse and fine powder under the air drag force, centrifugal force and gravity.
The centrifugal force on the fine particle is smaller than the air drag force. As a result, it will be drawn into the rotor cage with the airflow and be collected as the fine powder. The centrifugal force on the coarse particle is greater than the air drag force. Therefore it will move outside and collide with the guide vane or the volute, falling into the cone collector. Finally they are collected as the coarse powder. After the air enters the classifier from the airflow inlets, firstly, it passes through the volute. Therefore the volute plays an important role on the flow field distribution in the annular region. In order to improve the classification performance, the flow field of annular region should be well-distributed circumferentially, to ensure that the effects of the flow field on the same particles in different circumferential positions are same, conducive to improve the classification performance. The volute of the turbo air classifier includes the airflow inlet and the volute, the cross-section of the volute in turbo air classifier is shown in the Fig. 2. It is a centrosymmetric structure and there are two airflow inc and a0b0 d are the volute profile. The seclets: 1# and 2#. The section ab c and c0b0 d are airflow inlet straight channel. The dotted circle tion cb represents the section circle of the outer edge of the guide vane, dec (and a′ on a0b0) d is called the noted by Circle_M. The start point a on ab tongue and ∅0 is the tongue angle. In the prototype classifier, the volute profile is an involute. In order to design a reasonable volute profile to improve its flow-guiding effect, the motion of airflow in the turbo air classifier should be analyzed firstly. The motion of airflow in the classifier is shown in Fig. 3. The dotted arc is a part of cross-section line of the outer edge of the guide vanes, the solid c is the airflow particle's trajectory. The angle φ is defined as curve of BC the direction angle of airflow at the point B, which the angle between OC and OB. The flow will just pass by the C point when φ = 0. Suppose the inlet air volumetric flow rate is Q, the air volumetric flow rate passing through section AB is q'φ and the air volumetric flow rate passing through flow-guiding section AC is qφ which is coming from the section AB. Considering the centrosymmetric structure of the classifier, to achieve the well-distributed air flow circumferentially, a reasonable volute profile should ensure that the airflow enters the guide vanes passageway circumferentially uniformly, and it can be concluded as: qφ = Qφ/2π. In this case, when the amount of air flow from single airflow inlet is equal to that passing half of Circle_M (φ = 0~π), that is qφ = q'φ, mixed airflow in the volute from the two airflow inlets would be avoided and the stability of the flow field would be ensured, thus the volute profile should be: q0φ ¼ qφ ¼ Q
φ 2π
Fig. 1. The schematic diagram of a turbo air classifier.
ð1Þ
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Since steady-state and transient-state simulation results for this turbo air classifier model are in good agreement, the airflow streamline is approximated to the airflow's motion trajectory. It can be concluded that the airflow streamline in the volute should meet the logarithmic spiral line expressed in formula (6). Therefore, a volute with the profile of logarithmic spiral line will ensure a perfect guiding effect. When the operating condition is determined, the R corresponding to each φ can be calculated, so the position coordinates of the points on the airflow's motion trajectory can be obtained. The volute profile can be obtained by fitting these points. Since the change of the volute profile will change the cross section of the inlet, the inlet air volumetric flow rate is used in this paper, which is: Q ¼ 2abV 0 Fig. 2. The cross–section of the volute in a turbo air classifier.
