Fluid flow occurring in a venturi tube was numerically simulated with the Fluent software, and several factors to affect the mass flux and an asymmetric flow were analyzed, including the contraction ratio, ratio of the throat section length to diameter, the diffusion angle and the inlet and outlet pressure difference. Results show that the minimum pressure point occurs at the intersection between the contraction and throat sections in the venturi tube. As the contraction ratio increases, vacuum degree ascends, and mass flux rises. While both vacuum degree and mass flux reduces as the diffusion angle increases. In addition, an increment in the contraction ratio shortens a fully developed section of velocity in the diffusion section. At the contraction ratio less than 0.2 or the diffusion angle less than 35°, velocity in the diffusion section shows an asymmetric and skewed flow. However, as the inlet and outlet pressure difference increases, mass flux goes up, and thereby occurring a back-flowing in the throat section. The calculated results were compared with the reference’s data, both error is within 0.5% – -28%.

## I. INTRODUCTION

A venturi tube, of which the cross-section contracts firstly and then gradually expands, is composed of a contraction section, a throat section and a diffusion section. When the fluid flows through the throat section, the shrunken cross-section will accelerate the fluid accompanied by a pressure drop. This phenomenon is called as a Venturi effect, which will cause the fluid to occur a vacuum draw. In recent years, Venturi pipes have been widely applied in flow measurement, natural gas transmission, internal combustion engine pressurization system and industrial waste gas cleaning and dust removal. For example, in natural gas transmission, the use of Venturi tube jet-flow pressurization device achieves the mixture between a low pressure manufactured gas and a high pressure natural gas.^{1,2} In industrial waste gas cleaning, the venturi scrubber is aimed at atomizing water by a high speed gas at the throat section to remove dust.^{3} In internal combustion engine pressurization system, an exhaust gas recirculation technology in a pressurized diesel engine makes the exhaust gas circulation and flow driven by the vacuum degree at the throat section.^{4} Quiroz-Pérez et al.^{5} studied theoretically that the of the gas production caused by the venturi tube in the gas well. In a word, the application of venturi tube is helpful to effectively mix and improve chemical reaction, and thereby enhancing the energy efficiency. Therefore, to comprehend the fluid flow and pressure variation in the Venturi tube is of great significance for the realization of industrial energy saving.

Recently, many researchers experimentally and theoretically analyzed the influences of Venturi tube structural parameters on the velocity and pressure of the inner fluid.^{6–16} Rodio and Congedo.^{6} proposed a set of optimized parameters of the venture tube by means of the cavitation’s model. Gupta et al.^{7} carried out an experiment of air–water two–phase fluid flowing through a venturi channel in a 700MWe Indian Pressurized Heavy Reactor and found that a two-phase flow multiplier increases as the void fraction ascends. With an experimental and theoretical method, parameters of the venturi scrubber were investigated, including the throat pressure drop, the droplet dispersion and the dust collection efficiency. Among these parameters, the pressure drop is a function of the gas-liquid ratio, the throat gas velocity and the throat area.^{8–10} The effects of nozzle geometry and the fluid mass flux on the fume collection efficiency of diesel fume scrubbing was studied by Das and Biswas.,^{11} and both the hydrodynamic and mass transfer performances of an emulsion loop-venturi reactor in cocurrent downflow and upflow configurations was evaluated by Gourich et al.^{12} By means of a numerical method, Zhu et al.^{2} proposed that an increment in the diffusion angle can achieve more mass flux, and gave out an optimal diffusion angle 30°. Sun and Niu.^{13} numerically analyzed the effects of the contraction ratio and the diffusion angle on mass flux and vacuum degree in the venturi tube, and they suggested that the minimum pressure occurs at the intersection between the contraction and throat sections. Given the pressure difference between the inlet and outlet of the venture tube, an increase of the inlet pressure makes a throat pressure reduce. Moreover, given an inlet pressure, an increase of pressure difference between the inlet and outlet of venturi tube makes the throat pressure drop further. As both pressure difference between the inlet and outlet and the contraction ratio increases, mass flux increases as well.^{2,14} While an increase of the contraction ratio enhances the pressure loss in the venturi tube.^{15} They proposed that the contraction ratio ranges within 0.25–0.55 at the pressure drop of 60–83KPa. When Reynolds number is more than 2000 and the expansion ratio is more than 1.4, as the expansion ratio increases, the fluid flow appears an asymmetric distribution in the venturi tube, namely an obvious deflected flow.^{16} However, few researches considered the effects of the contraction ratio and the diffusion angle on an asymmetric flow.

