NUMERICAL ANALYSIS OF TURBULENT FLOWCHARACTERISTICS OF AN INCOMPRESSIBLE FLUID IN A

VENTURI-TYPE DEVICE

Natha M. Caetano and Luiz E. M. Lima

Mechanical Academic Department, Federal Technological University of Paran, 84016-210, Ponta

Grossa, PR, Brazil, lelima@utfpr.edu.br, http://www.utfpr.edu.br/pontagrossa

Keywords: Venturi, Numerical analysis, Turbulence.

Abstract. The Venturi is a device widely used in various industrial applications: automotive, food,

agricultural, oil, among others. The Venturi has circular cross section or polygonal, depending on your

application and it consists of three sequential parts: the convergent, the throat and the divergent. The

industrial applications of the Venturi can vary fromminor adjustments in the mechanism to more complex

engineering adaptations. The development of a computational model for flow in a Venturi constitutes an

additional tool for the analysis and determination of flow variables involved in the equipments which

apply the Venturi principle. This paper presents a numerical study of the characteristics of turbulent flow

of incompressible fluids in Venturi-type devices, through the use of different turbulence models. The

Reynolds decomposition process usually applied to incompressible flow was used as a mathematical tool

in the formulation of the turbulent flow. This decomposition provides the Reynolds Averaged Navier-

Stokes (RANS) equations. For the closing of the mean equations it is necessary to model the unknown

terms (Reynolds stresses) that arise from nonlinearities in the instantaneous mean flow equations. In

the present study, the Reynolds stresses were modeled using different versions of the k-epsilon model,

among others. For this study, Ansys/Fluent commercial software for Computational Fluid Dynamics

(CFD), which uses a finite volume method in the discretization of the governing equations, will be used.

To validate this computational model, their results will be compared against pressure experimental data.

The study of the flow field, the pressure distribution and the turbulent stresses is of great importance in

understanding the flows in these equipments, as well as in the improvement of some of its applications

and developing new applications of the Venturi principle.

1 INTRODUCTION

The Venturi is a device that was first used to solve simple problems and improve the hy-

draulics knowledge, years after its development it started to be used in some industrial appli-

cations, among them the flow measurement. Currently the Venturi principle is used for various

technological purposes in different applications, we highlight the air purifiers, gas-solid injec-

tors and jet pumps. The industrial applications of the Venturi vary from minor adjustments in

the mechanism to more complex engineering adaptations.

The Venturi has circular cross section or polygonal, depending on your application and it

consists of three sequential parts: the convergent, the throat and the divergent. These geometric

characteristics allows the pressure recovery occurs from the inlet to the outlet of the Venturi.

Due to the gradual reduction of area are not present certain phenomena, such as the vena con-

cracta (Fox et al., 2010), thus the flow is regular throughout the course of the Venturi when the

flow rate are relatively low. For higher flow rates, the separation points can occur along the

Venturi, which causes the occurrence of eddies, or counter flow, so that the pressure does not

fully recover (McDonald and Fox, 1966).

Equipments based on the Venturi principle are capable of performing the transformation of

pressure energy into velocity energy. This application is used extensively by industry to improve

air quality and also define its moisture, receiving the name of Venturi aeration (Baylar et al.,

2009). The air purifiers are generally used in the food industry, with the aim of removing

impurities and regulating the temperature, by a fluid that is injected in the throat region and

subsequently dispersed in the form of droplets in the environment in which it is desired to

purify (Puentes et al., 2012). For gas-solid injectors the same principle of the air purifiers is

used. The air circulating in the Venturi takes solid particles that are inserted in the throat region

carrying them to the desired locale (Domingues, 2006).

In the lift jet pumps technology the Venturi design requires a higher level of engineering. The

Venturi principle associated with this equipment is used in lift and flow of submerse fluids such

as water or oil. The operation of a lift jet pump is relatively simple. A motor fluid is injected

at the entrance of the Venturi-type device, which causes the fluid surrounding it is sucked into a

chamber, where the mixing occurs. The two fluids are mixed and then transported to the surface

through the duct using the thrust resulting from the motor fluid (Oliveira et al., 1996).

