computational modeling of the three-dimensional flow in a metallic stator progressing cavity pump
TRANSCRIPT
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Computational Modeling of the Three-Dimensional Flow in a Metallic Stator Progressing
Cavity Pump
Emilio E. Paladino; João A. Lima and Rairam F. Almeida
UFRN / DEM / PPGEM, Brazil
Benno W. Assmann
PETROBRAS / UN-RNCE, Brazil
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Introduction
• Since Moineau (1930), several approaches for evaluate PCP performance have been employed.
• Robello & Saveth (1998) , Olivet et al. (2002), Gamboaet al. (2002) and other works from these groups, constitute main references for this research field, theoretical or experimental
• Experiments are expensive and normally provide only global values
• Simplified approaches have been proposed, but could be inaccurate or fail in complex situations
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Introduction• Simplified models
– Quick responses to changes in operational variables or geometrical parameters
– Only global parameters could be obtained (like )
– Unusable for complex situations as multiphase flow (most common operation situation)
– Need for guessed parameters
• Three dimensional computational model
– Detailed knowledge of the flow field for geometry and operation optimization (too costly if done experimentally)
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Introduction
• Three dimensional computational model (cont.)
– Torque (and so power) can be calculatred from model, including hydraulic loosses
– Correct representation of the flow field (Hagen-Poiseulle flow hypothesis can be too strong in some cases)
– Multiphase flow can be simulated, having adequate models for interface morphology and momentum transfer
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Preliminary Analysis
• Hypotheses
–
– Hagen-Pouisuille flow in constant area channel for slip calculation
2
2 H
Lp f UD
ρ∆ = ⇒w
b
L
Flow
Flow
∆p
2 where ReReC Sf
bρµ
= =
38 bw pSC Lµ
∆=
22 34Lp f S
b wρ
∆ =
Pumped Displaced SlipV V V= −& & &
2
2 H
Lp f UD
ρ∆ = ⇒
• General aproach in simplified models:
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Preliminary Analysis
• Assuming that the volumetric flow can be calculated as,
• Some conclusions can be obtained– For laminar flow the slip depends linearly on ∆p and µ– The clearance (w) appears elevated to the cube, which
means it has a strong influence on the volumetric efficiency
– The channel length L is estimated in this kind of approaches but can be related to the pump length and has also a inverse linear influence on volumetric efficiency
{Depends on Geometry,Depends on Geometricp and Fluid PropertiesParameters and RPM
Pumped Displaced SlipV V V
∆
= −& & &14243 1 S
VolD
VV
η⇒ = −&
&
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Computational Model
• Main challenges– Mesh generation
– Mesh motion set-up
• Characteristics
– Full 3D, transient detailed model
– Complete Navier-Stokes equation solved within the fluid region (Allows for turbulence and multiphase modeling)
– Element Based Finite Volume Method used for equation discretization
– Fully coupled solver for pressure and velocity (mass and momentum equations)
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Computational Model
• The mesh generation process was a great challenge because of the element aspect ratio in near clearance regions
• Furthermore, mesh motion imposes huge element deformation along time
• Imposing the mesh motion directly in CFD code resulted in element distortion due to numerical diffusivity on the mesh motion calculation
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Computational Model• Mesh motion
– Imposed into the whole mesh (at each node)
– Meshes generated autimatically for each timestep
– FORTRAN CFX User routines needed
EnLithen Here
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Results and Discussion
• Model Validation
– Gamboa et al. (2002) experiments used to validate the model
– Some confusion with used parameters
– Experiments data:
• Geometry
3 (5) (?)Pitch number
0,187 mm (?)
Clearance
39.878 mmRotor Diameter
119.99 mmStator Pitch
• Fluid properties:
µ = 1 cPµ = 42 cP
ρ = 1000 kg/m3
ρ = 868 kg/m3
WaterOil
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• Volumetric flow vs. Pressure
Results and Discussion
0 20 40 60 80 100 120 140
∆P [psig]
0
50
100
150
200
250
QN
ET [b
pd]
Oil 42 cP 300 RPM
This work w = 0.185 mmThis work w = 0.370 mmGamboa et al, 2002
0 20 40 60 80 100 120 140
∆P [psig]
0
50
100
150
200
250
QN
ET [b
pd]
Oil 42 cP 300 RPM
3 pitches This work5 pitches This workGamboa et al, 2002
Different clearances Different number of pitches
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Results and Discussion
• Volumetric flow vs. Pressure
– Different RPM
0 20 40 60 80 100 120 140
∆P [psig]
0
50
100
150
200
250
QN
ET [b
pd]
Oil 42 cP300 RPM This work100 RPM This work300 RPM (Gamboa et al, 2002)100 RPM (Gamboa et al, 2002)
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Results and Discussion
• Volumetric flow vs. Pressure
– Water flow (1cP)
0 20 40 60
∆P [psig]
0
50
100
150
200
250
QN
ET [b
pd]
Water 1 cP300 RPM This work400 RPM This work300 RPM (Gamboa et al, 2003)400 RPM (Gamboa et al, 2003)
0 20 40 60
∆P [psig]
0
50
100
150
200
250
QN
ET [b
pd]
Water 1 cP300 RPM This work400 RPM This work300 RPM (Gamboa et al, 2003)400 RPM (Gamboa et al, 2003)
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Results and Discussion
• Volumetric flow vs. Pressure
– Eddy viscosity turbulent model (turbulence modeling study running on)
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Results and Discussion
• Pressure distribution EnLithen Here
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Results and Discussion
• Pressure distribution
Longitudinal slippage Transversal
slippage
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Results and Discussion• Velocity at clearance and pressure along the rotor
– Strong transient flow in sealing regions
EnLithen Here
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Conclusions
• A detailed CFD model for a rigid stator PCP, considering the rotor motion, was successfully implemented
• Provides detailed information about the pump fluid dynamics inside the PCP,
• This allows to calculate performance and can be used for geometrical and operational optimization
• Detailed pressure fields available allow the development of fluid-structure interaction models in order to study the elastomeric stator
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Further work
• Implementation of the Fluid-Structure Interaction into the model in order consider the elastomerstator
• Analysis of the influence of the turbulence modeling
• Multiphase flow modeling (Experimental support needed)
• Etc.