At the present work, a Fluent software was applied to numerically analyze the influences of the structural parameters on fluid flow and pressure in the Venturi tube, including the contraction ratio, the diffusion angle, the ratio of the throat section length to diameter and the pressure difference between the inlet and the outlet of venture tube. The characteristics of mass flux, vacuum degree and asymmetric flow were analyzed.

## II. ESTABLISHING MODEL AND NUMERICAL SOLUTION

The following assumptions were made in this study:

The fluid is an in-compressible Newton fluid.

Fluid properties are a function of temperature and include density, viscosity, surface tension coefficients. Physical properties are constant because the effect of temperature is not considered.

The viscous dissipation is negligible.

FIG. 1 shows a schematic diagram of a venturi tube structure, which is composed of the contraction section, the throat section and the diffusion section. Here, the contraction ratio is defined as the ratio of the diameters of the throat section to the contraction section. It is expressed as

Furthermore, the ratio of the venturi tube length to diameter is defined as

The pressure difference between the inlet and the outlet of venture tube is calculated with

In the Venturi tube, a single phase fluid flow in a three-dimensional stable state was numerically simulated. A set of mass and momentum conservation equations were described as follows:

A turbulent flow in the venturi tube was calculated with a standard *k* − *ε* two equations model.

Grid was divided with a Gambit pre-processing module in Fluent 6.3, each grid size selects 1mm, and 130 thousand meshes were generated. Here, grid skewness is within 0.7–0.85, and aspect ratio is 4:1. The calculated results are independent of mesh number. On the basis of the inspection of the grids in the x, y, z directions, the grid quality level could be determined. Here, grid quality is also checked up in Fluent software, a lower value is used as the evaluation index of the grid quality, which is thought as a good quality grid when the lower value is less than 0.4. At present generated grids, 99.28% of the lower value is less than 0.4. It indicates that the grid quality is satisfactory. The conservation equation groups were discretized with second order upwind difference scheme, a simple solver with velocity-pressure coupling was employed. The values assigned to the residuals for the different variables is 1×10^{-4} in the calculation. The convergence criterion was set as 1×10^{-4} for the momentum equation, the continuity equation and *k* − *ε* equation. In addition, a pressure inlet boundary condition is given by setting various pressure value, a constant pressure outlet boundary condition is given at the outlet, and no slip wall boundary condition was selected. Both Intensity and hydraulic diameter was given to *k* − *ε* equation, backflow turbulent intensity was 10%, and backflow hydraulic diameter was 0.02.

## III. COMPARISON OF CALCULATED RESULTS WITH REFERENCE DATA

Sun and Niu.^{5} summarized the relationship between the inlet and outlet pressure difference and the velocity in the Venturi tube, which is given out as follows

According to thirty groups of various Venturi tube structural parameters and the inlet and outlet pressure differences, the above correlation between the velocity coefficient and the flow pattern index was obtained.

Table I and Table II are structural parameters and pressures in the Venturi tube at the present simulation. FIG. 2 shows a comparison of the computed results to the reference data^{5} when the velocity coefficient is 0.5, and both error is within +0.5% – -28%. This is caused by several unknown parameters in the reference, they include the lengths of contraction section and diffusion section, and the diameter difference between the inlet and the throat sections. Because these unknown parameters is not in agreement with the references, causing the larger error between the computed results and the reference data. Therefore, this error caused by these certain unknown parameters is believed as a system error here, which could be avoided by adjusting these parameters setup. Based on these calculated results, it is verified that the present calculated method is reasonable and reliable.

. | D . | L . | l . | β . | α . |
---|---|---|---|---|---|

Model 1 | 16 | 60 | 10 | 21° | 10° |

Model 2 | 19.2 | 49 | 10 | 25° | 15° |

Model 3 | 21 | 49 | 10 | 30° | 20° |

. | D . | L . | l . | β . | α . |
---|---|---|---|---|---|

Model 1 | 16 | 60 | 10 | 21° | 10° |

Model 2 | 19.2 | 49 | 10 | 25° | 15° |

Model 3 | 21 | 49 | 10 | 30° | 20° |

## IV. RESULTS AND DISCUSSION

Fluid flow was numerically simulated at the contraction ratio of 0.2–0.8, the diffusion angle of 15°– 60° and the inlet and outlet pressure differences of 10–310kPa. Flow parameters were analyzed, including vacuum degree, mass flux, pressure and velocity. Here, the inlet and the outlet diameters of venturi tube are 0.02m, and the contraction section length is 0.1m.

