Wang Ji 2020a - Revision history

Rimni: /* 5.2 Simulation results for kinematics of rotor */

2021-02-12T14:09:53Z

‎5.2 Simulation results for kinematics of rotor

Rimni at 13:58, 12 February 2021

2021-02-12T13:58:40Z

Rimni: /* 3.1 Velocity and acceleration of the sliding vane */

2021-02-12T13:55:43Z

‎3.1 Velocity and acceleration of the sliding vane

Rimni at 13:53, 12 February 2021

2021-02-12T13:53:28Z

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Rimni at 13:45, 12 February 2021

2021-02-12T13:45:47Z

Rimni: /* 3.2 Velocity and acceleration of the rotor */

2021-02-12T13:44:54Z

‎3.2 Velocity and acceleration of the rotor

Rimni at 13:42, 12 February 2021

2021-02-12T13:42:54Z

Rimni at 12:37, 27 March 2020

2020-03-27T12:37:06Z

Rimni at 12:19, 27 March 2020

2020-03-27T12:19:54Z

Rimni at 12:07, 27 March 2020

2020-03-27T12:07:11Z

← Older revision		Revision as of 14:09, 12 February 2021
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−	Besides, different value of eccentric distance are set to evaluate the effects of eccentric distance on the kinematic behavior of the rotor, as shown in [[#img-10\|Figure 10]]0. It can noted in [[#img-10\|Figure 10]], the rotor rotates at a faster velocity, a larger angular velocity and angular acceleration when selecting a larger value of the eccentric distance.	+	Besides, different value of eccentric distance are set to evaluate the effects of eccentric distance on the kinematic behavior of the rotor, as shown in [[#img-10\|Figure 10]]. It can noted in [[#img-10\|Figure 10]], the rotor rotates at a faster velocity, a larger angular velocity and angular acceleration when selecting a larger value of the eccentric distance.

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← Older revision		Revision as of 13:58, 12 February 2021
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−	Besides, different value of eccentric distance are set to evaluate the effects of eccentric distance on the kinematic behavior of the rotor, ~~shown~~ as in Figure 10. It can noted in [[#img-10\|Figure 10]], the rotor rotates at a faster velocity, a larger angular velocity and angular acceleration when selecting a larger value of the eccentric distance.	+	Besides, different value of eccentric distance are set to evaluate the effects of eccentric distance on the kinematic behavior of the rotor, as shown in [[#img-10\|Figure 10]]0. It can noted in [[#img-10\|Figure 10]], the rotor rotates at a faster velocity, a larger angular velocity and angular acceleration when selecting a larger value of the eccentric distance.

	{\| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"		{\| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"

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 |}
-where <math>e</math> is the eccentric distance of the crankshaft and <math>r</math> is the radius of the rotor. Shown as in Figure 2, the minimum extension length of the sliding vane is zero when the crankshaft angle, <math>\theta</math>, equals to zero or <math>2\pi</math> while its maximum value is <math>2e</math> when the crankshaft angle equals to <math>\pi</math>. By differentiating the equation (1), the velocity of the sliding vane, <math>v_s</math>, and acceleration of the sliding vane, <math>a_s</math>, can be expressed as,
+where <math>e</math> is the eccentric distance of the crankshaft and <math>r</math> is the radius of the rotor. Shown as in [[#img-2|Figure 2]], the minimum extension length of the sliding vane is zero when the crankshaft angle, <math>\theta</math>, equals to zero or <math>2\pi</math> while its maximum value is <math>2e</math> when the crankshaft angle equals to <math>\pi</math>. By differentiating the equation (1), the velocity of the sliding vane, <math>v_s</math>, and acceleration of the sliding vane, <math>a_s</math>, can be expressed as,
 {| class="formulaSCP" style="width: 100%; text-align: center;"
@@ Line 98: / Line 98: @@
 |}
-where <math>\omega</math> is the angular speed of the crankshaft which can be obtained as <math>\omega =n\pi /30</math>, where <math>n</math> is the rotation rate of the pump. Shown as in Figure 3, the round end of the sliding vane that hinged into the rotor rotates reversely along with the rotor. Its relative angular velocity, <math>\omega_r</math>, can be expressed as,
+where <math>\omega</math> is the angular speed of the crankshaft which can be obtained as <math>\omega =n\pi /30</math>, where <math>n</math> is the rotation rate of the pump. Shown as in [[#img-3|Figure 3]], the round end of the sliding vane that hinged into the rotor rotates reversely along with the rotor. Its relative angular velocity, <math>\omega_r</math>, can be expressed as,
 {| class="formulaSCP" style="width: 100%; text-align: center;"

