System energy-saving self-air supply powder concentrator and self-air supply method thereof

Abstract

The application discloses a system energy-saving type self-air-supply powder concentrator and a self-air-supply method thereof, which comprises a shell, a first driving device, a first transmission shaft, a second driving device, a second transmission shaft, a rotating cage, guide vanes, a material returning device and an air outlet. The first transmission shaft is connected with the rotating cage, a plurality of first axial flow vanes are arranged on the first transmission shaft, the first axial flow vanes are arranged inside the rotating cage and are arranged at a certain angle with the first transmission shaft. A plurality of second axial flow vanes are arranged on the second transmission shaft, the second axial flow vanes are arranged between the rotating cage and the air outlet and are arranged at a certain angle with the second transmission shaft. When the self-air-supply is performed, the rotating speed of the second axial flow vanes is greater than or equal to the rotating speed of the first axial flow vanes, so that the rotational flow kinetic energy generated by the two groups of axial flow vanes and the rotating cage is used to discharge the separated materials from the air outlet. The self-air-supply purpose of the powder concentrator is achieved, the pressure value at the inlet of the system fan is reduced, and thus the system resistance and energy consumption are reduced.

Description

Technical Field

[0001] This invention relates to the field of material sorting technology, and in particular to a system-energy-saving self-supplying air classifier and its self-supplying air method. Background Technology

[0002] Common grinding processes consist of a complete system composed of grinding equipment, powder classifiers, dust collection equipment, and fans (air supply equipment). Among them, bed grinding equipment, represented by vertical roller mills and roller presses, has become the mainstream choice for different grinding systems.

[0003] In the power consumption of grinding systems, fan energy consumption accounts for a large proportion. Taking raw material grinding as an example, fan energy consumption accounts for about 40-50% in vertical roller mill systems and about 20-40% in roller press systems. Fan energy consumption is mainly determined by system resistance and air volume. Reducing fan energy consumption can be achieved by separating resistance and air volume from a system perspective, such as in a dual-fan grinding system. However, this process is relatively complex, and the construction and modification costs are high.

[0004] Vertical roller mill systems are widely used due to their simple process and ease of large-scale application, but they currently suffer from problems such as high system resistance and high power consumption. Taking raw material grinding as an example, overall, the power consumption of roller press systems is about 2-3 kWh / t lower than that of vertical roller mill systems, while the power consumption of the blowers in vertical roller mill systems is about 3-4 kWh / t higher than that in roller press systems. Therefore, in comparing vertical roller mill systems and roller press systems, blower power consumption has become one of the main factors restricting the selection of vertical roller mill systems. Summary of the Invention

[0005] One of the objectives of this invention is to provide a system-energy-saving self-supplying air classifier. This classifier adopts the form of adding axial flow blades inside the classifier drum and between the classifier drum and the air outlet to continue the swirling kinetic energy generated by the classifier drum and match the appropriate rotation speed between the two to achieve the purpose of self-supplying air for the classifier. This is equivalent to separating the function of the system fan, thereby effectively reducing the inlet pressure of the system fan. When selecting the system, the fan configuration can be reduced, thereby reducing system resistance and energy consumption.

[0006] Another objective of this invention is to provide a self-supply air method for a system-energy-saving self-supply air classifier.

[0007] The present invention is implemented as follows: a system energy-saving self-supplying air classifier includes a shell, a first drive device, a first transmission shaft, a rotating cage, guide vanes, a return material device, and an air outlet. The first drive device drives the first transmission shaft to rotate. The first transmission shaft is connected to the rotating cage. The rotation direction of the rotating cage is the same as that of the first transmission shaft. The rotating cage and the guide vanes are installed in the center of the shell and are coaxially arranged. The guide vanes are located between the shell and the rotating cage. The return material device is located below the guide vanes. The top end of the return material device is connected to the bottom end of the guide vanes. The air outlet is located above the rotating cage.