### A. Effects of the contraction ratio

FIG. 3 shows the effects of the contraction ratio on fluid flow. Pressure decreases along the flow direction at the contraction section, as shown in FIG. 3(a). An intensive change occurs at the intersection between the contraction and throat sections, where pressure reaches a minimum value. However, pressure in diffusion section increases along the flow direction. The difference between this minimum pressure and atmosphere is defined as a vacuum degree, and it is 78kPa at the contraction ratio of 0.5. As the contraction ratio increases, both the vacuum degree and mass flux increases, as shown in FIG. 3(b). Moreover, as the contraction ratio increases, fluid flow in the diffusion section requires more long distance to reach a fully developed state, as shown in FIG. 3(c). That is to say, the smaller contraction ratio is, the narrower the region of the diffusion section affected by venturi effect is. Moreover, it found that the flow was preferably deflected to the upper side of the diffusion section. This is because fluids appear bifurcation phenomenon and most of them lie in the lower side of the diffusion section when they flow from a narrow limited throat section to a wide free diffusion section. It makes it difficult to being fully developed. On the contrary, few fluids lie in the upper side of the diffusion section, where flow is fully developed. Therefore, fluid displays a deflected upward. By adjusting the size of diffusion angle and the length of diffusion section, the deflected is constrained. In the present calculation, the diffusion section length is 0.1 m; it found that the velocity at the outlet cross-section ascends as the contraction ratio increases. This velocity is up to 4m/s at the contraction ratio of 0.2, it reaches 25m/s at the contraction ratio of 0.4, while it is 49.9m/s at the contraction ratio of 0.6. As the contraction ratio reduces, the velocity occurs a deflection at the contraction ratio of 0.2. By comparison, the velocity shows a center symmetric contribution at the contraction ratio of 0.6. This is because the rigidity of the narrow high-speed fluid is poor and occurs a vortex at a lower contraction ratio, which is in agreement with the phenomenon of an asymmetric flow proposed by reference 7. They pointed out that an asymmetric distribution of velocity occurs at Re > 3700 due to a static bifurcation caused by the enforcement of turbulent fluctuation. In the present calculation, though Reynolds number is larger than 3700 at the diffusion section, fluid flow still shows a deflected when the contraction ratio is less than 0.2 or the diffusion angle is larger than 35°. This further verifies the structural parameters causes an asymmetric flow driven by the static or dynamic bifurcation. An asymmetric flow means the flow bifurcation and the presence of recirculating zone in the diffusion section. For pulverized coal fractional combustion, the flow bifurcation is helpful to realize the pulverized coal separation. In chemical reaction, the presence of recirculating zone is helpful to delay the chemical reaction time, and making chemical reaction fully finished.

### B. Ratio of the throat section length to diameter

FIG. 4 shows effects of the ratio of the throat tube length to diameter. Given the inlet and outlet pressure difference of 10kPa, intensive pressure variation in the venturi tube occurs at the intersection between the contraction and throat sections, where pressure is up to a minimum value. However, no variation of pressure occurs in the throat section. Subsequently, the pressure displays a continuous increment in the diffusion section, as shown in FIG. 4(a). As the ratio of the throat section length to diameter increases, the vacuum degree and mass flux reduces. In the present computation, the minimum pressure is 82kPa when the ratio of the throat section length to diameter is equal to 1, but it increases by 83kPa when the ratio of the throat section length to diameter is 5, the increasing amount is only 0.1kPa. Therefore, the effects of the ratio of the throat section length to diameter may be neglected. Furthermore, when the ratio of throat section length to diameter is 1.0, the maximum velocity in the throat section reaches 136m/s, while when it is 5.0, the maximum velocity here is 130m/s. So, the maximum velocity in the throat section is almost no variation, the velocity in the outlet cross-section is also without variation. Therefore, the effects of the ratio of the throat section length to diameter could be neglected, as shown in FIG. 4(c).

