Effect of working fluid temperature on flow characteristics of jet cavitation reactor

The discharge of chemical products such as fertilizers into natural bodies of water can lead to eutrophication and red tides. Algal blooms can pollute the water, making it cloudy and smelly. Drinking water containing toxic substances released by algae is detrimental to human health and may induce liver cancer.¹ Algal blooms can cause oxygen depletion in the water and block light, affecting the survival of other aquatic organisms; in addition, the toxins from algae can accumulate in aquatic organisms through the food chain.^2,3 Algae can be removed by chemical treatment or biological control. However, both chemical or biological methods have shortcomings: chemical algaecides tend to introduce new impurities into the water, and biological control is often a lengthy process and only effective for specific algal species.⁴ Therefore, research is now being directed toward investigations of the use of acoustic, hydrodynamic, and optical cavitation or other physical means to remove algae.⁵ 

Cavitation is a process in which gas dissolved in a liquid escapes or liquid vaporizes to form bubbles in regions with the pressure drops below the saturated vapor pressure (SVP) of the liquid and bubbles grow and then collapse as they move to normal-pressure areas. Cavitation is often harmful to rotating turbomachinery. The bubbles, if generated in large amounts, can congest the flow channel and reduce the pump head, and when the bubbles collapse, the microjets and shock waves generated can impact the impeller and thus cause vibration and noise. Long-term running of an impeller when cavitation occurs can also cause erosion damage. Very rapid collapse of bubbles can release huge amounts of energy, which is utilized in food processing,⁶ ship cleaning,⁷ sewage treatment,^8,9 biopharmaceutical production,¹⁰ chemical production,¹¹ and other industries.

Acoustic cavitation and hydrodynamic cavitation are two commonly used methods for inducing cavitation. Hydrodynamic cavitation can remove algae without producing new pollutants. It uses the local high temperatures and high pressures created when bubbles burst to cause physical damage to the algae. In addition, the collapse of bubbles can ionize the water to generate free radicals, which can oxidize algae and the toxins they secrete.¹ While acoustic cavitation tends to generate highly intense cavity collapse, hydrodynamic cavitation has the advantages of low cost, high sewage treatment efficiency, and the formation of large cavities.¹² 

Jet cavitation reactors (JCRs) rely on turbulent diffusion to achieve energy and mass exchange in fluids. Their structural design incorporating a sudden contraction section enables the production of local low pressure, which, combined with the shear flow of high-speed jets, facilitates cavitation.¹³ Therefore, JCRs are often used for removal of algae.^1,2,14 Cavitation intensity is related to a number of factors, including liquid air content, temperature, liquid flow rate, and liquid viscosity. Kim et al.¹⁵ were able to remove algal cells by ionizing water to increase its oxygen content and thus enhance the cavitating performance of venturis. They also verified that a design with a venturi nozzle could improve algal removal efficiency. Zezulka et al.¹⁶ conducted experiments to remove blue-green algae from samples collected in a water body where an algal bloom had occurred. High-pressure jets were used alone or in combination with hydrogen peroxide (H₂O₂). It was concluded that high-pressure cavitation could be improved with the addition of low-concentration H₂O₂. Ge et al.¹⁷ explored the effect of temperature on cavitation and cavity shedding in venturis. They analyzed cavitation at 24–85 °C and found that the cavity length reached a maximum at about 55 °C. The temperature of the working fluid has an important effect on algal removal, and increasing the temperature of the liquid within the appropriate temperature range is beneficial to increase the strength of cavitation.¹⁸ For heat-sensitive fluids or high-temperature water, however, the influence of thermodynamic effects on cavitation is enhanced, which is manifested as a decrease in cavitation strength with increasing liquid temperature,¹⁹ while, on the other hand, the water temperature also affects the degradation rate.²⁰ Most studies of hydrodynamic cavitation have involved water temperatures of 298–318 K,^2,21,22 while Kalumuck and Chahine²³ proposed that the optimal operating temperature of a water jet is about 315 K, and so the temperature range of subsequent studies in the present paper is 298–318 K.

Using a large eddy simulation (LES) method, we conduct numerical simulations of a JCR with water as its working medium in the temperature range of 298–318 K. The development of bubbles in the JCR at different temperatures is compared and analyzed, and the changes in the cavitating flow field inside the JCR at different temperatures are described and summarized. Our study can provide some theoretical basis for algal removal through cavitation using JCRs.

