The reactor for hydrodynamic cavitation was designed with a venturi-type geometry and started with computational fluid dynamics (CFD) simulation of the fluid dynamics using finite elements. The simulations were developed in Solid Work®.

For the simulation, it is fundamental to understand the physics associated with the phenomenon of cavitation, which can be defined as the formation of vapor or gas bubbles in a liquid due to the pressure variations to which it is subjected. The intensity of cavitation causes extreme phenomena to occur in the flow of a fluid ^[39], including mechanical effects, such as the generation of turbulence and the increase in the liquid-vapor phase transition on the boundary surface of the bubbles, generated due to the reduction of the pressure to below the vapor pressure; chemical effects, include the generation of hydroxyl radicals, ozone, and other chemical reactions; and thermal effects, as the increase temperature and pressure.

The intensity of cavitation is measured using a dimensionless parameter called the cavitation number, σ, which is mathematically deduced in a fluid flow from the Bernoulli equation, (1):

Where P_1 is the pressure at the inlet, ρ_1 is the fluid density at the inlet, v1 is the fluid velocity at the inlet, P₂ is the pressure at the outlet, ρ ₂ , is the fluid density at the outlet, v ₂ is the fluid velocity at the outlet, H ₁ is the fluid height at the inlet, H ₂ is the fluid height at the outlet, y g is the acceleration due to gravity. If it is assumed that the fluid is at the same height, terms H ₁ and H ₂ cancel out, so (1) is transformed into (2):

Rearranging (2) gives (3):

When divided by input velocity v^{1^2}, the relationship is transformed into (4):

The left-hand side term in (4) is known as the dispersion factor or cavitation number, σ _v . Suppose the pressure at the inlet of the restriction is low enough for the water to reach its vapor pressure, and the inlet velocity is that of the restriction (typically an orifice). In that case P₁=P_v y v₁=v_h, and the cavitation number can be expressed according to (5):

This number can be interpreted in two ways: first, it is the ratio between the energy of the fluid due to its pressure, which is associated with the term , and the maximum kinetic energy, which is associated with the term . Second, σ _v can be understood as the ratio between the total pressure drop and the dynamic pressure that occurs due to the inlet velocity. A change in absolute pressure is related to a change in the flow rate, so the dynamic pressure can be considered to define the size of the pressure drop, which results in the formation and growth of cavities. Alternatively, the cavitation number can be defined according to (6):

A low cavitation number means high cavitation intensity since the dynamic pressure forms the cavities. To ensure a low cavitation number, the denominator of (5) and (6) must be increased, and the numerator must be decreased, which is achieved by increasing the inlet pressure, P ₁ , increasing the velocity at the restriction, v _h , decreasing the outlet pressure, P ₂ , or increasing the vapor pressure, P _v , which can be achieved by increasing the temperature.

The adjustment of the cavitation process parameters generates two significant engineering problems:

If 𝑃₂−𝑃𝑣 is small, then the discharge pressure resembles the vapor pressure of the water so that it could erode the elements downstream of the fluid stream (elbows, valves, and others)

Bernoulli's conservation theorem shows that for a high velocity, it is necessary to increase the pump's capacity, which impels the fluid in pressure or flow rate. If 𝑃1−𝑃2 is required to be very large, more powerful pumps are needed to overcome this hydraulic loss, which would increase energy costs.

Therefore, a rigorous process of evaluating cavitation and disinfection parameters is necessary before carrying out experimental tests to avoid high investments and damage to equipment. For this, using CFD is fundamental as an analysis tool that enables the creation of complex models that make it possible to manipulate variables and parameters for decision-making. Through CFD, the behavior of a fluid in any system is calculated with precision so that its velocity fields, pressure, transported variables, reactions produced inside the fluid, the interaction between different phases, and, in short, any characteristic derived from the state and nature of the fluid can be known ^[40].

The CFD simulation with finite elements followed the general steps suggested in ^[41]. A Venturi shape was used for the disinfection element's geometry, as shown in Figure 3, after a comparative evaluation with other geometries, such as the orifice plate and fins.

Figure 3 Source: created by the authors.

Figure 4 shows the mesh refinement at specific geometry points, with five being the highest and 0 being the lowest. Discretization or meshing process, with refinements according to the overlapping areas of the geometry and considering the possibility of high gradients in the study values, yielded the following results:

Total cells and fluid cells: 119103.

Fluid cells in contact with solids: 67760.

Figure 4 Source: created by the authors.

To develop the fluid simulation, SolidWorks® numerically solves the Navier-Stokes equations, which are expressions of the conservation laws of mass, momentum, and energy (7), (8), and (9), ^{[42], [43],} where ρ is the fluid density, V its velocity, τ_ijthe viscous stress tensor, p its pressure, F the forces acting on the flow, e is the internal energy, Q is the heat source, t is the time, Φ is the dissipation and ∇.q is the heat lost by conduction. The simulation time was approximately 15 hours, which was necessary to observe the convergence of the desired parameters (pressure, velocity, density, vapor volume fraction) in 2810 iterations.

