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Development of a rotary clap mechanism for positive-displacement rotary pumps: Pump performance analysis

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Abstract

We have introduced a novel positive-displacement rotary pump named as rotary clap pump, and analyzed its working principles through a kinematic analysis in the previous study. That study mainly described fundamental design parameters of the rotary clap pump and their inter-relationships. As a follow-up research, this study presents the pump performance of the rotary clap pump such as the pressure, driving torque, and efficiency characteristics using related theories and some basic assumptions. In the pressure analysis, the effect of friction, mass acceleration, piping components, and gravity were considered. The forces acting on the pump components and the driving torque are calculated using vector equations based on the results of the previous study. The volumetric, torque, and overall efficiencies are analyzed by calculating the slip flow and frictional forces caused by fluid viscosity. We also present the conditions that minimize the input power and forces acting on the components. The experimental study for the rotary clap pump including comparison with analysis results is prepared to the follow-up paper.

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Abbreviations

ϕ :

Absolute angular displacement of the gear, rad

rc :

Crank radius, m

θc :

Angular displacement of the crank, rad

L:

Displacement between pins P1 and P2, m

rp1 :

Radius of pin P1 with respect to the center of rotor O, m

rp2 :

Radius of pin P2 with respect to the center of rotor O, m

θp1 :

Angular displacement of vector OP 1 , rad

θp2 :

Angular displacement of vector OP 2 , rad

Δpf1-2 :

Pressure head caused by friction, Pa

ρ:

Density of fluid, kg/m3

f1-2 :

Friction factor

l1-2 :

Distance between the two sides of the control volume, m

D1-2 :

Pipe diameter, m

Q1-2 :

Flow rate, m3/sec

A1-2 :

Pipe’s cross-section area, m2

Δpa1-2 :

Pressure head due to mass acceleration, Pa

\({\dot Q_{1 - 2}}\) :

Derivative with respect to the time of flow rate, m3/sec2

ΔpK1-2 :

Pressure head caused by minor losses, Pa

K:

Loss coefficient for pipe components

Δph1-2 :

Pressure head due to gravity, Pa

p2-p1 :

Total pressure head (differential pressure) of the pipe, Pa

k:

Number of control volumes

Σ(pk+1,s-pk,s):

Total pressure head in the suction lines of the pump, respectively, Pa

Σ(pk+1,d-pk,d):

Total pressure head in the discharge lines of the pump, respectively, Pa

θrel :

Relative angular displacement of the two rotors, θp1- θp2, rad

Wj :

Width of jaw, m

h:

Jaw height, m

N:

Number of jaws

ro :

Outer radius of rotor, m

\({\dot \theta _{p1}}\) :

Angular velocity of vector OP 1 , rad/sec

\({\dot \theta _{p2}}\) :

Angular velocity of vector OP 2 , rad/sec

\({\ddot \theta _{p1}}\) :

Angular acceleration of vector OP 1 , rad/sec

\({\ddot \theta _{p2}}\) :

Angular acceleration of vector OP 2 , rad/sec2

Zr :

Number of teeth on the fixed internal gear

Zp :

Number of teeth on the gear of shaft link

\({\dot \theta _c}\) :

Angular velocity of the crank, rad/sec

FR1 :

Force acting on the rotor 1, N

FR2 :

Force acting on the rotor 2, N

Fd :

Force caused by the discharging pressure, N

Fs :

Force caused by the suction pressure, N

TOR1 :

Torque acting on the rotor 1, N·m

TOR2 :

Torque acting on the rotor 2, N·m

ΣF SUM :

Summation of the force vectors acting on the gear and shaft link, N

ΣT c :

Summation of the torque vectors acting on the gear and shaft link, N·m

IR1 :

Moment of inertia for rotor 1, kg·m2

IR2 :

Moment of inertia for rotor 2, kg·m2

Ti :

Driving torque about point O

Dp = D/2π:

Displacement per degree, m3/rad

Tth :