The structural profile of the JCR is shown in Fig. 1. Our JCR consists primarily of an inlet tube, a nozzle, a suction chamber, a throat, a diffusion tube, and an outlet tube. It works as follows: when high-pressure working fluid flows from the inlet tube into the nozzle, its pressure decreases and its velocity increases as the flow channel becomes smaller; the suction chamber produces a low-pressure area to suck the fluid; and two streams of fluid mix in the throat. The detailed geometric parameters of the JCR are shown in Table I. The ratio of the throat area to the nozzle outlet area is high, reaching a value of 52. To ensure accuracy of the numerical calculations and control their cost, in our simulations, the JCR model is simplified by ignoring the curved inlet bend, extending the nozzle as the entrance of the high-pressure fluid, and extending the outlet section to make the flow uniform. ANSYS ICEM software is used to perform hexahedral meshing of the full flow domain of the JCR. To make the y⁺ value meet the requirements of LES, the number of elements is increased near the nozzle outlet, at the throat, and at other positions where it is necessary to capture the flow details, and the walls are refined. The computational model, grid details, and y⁺ distribution are shown in Fig. 2. It can be seen that the average y⁺ value is around 1, meeting the grid requirements of LES.

The grid independence analysis is performed using models with 1 190 000, 1 460 000, 1 900 000, 2 200 000, 3 020 000, and 4 010 000 elements, respectively, and the results are shown in Fig. 3. The flow ratio Q in the figure is a dimensionless number, which is commonly used to measure the performance of a JCR. It is defined as the ratio of the sucked fluid flow to the working fluid flow, and the monitored velocity is the jet flow rate at the nozzle outlet. It can be seen that Q fluctuates more widely for models with fewer elements, and that its fluctuation and the flow rate at the nozzle outlet stabilize as the number of elements continues to increase. Therefore, further refinement of the grid does not have much impact on the simulations of the JCR. To ensure the accuracy of calculations and reduce computational costs, our subsequent calculations are based on the grid with number of elements as indicated by the arrow in Fig. 3, i.e., 2 200 000 elements.

For calculations relating to cavitation in water, the evaporation coefficient F_vap = 50, the condensation coefficient F_con = 0.01, R = 10⁻⁶m, and α_nc = 5 × 10⁻⁴. The ZGB cavitation model assumes that cavitation is driven only by the difference between the local pressure and the cavitation pressure, i.e., the process is isothermal. Physical parameters of water at different temperatures are shown in Fig. 4, with the temperature range studied in this paper indicated by the vertical black dashed lines. At ambient and medium–high temperatures, the physical parameters of water and water vapor are not much affected by temperature change. However, at high temperatures, even with slight fluctuations in temperature, these parameters can change greatly. Therefore, for cavitation in thermosensitive fluids and high-temperature water, the effects of temperature change cannot be neglected. Cavitation models have been modified to take into account the effects of temperature.^26–30 In this paper, the SVP and density of the liquid medium, water, and the density of water vapor are modified to the values at the corresponding temperatures when calculating the cavitation characteristics of the JCR at different temperatures.

ANSYS-CFX software is used to simulate the jet cavitation generator, and water at 298, 308, 318, and 313 K near the optimal operating temperature as described above is selected for the calculations. It is assumed that the water flow is incompressible, the cavitation pressure is the SVP of water at the corresponding temperature, the bubbles generated by cavitation are all water vapor, and the mixed flow of the bubbles and water is uniform and multiphase flow. The inlet pressure of the working fluid is 0.803 MPa, the suction inlet pressure is 1 atm, the outlet pressure of the mixed fluid is 0.0217 MPa, the reference pressure value is set to 0, and the wall surface is considered as an adiabatic nonslip wall. The shear stress transport (SST) k-ω model is selected as the steady-state turbulence model, and LES is selected as the transient turbulence model, with a total time of 1.8 s and a time step size of 2 × 10⁻⁵ s. The average Courant number is 0.8, which meets the requirements of LES.