The calculation of σ _v used (5), considering P ₂ as the average pressure at the outlet of the computational domain of the simulation, P _v as the minimum pressure obtained in the simulation (which does not necessarily coincide with the vapor pressure of water at room temperature but must be equal to or less than), and v _h as the maximum velocity obtained in the simulation, which corresponds to the restriction and orifice designed.

Figures 5 and 6 detail the system assembly diagram. The main components used in the laboratory tests were: (1) the Venturi cavitation element, (2) a 6 HP centrifugal pump, (3) a 300 L domestic wastewater storage tank, (4) a flow diversion, (5) pressure gauges, (6) a sampling circuit, (7) the system water outlet, (8) the recirculation circuit and (9) a by-pass circuit. The system operated with a 6 HP pump power, a 2" suction and 1.5" discharge, and a flow rate of 0.00625 m3/s (6.25 L/s). With the implemented system, the designed cavitation equipment performance tests were carried out.

Figure 5 Source: created by the authors.

Figure 6 Source: created by the authors.

During the experimental stage, point sampling of wastewater was carried out in a discharge on the Fonce river in the municipality of San Gil, Santander, Colombia, on a property owned by the Santander Energy Company in the El Porvenir neighborhood. Wastewater samples were taken both upstream and downstream of the cavitation system. Table 1 shows the characterization of the discharge.

Table 1

Source: created by the authors.

In order to determine the performance of the system and its disinfection efficiency, laboratory analyses of the microbiological quality were carried out to count the CFU (Colony Forming Units) of total coliforms (Gram-negative bacteria, non-spore-forming) and fecal coliforms (specifically Escherichia coli, E. coli), according to the membrane filtration method, for all samples collected. The tests performed were filtered on a membrane and cultured in Chromoculth for 24 hours at 36.5 °C, with filtrate volumes for serial tubes of 10^-4 and 10^-5 of 9 ml with dilutions of 10^-4 and 10^-5, following the standards of the Institute of Hydrology, Meteorology and Environmental Studies (Sub directorate of Hydrology - Environmental Quality Laboratory Group, Total Coliforms and E. Coli by membrane filtration on Chromocult agar, August 2007), Resolution 2115 of 2007 of the Ministry of Social Protection, Ministry of Environment, Housing and Territorial Development, and SM 9222 J (Simultaneous Detection of Total Coliform and E. Coli by Dual-Chromogen Membrane Filter Procedure).

The growth of bacteria was evaluated in triplicate for three different amounts of water recirculation (n𝑝) in the cavitation system (1, 10, and 20). In each experiment, the system loading volume was 1000 mL of domestic urban wastewater (DUW) per 15 L of non-residual water in the tank. The total water volume processing was 200 L (12.5 L of DUW, diluted in 187.5 non-residual water). The number of recirculation was calculated measurement the time, knowing that for a flux of 6.25 L/s, with a tank of 200 L, one pass occurs each 32 s. Figure 7 shows an example of the bacterial growth obtained in the laboratory for the three amounts of water recirculation.

Figure 7 Source: created by the authors.

The methodology followed in the present investigation to evaluate the inactivation of contaminating microorganisms corresponds to the methods commonly used for this type of work ^[27]. Its scope goes up to evaluating index or indicator microorganisms, whose identification at certain levels reveals the potential presence of pathogenic microorganisms with taxonomic or physiological relationships. To evaluate each microorganism considered pathogenic in a specific medium in a separate form is beyond the limits set for the present study. As mentioned, most of the literature does not specify each pathogenic organism. However, studies have been done to characterize broad groups, such as the coliform group, which are fundamental indicators of contamination according to environmental standards. Generally, the literature reports result for E. coli. This study broadens that spectrum and presents results for the critical indicators of total and fecal coliforms. The research on fecal coliforms has been explicitly based on E. coli, the leading indicator of fecal contamination. Identification of parasites, protozoa, or viruses is beyond the scope of this study.

To minimize the matrix effect, i.e., the influence of the composition of a sample on the detection and quantification of microorganisms, in each test carried out, an analysis of blank samples has been performed, the sterility of the culture media and materials has been examined, and tests have been developed with a known concentration of microorganisms, following the standard rules for this type of tests, in order to minimize possible interferences that the analytical methods may cause.

Figure 8 shows the high and low levels of the hydrodynamic variable (in red and blue, respectively). These flow parameters give a better idea that the cavitation process is happening, and that the specific spatial location designed for the purpose of cavitation is taking place there and not in another place that could damage other components not designed for those conditions.

Figure 8 Source: created by the authors.

The simulation verified that the levels of the hydrodynamic variables obtained were consistent. Thus, for example, when detecting a cavitation zone at a pressure of 2300 Pa (vapor pressure at 20 °C), a value significantly below 1000 kg/m³ was found in the density parameter. These hydrodynamic parameters are beneficial for determining conditions that are associated with effective disinfection, including:

A. High velocity, near 35 m/s (Figure 8a).

B. Low pressure, below vapor pressure (<2300 Pa, Figure 8b).

C. Vorticity, or the ability of the flow to form vortices which is desirable if you want to increase the probability that an imploding cavitation bubble will encounter an E. Coli bacterium ^[44] (Figure 8e).