[0008] A plurality of first axial flow blades are mounted on the first drive shaft, and the first axial flow blades are located inside the rotating cage; the root of the first axial flow blade intersects with the first drive shaft and is set at a certain angle;

[0009] It also includes a second drive device, a second transmission shaft, and a second axial flow blade. The second drive device drives the second transmission shaft to rotate. Several second axial flow blades are installed on the second transmission shaft. The second axial flow blades are located between the rotating cage and the air outlet. The root of the second axial flow blade intersects with the second transmission shaft and is set at a certain angle.

[0010] Preferably, the angle α between the root of the first axial flow blade and the horizontal line is 10 to 80°; the angle β between the root of the second axial flow blade and the horizontal line is 10 to 80°.

[0011] Preferably, both the first drive shaft and the second drive shaft extend into the housing from above, and the first drive shaft and the second drive shaft are nested together. The first drive device is located outside the housing and is connected to the top end of the first drive shaft, and the second drive device is located outside the housing and is connected to the top end of the second drive shaft.

[0012] Preferably, the first drive shaft and the second drive shaft are arranged separately, with the first drive shaft located below the second drive shaft, and the first drive device located below the first axial flow blade and connected to the bottom end of the first drive shaft; the second drive shaft extends into the housing through the top of the housing, and the second drive device is located outside the housing and connected to the top end of the second drive shaft.

[0013] Preferably, several first axial flow blades are located at the same horizontal height, and several second axial flow blades are located at the same horizontal height.

[0014] Two sets of rotatable axial flow blades are installed inside the classifier's rotating cage and between the rotating cage and the air outlet. These two sets of axial flow blades are arranged at a certain angle to the drive shaft. The first axial flow blade inside the rotating cage rotates together with the rotating cage at the same speed. The second axial flow blade between the rotating cage and the air outlet is driven independently and is located above the rotating cage. The drive shafts of the first axial flow blade inside the rotating cage and the second axial flow blade above the rotating cage are nested together. The two drive units are located above the two sets of axial flow blades and the air outlet; alternatively, the two drive units can be arranged separately in different directions, located above and below the two sets of axial flow blades, respectively.

[0015] The self-supply air method of the energy-saving self-supply air classifier is as follows: the first drive device drives the first transmission shaft to rotate the rotating cage, providing kinetic energy for the powder to enter the sorting zone. The rotation of the rotating cage simultaneously drives the first axial flow blades to rotate. The second drive device drives the second transmission shaft to rotate the second axial flow blades. The first and second transmission shafts rotate in the same direction. The rotation speed of the second axial flow blades is greater than or equal to the rotation speed of the first axial flow blades, so that the first and second axial flow blades take over the swirling kinetic energy generated by the rotating cage and discharge the sorted material from the air outlet.

[0016] Preferably, the rotational speed of the first axial flow blade is n1, the rotational speed of the second axial flow blade is n2, and the ratio of n2 to n1 is n2 / n1 = 1 to 10.

[0017] The present invention has the following advantages and beneficial effects:

[0018] 1) This invention adds two sets of axial flow blades inside and above the classifier's rotating cage, making full use of the rotating kinetic energy of the classifier's rotating cage and matching the effective speed difference between the two sets of axial flow blades to achieve the purpose of self-supplying air for the classifier, reducing the pressure value at the system fan inlet, reducing the fan configuration, and thus reducing system resistance and energy consumption.

[0019] 2) The two sets of axial flow blades of the present invention are driven separately, which facilitates the adjustment of the speed difference.

[0020] 3) The two sets of drive devices of the present invention have different arrangement options, which facilitates different selection and matching. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the structure of the self-supplying air classifier provided in Embodiment 1 of the present invention;

[0022] Figure 2 This is a schematic diagram of the axial flow blade position provided in Embodiment 1 of the present invention;

[0023] Figure 3 This is a schematic diagram of the arrangement angle of the axial flow blades provided in Embodiment 1 of the present invention;

[0024] Figure 4 This is a schematic diagram of the structure of the self-supplying air classifier provided in Embodiment 2 of the present invention;

[0025] Figure 5 This is a schematic diagram of the axial flow blade position provided in Embodiment 2 of the present invention;

[0026] Figure 6 This is a schematic diagram of the arrangement angle of the axial flow blades provided in Embodiment 2 of the present invention;

[0027] Figure 7 This is a comparison chart showing the drag reduction effect of vertical roller mills with and without two sets of axial flow blades, calculated using CFD simulation of this invention.