To verify whether the selected turbulence models can simulate the cavitation evolution well, numerical simulations of the venturi test performed by Wang et al.³¹ are carried out. D_in1 and D_out1 are 50 mm, W and D_th1 are 10 mm, and α₁ and β₁ are 45° and 12°, respectively. The inlet and outlet segments are extended by a length that is eight times the inlet/outlet diameter to eliminate the influence of the boundary conditions, and the grids near the throat and the wall grid are refined. The details of the venturi test model and the grids are shown in Fig. 5.

Figure 6 compares the cavitation cloud evolution between the venturi test and the simulation. The left panel shows the test photographs (the white areas are bubbles) and the right panel shows the bubble volume fraction at the axial section of the venturi obtained from the simulation. It can be seen that the process of cavitation cloud development and shedding are simulated well. The cavitation cloud attached to the tube wall gradually thickens, piles up, and closes toward the center. Then, under the action of the re-entrant and main jest, the accumulated cavitation clouds are broken and move downstream, where they collapse and dissipate owing to high pressure. Then, a new cycle of cavitation cloud evolution starts in the venturi. The lengths of the cavitation clouds attached to the wall from the test and the simulation are compared in Fig. 7. As the gas phase insoluble in liquid is ignored in the simulation, the simulated cavitation cloud lengths are all slightly shorter than those from the test, with an error ranging from 3.1% to 9.1%. The cavitation cloud lengths from the test and simulation show similar trends, which verifies the feasibility of the turbulence model.

Figure 10 illustrates how the cavitation number, total bubble volume, and bubble volume fraction at the axial section of the JCR vary with working fluid temperature. When the inlet and outlet pressures are the same, increasing the working fluid temperature causes its SVP to increase, reducing the difference between local pressure and SVP, and resulting in a decrease in the cavitation number and a higher likelihood of cavitation. It can be seen from Fig. 10(a) that as the temperature increases, the total bubble volume increases, but at a lower rate. When the water temperature increases from 313 to 318 K, although the cavitation number is further reduced, the total bubble volume only increases slightly. The volume of bubbles generated by the JCR is close to its maximum value at 318 K. Figure 10(b) shows the bubble volume fraction at the axial section of the JCR at different temperatures. The length of the attached cavity continues to increase as the temperature rises, while more and more bubbles with small volume fraction appear inside the flow channel, and the gas–liquid interface inside the pump becomes unclear, as bubbles can escape from the liquid more easily. As already mentioned, when the water temperature increases from 298 to 308 K, the attached cavitation elongates significantly; however, as the temperature continues to increase from 308 to 318 K, there is no significant change in the length of the cavity, although the gas–liquid interface becomes even more indistinct. As the temperature rises, cavitation becomes more likely to occur, but when the temperature reaches a certain level, cavitation becomes stable and no longer changes significantly with temperature, indicating that the JCR has reached a stable limit state.

Figure 11 shows how the internal streamlines and central axis pressure of the JCR vary with temperature at 1.8 s. Figure 11(a) shows that the streamlines at the inlet and the throat are smooth at all four temperatures, indicating that the flow is uniform there. The differences in the streamlines are mainly in the diffusion tube and at the outlet. The streamline at 298 K is chaotic in the diffusion tube and at the outlet, with complex flow behavior such as flow separation, reflux, and vorticity; the streamlines at 308 and 313 K are similar, both with reflux at the wall surface of the diffusion tube; and the streamline at 318 K is most stable in general, with small zigzagging in the diffusion tube and at the outlet. As the temperature increases, the unstable flow structure in the cavitation reactor decreases and the flow becomes smooth. Figure 11(b) illustrates the pressure drop distribution along the center axis from the nozzle to the outlet. When the jet flows through the nozzle contraction section, which serves to reduce pressure, the jet pressure is reduced to the corresponding cavitation pressure at each temperature. Cavitation then occurs, and the generated bubbles congest the throat, slowing down the jet velocity, which causes the downstream pressure to increase. Thus, the throat outlet and pump outlet are two regions with sharp pressure fluctuations in the JCR. At 308, 313, and 318 K, the water pressure fluctuates within a small range at the throat outlet and the pump outlet. By contrast, at 298 K, the water pressure changes greatly at the two outlets, indicating that at that temperature, owing to bubble congestion, the downstream jet pressure fluctuations are greater. Increasing the temperature of the working fluid helps to reduce the internal pressure fluctuations of the JCR.