Ghassemi and Fasih (2011) study cavitating Venturis with three different throat diameters to

investigate the effect of Venturi size on its mass flow rate. They conducted three different sets of

experiments to investigate the performance of the Venturis. In the experiments, the mass flow

rates were examined under different downstream and upstream pressure conditions and time

varying downstream pressure. It is found that the Venturi size has no effect on its expecting

function to keep mass flow rate constant. Also, it is shown that by applying a discharge coeffi-

cient and using only upstream pressure, the cavitating Venturi can be used as a flow-meter with

a high degree of accuracy in a wide range of mass flow rate.

Blocken et al. (2011) used Computational Fluid Dynamics (CFD) to gain insight in the aero-

dynamic performance of a Venturi-shaped roof (called VENTEC roof). The simulations are

performed with the 3D steady Reynolds-averaged Navier-Stokes (RANS) equations and the

Renormalization Group (RNG) k model. A detailed analysis is conducted of the influenceof the so-called Venturi-effect and the wind-blocking effect on the aerodynamic performance

of the VENTEC roof. The results indicate that because of the wind-blocking effect, the highest

contraction ratio does not provide the best aerodynamic performance and the largest negative

pressure, which is a counter-intuitive result.

This works presents a numerical study of the characteristics of turbulent flow of incompress-

ible fluids in Venturi-type devices, through the use of different turbulence models. The aim of

this study is to obtain a computational model of the flow in a Venturi that allows the analysis of

this device in several applications. For this study, Ansys/Fluent commercial software for Com-

putational Fluid Dynamics (CFD), which uses a finite volume method in the discretization of

the governing equations, will be used. To validate this computational model, their results will

be compared against pressure experimental data.

2 GOVERNING EQUATIONS AND NUMERICAL MODEL

The present numerical study of turbulent flows of incompressible fluids in a Venturi-type

device was done using the commercial software for Computational Fluid Dynamics (CFD) An-

sys/Fluent version 14.5. The numerical model is based on the solution of the Reynolds averaged

Navier-Stokes (RANS) equations for incompressible flows using a finite volume method on

non-structured non-uniform grid. The turbulent stress terms were closed with a two equations

k turbulence model, that will be presented below.

2.1 Reynolds Averaged Navier-Stokes (RANS) equations

The RANS equations are time averaged Navier-Stokes equations written for the instanta-

neous velocity decomposed in a mean value and a fluctuation. For an incompressible Newtonian

fluid, these equations can be written as:

uixi

= 0, (1)

uit

+

xj(uj ui) = fi +

xj

[p

ij +

(uixj

+ujxi

) uiu

j

], (2)

where u is the velocity, x is the space coordinate, t is the time, fi is the volume force, p is thepressure, is the specific mass, ij is the delta of Kronecker and is the kinematic viscosity. Theleft side of Eq. (2) represents the time variation of momentum due to the transient regime and

the convection in the mean flow. The transient term is kept for numerical integration purposes.

This variation is balanced by the mean volume force, the average pressure gradient, the viscous

stresses and the apparent viscous stresses (uiu

j) due to fluctuations in the velocities field,generally known as the Reynolds stresses.

2.2 Turbulence models

The turbulence models used for the simulation of the flow in Venturi in this work are: the

standard k , the RNG k and the realizable k .In the standard k model the turbulent kinetic energy, k, is derived from the exact equa-

tion, while the dissipation rate of the turbulent kinetic energy, , is obtained by reasoning aboutphysical phenomena. The RNG k model is derived using statistical techniques called renor-malization group theory and has an extra term in the dissipation rate that optimizes the accuracy

of the results for fluids subjected to tension quickly. The realizable k model differs fromthe standard model to contain an alternative formulation for the turbulence model and present

an motion equation for the dissipation rate modified, derived from the exact equation for the

motion to the main area of vorticity change. The transport equations for standard k modelare presented below (Launder and Spalding, 1974).

