GEOMETRY AND HEAD LOSS IN VENTURI INJECTORS THROUGH COMPUTATIONAL FLUID DYNAMICS

To determine the influence of geometry on the hydrodynamic behavior of Venturi injectors, using computational fluid dynamics techniques, we studied, at the Universitat Politècnica de València, Valencia, Spain, the geometric parameters that exert the most influence on head losses: the relationship between throat diameter and nozzle (β), nozzle angle (α1) and diffuser angle (α2). In addition, three throat morphologies (B1: nozzle-throat and throat-diffuser with a sharp edge; B2: nozzle-diffuser with a zerolength, sharp-edge throat; B3: nozzle-throat and throat-diffuser with rounded edge). We analyzed their influence on the velocity distribution and differential pressure between inlet and throat (DP/γ), throat and outlet (Δhv/γ), and outlet and throat ((P3-P2)/γ). The development of the velocity profile from the throat is slower the greater β is and the lower α2 is. DP/γ decreases with β, increases with α1 and varies little with α2. Δhv/γ decreases with β and increases with α1 and α2. (P3-P2)/γ decreases with β and increases with α1 and α2. Geometry B3 decreases the losses and delays the onset of cavitation. Thus, the lower β and the higher α2, the greater the losses; however, the influence of α1 is less clear. The rounded edges produce lower head losses.


INTRODUCTION
The contribution of chemicals in the water, referred to as chemigation, is a technique that is currently often developed in pressurized irrigation methods (SANTOS et al., 2012) such as a sprinkling (DANTAS NET et al., 2013) and localized irrigation (REZENDE et al, 2010;. URIBE et al, 2013).
An injection device that is often used in chemigation, in small and medium agronomic crops, is the Venturi nozzle (DIMITRIOS et al., 2014).It is an economical, robust hydraulically operated system, without requiring external energy input (SANTOS et al., 2012).Nevertheless, the high head losses caused by its operation (SUN & NIU, 2012) correspond to the least 30% of the inlet pressure (ARVIZA, 2001).It may also present problems regarding regulation, air injection, or cavitation (MANZANO, 2008).
Venturi-type injectors initially based their characteristics on flowmeters based on the same hydraulic effect, where certain angle values are recommended for the throat (α 1 = 21°±1, 7° ≤ α 2 ≤ 15°), enabling production of minimum losses (INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, 2003).Nevertheless, in commercial equipment, these angles are greater, in particular α 1 .This angular increase is associated with reduced length (cost reduction), although there is an increase in losses.Commercial values for the relationship of diameters ( range between 0.12 and 0.5.For the nozzle angle (α 1 ), commercial values range between 10° and 75°.Regarding the diffuser angle (α 2 ), commercial values range between 5 and 31 (MANZANO, 2008).
Other important geometrical characteristics are the junctions of the nozzle with the throat and the diffuser, which may affect the total head loss and risk of cavitation.The International Organization for Standardization (2003) establishes a throat length (L g ) of D 2 ±0.03 D 2 and, depending on the construction material, recommends the rounding of edges.The throat length given by commercial manufacturers varies greatly and junctions frequently have sharp edges.
The computational fluid dynamics (CFD) techniques provide numerical solutions for problems in fluid mechanics with the aid of computers (BAYLAR et al., 2009;WENDT, 2009).This technique is widely used in Hydraulic Engineering, following the example of fertilizer injection systems (YEOH et al., 2012), showing the effect of geometry to obtain the values of the system characteristic variables.
In summary, the phases of a CFD method consist of preprocessing (problem definition), processing (solution) and post-processing (analysis of results).The preprocessing phase defines the specific geometry of the system being simulated, discretizing the computational domain with the mesh generation.The following are defined : physical aspects of the problem; governing equations and models for processes taking place in the system; chemical reactions; and initial and boundary conditions.Finally, numerical calculation parameters should be established.The processing phase consists of approximating the unknown variables by simple functions and their replacement in the governing equations.The post-processing phase defines the analysis of the results through a graphical representation (MANZANO, 2008).
The results developed by the CFD techniques are approximate values of the behavior of the thermodynamic variables.When theoretical models for checking the accuracy of these values are not available, experimental tests are required (LODOÑO et al., 2004).Therefore, the suitability of CFD techniques to describe the hydraulic behavior of Venturi injectors has been proven by MANZANO & PALAU (2005), as the experimental results and those obtained by computer were very similar.
In this paper, we employed CFD techniques to analyze the geometric parameters that characterize the Venturi injector and have the greatest impact on the head loss.We thus intended to determine their influence on the hydrodynamic behavior of the element.As an associated objective, we refined the computational calculation methodology, which has proven to be an effective tool for improving elements and devices in agricultural hydraulic applications.