@@ Line 237: / Line 237: @@
 ===4.1 Force model for sliding vane===
-The forces acting on the sliding vane are defined to be positive when their directions are the same as the positive direction of the <math>X</math>-axis or <math>Y</math>-axis of the established coordinate system <math>XOY</math>, shown as in Figure 5. The forces acting on the sliding vane include:
+The forces acting on the sliding vane are defined to be positive when their directions are the same as the positive direction of the <math>X</math>-axis or <math>Y</math>-axis of the established coordinate system <math>XOY</math>, shown as in [[#img-5|Figure 5]]. The forces acting on the sliding vane include:
 * The normal force (<math>F_n</math>) and tangential force (<math>F_t</math>) at the round end of the sliding vane.
@@ Line 329: / Line 329: @@
-Different pressure exist between the intake chamber and discharge chamber of the pump during its application. The pressure difference induced force would loaded on the rotor during the application of the pump, shown as in Figure 6. The value of the force can be obtained as,
+Different pressure exist between the intake chamber and discharge chamber of the pump during its application. The pressure difference induced force would loaded on the rotor during the application of the pump, shown as in [[#img-6|Figure 6]]. The value of the force can be obtained as,
 {| class="formulaSCP" style="width: 100%; text-align: center;"

← Older revision		Revision as of 13:44, 12 February 2021
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−	The movement at point <math>A</math> is rotating around the rotational coordinate system <math>X_1 O_1 Y_1</math>. Then, the relative velocity at point <math>A</math> is vertical to <math>O_1 A</math> and its value can be obtained as,	+	The movement at point <math>A</math> is rotating around the rotational coordinate system <math>X_1 O_1 Y_1</math> ([[#img-4\|Figure 4]]). Then, the relative velocity at point <math>A</math> is vertical to <math>O_1 A</math> and its value can be obtained as,