[0028] In the figure: 1-First driving device; 2-Second driving device; 3-Second axial flow blade; 4-First axial flow blade; 5-Rotating cage; 6-Guide blade; 7-Shell; 8-Returning device; 9-Air outlet; 10-Second transmission shaft; 11-First transmission shaft. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments and accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0030] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0031] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0032] An embodiment of the present invention provides a system-energy-saving self-supplying air classifier, including a housing 7, a first drive device 1, a first transmission shaft 11, a rotating cage 5, guide vanes 6, a return material device 8, and an air outlet 9. The first drive device 1 drives the first transmission shaft 11 to rotate. The first transmission shaft 11 is connected to the rotating cage 5. The rotation direction of the rotating cage 5 is the same as that of the first transmission shaft 11. The rotating cage 5 and the guide vanes 6 are installed in the center of the housing 7 and are coaxially arranged. The guide vanes 6 are located between the housing 7 and the rotating cage 5. The return material device 8 is located below the guide vanes 6. The top end of the return material device 8 is connected to the bottom end of the guide vanes 6. The air outlet 9 is located above the rotating cage 5.

[0033] A plurality of first axial flow blades 4 are mounted on the first drive shaft 11. The plurality of first axial flow blades 4 are located at the same horizontal height. The first axial flow blades 4 are located inside the rotating cage 5. The first axial flow blades 4 and the rotating cage 5 rotate together at the same speed. The root of the first axial flow blade 4 intersects the first drive shaft 11 and is set at a certain angle. Specifically, the angle α between the root of the first axial flow blade 4 and the horizontal line is 10 to 80°.

[0034] It also includes a second drive device 2, a second transmission shaft 10, and a second axial flow blade 3. The second drive device 2 drives the second transmission shaft 10 to rotate. Several second axial flow blades 3 are installed on the second transmission shaft 10. The several second axial flow blades 3 are located at the same horizontal height. The second axial flow blades 3 are located between the rotating cage 5 and the air outlet 9. The root of the second axial flow blade 3 intersects the second transmission shaft 10 and is set at a certain angle. Specifically, the included angle β between the root of the second axial flow blade 3 and the horizontal line is 10 to 80°.

[0035] Both the first drive shaft 11 and the second drive shaft 10 extend into the housing 7 from above, and are nested together. The first drive device 1 is located outside the housing 7 and connected to the top end of the first drive shaft 11, while the second drive device 2 is located outside the housing 7 and connected to the top end of the second drive shaft 10. Alternatively, the first drive shaft 11 and the second drive shaft 10 are arranged separately. The first drive shaft 11 is located below the second drive shaft 10, and the first drive device 1 is located below the first axial flow blade 4 and connected to the bottom end of the first drive shaft 11. The second drive shaft 10 extends into the housing 7 from above, and the second drive device 2 is located outside the housing 7 and connected to the top end of the second drive shaft 10.

[0036] Two sets of rotatable axial flow blades are installed inside the classifier drum 5 and between the classifier drum 5 and the air outlet 9. The two sets of axial flow blades are arranged at a certain angle to the drive shaft. The first axial flow blade 4 inside the classifier drum 5 rotates together with the classifier drum 5 at the same speed. The second axial flow blade 3 between the classifier drum 5 and the air outlet 9 is driven separately and is located above the classifier drum 5. The drive shaft of the first axial flow blade 4 inside the classifier drum 5 and the drive shaft of the second axial flow blade 3 above the classifier drum 5 are nested together. The two sets of drive devices are above the two sets of axial flow blades and the air outlet 9. The two sets of drive devices can also be arranged separately in different directions, located above and below the two sets of axial flow blades, respectively.