Theoretical torque, N·m

p:

Discharge pressure, Pa

v:

Velocity in the direction of the x axis, m/sec

τ:

Shear stress on a plane parallel to the xz plane, N/m2

μ:

Coefficient of the fluid viscosity, N·sec/m2

A:

Area of the flat plate, m2

τm :

Shear stress at the moving plate located at y = δ, N/m2

τf :

Shear stress at the fixed plate located at y = 0, N/m2

l:

Length of the plate, m

ΔQs :

Slip flow of a conventional positive-displacement pump, m3/sec

Δp:

Pressure drop through the passage, Pa

Cs :

A dimensionless coefficient

Tv :

Viscous torque, N·m

Cd :

Coefficient of the viscous drag dependent on the pump geometry

Tf :

Pressure-dependent frictional torque, N·m

Cf :

Coefficient of friction dependent on the pump geometry

(Qsc1)tot :

Total slip flow between the upper and lower surfaces of jaw 1 and the chamber, m3/sec

(Qss1)tot :

Total slip flow between the side surfaces of jaw 1 and the chamber, m3/sec

Qss1f :

Slip flow between the front side surface of jaw 1 and the chamber, m3/sec

Qss1b :

Slip flow between the back side surface of jaw 1 and the chamber, m3/sec

(Qsc2)tot :

Total slip flow between the upper and lower surfaces of jaw 2 and the chamber, m3/sec

(Qss2)tot :

Total slip flow between the side surfaces of jaw 2 and the chamber, m3/sec

(F’sc1)tot :

Total forces at jaw 1 caused by the fluid viscosity between the upper and lower surfaces of jaw 1 and the chamber, N

(F’ss1)tot :

Total forces at jaw 1 caused by fluid viscosity between the side surfaces of jaw 1 and the chamber, N

F’ss1f :

Forces at jaw 1 caused by the fluid viscosity between the front side surface of jaw 1 and the chamber, N

F’sc1b :

Forces at jaw 1 caused by the fluid viscosity between the back side surface of jaw 1 and the chamber, N

(F’sc2)tot:

Total forces at jaw 2 caused by the fluid viscosity between the upper and lower surfaces of jaw 2 and the chamber, N

(F’ss2)tot:

Total forces at jaw 2 caused by the fluid viscosity between the side surfaces of jaw 2 and the chamber, N

References

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Author information

Authors and Affiliations

  1. Upland-field Machinery, Research Center, Kyungpook National University, 80, Daehak-ro, Buk-gu, Daegu, 41566, South Korea

    Sung-Bo Shim

  2. Department of Biosystems and Biometerials Science and Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

    Young-Jun Park & Kyeong-Uk Kim

  3. Research Institute for Agriculture and Life Sciences, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

    Young-Jun Park

  4. Department of Biosystems Engineering, Kangwon National University, 1 Kangwondaehak-gil, Chuncheon, Gangwon-do, 24341, South Korea

    Ju-Seok Nam

  5. Department of System Reliability, Korea Institute of Machinery and Materials, 1156, Gajeongbuk-ro, Yuseong-gu, Daejeon, 34103, South Korea

    Su-Chul Kim

  6. ClapMC Co., Ltd., 156, Gajeongbuk-ro, Yuseong-gu, Daejeon, 34103, South Korea

    Jong-Mun Kim

Authors
  1. Sung-Bo Shim
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  2. Young-Jun Park
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  3. Ju-Seok Nam
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  4. Su-Chul Kim
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  5. Jong-Mun Kim
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  6. Kyeong-Uk Kim
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Correspondence to Sung-Bo Shim.

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Shim, SB., Park, YJ., Nam, JS. et al. Development of a rotary clap mechanism for positive-displacement rotary pumps: Pump performance analysis. Int. J. Precis. Eng. Manuf. 18, 575–585 (2017). https://doi.org/10.1007/s12541-017-0069-5

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  • DOI: https://doi.org/10.1007/s12541-017-0069-5

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