MATERIAL AND METHODS
The test was conducted in the Hydraulics and Localized Irrigation Laboratory of the Department of Rural and Agrifood Engineering of the Universitat Politècnica de València, Valencia, Spain (39°29'N, 0°23'20"W).
GAMBIT has been employed in the construction of the geometry and meshing (Figure 3A).The mesh was decomposed into different subdomains, combining meshes in structured tetrahedral and prismatic structures.The size of each cell is between 0.3 mm 3 and 0.2 mm 3 and the total number of cells was greater than 5 10 5 .We tested different mesh sizes by comparing the results obtained with each of them.The mesh was built in a structured (hexahedral) way, according the main direction of the flow throughout the domain, except in areas of pipe connection (not allowed by the software).In these cases, we intercalated unstructured (tetrahedral) meshes, resulting in a hybrid meshing type (Figure 3B).Near the walls of the Venturi, the mesh was refined for better resolution of the boundary layer (Figure 3C).All geometries were modeled in three dimensions, reproducing as accurately as possible the internal dimensions of the tested prototypes (Figure 3D).The Cartesian coordinate system was used, and we defined the origin at the point of confluence of the Venturi axis and the suction axis.FLUENT was used to define the Solver, performing the analysis with three dimensions and double precision.After the definition, we imported the mesh generated by GAMBIT, checking it for connectivity and scaling.As boundary conditions, we set the pressure in the outlet section (15 m.c.a.) and the average inlet speed of the Venturi (1.5 m s -1 ), considering null the injection flow.
The Solver formulation selection was performed through the governing equations of continuity and momentum (VASATA et al., 2011).The selection of the mathematical model for the formulation was made considering the turbulent flow, being added to the above governing equations.The Reynolds-Averaged Navier-Stokes (RANS) equation modelcurrently one two most widely used (CHAN et al., 2014;SANDERS et al., 2011) was employed.In the RANS model, we employed the Reynolds Stress Model (RSM) (ALPTEKIN et al., 2014), with standard functions for the wall treatment, selecting as the basis for the calculation the turbulence intensity (5%) and the hydraulic diameter of the upstream flow in the inlet and outlet sections of the Venturi injector.The equations above were discretized using the finite volume method (FVM) (MELLADO et al., 2013), using the Tridiagonal Matrix Algorithm (TDMA) (AL-HASSAN, 2005) with a sequential (segregated) resolution.
TECPLOT was used to define the graphical representation of all calculated, scalar or vector variables.Each model provided complete graphical and numerical information.
Thus, first, we modeled the operation of the injector for variables β, α 1 and α 2 while maintaining constant the Venturi injector nozzle diameter and length.With the resulting quantitative data, we determined the speed distribution and the influence of each geometric variable in DP/γ, Δh v /γ, and (P 3 -P 2 )/γ.The DP/γ variable is the differential pressure between the inlet and throat ((P 1 -P 2 )/γ); Δh v /γ are total losses in the injector or the pressure difference between the throat and the outlet ((P 1 -P 3 )/γ); and (P 3 -P 2 )/γ is the pressure difference between the outlet and the throat.The weight of variables β, α 1 and α 2 in DP/γ, Δh v /γ and (P 3 -P 2 )/γ, from the quantitative data obtained with the CFD was obtained with the analysis of variance and multiple regression (1% probability, F test), through the Statgraphics Plus 5.1 software application.
Second, for the same boundary conditions, we obtained the pressure and speed distribution in a vertically symmetrical plane in the throat.The pressures analyzed were P 1 /γ (injector inlet), P 2 /γ (suction point), P 3 /γ (injector outlet), DP/γ (P 1 /γ -P 2 /γ), Δh v /γ (P 3 /γ -P 2 /γ) and P min /γ (pressure at the lowest analyzed volume, which is obtained at the wall in all cases).The results obtained with the CFD techniques were as expected according to hydrodynamics.The development of the speed profile from the throat is slower as β increases and α 2 decreases.A more gradual convergence decreases flow disturbances.DP/γ decreases with β, increases with α 1 and varies little with α 2 with a minimum of 50°.Δh v /γ losses decrease with β and increase with α 1 and α 2 .(P 3 -P 2 )/γ decreases with β and α 1 , increasing with α 2 .