[0037] The self-supplying air method of the energy-saving self-supplying air classifier is as follows: a first drive device 1 drives a first transmission shaft 11 to rotate a rotating cage 5, providing kinetic energy for the material to enter the sorting zone. Simultaneously, the rotation of the rotating cage 5 drives the first axial flow blade 4 to rotate. A second drive device 2 drives a second transmission shaft 10 to rotate the second axial flow blade 3. The first and second transmission shafts 11 and 10 rotate in the same direction. The rotational speed of the second axial flow blade 3 is greater than or equal to the rotational speed of the first axial flow blade 4. This allows the first and second axial flow blades 4 and 3 to utilize the swirling kinetic energy generated by the rotating cage 5, discharging the sorted material from the outlet 9 and sending it to the dust collection equipment. This reduces the pressure at the system fan inlet, achieving energy saving and consumption reduction. Specifically, the rotational speed of the first axial flow blade 4 is n1, and the rotational speed of the second axial flow blade 3 is n2, with the ratio of n2 to n1 being n2 / n1 = 1 to 10.

[0038] Example 1

[0039] Please see Figure 1 , Figure 2 , Figure 3 The energy-saving self-supplying air classifier of this embodiment includes a housing 7, a rotating cage 5, guide vanes 6, a return material device 8, a first drive device 1, a first transmission shaft 11, a first axial flow vane 4, a second drive device 2, a second transmission shaft 10, a second axial flow vane 3, and an air outlet 9. The rotating cage 5 and the guide vane 6 are installed in the center of the housing 7 and are coaxially arranged. The guide vane 6 is located between the housing 7 and the rotating cage 5. The return material device 8 is located below the guide vane 6. The top end of the return material device 8 is connected to the bottom end of the guide vane 6. The air outlet 9 is located above the rotating cage 5.

[0040] The first drive shaft 11 and the second drive shaft 10 are located in the middle of the housing 7. Both the first drive shaft 11 and the second drive shaft 10 extend into the housing 7 from above, and are nested together. The first drive shaft 11 passes through the interior of the second drive shaft 10. The first drive device 1 is located outside the housing 7 and connected to the top end of the first drive shaft 11. The second drive device 2 is located outside the housing 7 and connected to the top end of the second drive shaft 10. The first drive device 1 and the second drive device 2 are located above the first axial flow blade 4 and the second axial flow blade 3. The two drive devices are arranged in the same direction, which facilitates maintenance and allows for flexible selection of motor configurations.

[0041] The first drive shaft 11 is connected to the rotating cage 5, and the rotation direction of the rotating cage 5 is the same as that of the first drive shaft 11. A plurality of first axial flow blades 4 are mounted on the first drive shaft 11, and the plurality of first axial flow blades 4 are located at the same horizontal height. The first axial flow blades 4 are located inside the rotating cage 5, and the first axial flow blades 4 rotate together with the rotating cage 5 at the same speed. In this embodiment, the angle α between the root of the first axial flow blade 4 and the horizontal line is 30°. The first drive device 1 drives the first drive shaft 11 to rotate, thereby causing the rotating cage 5 and the first axial flow blades 4 to rotate.

[0042] A plurality of second axial flow blades 3 are mounted on the second drive shaft 10. The plurality of second axial flow blades 3 are located at the same horizontal height and are positioned between the rotating cage 5 and the air outlet 9. In this embodiment, the angle β between the root of the second axial flow blade 3 and the horizontal line is 30°. The second drive device 2 drives the second drive shaft 10 to rotate, thereby driving the second axial flow blades 3 to rotate.

[0043] When self-supplying air is used, the first drive device 1 drives the first transmission shaft 11 to rotate the rotating cage 5, providing kinetic energy for the powder to enter the sorting zone. Simultaneously, the rotation of the rotating cage 5 drives the first axial flow blade 4 to rotate. The second drive device 2 drives the second transmission shaft 10 to rotate the second axial flow blade 3. The rotational speed of the second axial flow blade 3 is greater than or equal to the rotational speed of the first axial flow blade 4. This allows the first and second axial flow blades 4 and 3 to utilize the swirling kinetic energy generated by the rotating cage 5, discharging the sorted material from the outlet 9 and sending it into the dust collection equipment. This reduces the pressure value at the system fan inlet, achieving the goal of energy saving and consumption reduction. In this embodiment, the rotational speed of the first axial flow blade 4 is n1, and the rotational speed of the second axial flow blade 3 is n2. The ratio of n2 to n1 is n2 / n1 = 4.