When cavitation occurs, the vorticity in the JCR is related to the development of cavitation, and the region where vorticity is distributed is closely linked to the region where cavitation occurs.³²  Figure 12 illustrates the vortex distribution as analyzed by the vortex transport equation at different temperatures. It can be seen that the vorticity is mainly distributed at the center of the diffusion tube and the pump outlet. The vortex structure from the nozzle outlet to the throat outlet is continuous and orderly, and the vorticity here is obviously less than that in the diffusion tube and at the outlet, which indicates that the flow of the high-speed jet from the nozzle is stable and that temperature change has no effect on the vorticity distribution here. As the jet continues to move down to the inlet of the diffusion tube, the vortex behavior is characterized by an increase in vorticity, vortex merging, vortex elongation, and the development of a chaotic vortex structure. There is significantly higher vorticity in the diffusion tube at 298 K when compared with other temperatures, indicating a buildup of bubbles clogging the flow and disturbing it. A smaller increase in vorticity is found in the diffusion tube at other temperatures. Bubble clouds are shedding and collapsing at the outlet, and the flow is disturbed by the development of bubbles, resulting in a fragmented vortex structure. The vortex distributions at the outlet are similar at the four different temperatures. Overall, the vorticity distribution decreases with increasing temperature, and lower vorticity means that the fluid flow is less subject to disturbance from bubbles and so is more uniform.

Sun et al.³³ proposed the use of the total bubble volume as a parameter to measure cavitation intensity. A larger total bubble volume generated indicates a higher cavitation intensity. As indicated by the steady-state analysis, at a higher working fluid temperature, more bubbles can be generated, which is helpful for algal removal; and the total bubble volume will not increase significantly once the temperature has reached a certain level. In addition, at a higher working fluid temperature, the streamlines of the JCR become smooth, the unstable flow structure is reduced, the pressure fluctuations and vorticity at the central axis are reduced, and the internal flow becomes more stable.

The JCR flow is highly nonstationary, and a transient-state analysis of the JCR simulations is required to investigate the effect of cavitation on the flow inside the JCR. Figure 13 illustrates the changes in the total bubble volume in 1.8 s when cavitation occurs at different working fluid temperatures. It can be seen that the total bubble volume change at each temperature is quasi-periodic in nature: the total bubble volume increases owing to bubble accumulation and decreases owing to bubble collapse. From Fig. 13(a), it can be seen that there is a large fluctuation (0.002 059–0.011 96 m³) in total bubble volume at 298 K and that the fluctuations in the total bubble volume at the other three temperatures did not differ much, revealing an overall trend of total bubble volume increase with increasing water temperature. From Fig. 13(b), it can be seen that the total bubble volume increases in a shorter time than the time taken to decrease, that is, the bubble clouds accumulate more quickly than they collapse. In addition, at a higher temperature, it takes a longer time for bubbles to collapse, indicating that bubbles can be supplemented in a timely manner after collapse and thus slow down the reduction in their total volume. By contrast, temperature changes have an insignificant effect on the time for the bubble volume to accumulate. In general, as the temperature rises, the minimum total bubble volume increases, the total volume fluctuates less violently, and the total bubble volume decreases over a longer time span.