The whole section of AB is filled with effective airflow and the total amount is: Z q0φ ¼
R
bV t dr Rh
ð2Þ
Where R– radius of the located fluid element (m); Rh– radius of the outer edge of the guide vanes (m); Vt– tangential velocity of the fluid element with radius R (m/s); b– height of the volute (m). Ignoring the influence of friction, the airflow in the volute is not subjected to the external force and is accorded with the law of conservation of moment of momentum, there is: Rh V ht ¼ RV t ¼ constant
ð3Þ
Where Vht – tangential velocity of the fluid element with radius Rh (m/s). Combining formula (3) and (2), there is: q0φ
Z ¼
R
Rh
R V R b h ht dR ¼ bRh V ht ln Rh R
ð4Þ
R can be expressed as: q0φ
ð5Þ
R ¼ Rh ebRh V ht
Combining formula (1) and (5), the airflow streamline equation in the volute can be obtained: Q
R ¼ Rh e2πbRh V ht
φ
ð6Þ
ð7Þ
Where a, b– width and height of volute; V0– air inlet velocity. In the prototype structure, a is 0.062 m, b is 0.096 m, and the air inlet velocity V0 is 12 m/s. So the design conditions are: rotor's rotating speed is 1200 r/min and the inlet air volumetric flow rate Q is 0.1428 m3/s. 2.2. The calculation of volute profile According to mass conservation law, air volume is Q in the classifier. ′ after entering the guide vanes passageway can The air radial velocity Vhr be calculated by formula (8): Q V 0hr ¼ δ n1 b 2πRh − sinθ
ð8Þ
Where δ– the thickness of guide vanes, δ = 0.002 m; n1– the number of guide vanes, n1 = 24; θ– setting angle of the guide vanes, θ = 15; Rh– the radius of the outer edge of the guide vanes, Rh = 0.142 m. The tangential velocity of the air at the outer edge guide vanes is: V 0ht ¼ V 0hr cotθ
ð9Þ
′ and Vht ′ , they can be calculated Then according the expression of Vhr and Vhr ′ = 2.11 m/s and Vht ′ = 7.86 m/s. And the volute profile can be obtained as: Q
φ
7:142410‐2
R ¼ Rh e2πbRh V ht ¼ Rh eπ0:0960:1427:86φ ¼ Rh e0:212φ
ð10Þ
0, π/6, π/3, π/2, 2π/3, 5π/6 and π are assigned to φ in order to calculate the volute profile points, and the outputs are listed in Table 1. Keeping unchanged prototype volute tongue angle ∅0, the start point of the volute profile is determined. These points on the volute profile are fitted in sequence, and the logarithmic spiral volute which is suitable to the airflow characteristics can be obtained. The comparison of the cross section of the prototype volute and the calculated logarithmic spiral volute is shown in Fig. 4. 3. Numerical simulation and analysis To simulate the distribution of flow field in the turbo air classifier with this logarithmic spiral volute, Gambit 2.2.30 and ANSYS-FLUENT 17.0 were used to establish the model of a turbo air classifier and simulate its inner airflow field. The model was designed to describe the main classification regions, including the volute, the rotor cage and the center section. Structured Hex&Wedge meshes were applied to these regions Table 1 The calculated discrete points on the volute profile.
Fig. 3. Analyses of the motion of airflow in the volute.
φ (rad)
0
π/6
π/3
π/2
2π/3
5π/6
π
R (m)
0.142
0.159
0.177
0.198
0.221
0.247
0.276
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Y. Yu et al. / Powder Technology 348 (2019) 65–69
Logarithmic spiral volute profile Prototype volute profile
Fig. 4. The comparison of the two different volutes' profiles.
and the Cooper algorithm was selected to create volumetric meshes. Before the primary simulations were conducted, the verification of grid independence was implemented [11]. In this study, the mesh with 1,550,012 nodes was selected to conduct the required simulations. The RNG k-ε turbulence model was adopted to describe the air flow [12]. To guarantee the same design operating conditions with those of the prototype classifier, the inlet air volumetric flow rate Q of 0.1428 m3/s and the rotor cage rotary speed of 1200 rpm were set. 3.1. The simulation and analysis of the continuous phase 3.1.1. The velocity distribution in the volute The airflow velocity distribution of in the XOY plane (z = 50) of the turbo air classifier is shown in Fig. 5. The air velocity is well-distributed in the annular region including the location near volute tongue. The velocity gradient is from 4 to 8 m/s. When the classifier is working, the powder materials to be classified will be thrown into the annular region from the spreading plate, the circumferentially well-distributed velocity distribution can ensure the same classification effect for these particles in different circumferential positions, which can improve the classification performance. 3.1.2. The velocity distribution in the annular region The velocity distribution in the annular region is analyzed in XOY plane (Z = 50). Fig. 6 shows the tangential velocity distribution in the annular region. It shows that the tangential velocity is well-distributed in the annular region and the tangential velocity in the same circular is almost same, thus the tangential velocity in different circumferential positions can maintain same, which devotes to the improvement of the classification performance. The radial velocity distribution in
Fig. 5. The velocity magnitude contour in XOY plane (z = 50) of the classifier with log spiral volute.