The turbulence kinetic energy, k, and its dissipation rate, , are obtained from the followingtransport equations:

t(k) +

xi(kui) =

xj

[(+

tk

)k

xj

]+ Pk + Pb YM + Sk, (3)

and

t() +

xi(ui) =

xj

[(+

t

)

xj

]+ C1

k(Pk + C3Pb) C2

2

k+ S. (4)

In Eqs. (3) and (4), Pk represents the production of turbulence kinetic energy due to the meanvelocity gradients. Pb is the production of turbulence kinetic energy due to buoyancy. YMrepresents the contribution of the fluctuating dilatation in compressible turbulence to the overall

dissipation rate. C1, C2, and C3 are model constants. k and are the turbulent Prandtlnumbers for k and , respectively. Sk and S are user-defined source terms.

The turbulent (or eddy) viscosity, t, is computed by combining k and as follows:

t = Ck2

, (5)

where C is a constant.The production of kinetic energy Pk is given by:

Pk = uiu

j

ujxi

tS2, (6)

where S 2tSij Sij is the modulus of the mean rate-of-strain tensor considering the

Boussinesq hypothesis.

The effect of buoyancy Pb is given by:

Pb = gitPrt

T

xi, (7)

where T is the temperature, Prt is the turbulent Prandtl number for energy and gi is the compo-nent of the gravitational vector in the ith direction. For the standard and realizable models, the

default value of Prt is 0.85. = (1/)(/T )p is the coefficient of thermal expansion. Themodel constants are defined as: C1 = 1.44, C2 = 1.92, C3 = 0.33, C = 0.09, k = 1.0and = 1.3.

3 EXPERIMENTAL APPARATUS AND DATA

The experimental apparatus used in this work was made by Edibon Technical Teaching

Equipment with purposes of study and measurement of head loss in pipes and accessories

(Edibon, 2012). The components of this experimental facility are schematically shown in Fig. 1.

A centrifugal pump supplies the water to the experimental circuit. After pass by the experimen-

tal circuit the water flows downward to a collecting tank of 165 l. The water exits the collectingtank to feed the centrifugal pump in a closed loop. The tests were conducted at nearly atmo-

spheric pressure of 1021 mbar and ambient temperature of 18C. The water flow rate measure-ment uses a rotameter calibrated at100 l/h of uncertainty operating within the range of 600 l/hto 6000 l/h. The Venturi is made of acrylic and your dimensions are shown in the Fig. 1.

QP3

Centrifugalpump

Rotameter(flow meter)

Valve

Venturi(test section)

Waterreservoir

Bourdonpressure gauge

60 mm 50 mm20 mm

32 mm 32 mm20 mm

P2P1

U-tubemanometers

Water recycling circuit

Inlet Outlet

ThroatConvergent Divergent

Watercircuit

Figure 1: Schematic representation of the experimental facility.

The pressure taps are localized at three axial positions of the Venturi: inlet, throat and outlet,

see Fig. 1. Two U-tube manometers are used to measuring the pressure differences between

inlet and throat and between throat and outlet. A Bourdon pressure gauge measures the pres-

sure at outlet relative to atmosphere. The pressure uncertainty was estimated at approximately

20 mbar. The atmospheric pressure reading comes from the weather service provided bySimepar Technological Institute (available at http://www.simepar.br/site/).

3.1 Experimental data

The experimental test grid consists of one sets with 14 values of water flow ratesQmeasuredby the rotameter shown in Fig. 1, see Table 1. The flow rates range encompasses the region of

turbulent flow occurrence. In Table 1 the variables P1, P2 and P3 correspond to the absolutepressures at the inlet, the throat and the outlet of the Venturi.

Table 1: Experimental test grid data.

Q Re P1 (abs.) P2 (abs.) P3 (abs.)[l/h] [] [Pa] [Pa] [Pa]600 6552 108149 108051 108100

800 8737 108198 108012 108100

1000 10921 110208 109943 110100

1200 13105 112237 111865 112100

1400 15289 116257 115747 116100

1600 17473 120306 119639 120100

1800 19657 124031 123551 124100

2000 21842 128433 127374 128100

2200 24026 132522 131237 132100

2400 26210 138590 137080 138100

2600 28394 144561 142874 144100

2800 30578 150747 148678 150100

3000 32762 156885 154462 156100

3200 34947 164943 162247 164100

4 NUMERICAL RESULTS AND ANALYSIS

The computational domain used in the simulations corresponds to the internal region of the

Venturi geometry defined in Fig. 1, using boundary condition of symmetry around the revolution

z axis. The boundary conditions used as input parameters in the simulation are the inlet velocity,based on Q, and the outlet absolute pressure, P3, obtained experimentally, see Table 1.