D. The density of water under environmental conditions at 1 atmosphere and 20 °C is 998 kg/m3 (Figure 8c). Because water is considered incompressible, a low density implies that there are zones within the computational domain of the simulation that have already transitioned to a vapor-liquid mixture state (Figure 8d). In the case of the simulation, as can be seen in Table 2, there were zones where the water reached 5.74 kg/m3, which indicates that the process is already generating cavitation bubbles.

Table 2

Source: created by the authors.

Once the hydrodynamic parameters of cavitation were determined, the cavitation number was calculated, as detailed in Table 2, obtaining a result of σ _v =0.07. This value of the cavitation number (0.07) is close to the lower limit reported by ^[45], who refers for microorganism reduction, an optimal interval for σ _v between 0.1 and 0.54. Likewise, ^[33] shows how σv lower than 0.2 is related to a more significant logarithmic reduction of microorganisms. Whether this σ _v value causes a critical cavitation in the experimental reactor that affects its structure has not been determined. The most probable cavitation zone is shown in Figure 9.

Figure 9 Source: created by the authors.

How hydrodynamic cavitation affects microorganisms obeys a sequence of abrupt generation and collapse of bubbles ^[31] because of pressure variations in the liquid, which are generated in turn by the speed variations caused by the reactor. As the velocity increases, the pressure decreases and bubbles emerge. Then, as the velocity decreases, the pressure increases, and the bubbles collapse. This abrupt generation and collapse of bubbles inside the reactor produces increases in temperature and pressure, which can reach values close to 10000 K and 1000 atm, in time instants of the order of microseconds. These values are sufficient to generate ruptures in the cell membrane of the microorganisms present in the water and generate free radicals that can contribute to altering the DNA of the microorganisms present.

For the σ _v value obtained in simulation (0.07), and with a registered pressure delta of 54 psi, the microbiological test data determined for n _p =1, n _p =10, and n _p =20, correspond to those detailed in Tables 3 and 4, where C and C0 are the number of coliforms measured in UFC/100 mL (colony forming units per 100 mL) after and before cavitation, respectively. C/C0 is the ratio between the number of coliforms after and before cavitation, GIR is the growth inhibition rate calculated according to (10), and LR is the logarithmic reduction calculated according to (11).

The best results were obtained by Experiment 1 with dilution of 10^-5, reaching a GIR of 93.40 % and a LR of 1.18 for Total Coliforms, and a GIR of 95.12 and a LR of 1.31 for E. coli. Averages of disinfection ratios (C/C₀) and average of GIRs for one, ten, and twenty water recirculation for both total and fecal coliforms and dilutions 10-4 and 10-5 can be seen in Figure 10 and Figure 11, respectively. The average growth rates for one, ten, and twenty recirculation were 31.72 %, 59.45 %, and 84.53 %, respectively, reached in approximate times of 32, 320, and 640 seconds, considering the system's flow rate. In ^[46] with an HCR with an orifice plate, after 1800 seconds, the removal rate was 41.57 % for an initial E-coli density of 0.16x10⁶/100 mL, reaching, however, a removal greater than 98 % after 60 minutes. On the other hand, when comparing the results with ^[27], it is evident that the C/C ₀ levels for E-coli reported in this work for disinfection reactors with an orifice plate are approximately 50 % higher than those determined in the present research for comparable initial C ₀ conditions.

Table 3

Source: created by the authors.

Table 4

Source: created by the authors.

Figure 10 Source: created by the authors.

Figure 11 Source: created by the authors.

The following table (see Table 5) compares the results of this research and those of other related works for the specific indicator of E. coli. The GIR results of this research are close to those obtained by other laboratory studies that were realized with artificially contaminated distilled water samples and for a smaller volume of water. It could be helpful for future experiments to mix HC with advanced oxidation methods to increase the LR value.

On the other side, after cavitation, the mean pH measurements in the tank's water were 7.80. Before cavitation, the pH of the 187.5L mixed with the 12.5L of DUW was 7.73, and 7.68 in the direct sample of DUW. This increase in pH after cavitation could be understood by the formation of free radicals of OH-1 during the HC.

Table 5

Source: created by the authors.

From the results obtained, it was also possible to determine the CFU/J, or colony-forming units dead per Joule of energy. Considering that the pump operates in three-phase mode with a line voltage of 220 V, a line current of 11 A, and a power factor of 0.86, its electrical power was calculated at 3730.4 W. With this power, and given that the system's flow rate (6.25 L/s) empties the 200 L tank in 32 seconds, the Joules consumed (J _C ) for one pass were calculated at 119.375,7. Now, knowing that the discharge water has 4.88x10⁶ CFU/100 mL (CFU_100mL), that the liters of domestic urban wastewater (L_udw) used in each experiment were 20, and that the average GIR for one pass (𝐺𝐼𝑅𝑎𝑣𝑔) can be estimated from Table 3 and 4 at 31.2 %, the CFU/J can be calculated according to (12), at 2327.6. This result is higher than that reported by ^[47], which reports an approximate value of 1038 CFU/J, with only cavitation.