Fig. 6. The tangential velocity contour in XOY plane (z = 50) of the annular region.
annular region is shown in Fig. 7. The minus sign means that the velocity points to the center. It shows that the radial velocity is well-distributed in the annular region, which is more favorable for classification.
3.2. The simulation results of the discrete phase The flow field distribution in the classifier directly determines the movement of the particles. Since the particle volume fraction in the classifier is less than 10%, the particles' trajectories in the in this numerical analysis can be simulated using the Discrete Phase Model [13]. To observe the particle's trajectory clearly, the single particle with size of 21.8 μm is released from point A and B and the simulation results are shown in the Fig. 8. The red curve is the particle trajectory released from point A and the blue curve is the particle trajectory released from point B. The particles of the same size at the different position A and B will enter the cage and collected as fine powder, because the air flows into the annular region through the guide vanes circle uniformly, which will improve the classification performance.
Fig. 7. The radial velocity contour in XOY plane (z = 50) of the annular region.
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What is worth mentioning is, the further promotion of this volute design method for a turbo air classifier to industry will be done soon and then the reports on the industrial application and verification will be tracked. Acknowledgement This project is supported financially by the National Natural Science Foundation of China (No. 51204009). References
Fig. 8. The particles' trajectories in the turbo air classifier.
4. Conclusions A theoretical design method of logarithmic spiral volute profile is put forward, which can obtain a well-distributed flow field distribution in the annular region for the turbo air classifier. It is based on the design theory of the turbine machinery and the particles' motion characteristics in turbo air classifier. The logarithmic spiral volute profile can be expressed as the following formula: Q
R ¼ Rh e2πbRh V ht
φ
Both the continuous phase and discrete phase simulations indicate that the logarithmic spiral volute has a perfect flow-guiding effect and improve the velocity distribution uniformity in the annular region obviously and it is feasible to improve the classification performance.
[1] W. Xing, Y. Wang, H. Zhang, et al., Experimental study on velocity field between two adjacent blades and gas–solid separation of a turbo air classifier, Powder Technol. 286 (2015) 240–245. [2] C. Eswaraiah, S.I. Angadi, B.K. Mishra, Mechanism of particle separation and analysis of fish-hook phenomenon in a circulating air classifier, Powder Technol. 218 (2012) 57–63. [3] O. Altun, A. Toprak, Multi component modeling of an air classifier, Miner. Eng. 93 (2016) 50–56. [4] Y. Yu, J. Liu, A parametric cut size prediction model for a turbo air classifier, Mater. Wiss. Serkstofftechnik 49 (2018) 1510–1519. [5] Q. Huang, J. Liu, Y. Yu, Turbo air classifier guide vane improvement and inner flow field numerical simulation, Powder Technol. 226 (2012) 10–15. [6] R. Liu, J. Liu, Y. Yu, Effects of axial inclined guide vanes on a turbo air classifier, Powder Technol. 280 (2015) 1–9. [7] Z. Sun, G. Sun, J. Liu, X. Yang, CFD simulation and optimization of the flow field in horizontal turbo air classifiers, Adv. Powder Technol. 28 (2017) 1474–1485. [8] D. Zhao, C. Tong, X. Diao, X. Li, Experiment on classification performance of SCX classifiers with different feeding types, Mach. Des. Manufact. 3 (2014) 142–144. [9] H. Yoshida, Y. Inada, Improvement of gas-cyclone performance by use of local fluid flow control method, Powder Technol. 