Modelling of flow in pipes and ultrasonic flowmeter bodies

The contribution using CFD system ANSYS/FL flow parts flow and selected velocity profiles in smooth p selected results of the numer partially comparison with exp


Introduction
Ultrasonic flowmeters are used more tha are applicable to liquids, gases and mul but their applicability has limits [1].T describes selected results obtained du research project concerning flow par flowmeter bodies for industrial applicati The ultrasonic flowmeter mostly con and of the electronic control unit.The f determined from the difference between of ultrasonic waves propagating in the m and against the flow direction.
The work on the project was divi stages; selected of these are presented in The first one is the solution of velo the developed flow in the circular pipe.the modelling of flow in the flowmete and with hydraulic perturbations.Very the modelling of flow in the body o ultrasonic flowmeter.
The goal of the work was to obtain and velocity profiles for development bodies and software algorithms for e units.The project was also focused the hydraulic perturbations of liquids to measured values.Numerical modelling research was performed during the proj about behaviour of flow in measuring in 2 Flow in parts of ultrasonic Bodies of ultrasonic flowmeters can a shaped casting or a weldment, both de by precision machining.The shape of th simple for efficient manufacturing an cu.cz flowmeter n be designed as esign are finished he body should be nd to have low influence to the flow field.includes inlet and outlet cone.Ultrasonic probes are a The figure 1 shows some exa with pockets for probes.

Flow in pipe
The flowmeters are mounted i the straight section before sho stabilize the flow.The pipe a basic shape of the flowmete crucial for accuracy of the flo path flowmeters are calibrate and the calibration curve is e case of multi-path flowmeter more complicated problem.
Multi-paths arrangement information about flow and t higher accuracy.The software probes of individual paths, var suitable method is, for The software in instrument can dies ultrasonic flowmeters create CFD models of mmarizes the results of second part describes flowmeters and their In some cases, the body dded to the main body.amples of flowmeter bodies bodies.
into pipes and the length of ould be sufficiently long to can be also supposed as er body.Velocity profile is owmeter.The oneor two- ed in the testing laboratory entered into control unit.In rs it is necessary to solve t gives markedly wide the flowmeter can achieve e integrates the values from rious methods are used, and example, OWICS [2].n make corrections of flow- rate with the help of values from single paths and perhaps even data from thermometer and viscosimeter.The computational procedures take into account Reynolds number, temperature and viscosity of the fluid and flow disturbances.
The basic turbulent velocity profile is the profile of developed flow without disturbances.Several methods were used to obtain this type of profile.The profiles were compared only in main flow, because the area close the wall wasn't important for that purpose.

Analytical velocity profiles
The formula for developed flow profile in smooth pipe can be found in various forms.
The first one is the power law profile.The formula for the velocity u is simple and the relationship 1 can be written in the following form: More complicated power law are defined as: Figure 3. Velocity profiles -relationship 2.
Another form of the relationship is the logarithmic law of the profile: The profile should interpolate the experimental results and for the practical using seems usable.Interesting solution of the analytical velocity profile is described in [3].It regards the power law profile depending on the pressure gradient.
The advantage of the relationship is the simplicity and wide use.The disadvantage is the need to know the pressure drop and inaccuracy in the published version for now, see Figure 5.The value for the pressure gradient in (13) was obtained from CFD computations because the experimental values weren't available.The profiles seem to be too flat, but the development of the relationship is still in progress.

Shape of the velocity profiles d theory of large eddies
Among the others mathematical m investigated model found in [4].Base Stokes equation and on the assumption eddies plays crucial role for the final s profile, there was in [4] derived new ma to express the shape of velocity prof between the plates.The most interesting seemed to be that this model could completed with easy measured data velocity of flow in pipes or among the p equation for pipes is shown below (14).

‫ܥ‬ ‫ݒ‬
Where A,B,C are constant, r is pipe radi V cl is velocity at the center of flow i.e. c velocity profiles were computed methodology presented in [4].But th about specific constants A, B in this m reason for that was that these constants based on "numerical experiments".Henc if the results were unambiguously.Any approximated the shape of velocity the conclusion of this experiment co follows: if there will be some methods d physical nature of the phenomena to acq and B, the equation stated above has a describe the shape of the velocity profile        The graphs show different beh relationships and turbulent models.V the experimental results can be expected but for lower Re you can see the discont in the centre of the tube.From these r disadvantages relations 1, 2 (too sharp (too flat profile for published parame stated, that the relationship 1 can be use relatively exact for "engineering" applica The simple numerical models differences than relationships, but even differ.After evaluating the results, it see reliable results give the models SSTk-ω

Flow in ultrasonic flowmeter bo
The turbulent flow in bodies of ultrasoni simulated, similar simulations are perfor The geometries were based the industrial partner.The following para aviour for used Values closest to d in relationship 3, tinuous derivative results, it is seen p profiles) and 4 eters).It can be ed as a simple and ation.
show smaller n here the values ems that the most and RSM.odies ic flowmeters was rmed [5,6] on data from agraphs show one of the many variants that were of the flowmeter bodies were f The computational mes were 3D tetrahedral or hybrid The number of cells was about unsteady flow of incompres the boundary conditions w the required conditions.
The published results w flow meter DN 80 (2-pat equipped with a simple "cr Figure 1

Influence of the flow p
The flow perturbations can the flowmeter.They can be practice produce a number of f It turned out that for the ultrasonic flowmeters is v swirl perturbation, see Figu the measurements using ery dangerous the so called ure 14.The effect of this perturbation is again dependent on the conditions and in particular on the configuration of the body.