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 ==2. Structural characteristics and working principle==
-Shown as in Figure 1, the proposed ERMP consists of a rotor, a sliding vane, a housing case, and a crankshaft. The rotor is eccentrically assembly in the cylinder that is assembly with the housing case. Due to the outside wall of the rotor and the inside wall of the cylinder are tangent to each other, a crescent-shaped working chamber is formed by the inside wall of the cylinder and the outside wall of the rotor. The upper end the sliding vane is inserted in the groove of the housing case while the lower end is assembly with the rotor by a joint. In such case, the formed crescent-shaped chamber is divided into an intake chamber and a discharge chamber by the sliding vane. The intake port and discharge port of the pump are connected to the intake chamber and discharge chamber, respectively.
+Shown as in [[#img-1|Figure 1]], the proposed ERMP consists of a rotor, a sliding vane, a housing case, and a crankshaft. The rotor is eccentrically assembly in the cylinder that is assembly with the housing case. Due to the outside wall of the rotor and the inside wall of the cylinder are tangent to each other, a crescent-shaped working chamber is formed by the inside wall of the cylinder and the outside wall of the rotor. The upper end the sliding vane is inserted in the groove of the housing case while the lower end is assembly with the rotor by a joint. In such case, the formed crescent-shaped chamber is divided into an intake chamber and a discharge chamber by the sliding vane. The intake port and discharge port of the pump are connected to the intake chamber and discharge chamber, respectively.
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@@ Line 42: / Line 42: @@
-During the operation of the pump, the rotor is driven by the crankshaft, which is rotate clockwise around its geometrical axis, to swing in the cylinder and change the volume of the crescent-shaped working chamber. At the same time, the sliding vane reciprocate straightly in the vane slot. Due to the compound motion of the vane, the volumes of the divided intake chamber and discharge chamber vary gradually, and thus the intake -discharge process is resulted, shown as in Figure 2. The volume of the intake chamber increase with the crankshaft angle of ''θ ''and result in a vacuum in this area during the intake process. Meanwhile, the volume of the discharge chamber decrease with the crankshaft angle of ''θ ''during the discharge process. In such case, the pump inhales the multiphase fluid continuously into the intake chamber through the intake port of the pump during the intake process and discharge the multiphase fluid out of the pump through the discharge port during the discharge process.
+During the operation of the pump, the rotor is driven by the crankshaft, which is rotate clockwise around its geometrical axis, to swing in the cylinder and change the volume of the crescent-shaped working chamber. At the same time, the sliding vane reciprocate straightly in the vane slot. Due to the compound motion of the vane, the volumes of the divided intake chamber and discharge chamber vary gradually, and thus the intake -discharge process is resulted, shown as in [[#img-2|Figure 2]]. The volume of the intake chamber increase with the crankshaft angle of <math>\theta</math>  and result in a vacuum in this area during the intake process. Meanwhile, the volume of the discharge chamber decrease with the crankshaft angle of <math>\theta</math> during the discharge process. In such case, the pump inhales the multiphase fluid continuously into the intake chamber through the intake port of the pump during the intake process and discharge the multiphase fluid out of the pump through the discharge port during the discharge process.
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@@ Line 54: / Line 54: @@
 ===3.1 Velocity and acceleration of the sliding vane===
-The rotor driven by the crankshaft, which rotates at a uniform speed, exhibits a composite planar motion. Simultaneously, the sliding vane driven by the rotor reciprocates along the vane slot. In order to analyze the kinematic characteristics of the sliding vane and the rotor, a fixed coordinate system and a rotational coordinate system have been established. Shown as in Figure 3, the fixed coordinate system <math>X O Y</math> locates the origin point at the centrum of pump’s cylinder and <math>Y</math>-axis crossing through the centerline of sliding vane. The rotational coordinate system <math>X_1 O_1 Y_1</math> locates the origin point at the centrum of the rotor and <math>Y_1</math>-axis crossing the center of round end of the sliding vane. The established rotational coordinate system <math>X_1 O_1 Y_1</math> rotates synchronously with the rotor based on the radius of the eccentric distance of the crankshaft.
+The rotor driven by the crankshaft, which rotates at a uniform speed, exhibits a composite planar motion. Simultaneously, the sliding vane driven by the rotor reciprocates along the vane slot. In order to analyze the kinematic characteristics of the sliding vane and the rotor, a fixed coordinate system and a rotational coordinate system have been established. Shown as in [[#img-3|Figure 3]], the fixed coordinate system <math>X O Y</math> locates the origin point at the centrum of pump’s cylinder and <math>Y</math>-axis crossing through the centerline of sliding vane. The rotational coordinate system <math>X_1 O_1 Y_1</math> locates the origin point at the centrum of the rotor and <math>Y_1</math>-axis crossing the center of round end of the sliding vane. The established rotational coordinate system <math>X_1 O_1 Y_1</math> rotates synchronously with the rotor based on the radius of the eccentric distance of the crankshaft.
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@@ Line 570: / Line 570: @@
 ==References==
 [1] Porto F., Larson A.  Multiphase pump field trials demonstrate practical applications for the technology. SPE Prod. Facil., 12(3):159–164, 1996.
@@ Line 600: / Line 601: @@
 [15] Muller L.D., Rohlfing G., Spelter H.  Twin screw pumps help improving oil recovery in mature fields and transfer heavy crude oil over long distances. Oil Gas Eur. Mag., 35(3):127–131, 2009.