193 (2009) 6–14. [10] Y. Li, C. Zhao, F. An, Numerical optimization on the volute configuration of a centrifugal fan via variable helical angle, Chinese J. Appl. Mech. 29 (2012) 398–403. [11] Y. Yu, M. Saadat, A. Untaroiu, et al., Prediction of turbo air classifier cut size based on particle trajectory, Proceedings of ASME Turbo Expo 2016: Turbo-Machinery Technical Conference and Exposition, GT2016-57903 2016, pp. 1–11. [12] R.X. Hu, S.T. Kang, FLUENT 16.0 Flow Field Analysis from Novice to Professional, China Machine Press, Beijing, 2016. [13] S. Atas, U. Tekir, Numerical and experimental analysis of pulverized coal mill classifier performance in the Soma B power plant, Fuel Process. Technol. 126 (2014) 441–452.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Short communication
A new volute design method for the turbo air classifier Yuan Yu a, Wenjing Ren b, Jiaxiang Liu c,⁎ a b c
College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaan'xi, China Beijing Key Laboratory of Electrochemical Process and Technology for Materials, Beijing University of Chemical Technology, Beijing 100029, China
a r t i c l e
i n f o
Article history: Received 10 December 2018 Received in revised form 5 March 2019 Accepted 8 March 2019 Available online 12 March 2019 Keywords: Turbo air classifier Volute profile Logarithmic spiral Volute design method
a b s t r a c t Volute profile plays an important role in guiding the airflow for a turbo air classifier. The traditional volute design is based on the method of analogue and there is a lack of uniform theoretical design basis and guidance. To meet the needs of guiding the airflow better, a logarithmic spiral volute design method is put forward based on the analyses of airflow motion in the volute and classification characteristics of the turbo air classifier. The numerical simulations on flow field distribution in the turbo air classifier show that the logarithmic spiral volute has a good effect on guiding the airflow and can form a well-distributed flow field in the classifier, which is conducive to improve the classification performance. The single particle trajectory verifies that the logarithmic spiral volute makes the airflow flow along the guide vanes circumferentially uniformly, forming a well-distributed flow field in the annular region of the classifier. So the classification results for the particles with the same size are in correspondence when the logarithmic spiral volute is applied. The numerical simulations of both gas phase and discrete phase indicate that the logarithmic spiral volute can provide a well-distributed flow field for the classification and this volute deign method for turbo air classifier is feasible. © 2019 Published by Elsevier B.V.
1. Introduction The turbo air classifier is widely used in the fields of fine chemical industry, ceramic and composite material manufacturing due to its simple structure and adjustable operating parameters [1–4]. In recent years, with the development of powder technology, the performance of the classifier has been continuously improved, especially in the refinement and narrow distribution fields. The separation of coarse and fine particles is implemented in the turbo air classifier under the influence of the airflow field which influences classification performance of the classifiers directly. When the operating parameters are constant, the classifier structure determines the flow field distribution, even the classification performance. Comparing to the airflow distribution using positive bending, reverse bending and straight guide vanes, Huang Qiang concluded that the positive bending blades can reduce the swirl in the blade passages of the rotor cage, making the flow field welldistributed, improving classification accuracy, as well as reducing the cut size [5]. Liu Rongrong pointed out that the axial guide vanes with 2.5° are favorable to keep the flow field well-distributed and the ⁎ Corresponding author. E-mail address: [email protected] (J. Liu).
https://doi.org/10.1016/j.powtec.2019.03.015 0032-5910/© 2019 Published by Elsevier B.V.