Figure 14 shows how an isosurface with bubble volume fraction of 0.1 changes during one cycle at 298 K. At t = 0.370 64 s, the bubbles fill the pump, the total bubble volume reaches its maximum value, and bubbles accumulate inside the throat as indicated by the throat profile. The bubbles inside the throat are in two morphologies: thin and stable annular cavitation layers adhering to the wall, which have a smaller influence on the main flow, and cavitation clouds that can move downstream along with the jet. Cavitation clouds at the center of the throat have more regular and annular shapes, since the axisymmetric low pressures generated by the high-speed jet make it easier for cavitation to occur around the high-speed jet,³⁴ as shown in Fig. 14(a). Cavitation clouds accumulating in the throat can block it, reducing the mainstream flow rate, and then the pressure inside the throat will increase to prevent the occurrence of cavitation, at which point, the ability of the JCR to produce bubbles will be weakened. At the same time, under the action of the re-entrant flow in the opposite direction to the mainstream, cavitation clouds constantly divide, and shedding cavitation clouds are pushed downstream by the mainstream and burst at the outlet. In this way, the total bubble volume inside the JCR decreases continuously to its lowest value at t = 0.6212 s, as shown in Figs. 14(b)–14(f). Cavitation clouds inside the throat are continuously transported downstream and decreased in extent, and the stable cavitation layer attached to the wall develops downstream from the entrance of the throat, reducing the congestion and thereby increasing the jet velocity again. The ability of the JCR to generate cavitation is thus restored, bubbles start to accumulate, and their total volume starts to increase in a new cycle, as shown in Figs. 14(g) and 14(h). At 298 K, the cavitation inside the JCR is in an unstable limit state, and, owing to bubble congestion inside the throat, the rate of bubble growth does not match the rate of bubble shedding and collapse, as a consequence of which the length of the cavitation clouds inside the reactor exhibits pulsating behavior. Bubble congestion inside the throat has been studied in detail in Ref. 35.

Figures 15–17 show the limiting cavitation states at 308, 313, and 318 K, respectively. It can be seen that the changes in the bubble volume fraction isosurfaces at the three temperatures are quite different from those at 298 K. At 298 K, the length of the cavitation clouds exhibits obvious pulsations in one cycle. By contrast, at 308, 313, and 318 K, the length of the cavitation clouds remains stable in one cycle, with only shedding and collapse of bubbles at the tail. This cavitation state is called stable limit cavitation and is characterized by the small influence of cavitation development on the cavitation cloud. Although a large number of bubbles are generated in the throat at all three temperatures, when the SVP is high, cavitation occurs readily downstream to produce a large number of bubbles, thus weakening the effect of throat blockage in the downstream region. Stable cavitation clouds fill the throat and the expanding section of the cavitation reactor. The main difference between the bubble volume fraction isosurfaces at the three temperatures lies in the length of stable cavitation clouds. To the left of the red dashed lines in Figs. 15–17, there are stable cavitation clouds, while to the right of these lines, the cavitation clouds can be seen to collapse. The lengths of the cavitation clouds at 308, 313, and 318 K account for 81%, 84%, and 95%, respectively, of the total length of the JCR from the nozzle to the outlet, indicating that the percentage increases with increasing temperature. The stable cavitation cloud at 318 K is the longest among the three temperatures, and the JCR reaches its maximum cavitation capability around this temperature.

Figure 18 illustrates the variation in mean bubble volume fraction over one cycle for planes 1 and 2 indicated in Fig. 14(a). The distance between plane 1 and the nozzle outlet is 78 mm, and the distance between the planes is 50 mm. The same positions are monitored for the other three temperatures. The mean bubble volume fraction at plane 1 remains almost unchanged at all four temperatures, indicating that the development of cavitation at this position is not affected by the flow and that the annular cavitation layers are stable. The mean bubble volume fraction at plane 2 changes more significantly over one cycle. It increases owing to the accumulation of bubbles, and then decreases when congestion is reduced by the pushing action of jets and the cutting action of re-entrant jets. Subsequently, the bubble development process (accumulation and collapse) repeats. The rate of change of the mean volume fraction of bubbles at plane 2 decreases as the temperature increases. The rate of change at plane 2 is smallest at 318 K among the four temperatures.

As demonstrated by the transient-state analysis, bubble development in the JCR exhibits quasi-periodicity, with large fluctuations in total bubble volume and a pulsating change in cavitation cloud length at 298 K. When the water temperature rises, the minimum total bubble volume increases and the time taken for the total bubble volume to decrease becomes longer, indicating that more bubbles are generated to delay the reduction in total bubble volume and thereby stabilize the length of cavitation clouds. The higher the water temperature, the greater is the length of stable cavitation clouds. Inside the JCR, cavitation clouds are in two states in the throat: stable annular cavitation layers attached to the pipe wall, which are not affected by the development of downstream cavitation, and irregular cavitation clouds clogging the throat, which move downstream when pushed by the jets and eventually collapse. New irregular cavitation clouds can grow continuously to clog the throat.