[0044] The working principle of this embodiment: During the rotation of the classifier's rotating cage 5, a high-speed swirling airflow is generated. This airflow provides kinetic energy for carrying the classified material into the sorting zone, while simultaneously generating swirling resistance. This resistance increases the inlet pressure of the system fan, leading to an oversized fan and increased energy consumption during operation. This invention adds a first axial flow blade 4 and a second axial flow blade 3 inside the classifier's rotating cage 5 and between the rotating cage 5 and the outlet 9 to fully utilize the swirling kinetic energy of the classifier's rotating cage 5, allowing the classified material to continue entering the dust collection equipment, thus reducing the fan inlet pressure and achieving system energy saving.

[0045] Example 2

[0046] Please see Figure 4 , Figure 5 , Figure 6 Unlike Embodiment 1, in this embodiment, the first drive shaft 11 and the second drive shaft 10 are arranged separately. The first drive shaft 11 is located below the second drive shaft 10, and the first drive device 1 is located below the first axial flow blade 4 and connected to the bottom end of the first drive shaft 11. In this embodiment, the first drive shaft 11 is mounted on an inverted cone inside the rotating cage 5, and the first drive device 1 is located inside the inverted cone and connected to the bottom end of the first drive shaft 11. The second drive shaft 10 extends into the housing 7 through the top of the housing 7, and the second drive device 2 is located outside the housing 7 and connected to the top end of the second drive shaft 10. The second drive shaft 10 is located above the first drive shaft 11, the first drive device 1 is located below the first axial flow blade 4, and the second drive device 2 is located above the second axial flow blade 3. The two drive devices are arranged separately in two directions, which helps to reduce the height of the classifier.

[0047] To verify the core technical points of this invention in principle, taking the improved classifier of this invention nested inside a vertical roller mill system as an example, a calculation model of the vertical roller mill is constructed according to the design method. The drag reduction effect of different scheme models under the same operating conditions is numerically solved using CFD theoretical calculation methods. The drag reduction effect is compared with... Figure 7 As shown.

[0048] With an air volume of 1,000,000 m³ 3 Taking / h as an example, the boundary conditions are calculated as shown in Table 1 below:

[0049] Table 1 Calculation boundary conditions

[0050] boundary <![CDATA[Area (m 2 )]]> Hydraulic diameter (m) Wind speed (m / s) Static pressure (Pa) Mill air inlet 1 9.2496 2.974 15.0 inverse search Mill air inlet 2 9.2496 2.974 15.0 inverse search Mill air outlet 9 16.47 3.795 inverse search -3000

[0051] The rotational speed of the classifier drum in the original vertical roller mill is set to 53 rpm, and the rotational speed of the second axial flow blade 3 above the classifier drum 5 in this invention, n2, is set to 212 rpm. The calculation results using the vertical mill model of the invented classifier and the original vertical mill model are shown in Table 2 below:

[0052] Table 2 Comparison of calculation results between the vertical mill model and the original vertical mill model of the air classifier of this invention.

[0053] Original vertical mill The vertical mill of the air classifier of this invention Static pressure (Pa) at the mill inlet -517 -1433 Static pressure (Pa) at the mill inlet. -517 -1433 Static pressure at the outlet of the air ring (Pa) -1988 -2898 Static pressure at the mill outlet (Pa) -3000 -3000 Resistance from mill inlet to air ring outlet (Pa) 1470 1466 Resistance from mill inlet to mill outlet (Pa) 2483 1568 Resistance from the air ring outlet to the mill outlet (Pa) 1012 102

[0054] Through Table 2, Figure 7 It can be seen that the internal pressure distribution of the vertical roller mill using the classifier of the present invention has been greatly improved. Under the same working conditions, the internal resistance of the vertical roller mill of the classifier of the present invention is reduced by nearly 90% in the area from the air ring outlet to the mill outlet, which includes the classifier, and the resistance reduction effect is obvious.