classification force field is enhanced to improve the dispersion of the powders, which leads to an improved classification performance [6]. Sun Zhanpeng compared and analyzed the effect of air-inlet direction on the performance of classifier through powder classification experiments [7]. Zhao Dongmei did some researches on the influences of material feeding types on the classification performance [8]. Hideto Yoshida improved the air inlet structure of the cyclone separator and the new inlet provided a smaller cut size and a higher classification accuracy [9]. At present, the structure improvement of classifier is mainly focused on the rotor cage, guide vanes and spreading plate. However, there are few reports on the volute of the turbo air classifier. Before the air flows into the annular classification region, it will pass through the volute firstly. The structure of the volute determines the distribution of the airflow, the stability of the flow field and the classification performance. Since there is a lack of clear design method for the volute, the analogy method is often used to determine the volute profile of a turbo air classifier. The common volute profile types include involute, multi-arcs and approximate logarithmic spiral. However, in the turbine machinery such as centrifugal blower and gas turbine compressor, there is a set of complete volute design theory to standardize industrial applications [10]. In this paper, the volute design theory of turbine is
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Y. Yu et al. / Powder Technology 348 (2019) 65–69
Nomenclature a b θ ∅0 φ Q q'φ qφ R Rh Vt Vht V0 Vhr′ δ n1 Vht′
width of the volute (mm) height of the volute (mm) setting angle of the guide vanes (°) tongue angle (°) direction angle (°) inlet air volumetric flow rate (m3/s) air volumetric flow rate passing through the section of AB (m3/s) air volumetric flow rate passing through the section AC (m3/s) radius of the located fluid element (m) radius of the outer edge of the guide vanes (m) tangential velocity of the fluid element with radius R (m/s) tangential velocity of the fluid element with radius Rh (m/s) air inlet velocity (m/s) air radial velocity at the outer edge of guide vanes (m/s) thickness of the guide vanes(m) number of the guide vanes air tangential velocity at the outer edge of guide vanes (m/s)
introduced and applied to the turbo air classifier, combining its classification characteristics. A logarithmic spiral volute design method for the turbo air classifier is proposed. The well-distributed flow field of the air turbo classifier with the logarithmic spiral volute is feasible to improve the classification performance. 2. Theoretical design of volute 2.1. The formula derivation of volute profile The structural scheme of the turbo air classifier used in the present study is shown in Fig. 1. Under central negative pressure, the airflow enters the annular classification region through the guide vanes from two horizontally symmetrical airflow inlets, forming a rotating velocity field. At the same time, the powder materials to be classified are fed onto the feeding plate, which is rapidly rotating together with the rotor cage. The particles are thrown outward into the annular region, which is a cylindrical space between the outer edge of the rotor cage and the inner edge of the guide vanes. The powder materials are separated into coarse and fine powder under the air drag force, centrifugal force and gravity.
The centrifugal force on the fine particle is smaller than the air drag force. As a result, it will be drawn into the rotor cage with the airflow and be collected as the fine powder. The centrifugal force on the coarse particle is greater than the air drag force. Therefore it will move outside and collide with the guide vane or the volute, falling into the cone collector. Finally they are collected as the coarse powder. After the air enters the classifier from the airflow inlets, firstly, it passes through the volute. Therefore the volute plays an important role on the flow field distribution in the annular region. In order to improve the classification performance, the flow field of annular region should be well-distributed circumferentially, to ensure that the effects of the flow field on the same particles in different circumferential positions are same, conducive to improve the classification performance. The volute of the turbo air classifier includes the airflow inlet and the volute, the cross-section of the volute in turbo air classifier is shown in the Fig. 2. It is a centrosymmetric structure and there are two airflow inc and a0b0 d are the volute profile. The seclets: 1# and 2#. The section ab c and c0b0 d are airflow inlet straight channel. The dotted circle tion cb represents the section circle of the outer edge of the guide vane, dec (and a′ on a0b0) d is called the noted by Circle_M. The start point a on ab tongue and ∅0 is the tongue angle. In the prototype classifier, the volute profile is an involute. In order to design a reasonable volute profile to improve its flow-guiding effect, the motion of airflow in the turbo air classifier should be analyzed firstly. The motion of airflow in the classifier is shown in Fig. 3. The dotted arc is a part of cross-section line of the outer edge of the guide vanes, the solid c is the airflow particle's trajectory. The angle φ is defined as curve of BC the direction angle of airflow at the point B, which the angle between OC and OB. The flow will just pass by the C point when φ = 0. Suppose the inlet air volumetric flow rate is Q, the air volumetric flow rate passing through section AB is q'φ and the air volumetric flow rate passing through flow-guiding section AC is qφ which is coming from the section AB. Considering the centrosymmetric structure of the classifier, to achieve the well-distributed air flow circumferentially, a reasonable volute profile should ensure that the airflow enters the guide vanes passageway circumferentially uniformly, and it can be concluded as: qφ = Qφ/2π. In this case, when the amount of air flow from single airflow inlet is equal to that passing half of Circle_M (φ = 0~π), that is qφ = q'φ, mixed airflow in the volute from the two airflow inlets would be avoided and the stability of the flow field would be ensured, thus the volute profile should be: q0φ ¼ qφ ¼ Q
φ 2π
Fig. 1. The schematic diagram of a turbo air classifier.
