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Design of a hydrodynamic cavitating reactor
Accepted Manuscript Title: Design of a Hydrodynamic Cavitating Reactor Authors: Narotam Jangir, Prateek Diwedi, Sumana Ghosh PII: DOI: Reference:
S0255-2701(17)30598-6 https://doi.org/10.1016/j.cep.2017.10.008 CEP 7092
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
22-6-2017 6-10-2017 8-10-2017
Please cite this article as: Narotam Jangir, Prateek Diwedi, Sumana Ghosh, Design of a Hydrodynamic Cavitating Reactor, Chemical Engineering and Processing https://doi.org/10.1016/j.cep.2017.10.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Design of a Hydrodynamic Cavitating Reactor Narotam Jangir, Prateek Diwedi and Sumana Ghosh* Department of Chemical Engineering, IIT Roorkee, Roorkee 247667, India Email: [email protected] *Corresponding author: Tel.: +91-01332-284803
Graphical Abstract
Water, Us= 2 m/s
Ethyl alcohol, Us= 2 m/s Cavitation of different liquid
Fuel oil, Us= 2 m/s
Us= 0.5 m/s
Us= 1 m/s Caviation with water at different velocities
Us= 2 m/s
Research Highlights:
CFD simulation of hydrodynamic cavitation in horizontal pipe fitted with sudden contractions Three different liquids of different vapor pressure are considered Phase velocity of the liquids varied from 0.5 to 16 m/s Diameter ratio varied from 0.2 to 0.6 Radial averaged volume fraction and pressure are compared for different situations
Abstract In the present work, a computational fluid dynamic simulation has been performed to investigate hydrodynamic cavitation in sudden contraction. Hydrodynamic cavition of water, ethyl alcohol and fuel oil have been simulated using commercial CFD soft ware package ANSYS FLUENT 1
16.A satisfactory match between the simulated data and experimental results have been obtained. A detailed study has been performed to obtain the influence of liquid velocity, diameter ratio and liquid properties on average vapor volume fraction. A critical condition is identified for a specific geometry and liquid vapor pressure with respect to average volume fraction. Keywords: Hydrodynamic cavitation; sudden contraction; choking; CFD 1. Introduction Hydrodynamic cavitation is a tool of process intensification. In case of hydrodynamic cavitation the bubbles formed when the liquid pressure decreases due to a change in area of its flow path. Bubbles collapse during recovery of pressure. Collapses of cavities or bubbles in liquid results in very high local temperature and pressure. However, the total temperature and pressure of the liquid remain unaffected. At the same time free radicals are released from the collapse of bubbles. It also produces local turbulence and micro-circulation in the reactor. All these factors enhances the rate of any chemical reaction (Gogate 2008). As a result, hydrodynamic cavitation has been found to be efficient in producing the desired chemical changes in different applications i.e. biomedical, waste water treatment (Wu et al. 2007, Brauetigam et al. 2009, Joshi and Gogate 2012, Patil and Gogate 2012) and production of biodiesel (Gogate 2008, Kelker et al. 2008, Pal et al. 2010, Ghayal et al. 2013, Gole et al. 2013) etc. It is reported in literature that hydrodynamic cavitation is more energy efficient than acoustic cavitation (Gore et al. 2014, Ji et al. 2006). A review of past literature, shows that hydrodynamic cavitation has a potential to enhance chemical reactions. Also it can handle larger volumes of reactants. As a result, it could be easily scaled up for industrial purposes than acoustic cavitation. The intensity of cavitation in this case, majorly depends on the pressure drop at plane of area change as well as the liquid characteristics. The design of the reactor plays an important role in cavitation intensity. In most of the past 2