The cavitation rate and disinfection rate can be used to assess the cavitation and disinfection performance of the JCR and compare the results with those of other studies. The cavitation rate is the ratio of the total bubble volume to the total volume of the fluid domain, and the disinfection rate is the ratio of the algal concentration before and after cavitation and disinfection. The results of the comparison are shown in Table II. Owing to the presence of internal shear flows, which have strong cavitation-inducing effects, the cavitation rate and total bubble volume of jet and rotary cavitation reactors are higher than those of traditional orifice plates and venturis, indicating a higher efficiency of algal removal. In particular, the disinfection rate of a rotary cavitation reactor can reach as high as 96.4%. Although algal removal experiments have not been conducted in the present study, the potential of the JCR as an algal removal device based on cavitation can also be seen by comparing the results of other tests.

In this paper, numerical simulations of the cavitation state inside a JCR have been carried out using LES to explore its cavitation characteristics at different temperatures. The following main conclusions can be drawn from the results of this study:

1. When the pressures at the inlet and outlet are same, as the temperature rises, the liquid’s SVP increases, and the cavitation performance of the JCR is enhanced. The total volume of bubbles increases significantly between water temperatures of 298 and 313 K, but ceases to increase significantly once the temperature has reached 318 K. Eddy generation is closely related to bubble development. A large number of vortices can be generated in areas where cavitation clouds accumulate, shed, and burst. Fewer vortices are distributed and internal flows become more uniform as the temperature of the working fluid increases.

2. The total bubble volume exhibits quasi-periodic behavior, changing most dramatically at 298 K. As the water temperature rises further, volume fluctuations become milder, and the total bubble volume decays over a longer time span. Owing to congestion of bubbles and cutting of cavitation clouds by re-entrant jets, these clouds are unstable and exhibit quasi-periodic pulsations at 298 K. At 308, 313, and 318 K, there are stable cavitation clouds, the lengths of which account for 81%, 84%, and 95%, respectively, of the length from the throat to the outlet.

3. Taking account of the total volume of bubbles and the length of stable cavitation clouds, the cavitation performance of a JCR, and thus its ability to remove algae, can be enhanced by increasing the working fluid temperature appropriately.

4. JCRs have the advantages of high cavitation rate and large total bubble volume when compared with traditional cavitation reactors such as orifice plates and venturis. Comparisons with previous studies of cavitation and algal removal indicate that the JCR considered in this paper has the potential to achieve efficient algal removal.

The authors have no conflicts to disclose.

Jinlan Gou: Conceptualization (equal); Investigation (equal). Qi Xiao: Conceptualization (equal); Investigation (equal). Zhenhai Zou: Conceptualization (supporting); Investigation (supporting). Bangming Li: Conceptualization (supporting); Investigation (supporting).

The data that supports the findings of this study are available within the article.

$ṁ$

Mass transfer rate for cavitation

$p̄$

Pressure

$ūi$

Fluid velocity components in Cartesian coordinate system

F_con

Condensation coefficient

F_vap

Evaporation coefficient

h

Pressure ratio

Q

Flow ratio

R

Bubble radius

t

Time

V_B

Bubble volume

x_i

Cartesian coordinates in flow field

Greek

α_l

Fluid volume fraction

α_v

Bubble volume fraction

γ

Surface tension of liquid

η

Efficiency

μ

Mixed viscosity

μ_l

Liquid viscosity

μ_v

Vapor viscosity

ρ

Gas–liquid mixed density

ρ_l

Liquid density

ρ_v

Vapor density

σ

Cavitation number

τ_ij

Subgrid stress

$ṁ$

Mass transfer rate for cavitation

$p̄$

Pressure

$ūi$

Fluid velocity components in Cartesian coordinate system

F_con

Condensation coefficient

F_vap

Evaporation coefficient

h

Pressure ratio

Q

Flow ratio

R

Bubble radius

t

Time

V_B

Bubble volume

x_i

Cartesian coordinates in flow field

Greek

α_l

Fluid volume fraction

α_v

Bubble volume fraction

γ

Surface tension of liquid

η

Efficiency

μ

Mixed viscosity

μ_l

Liquid viscosity

μ_v

Vapor viscosity

ρ

Gas–liquid mixed density

ρ_l

Liquid density

ρ_v

Vapor density

σ

Cavitation number

τ_ij

Subgrid stress