ð1Þ
Y. Yu et al. / Powder Technology 348 (2019) 65–69
67
Since steady-state and transient-state simulation results for this turbo air classifier model are in good agreement, the airflow streamline is approximated to the airflow's motion trajectory. It can be concluded that the airflow streamline in the volute should meet the logarithmic spiral line expressed in formula (6). Therefore, a volute with the profile of logarithmic spiral line will ensure a perfect guiding effect. When the operating condition is determined, the R corresponding to each φ can be calculated, so the position coordinates of the points on the airflow's motion trajectory can be obtained. The volute profile can be obtained by fitting these points. Since the change of the volute profile will change the cross section of the inlet, the inlet air volumetric flow rate is used in this paper, which is: Q ¼ 2abV 0 Fig. 2. The cross–section of the volute in a turbo air classifier.
The whole section of AB is filled with effective airflow and the total amount is: Z q0φ ¼
R
bV t dr Rh
ð2Þ
Where R– radius of the located fluid element (m); Rh– radius of the outer edge of the guide vanes (m); Vt– tangential velocity of the fluid element with radius R (m/s); b– height of the volute (m). Ignoring the influence of friction, the airflow in the volute is not subjected to the external force and is accorded with the law of conservation of moment of momentum, there is: Rh V ht ¼ RV t ¼ constant
ð3Þ
Where Vht – tangential velocity of the fluid element with radius Rh (m/s). Combining formula (3) and (2), there is: q0φ
Z ¼
R
Rh
R V R b h ht dR ¼ bRh V ht ln Rh R
ð4Þ
R can be expressed as: q0φ
ð5Þ
R ¼ Rh ebRh V ht
Combining formula (1) and (5), the airflow streamline equation in the volute can be obtained: Q
R ¼ Rh e2πbRh V ht
φ
ð6Þ
ð7Þ
Where a, b– width and height of volute; V0– air inlet velocity. In the prototype structure, a is 0.062 m, b is 0.096 m, and the air inlet velocity V0 is 12 m/s. So the design conditions are: rotor's rotating speed is 1200 r/min and the inlet air volumetric flow rate Q is 0.1428 m3/s. 2.2. The calculation of volute profile According to mass conservation law, air volume is Q in the classifier. ′ after entering the guide vanes passageway can The air radial velocity Vhr be calculated by formula (8): Q V 0hr ¼ δ n1 b 2πRh − sinθ
ð8Þ
Where δ– the thickness of guide vanes, δ = 0.002 m; n1– the number of guide vanes, n1 = 24; θ– setting angle of the guide vanes, θ = 15; Rh– the radius of the outer edge of the guide vanes, Rh = 0.142 m. The tangential velocity of the air at the outer edge guide vanes is: V 0ht ¼ V 0hr cotθ
ð9Þ
′ and Vht ′ , they can be calculated Then according the expression of Vhr and Vhr ′ = 2.11 m/s and Vht ′ = 7.86 m/s. And the volute profile can be obtained as: Q
φ
7:142410‐2
R ¼ Rh e2πbRh V ht ¼ Rh eπ0:0960:1427:86φ ¼ Rh e0:212φ
ð10Þ
0, π/6, π/3, π/2, 2π/3, 5π/6 and π are assigned to φ in order to calculate the volute profile points, and the outputs are listed in Table 1. Keeping unchanged prototype volute tongue angle ∅0, the start point of the volute profile is determined. These points on the volute profile are fitted in sequence, and the logarithmic spiral volute which is suitable to the airflow characteristics can be obtained. The comparison of the cross section of the prototype volute and the calculated logarithmic spiral volute is shown in Fig. 4. 3. Numerical simulation and analysis To simulate the distribution of flow field in the turbo air classifier with this logarithmic spiral volute, Gambit 2.2.30 and ANSYS-FLUENT 17.0 were used to establish the model of a turbo air classifier and simulate its inner airflow field. The model was designed to describe the main classification regions, including the volute, the rotor cage and the center section. Structured Hex&Wedge meshes were applied to these regions Table 1 The calculated discrete points on the volute profile.