@@ Line 571: / Line 571: @@
 ==References==
-[1] Porto F., Larson A. 1996. Multiphase Pump Field Trials Demonstrate Practical Applications for the Technology. SPE Prod. Facil., 12(3): 159–164.
+[1] Porto F., Larson A.  Multiphase pump field trials demonstrate practical applications for the technology. SPE Prod. Facil., 12(3):159–164, 1996.
-[2] Chynoweth E. 1986. Twin Screw Pump is Developed for Multiphase Applications. Process Eng. London, 67(12): 27.
+[2] Chynoweth E.  Twin screw pump is developed for multiphase applications. Process Eng. London, 67(12):27, 1986.
-[3] Neumann W. 1991. Efficient Multiphase Pump Station for Onshore Application and Prospects for Offshore Application. Proceedings of the Eighth International Pump Users Symposium, Texas A&M Univ., College Station, TX: 43–48.
+[3] Neumann W.  Efficient multiphase pump station for onshore application and prospects for offshore application. Proceedings of the Eighth International Pump Users Symposium, Texas A&M Univ., College Station, TX, 43–48, 1991.
-[4] Beran W. T. 1994. On the Threshold: Subsea Multiphase Pumping. Proceedings of the 1994 SPE Annual Technical Conference and Exhibition, SPE, New Orleans: 569–581.
+[4] Beran W.T.  On the threshold: subsea multiphase pumping. Proceedings of the 1994 SPE Annual Technical Conference and Exhibition, SPE, New Orleans, 569–581, 1994.
-[5] Salis D. J., Cordner M., Birnov M. 1998. Multiphase Pumping Comes of Age. World Pumps, 384: 53–54.
+[5] Salis D.J., Cordner M., Birnov M.  Multiphase pumping comes of age. World Pumps, 384:53–54, 1998.
-[6] Leporcher E., Delaytermoz A., Renault J. F., Gerbier A., Burger O. 2001. Deployment of Multiphase Pumps on a North Sea Field. Proceedings of the 2001 SPE Annual Technical Conference and Exhibition, SPE, New Orleans: 1755–1766.
+[6] Leporcher E., Delaytermoz A., Renault J.F., Gerbier A., Burger O. Deployment of multiphase pumps on a north sea field. Proceedings of the 2001 SPE Annual Technical Conference and Exhibition, SPE, New Orleans, 1755–1766, 2001.
-[7] Dogru A. H., Hamoud A. A., Barlow S. G. 2004. Multiphase Pump Recovers More Oil in a Mature Carbonate Reservoir. J. Petrol. Technol., 56(2): 64–67.
+[7] Dogru A.H., Hamoud A.A., Barlow S.G.  Multiphase pump recovers more oil in a mature carbonate reservoir. J. Petrol. Technol., 56(2):64–67, 2004.
-[8] Bornemann P. 2009. Multiphase Pumps – the Path to Success. World Pumps, 511: 18–20.
+[8] Bornemann P.  Multiphase pumps – the path to success. World Pumps, 511:18–20, 2009.
-[9] Cao S., Peng G., Yu Z. 2005. Hydrodynamic Design of Rotodynamic Pump Impeller for Multiphase Pumping by Combined Approach of Inverse Design and CFD Analysis. ASME J. Fluids Eng., 127(2): 330–338.
+[9] Cao S., Peng G., Yu Z.  Hydrodynamic design of rotodynamic pump impeller for multiphase pumping by combined approach of inverse design and cfd analysis. ASME J. Fluids Eng., 127(2):330–338, 2005.
-[10] Cao F., Peng X., Xing Z., Shu P. 2001. Thermodynamic Performance Simulation of a Twin-Screw Multiphase Pump. Proc. Inst. Mech. Eng., Part E, 215(2): 157–163.
+[10] Cao F., Peng X., Xing Z., Shu P.  Thermodynamic performance simulation of a twin-screw multiphase pump. Proc. Inst. Mech. Eng., Part E, 215(2):157–163, 2001.
-[11] Chynoweth E. Twin screw pump is developed for multiphase applications. Process Eng (London) 1986; 67(12): 27–31.
+[11] Chynoweth E. Twin screw pump is developed for multiphase applications. Process Eng. London, 67(12):27–31, 1986.
-[12] Dal P. D., Larson L. A. 1996. Multiphase pump field trials demonstrate practical applications for the technology. SPE Prod Facilities. 12(3): 159–164.
+[12] Dal P.D., Larson L.A.  Multiphase pump field trials demonstrate practical applications for the technology. SPE Prod. Facilities. 12(3):159–164, 1996.
-[13] Ryazantsev V.M., Plyasov V.V., Shumakov N. D. 2004. Twin-screw pumps for transferring petroleum-water-gas multiphase mixture or diesel fuel. Chem Petrol Eng, 40(8): 407–410.
+[13] Ryazantsev V.M., Plyasov V.V., Shumakov N.D.  Twin-screw pumps for transferring petroleum-water-gas multiphase mixture or diesel fuel. Chem. Petrol. Eng., 40(8):407–410, 2004.
-[14] Nakashima C. Y., Oliveira S. 2006. Heat transfer in a twin-screw multiphase pump: thermal modeling and one application in the petroleum industry. Energy, 31(15): 3415–3425.
+[14] Nakashima C. Y., Oliveira S.  Heat transfer in a twin-screw multiphase pump: thermal modeling and one application in the petroleum industry. Energy, 31(15):3415–3425, 2006.
-[15] Muller L. D., Rohlfing G., Spelter H. 2009. Twin screw pumps help improving oil recovery in mature fields and transfer heavy crude oil over long distances. Oil Gas Eur Mag, 35(3): 127–131.
+[15] Muller L.D., Rohlfing G., Spelter H.  Twin screw pumps help improving oil recovery in mature fields and transfer heavy crude oil over long distances. Oil Gas Eur. Mag., 35(3):127–131, 2009.