literature, the hydrodynamic cavitation is investigated by using either an orifice plate or venturi in the test rig. Recently some innovative designs are suggested for establishing hydrodynamic cavitation. Badve et al. (2015a) used a slit venturi along with circular venturi. Further, Badve et al. (2015b) also used rotor stator assembly to establish hydrodynamic cavitation. Dular et al.(2016) used a shear induced hydrodynamic cavitation reactor, which consists of two rotor with grooves. The major challenge in this field is to identify and control the parameters those influence cavitation. Inlet pressure, geometry of orifice plate and venturi are identified as controlling parameters. Although search of literature reveals that majority of the numerical study carried out in past are focused on bubble dynamics. In some initial studies, Rayleigh Plasset equation is solved without a consideration of heat and mass transfer ( Moholkar and Pandit 1997). Later effect of heat transfer (Arrojo and Benito 2008) is included. Sharma et al. (2008) modeled an orifice based hydrodynamic reactor based on bubble dynamics and reaction occurring in air water interface. They concluded that inlet pressure, initial bubble radius and orifice to pipe diameter ratio influence the final radius achieve before collision and the collapse pressure. Similar study also reported by Zhang et al.(2008) on venturi based hydrodynamic cavitation reactor. Gogate et al.(2014, 2015) effectively modeled and showed that presence of a gaseous species and its type influences cavitational yield of a chemical reaction in a sonochemical reactors. Badve et al.(2015b) modeled the rotor-stator hydrodynamic caviation reactor. They concluded the shear rate and pressure distribution, have a strong dependence on speed of rotation. These studies, effectively show the cavitation yield with various input parameters. Howeve,r the phase distribution inside the reactor is not discussed. Recently few studies on hydrodynamic cavitation in diesel injection( Qiu et al 2016, Salvador et al. 2017) and hydrofoil (Roohi et al 2013, Srinivasan et al. 2009) use commercial CFD software to simulate phase distribution inside these devices.
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In the present study, an interest is felt to investigate if hydrodynamic cavitations can be initiated in a horizontal pipe fitted with sudden contraction, which is very common pipe fitting. For this purpose, an experimental set up is designed fitted with two successive sudden contractions. Initial experiments are carried at lower water velocities. However it is difficult to find an optimum operating condition at which cavitation is occurring and the corresponding inner flow field hydrodynamics. Therefore, a numerical 3D model is developed. As discussed by Sarc et al.(2017) that caviation number cannot be sole criteria to define cavitation. They also pointed out that there is a huge importance of geometry, liquid and liquid velocities on the extent of cavitation. Hence, the present work tried to investigate the influence of all these parameters to design a hydrodynamic cavition reactor.
2. Modeling: Fig.1 depicts the geometry of the flow passage considered for computational modeling. The geometry consists of three tubes. The diameters of larger tubes are of 0.03 m and 0.01 m respectively. Hence, the first contraction diameter ratio is fixed for all cases i.e. 0.33. The diameter of the smallest pipe is varied from 0.002 m to 0.006 m. The diameter ratio for the second contraction, defined as β, is varied from 0.2, 0.3, 0.4 and 0.6. The total length of the computational domain is 0.5 m. This ensures enough axial length needed for the development of flow. Finite volume based commercial CFD software ANSYS FLUENT 16 (2013) has been used for the simulation. Finite volume
technique is used to discretize the governing equations. After
discretization, the governing equations are solved by using segregated solver. The computation has been performed for unsteady flow to investigate the initiation of cavitation in sudden contraction. The assumptions include unsteady flow, homogenous mixture of liquid and vapor, constant liquid properties etc. 4
2.1. Governing equations A 3D homogenous model, is used for modeling the phenomenon. In this technique, a single set of momentum equation is shared by both the liquid and its vapor. It assumes no slip between the phases. In the present study, three different liquids are used namely water, ethyl alcohol and fuel oil in order to find out the effect of vapor pressure of liquid on cavitation characteristics.
The governing equations are:
Continuity:
m t
.( mU m ) 0
(1)
where, m , U m ,t, are mixture density, velocity and time respectively.