RESULTS AND DISCUSSION
With the results, we can see that the pressure loss relates to the geometry of the injector.We can see that the lower the relationship of diameters, the greater the loss.For the diffuser angle, we also note a clear trend of increasing losses with the angle.Nevertheless, the influence of the nozzle angle is not so clear.
In addition, other experiments investigated the influence of geometric parameters on the hydrodynamic behavior of the Venturi injectors using CFD techniques.Huang et al. (2009) used is the CFD method for simulating the internal flow field of Venturi injectors and the relationships between some of the structure parameters: diameter (D 2 ) and throat length (L g ), diameter of the top of the suction pipe (D a ), and suction capacity (q).The results showed that when the inlet pressure and the D a position remained unchanged, q increased with the decrease in D 2 and L g and increase in D a .While D a , D 2 and L g remained unchained, the greater inlet pressure increased suction capacity.
SUN & NIU (2012), using the CFD techniques, investigated the effects of geometric parameters (relationship between throat length and diameter (λ) and between throat and nozzle diameters (β)) in the performance of a Venturi injector (average output rate, low and critical pressures, coefficient of local head loss, and fertilizer absorption ratio).The results indicated that β was the main factor in the performance of the Venturi injector, which was positively correlated with the output rate and negatively correlated with the critical and minimum pressures, the coefficient of local head loss, and the fertilizer absorption ratio.
Figure 6 shows pressure and speed distribution in a vertically symmetrical plane in the throat for models B1, B2 and B3.In geometries B1 and B2, the minimum pressures were presented in the junction edges.In geometry B3, they were presented in the rounded joints, with higher minimum pressures.
The head losses are similar in all three-throat geometries, while the pressure difference between the inlet and the throat is lower in geometry B2.The increased pressure in the throat, which corresponds to a lower injection flow, is given in geometry B2 while geometries B1 and B3 would be more favorable from the standpoint of the injected flow.Geometry B3 is the one that least favors the occurrence of cavitation.In summary, the rounding of the nozzle-throat and throatdiffuser junctions delays the occurrence of cavitation and reduces losses.

CONCLUSIONS
1. Based on the CFD analysis, we can conclude that the relationship of diameters is the parameter that exerts the greatest influence on the head loss in the injector.Regarding the angles, it should be pointed out that the value of the nozzle does not have a significant influence, although there is a high correlation between it and the diffuser angle.
2. The design and geometry of these devices are simple, but the geometric parameters should be controlled to achieve the best hydraulic efficiency within a specific range of operation.Thus, it will be important to select the largest possible relationship of diameters to enable the injection, and ensure that the diffuser angle is as small as possible.
3. The rounding of junctions in the morphology between nozzle-throat and throat-diffuser junctions is the most recommended one, as it reduces head losses and delays the occurrence of cavitation.

FIGURE 2 .
FIGURE 2. Diagrams of the three compared throat geometries of the Venturi nozzle, Valencia, Universitat Politècnica de València, 2008.B1: nozzle-throat and throat-diffuser junctions with a sharp edge; B2: nozzle-diffuser junction with zero length and a sharp edge; B3: nozzle-throat and throat-diffuser junctions with a rounded edge.

FIGURE 3 .
FIGURE 3. Diagram of the geometry of a Venturi injector (A), detail of the structured and unstructured areas (B), detail of the bo undary layer (C), and example of meshing of model A3 (D), Valencia, Universitat Politècnica de València, 2008.

FIGURE 6 .
FIGURE 6. Pressure and speed distribution in the Venturi injector throat, Valencia, Universitat Politècnica de València, 2008.B1: nozzle-throat and throat-diffuser junctions with a sharp edge; B2: nozzle-diffuser junction with throat zero length and a sharp edge; B3 : nozzle-throat and throat-diffuser junctions with a rounded edge.