### C. Effects of the diffusion angle

FIG. 5 shows the effects of the diffusion angle in the venturi tube. An intensive pressure change occurs at the intersection between the contraction and throat sections, where the pressure reaches the minimum value. The vacuum degree is 84kPa at the diffusion angle of 22.5°, while it is 86kPa at the diffusion angle of 37.5°, as shown in FIG. 5(a). Therefore, the diffusion angle affects significantly the vacuum degree in the Venturi tube. As the diffusion angle increases, the vacuum degree decreases sharply, but mass flux ascends, as shown in FIG. 5 (b). The minimum velocity in the Venturi tube is 10m/s at the diffusion angle of 22.5° and the velocity distribution in the Venturi tube shows an uneven development. However, it reaches 5m/s at the diffusion angle of 37.5°, and the velocity distributes symmetrically. This is because the backflow is formed at the diffusion section as the diffusion angle decreases. In addition, the velocity at the venturi tube outlet decreases as the diffusion angle increases.

### D. Inlet and outlet pressure difference

Given the inlet and outlet pressure difference as 90KPa and various inlet pressure, the influences of the inlet and outlet pressure difference on flow parameters were calculated, as shown in FIG. 6. At the inlet and outlet pressure difference of 110KPa, the minimum pressure at the throat section is -20kPa. At the inlet and outlet pressure difference of 210KPa, the minimum pressure at the throat section is -100kPa, as shown in FIG. 6(a). So, the inlet and outlet pressure difference affects significantly the vacuum degree.

As the inlet and outlet pressure difference increases, the minimum pressure in venturi tube reduces and shows a negative value, which is in agreement with the results of Sun and Niu,^{4} shown in Fig. 6(b). It is well known that zero adiabatic pressure is equal to -101.325KPa at zero vacuum degree, which can be obtained at the inlet and outlet pressure difference of -160KPa. When it is larger than 160KPa, the minimum pressure in the throat section is negative, its absolute value is larger than 101.325KPa and gradually increases. It indicates that the back flow occurs in the venturi tube under the push of negative pressure difference. By comparison with the inlet and outlet pressure difference of 210KPa, the velocity reduces obviously at the inlet and outlet pressure difference of 110KPa, as shown in FIG. 6(c). It indicates that the inlet and outlet pressure difference affects slightly the velocity at the throat section.

## V. CONCLUSION

In the present work, a numerical analysis was done with the Fluent software in order to show pressure and velocity in the venturi tube. Vacuum degree, mass flux, velocity and pressure were obtained at various venturi tube structural parameters, including the contraction ratio, the diffusion angle, the ratio of the throat section length to diameter and the inlet and outlet pressure difference. It comes to conclusions as follows:

The minimum pressure occurs at the intersection between the contraction and the throat sections in the venturi tube, where pressure varies intensively.

Main structural parameters that affect a pressure distribution in the venturi tube involve of the contraction ratio, the diffusion angle and the pressure difference between the inlet and outlet. Vacuum degree in the venturi tube shows a negative linear variation with the contraction ratio and the diffusion angle. As the contraction ratio increases, both vacuum degree and mass flux ascends. As the diffusion angle increases, both vacuum degree and mass flux drops. As the inlet and outlet pressure difference increases, the minimum pressure increases, causing a backflow phenomenon. However, the ratio of throat section length to diameter affects slightly vacuum degree and mass flux.

The main structural parameters affecting velocity in the Venturi tube are the contraction ratio and the inlet and outlet pressure difference. As the contraction ratio increases, the velocity in the Venturi tube ascends rapidly, and the velocity full development length in the diffusion section becomes shorter. With the increasing of the inlet and outlet pressure difference, the velocity in the venturi tube gradually increases. While the ratio of throat section length to diameter affects slightly the velocity.

When the contraction ratio is less than 0.2 or the diffusion angle is less than 35°, the velocity shows an asymmetric distribution in the venturi tube.

## ACKNOWLEDGMENTS

This work was financially supported by the Project of National Natural Science Foundation of China (Grant No. 51406176)

## NOMENCLATURE

*b*throat section length, m

*D*venturi tube inlet and outlet diameter, m

*d*throat section diameter, m

*k*velocity coefficients

*L*overall length, m

*m*ratio of venture tube length to diameter

*p*pressure, Pa

- Δ
*p* inlet and outlet pressure difference

*u*velocity in

*x*coordinated, m.s^{-1}*u*_{ax}average velocity, m.s

^{-1}*v*velocity in

*y*coordinated, m.s^{-1}*w*velocity in

*z*coordinated, m.s^{-1}*X*flow pattern index

*x**x*coordinated*y**y*coordinated*z**z*coordinated*β*diffusion angle,

*γ*contraction ratio