The computational mesh used was refined near the surface where the gradients are more

significant and the rest of the field was refined enough to provide a good convergence of the

results, see Fig. 2. All simulations were performed for permanent regime. The pressure-velocity

coupling was performed using the Simple method (Patankar and Spalding, 1972).

Figure 2: Computational mesh used.

The Fig. 3 shows a comparison of the numerical (num.) results against the experimental

(exp.) results for absolute pressure at the inlet, P1, and the throat, P2, as a function of flow rateQ. These numerical results were obtained using the standard k model.

Figure 3: Comparison of numerical (num.) and experimental (exp.) results for absolute pressure values at inlet, P1(left), and at throat, P2 (right), as a function of flow rate Q.

The results presented in the Fig. 3 show a good agreement between numerical simulation and

experimental data. The three turbulence models used presented a smaller relative deviation than

1% compared with the experimental data. This is due to the fact that the Venturi geometry is rel-

atively straightforward and hence the turbulence models used tends to show good performance.

Therefore, the results obtained in this work by these three turbulence models for simulation of

turbulent flows in the Venturi-type device are similar.

The Fig. 4 shows the distribution of the absolute pressure and the velocity through the Ven-

turi at flow rate of 3200 l/h. These results show the reduction of pressure in the throat, andsubsequent recovery of pressure in the outlet of the Venturi, as expected in this type of device.

Figure 4: Distribution of the absolute pressure (left) and velocity (right) through the Venturi at flow rate of 3200 l/h.

The values of the absolute pressure and the velocity are in Pa and m/s, respectively.

Near the Venturi outlet is possible to observe the existence of a counterflow, see Fig. 5. This

phenomenon occurs due to vortices formation caused by non-slip condition on the wall in the

region downstream of the throat where the velocity magnitude is reduced. For the lower values

of flow rate this counterflow is negligible, thus the flow is regular throughout the Venturi.

Figure 5: Detail of the counterflow occurrence in the velocity distribution.

The Fig. 6 shows the distribution of the turbulent kinetic energy and the turbulent viscosity

through the Venturi at flow rate of 3200 l/h. These results show an increase in the turbulentkinetic energy after the throat. This increase in turbulent kinetic energy explains the vortices

formation in the divergent section after the throat. This can also be observed by an increase in

the turbulent viscosity at this divergent section.

For all other values of flow rate presented in Table 1, the numerical results are similar to

those obtained with the flow rate of 3200 l/h with proportional values for each of the flowcharacteristics shown in Figs. 4 and 6.

Figure 6: Distributions of turbulent kinetic energy (left) and turbulent viscosity (right) through the Venturi at flow

rate of 3200 l/h. The values of the turbulent kinetic energy and the turbulent viscosity are in m2/s2 and kg/(m.s),

respectively.

5 CONCLUSIONS

This work presented a numerical analysis of turbulent flow in a Venturi-type device. The

results were obtained with three different versions of the k turbulence model: standard,RNG and realizable.

The three turbulence models presented good results for the Venturi topology once this geom-

etry is relatively straightforward. The validation of the computational model presented a good

level of agreement with experimental results.

The divergent section in the Venturi presents higher values of turbulent kinetic energy and

turbulent viscosity. This characteristics can be used to maximize the mixture level after the

throat in some industrial applications of this device.

This study allowed a better understand for the behavior of turbulent flow in a Venturi device.

Next steps will be introducing complex phenomena in this analysis of Venturi-type devices, for

example: multiphase flow, particle injection, cavitation, etc.

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INTRODUCTIONGOVERNING EQUATIONS AND NUMERICAL MODELReynolds Averaged Navier-Stokes (RANS) equationsTurbulence models

EXPERIMENTAL APPARATUS AND DATAExperimental data

NUMERICAL RESULTS AND ANALYSISCONCLUSIONS