COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Computation of Turbulent Flows in Natural Gas Pipes with Different
Rectifiers
Z. L. Li*, Y. X. Zhang
Department of Mechanical and Electronic Engineering, China University of Petroleum-Beijing, 102249 China
Email: [email protected]
Abstract With the development of natural gas industry, improving the accuracy of the flowmeter systems is becoming
the common concerned problem both corporations and customers. Many experiments demonstrate that the different
flow field structures in pipes with diverse baffle installations have great influence on the measure accuracy of
flowmeters. In order to measure the flux in pipes more accurate, the flowmeters must be installed downstream the
baffles far away so that the irregular flows induced by baffles have less influence on the flowmeters. However, the
installation lengths downstream baffles for flowmeters in ISO are usually much longer than the allowable lengths for
the local flowmeters. To decrease the installation lengths and loss measure accuracy of flowmeters as little as possible,
it is necessary to study the flows in pipes with baffles. CFD is a good tool for the study. Here, the flows in a diffusive
pipe with various rectifiers are computed as examples. The lengths of the irregular flows induced by the diffuser and
rectifier are shown. By analyzing and comparison the numerical results, the installation lengths for flowmeters and the
rectification of the different rectifiers are confirmed. The study conclusions will be very useful for guiding the local
flowmeter selection and installation in the future.
Key words: natural gas measurement, CFD, rectifier, flowmeter, diffusive pipe
INTRODUCTION
It is necessary and important to measure the flux of natural gas during its exploitation, transportation and
consumption. The accurate, credible and just natural gas measurement directly influences the economic benefit both
providers and consumers. Many experiments have been carried on natural gas measurement based on diverse
domestic and foreign flowmeters in recent years. The results of these experiments show that the measure accuracy of
flowmeters are influenced by many factors, but the different flow fields in pipes with diverse baffle installations
have greater influence than the other factors. The flux is usually measured by means of experiential formulas or
mathematic models based on ideal flows for almost all flowmeters except the volume flowmeters. The measurement
accuracy of flowmeters is determined mainly on the agreement between real flows and ideal models. The study
methods for flows include theoretic analysis, experimental investigation and numerical simulation. The numerical
simulation of flows is achieved by CFD (computational fluid dynamics). CFD needs lower cost and shorter period
contrast to theoretic analysis and experimental investigation. Otherwise, CFD has good repetition, agility and
anti-jamming, it is limited much less than experiment. CFD presents the orientation of flow study. In this paper, the
flows in a diffusive pipe with diverse rectifier installations as examples are computed by CFD. At present, the
standard installation lengths downstream the classic baffles are usually much longer than the allowable lengths for
the local flowmeters. Decreasing the installation length and increasing the measurement precision is the purpose of
the study. The diffusive pipe computed is classic because its diffusive ratio is 50 millimeter to 100 millimeter which
is bigger than another applicable diffusive pipe with diffusive ratio of 100 millimeter to 150 millimeter. The bigger
diffusive ratio means stronger contrary pressure grads. The stronger contrary pressure grads means the greater
probability of flow separation and recirculation. For a contractive pipe, the pressure grads is plus, the irregular flow
length induced by flow separation and recirculation must be much shorter than the diffusive pipe.
By analysis and comparison the numerical results of the diffusive pipe with diverse rectifier installations, some
valuable conclusions were summarized. The conclusions are useful to guide the local flowmeter selection and
installation to improve the measurement accuracy of natural gas.
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MATHEMATIC MODEL
The average velocity at the inlet is V = 8m / s . The environmental temperature is 22℃. The pressure is approximate
0.8MPa. The density of the natural gas in pipe is 0.68 Kg/m3 . The kinetic coefficient is 1.603 × 10 −5 m 2 / s . The
velocity of sound in natural gas is 450m / s . The corresponding Mach number is much less than 0.3. The nature gas
flow should be computed as incompressible flow. Considering the computation services for measurement, the
steady results can be satisfactory to engineering demand.
The governing equations of steady incompressible turbulent flows can be written in uniform as follows, the
standard k − ε turbulent model is adopted.
∂ (φ u j )
∂x j
=
∂
∂x j
⎛ ∂φ ⎞
⎜⎜ Γφ
⎟⎟ + Sφ
⎝ ∂x j ⎠
(1)
Here, φ is a universal value in equation (1), u j is velocity component, Γ is general diffusion coefficient. While
φ is 1, (u,υ , w) , k and ε respectively, the Eq. (1) becomes continuity equation, three momentum component
equations, turbulent kinetic energy equation and turbulent dissipation rate equation.