U 2
Um
1
1 1
1
m
(2)
and
m 1 11 2
(3)
Where 1 , 1 , U1 are the vapor phase fraction, density and velocity. Momentum: A single momentum equation is solved throughout the domain and the resulting velocity field is shared among the phases. Assuming turbulent flow, the momentum equation can be written as:
mU m t
.( mU m .U m ) P . m U m U m T ( m g ) F
(4)
where, P, g, F, μm are pressure in the flow field, acceleration due to gravity, body force acting on the system and viscosity of the flow system respectively. 2
m 11 1
2.2 Cavitation Model: 5
(5)
Unsteady cavitation phenomenon based on Schnerr and Sauer (2012) has been used for the present study. The governing equations are as follows: -
Vapour phase:
D1 ( 11 ) . 11U m 1 2 t m Dt
(6)
The net mass source term R is given as: R
12 d1 m dt
(7)
Vapor volume fraction 1 can be related to number of cavities in liquid as 4 nb RB3 3 1 4 1 nb RB3 3
(8)
where, RB is the bubble radius. It is can be calculated as
3 1 RB 1 1 1 4 n
(9)
The source term in equation (7) can be obtained as (ANSYS FLUENT user guide 2013)
R
1 2 3 1 (1 1 ) m RB
2(P1 P) 3 2
(10)
2.3. Turbulence model There are several turbulent models available however as an initial attempt to simulate such flow condition both standard and RNG k- models have been used. This model estimate the turbulent kinetic energy and viscous dissipation rates and they used to obtain the turbulent viscosity in the flow field. a) k- turbulence model
( k ) ( kU ) ( t .k ) 2t Eij . Eij . t k 6
(11)
( ) 2 ( U ) ( t . ) C1 2t Eij . Eij . C2 t k k
t C
k2
(12)
(13)
where, k, , t are the turbulent kinetic energy, dissipation rate and eddy viscosity respectively . Eij is defined as
1 U i U j Eij 2 X j X i
(14)
The constant are taken as C 0.09, k 1, 1.3, C1 1.44, C2 1.92 . b) RNG k-ɛ turbulence model ( k ) ( kU ) (k eff .k ) Gk Gb YM t
( ) 2 ( U ) ( eff . ) C1 Gk C3 Gb C2 R t k k
(15)
(16)
In the above equations, k and are the inverse effective Prandtl numbers for k and , respectively. 2.4. Initial and Boundary condition In all the cases the flow has been initialized from inlet. The boundary conditions are reported below: Inlet Boundary condition Velocity of liquid under consideration is specified at the inlet of the largest pipe. Wall Boundary conditions 7
A stationary, no-slip, no penetration boundary is imposed on the wall of the pipe. Uz = 0 (No slip) and Ur = 0 (No penetration) In addition, contact angle between water and pipe wall material is provided at the wall. The contact angle of liquid is measured with pipe wall material (stainless steel) using a contact angle goniometer (Kruss DSA258). For water it is found to be 720. This angle, is then provided as an input parameter while specifying the wall boundary. Outlet Boundary condition At the outlet, pressure is specified and the diffusion fluxes for the variables in exit direction are set to zero. The range of pressure at outlet is specified as 101 kPa to 30kPa. 3. Numerical simulation 3.1. Meshing of the model The meshing of the models has been done using a software GAMBIT. As a vapor film formation is expected just after the contraction near the wall, smaller adaptive meshes are generated near the wall of the smallest pipe. Fig.2 shows the zoomed meshed geometry for the up and downstr. To ensure the grid independence of the results, numerical time averaged pressure at downstream of the plane of area change for β 0.6 are estimated by varying number of meshes. Fig.3 depicts the grid independence result. Based on the optimum performance, in terms of accuracy and computational effort, 397649 hexahedral elements and 78708 nodes are chosen for the geometry for β=0.6. As β decreases from 0.6 to 0.2, the geometry changes so also the number of nodes. Hence the grid independence test is carried out for each of the geometry. For β=0.4, 0.3 and 0.2 respective values are 61465, 59067 and 57830 respectively.