Numerical model
Numerical model of the swirl perturbation (and perturbations generally) was prepared as modular as to minimize the time required to prepare.The tetrahedral mesh was used and the model was added to the model of flowmeter body without perturbation.The length of pipe between the perturbation and flowmeter was 5D for 2-paths flowmeters, 10D for 1-path flowmeters and was tested also the configuration with short length 1.5D.

Results
In the Table 1 and in Figure 15 you can see the comparison of results with and without swirl perturbation for case from section 2.2.

Table 1. Averaged velocities and their RMS values
on the flow paths.It is possible to observe that the results with and without disturbances are relatively similar.It is a consequence of the flowmeter is equipped with a simple flow conditioner, the difference is roughly twice without this add-on.

Model the 3-path flowmeter body
The 3-path flowmeter body has been developed taking into account a number of recommendations obtained by CFD and measurements on simpler flowmeter.Here are some results of dimension DN 100, which was the basic dimension for the project.

Numerical model
In Figure 16 you can see the entire modular model of the computational domain, including pipelines, flow conditioner, body flow and output section including dampers.This area was covered with computational mesh with the number of cells around 12 million.The setting of the model parameters was similar as in section 2.2.
Figure 16.Geometry of the simulated area and surface mesh of the 3-path flowmeter body and flow conditioner.

Results
In the Figure 17    In the Figure 18 are depicted the time averaged flow fields in the computational domain and in the flowmeter body.Figure 19 shows a relatively small effect of recesses for the probes on the flow field.Figure 20 and Table 2 show the difference between the model SST k-ω and LES.It is seen that the calculated velocities of flow on ultrasonic paths are virtually the same.Table 2. Averaged velocities on the flow paths.

Conclusions
It was solved and analyzed the flow in a smooth pipe and the bodies of the ultrasonic flowmeters.Based on the results it can be stated several findings.The developed turbulent flow in the smooth pipe for various Reynolds numbers was solved as the first problem.The relationship 1 e.g.equations ( 1) and ( 2) was chosen as a suitable compromise describing the velocity profile.For the numerical simulations was chosen the two equation model SST k-ω.
The simulation of ultrasonic flowmeter bodies has shown the flow field and its changes by influence of the hydraulic perturbations.The design modification has been also tested and optimised.
The model of the 3-path flowmeter body is very complex and calculation detailed maps flow behaviour under various conditions, and it is further continued.
It has been prepared the comparison between simulations and experimental testing of flow perturbations effects.The research should continue to bring as much information about the field described.

pes and ultrasonic flowmeter bod d Tomas Syka 1 n
, NTC, Univerzitni 8, 306 14 Plzen, Czech Republic gives a summary of the flow modelling in flow parts of LUENT.The article describes the basic techniques used to results of the flow fields.The first part of the article sum ipes for various turbulent models and used relations.The rical modelling of flow in the flow parts of the ultrasonic perimental results.

2. 1 . 3
Numerical computed velocity pNumerical methods are currently widely of developed turbulent flow fields.App models can help to solve relatively c structures, but in this case it is necessar basic problems in fluid dynamics -dev flow in the smooth tube.The work direc stationery axisymmetric model, see FiguThe system ANSYS/FLUENT simulations.The model for the solution the rectangle computed domain was m mesh, the boundary condition on the inl set as periodic with defined mass flow r Reynolds number (Re) and the fluid incompressible.The following RANS were tested: k-ε, RNGk-e, SSTk-ω an smaller than 2⋅10 4 were tested the models for low Reynolds numbers.

Figure 7 .
Figure 7. Velocity profiles -RNG In Figure 8 are depicted "engineering" model SSTk-w the recent years very popular.

Figure 13 .
Figure 13.Contours of mean v velocity in the slice of the model o Calculated results generally minimizing the recesses fo the sensitivity of the flowme other geometric parameters.
e simulated.The dimensions from DN 50 to DN 200.shes used for simulations d with the boundary layer.t 7 millions.The steady and sible fluid was simulated, were set depending on were obtained for the model ths).The flowmeter was rosswise" conditioner (see was modelled as unsteady et 21.4 kg/s.The pressurebetter describe the complex ons can be in same cases was preferred in simulations etries".In some cases were LES method.can see the flow field in d is in this design relatively ve unsteady flow in the rear vels of RMS values.velocity magnitude and RMS of 2-path flowmeter.y showed the need for or ultrasonic probes and eter bodies to a number of perturbations n affect the accuracy of of different types and in factors.

Figure 14 .
Figure 14.Numerical model of the swirl perturbation.

Figure 15 .
Figure 15.Distribution of velocity along flow paths for situation without and with the swirl perturbation.
you can see the instantaneous unsteady flow structure in the duct.