Fig. 3. Analyses of the motion of airflow in the volute.
φ (rad)
0
π/6
π/3
π/2
2π/3
5π/6
π
R (m)
0.142
0.159
0.177
0.198
0.221
0.247
0.276
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Logarithmic spiral volute profile Prototype volute profile
Fig. 4. The comparison of the two different volutes' profiles.
and the Cooper algorithm was selected to create volumetric meshes. Before the primary simulations were conducted, the verification of grid independence was implemented [11]. In this study, the mesh with 1,550,012 nodes was selected to conduct the required simulations. The RNG k-ε turbulence model was adopted to describe the air flow [12]. To guarantee the same design operating conditions with those of the prototype classifier, the inlet air volumetric flow rate Q of 0.1428 m3/s and the rotor cage rotary speed of 1200 rpm were set. 3.1. The simulation and analysis of the continuous phase 3.1.1. The velocity distribution in the volute The airflow velocity distribution of in the XOY plane (z = 50) of the turbo air classifier is shown in Fig. 5. The air velocity is well-distributed in the annular region including the location near volute tongue. The velocity gradient is from 4 to 8 m/s. When the classifier is working, the powder materials to be classified will be thrown into the annular region from the spreading plate, the circumferentially well-distributed velocity distribution can ensure the same classification effect for these particles in different circumferential positions, which can improve the classification performance. 3.1.2. The velocity distribution in the annular region The velocity distribution in the annular region is analyzed in XOY plane (Z = 50). Fig. 6 shows the tangential velocity distribution in the annular region. It shows that the tangential velocity is well-distributed in the annular region and the tangential velocity in the same circular is almost same, thus the tangential velocity in different circumferential positions can maintain same, which devotes to the improvement of the classification performance. The radial velocity distribution in
Fig. 5. The velocity magnitude contour in XOY plane (z = 50) of the classifier with log spiral volute.
Fig. 6. The tangential velocity contour in XOY plane (z = 50) of the annular region.
annular region is shown in Fig. 7. The minus sign means that the velocity points to the center. It shows that the radial velocity is well-distributed in the annular region, which is more favorable for classification.
3.2. The simulation results of the discrete phase The flow field distribution in the classifier directly determines the movement of the particles. Since the particle volume fraction in the classifier is less than 10%, the particles' trajectories in the in this numerical analysis can be simulated using the Discrete Phase Model [13]. To observe the particle's trajectory clearly, the single particle with size of 21.8 μm is released from point A and B and the simulation results are shown in the Fig. 8. The red curve is the particle trajectory released from point A and the blue curve is the particle trajectory released from point B. The particles of the same size at the different position A and B will enter the cage and collected as fine powder, because the air flows into the annular region through the guide vanes circle uniformly, which will improve the classification performance.
Fig. 7. The radial velocity contour in XOY plane (z = 50) of the annular region.
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What is worth mentioning is, the further promotion of this volute design method for a turbo air classifier to industry will be done soon and then the reports on the industrial application and verification will be tracked. Acknowledgement This project is supported financially by the National Natural Science Foundation of China (No. 51204009). References
Fig. 8. The particles' trajectories in the turbo air classifier.
4. Conclusions A theoretical design method of logarithmic spiral volute profile is put forward, which can obtain a well-distributed flow field distribution in the annular region for the turbo air classifier. It is based on the design theory of the turbine machinery and the particles' motion characteristics in turbo air classifier. The logarithmic spiral volute profile can be expressed as the following formula: Q
R ¼ Rh e2πbRh V ht
φ
Both the continuous phase and discrete phase simulations indicate that the logarithmic spiral volute has a perfect flow-guiding effect and improve the velocity distribution uniformity in the annular region obviously and it is feasible to improve the classification performance.
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