[0055] In summary, by adding two sets of axial flow blades inside and above the classifier's rotating cage 5, this invention fully utilizes the rotational kinetic energy of the classifier's rotating cage 5 and matches the effective speed difference between the two sets of axial flow blades to achieve the purpose of self-supplying air for the classifier. This reduces the pressure value at the system fan inlet, allowing for a smaller fan configuration, thereby reducing system resistance and energy consumption.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A system-energy-saving self-supplying air classifier, comprising a housing, a first drive device, a first transmission shaft, a rotating cage, guide vanes, a material return device, and an air outlet, wherein the first drive device drives the first transmission shaft to rotate, the first transmission shaft is connected to the rotating cage, the rotating cage rotates in the same direction as the first transmission shaft, the rotating cage and the guide vanes are mounted in the center of the housing and coaxially arranged, the guide vanes are located between the housing and the rotating cage, the material return device is located below the guide vanes, the top end of the material return device is connected to the bottom end of the guide vanes, and the air outlet is located above the rotating cage; characterized in that: A plurality of first axial flow blades are mounted on the first drive shaft, and the first axial flow blades are located inside the rotating cage; the root of the first axial flow blade intersects with the first drive shaft and is set at a certain angle; It also includes a second drive device, a second transmission shaft, and a second axial flow blade. The second drive device drives the second transmission shaft to rotate. Several second axial flow blades are installed on the second transmission shaft. The second axial flow blades are located between the rotating cage and the air outlet. The root of the second axial flow blade intersects with the second transmission shaft and is set at a certain angle.

2. The energy-saving self-supplying air classifier as described in claim 1, characterized in that, The angle α between the root of the first axial flow blade and the horizontal line is 10 to 80°; the angle β between the root of the second axial flow blade and the horizontal line is 10 to 80°.

3. The energy-saving self-supplying air classifier as described in claim 1 or 2, characterized in that, Both the first drive shaft and the second drive shaft extend into the housing from above. The first drive shaft and the second drive shaft are nested together. The first drive device is located outside the housing and is connected to the top of the first drive shaft. The second drive device is located outside the housing and is connected to the top of the second drive shaft.

4. The energy-saving self-supplying air classifier as described in claim 1 or 2, characterized in that, The first drive shaft and the second drive shaft are arranged separately. The first drive shaft is located below the second drive shaft. The first drive device is located below the first axial flow blade and is connected to the bottom end of the first drive shaft. The second drive shaft extends into the housing through the top of the housing. The second drive device is located outside the housing and is connected to the top end of the second drive shaft.

5. The energy-saving self-supplying air classifier as described in claim 1, characterized in that, Several first axial flow blades are located at the same horizontal height, and several second axial flow blades are located at the same horizontal height.

6. A self-supplying air method for an energy-saving self-supplying air classifier based on any one of claims 1 to 5, characterized in that, The self-supplying air method involves a first drive device driving a first transmission shaft to rotate a rotating drum, providing kinetic energy for the powder material to enter the sorting zone. The rotation of the rotating drum simultaneously drives the first axial flow blades to rotate. A second drive device drives a second transmission shaft to rotate the second axial flow blades. The first and second transmission shafts rotate in the same direction. The rotational speed of the second axial flow blades is greater than or equal to the rotational speed of the first axial flow blades, allowing the first and second axial flow blades to continuously generate kinetic energy from the rotating drum, thus discharging the sorted material from the air outlet.

7. The self-supply air method for the energy-saving self-supply air classifier as described in claim 6, characterized in that, The rotational speed of the first axial flow blade is n1, the rotational speed of the second axial flow blade is n2, and the ratio of n2 to n1 is n2 / n1 = 1 to 10.

Images