← Older revision		Revision as of 12:07, 27 March 2020
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−	In this study, four points on the contour of rotor (<math>C_2</math>, <math>C_3</math>, <math>C_4</math> and <math>C_5</math>) and four points on the middle position of end surface of rotor (<math>B_2</math>, <math>B_3</math>, <math>B_4</math> and <math>B_5</math>) are selected to simulate velocity of rotor on the end surface, shown as in Figure 8. Figure 9 shows the velocity variations of each selected points on the end surface of rotor. The velocities of each selected points vary with the rotation of the crankshaft in a same trend. The points located at <math>3\pi /2</math> position of the rotor, such as points <math>C_5</math> and <math>B_5</math>, have larger velocities compared with the points in other area. Besides, the more the points approach to the center of the rotor, the smaller velocities they have. Then, the area located at opposite of the sliding vane (<math>3\pi /2</math> position of the rotor) and located at contour part of the rotor, such as area of point <math>C_5</math>>, have wear problem during application of the pump and attention need to be paid.	+	In this study, four points on the contour of rotor (<math>C_2</math>, <math>C_3</math>, <math>C_4</math> and <math>C_5</math>) and four points on the middle position of end surface of rotor (<math>B_2</math>, <math>B_3</math>, <math>B_4</math> and <math>B_5</math>) are selected to simulate velocity of rotor on the end surface, shown as in Figure 8. Figure 9 shows the velocity variations of each selected points on the end surface of rotor. The velocities of each selected points vary with the rotation of the crankshaft in a same trend. The points located at <math>3\pi /2</math> position of the rotor, such as points <math>C_5</math> and <math>B_5</math>, have larger velocities compared with the points in other area. Besides, the more the points approach to the center of the rotor, the smaller velocities they have. Then, the area located at opposite of the sliding vane (<math>3\pi /2</math> position of the rotor) and located at contour part of the rotor, such as area of point <math>C_5</math>, have wear problem during application of the pump and attention need to be paid.

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