Considering the present natural gas pipes with baffles have complicated boundaries, it is necessary to transform the
complicated physical space ( x, y, z ) to regular computational space ( ξ ,η , ζ ). In the computational space, the
governing equations are discretized by finite volume method. The equations discretized are solved by SIMPLEC
method [1]. To improve the numerical stability and precision, the convection terms of momentum equations are
discretized by QUICK scheme [2], the convection terms of k and ε equations are discretized by second-order
upwind scheme. The convergence criterion was the maximal relative error of the continuity equation, u , υ , w , k
and ε which was less than 10−4 .
The boundary conditions and governing equations together form the integrated mathematic model for the present
flows. The uniform velocity profile is given on the inlet boundary. The no-slip condition is given on the solid
boundaries. The k and ε on the inlet boundary are given directly by the velocity profile. On the solid boundary,
k and ε are determined by wall function [3]. All of the other boundaries are given Neumann condition.
NUMERICAL RESULTS
In order to measure the flux in diffusive pipe with diverse rectifiers more accurate, the flowmeter must be installed
downstream the diffuser and rectifiers far away so that the irregular flows induced by them have less influence. For
some classic baffles, the standard installation lengths are given through many experiments and much practice. For
example, for the new orifice-plate flowmeter, the standard installation length of confluent pipe is 145D which
sometimes is too long to install flowmeter because of limited local space. Computing the flows in pipes by CFD, it
takes less time and cost to select the shorter installation length and loss less measure accuracy of flowmeter.
The structure of natural gas flow field in pipe has great influence on the measurement. To improve the measurement
accuracy, the flowmeter must be installed downstream the baffles such as diffuser and rectifier far away to avoid the
irregular flow regions which include flow separation, recirculation, vortex shedding and so on. Therefore,
ascertaining the irregular flow regions of diffusive pipe with diverse rectifiers are an emphases for numerical
simulation.
500
Φ=100
inlet
Φ=50
The first task of CFD is grid generation. The diffusive pipe with the plate rectifier is shown as example. Fig. 1 shows
its structure and size. The origin of coordinates is at the center of the inlet. There are 35 orifices distributed
symmetrically on the plate rectifier. The diameters of the orifices are equal to 12 millimeter. Some classic cross
section grids are shown in Fig. 2.
13
rectifier
250
82
y
3000
x
z
Figure 1: The diffusive pipe with the plate rectifier
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outlet
z = 200
z = 300
z = 832
z = 2000
Figure 2: The cross section grid of the diffusive pipe with the plate rectifier
w/ (m/s)
w/ (m/s)
w/ (m/s)
Fig. 3 shows the velocity w distributions on x = 0 section of the diffusive pipe without rectifier. It indicates that w
distribution changes obviously at the diffuser and its downstream region which extends for approximate 5-6 times of
diameter. There is flow recirculation at the diffuser. At the diffuser, with the increasing of the flow cross section area,
the velocity w is decreasing. It can be derived form Bernoulli equation that the pressure is increasing, the contrary
pressure grads is formed which is the leading reason for flow separation and recirculation. Downstream the diffuser,
the w distribution resumes uniform for about 17 times of diameter which can be selected as the installation length for
flowmeter.
y / (m)
y / (m)
z = 300
z = 600
y / (m)
w/ (m/s)
w/ (m/s)
w/ (m/s)
z = 200
y / (m)
y / (m)
z = 1000
y / (m)
z = 1500
z = 2000
u / (m/s)
v / (m/s)
Figure3: The w distribution on x = 0 section of the diffusive pipe without rectifier
y / (m)
y / (m)
Figure 4: The velocity distribution of u and v on x = 0 section of the diffusive pipe without rectifier
Fig. 4 shows the velocity
u
and
v
distribution on x = 0 section of the diffusive pipe without rectifier. The curve 1,
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2 and 3 are at z = 330 , z = 1000 and z = 2000 respectively. The velocity u and v are great at z = 330 because of
the diffuser. Downstream the diffuser, u and v are decreasing gradually until they are very little where the flow
resumes uniform. u and v are greater near the pipe boundary than interior because of the viscous boundary layer.
y / (m)
w/ (m/s)
w/ (m/s)
w/ (m/s)
Fig. 5 shows the velocity w distribution on x = 0 section of the diffusive pipe with the plate rectifier shown in
figure 2. The w distribution is comparatively symmetrical through rectifier. Extending for about 12 times of diameter
downstream the plate rectifier, the w distribution resumes uniform. Compare with flow fields of the diffusive pipe
without rectifier, the recirculation at the diffuser is weaker because of the blockage of the plate rectifier which make
the contrary pressure grads at the diffuser is less, the length for resuming uniform flow downstream the plate rectifier
is shorter. In other words, the installation length for flowmeter is shorter.
y / (m)
z = 832
w/ (m/s)
w/ (m/s)
z = 300
w/ (m/s)
z = 200
y / (m)
y / (m)
y / (m)
z = 900
y / (m)
z = 1500
z = 2000
Figure 5: The w distribution on x = 0 section of the diffusive pipe with the plate rectifier
v / (m/s)
u / (m/s)
Fig. 6 shows the velocity u and v distribution on x = 0 section of the diffusive pipe without rectifier. The curve 1,
2 and 3 are at z = 330 , z = 860 and z = 2000 respectively. The velocity u and v are greatest at z = 330 because of
the diffuser, they take second place at z = 860 because of the plate rectifier, they are lest at z = 2000 . Downstream
the plate rectifier, u and v are decreasing enormously.
y / (m)
Figure6. The
u
and
v
y / (m)
distribution on x = 0 section of the diffusive pipe with the plate rectifier
Fig. 7 shows the velocity w distribution on x = 0 section of the diffusive pipe with the tube rectifier. There are 19
orifices in the tube rectifier. The diameter of all orifices is 20 millimeter. The total length of the tube rectifier is 220
millimeter. Extending for about 6 times of diameter downstream the tube rectifier, the w distribution resumes
uniform. Compare with Fig. 5. The recirculation is hardly seen at the diffuser. The length for resuming uniform flow
downstream the tube rectifier is shorter. The velocity u and v distribution characteristics are similar to Fig. 6.
Fig. 8 shows the velocity w distribution on x = 0 section of the diffusive pipe with the tube-plate rectifier. The
length of the tube rectifier is 40 millimeter. The length of the plate rectifier is 13 millimeter. The total length of the
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w/ (m/s)
w/ (m/s)
w/ (m/s)
y / (m)
y / (m)
w/ (m/s)
z = 1052
w/ (m/s)
z = 300
w/ (m/s)
z = 200
y / (m)
y / (m)
y / (m)
z = 1100
y / (m)
z = 1600
z = 2000
w/ (m/s)
w/ (m/s)
w/ (m/s)
Figure 7: The w distribution on x = 0 section of the diffusive pipe with the tube rectifier
y / (m)
z = 0.3
z = 832
w/ (m/s)
w/ (m/s)
y / (m)
z = 900
w/ (m/s)
y / (m)
y / (m)
y / (m)
z = 1187
z = 1200
y / (m)
z = 1700
Figure 8: The w distribution on x = 0 section of the diffusive pipe with the tube-plate rectifier
tube-plate rectifier is 355 millimeter. Extending for about 5 times of diameter downstream the tube-plate rectifier, the
velocity w on cross section is almost constant. The velocity distribution is in favor of the natural gas measurement.
The velocity u and v distribution characteristics are similar to Fig. 6.
The flow fields on other sections of the diffusive pipe with diverse rectifier installations are also simulated and
analyzed. It demonstrates that the flows in pipes are 3-D turbulence though the diffusive pipes with rectifiers are
symmetry. It demonstrates that the flows in diffusive pipe with diverse rectifiers are 3-D turbulent flows.
The experiments will be done soon to verify the numerical results. If the numerical results derived from suitable
mathematic model are in good agreement with the experiments, the CFD will become the leading method to guide
the local flowmeter selection and installation in the future.
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CONCLUSIONS
(1) The flows in diffusive pipe with diverse rectifiers are 3-D turbulence. The flows resume uniform for several
times of diameter downstream the baffles.
(2) To measure nature gas flux accurately, it is necessary to install flowmeter downstream the irregular regions
induced by baffles. The length of irregular flow region downstream the diffuser for diffusive pipe without rectifier is
about 17 times of diameter
(3) Although the rectifiers induce irregular flows, their rectification is prominent. Downstream the rectifiers, the
flows become symmetry and resume uniform in shorter length. The lengths for resuming uniform flow of the
diffusive pipe with the plate rectifier, tube rectifier and tube-plate rectifier are 12, 6 and 5 times of diameter
respectively downstream the rectifiers.
(4) The rectification of the tube-plate rectifier is best among the present rectifiers. The tube rectifier takes the second
place.
REFERENCES
1.
Van Doormaal JR, Raithby GD. Enhancement of the SIMPLE method for predicting incompressible fluid
flows. Num. Heat Transfer, 1984; 7: 147-163.
2.
Leonard BP. A stable and accurate convective modeling procedure based on quadratic upstream interpolation.
Comp Meth. Appl. Mech. Eng., 1979; 29: 59-98.
3.
Chieng CC, Launder BE. On the calculation of turbulent heat transport downstream from an abrupt pipe
expansion. Num. Heat Transfer, 1980; 3: 189-207.
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