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3.2. Discretization method Due to the dynamic nature of cavitation phenomenon variation in both time and space has been considered. A transient simulation with a time step of 0.00001s is taken for computation. Simulations are carried out for 10E5 time steps. Equation of continuity has been discretized by PRESTO (Patankar (1980). On the other hand, momentum, turbulent kinetic energy and dissipation rate equations are discretized by first order upwind method. For pressure velocity coupling in the present model, PISO algorithm (Issa 1986) is used. 3.2. Convergence criterion The convergence criterion is chosen based on the residual value of the calculated variables, namely mass, velocity and volume fraction. For the present model, the numerical computation is said to be converged if the residuals of the different variables are lowered by three orders of magnitude. However in case of turbulent energy and dissipation rate, residuals should lowered by five order of magnitude. 4. Experimentation and Validation In order to validate the model performance, the numerical result is compared with that obtained from an existing experimental set up. This setup, is operated with water as test liquid. A schematic of the experimental setup, has been presented in Fig.4. It comprised off a test rig made up of three tubes of different cross-sectional area. Largest tube has an inner diameter of 0.03 m. It is followed by another tube with inner diameter of 0.01 m. The tube at the end has a smallest inner diameter of 0.006 m corresponds to β=0.6. Last two tubes are made up of stainless steel and each has a length of 1 m. Water is pumped from a tank (T) of 80 liter capacity by a centrifugal pump. The flow rate is measured using is rotameter (F). The range of the rotameter is from 0 to 30 LPM with
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a least count of 1 LPM. As water encounters a change in area of its flow path, its pressure reduces drastically just downstream of second constriction. This reduction in pressure, produces the cavities. The cavities collapse as the pressure recovers along the length of the downstream pipe ( i.e. 0.006 m id ). After it flows through the test rig, water is collected in the same tank. The flow rate of water in test rig, is controlled by the help of two valves. One is present on the bypass line and other one is present on the main line just before the rotameter. Two pressure sensors (Range 0 to 6 bar) are used to measure the downstream pressure for first and second contraction. Both sensors, are placed at a distance of 0.1 m at the downstream of first and second contraction respectively. Signals from pressure sensors are transferred to the data acquisition. From data acquisition, voltage signals are generated and recorded in PC. In order to validate the simulation, the results are compared with the experimental data obtained with water. Experimental superficial velocity of liquid ( U s ), is estimated from the volumetric flow rate and cross sectional area of the largest pipe (i.d 0.03 m). Experiments are performed at lower
U s ranges from 0.05 m/s to 0.25 m/s. For this range of U s , the simulated data on time averaged downstream pressure are compared with experiments in Table 1. In numerical simulations, cavitation is noticed only after the second contraction. Hence, in Table 1, numerical pressure data, corresponds to experimental data obtained from the sensor at the downstream of the second constriction is provided. It is a checking for two phase flow pressure drop which validates the multiphase model used in the present study. Table 1 shows the pressure data comparison both for standard and RNG k-ɛ model. It is noticed that both the model predict the experimental data within ± 10%. Hence the standard k-ɛ model is used for the further simulation as discussed in the next section. 5. Results and Discussion: 10
After the validation, simulations are carried out at higher superficial velocities and different geometries as well as with different liquids to explore the effect of all these parameters on cavitation characteristics. As like the experiments, the liquid velocity specified at the largest pipe is termed as superficial velocities ( U s ). On the other hand, average velocity with which the liquid is flowing at the smallest pipe (0.006 m i.d) is defined as the throat velocity U th . The up and downstream distance after the second contraction is expressed in terms of positive and negative L/D ratios where, D is the diameter of the smallest pipe. Simulations are carried out for the entire length as shown in Fig.1. However, as mentioned earlier cavitation is noticed only after second constriction. Hence, the results are shown for second constriction in the following section. 5.1 Development of caviation in flow field In Fig.5a, the picture sequence depicts the formation of vapor film at L/D 0.083 with time during flow of water in geometry with β 0.6 at a U s of 2 m/s. Fig 5b shows the longitudinal profile for the same flow situation at 1 s. A gradual development of vapor zone with time can be noted from this figure. The red color indicates presence of only vapor and blue is the water. It can be seen from the figures, that with time vapor layers are present at the inner wall of the smallest pipe while the liquid remains at the centre core. Next, the cross sectional contours of phase distribution at different axial locations at 0.3 s for U s 2 m/s along with the corresponding pressure profile is depicted in Fig.6a. Fig.6b shows the longitudinal pressure contour. It can be seen from the figure, that at the plane of area change there is no significant formation of vapor layers. However just after the plane of area change at 0.5 mm, an intense vapor layer is observed at the inner wall. It can be resulted from the formation of vena contracta at this location. At this point, (0.5 mm from the
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plane of second contraction) the U th increases to 50 m/s and the pressure drop of 1.2 MPa are noticed. As a result, the local static pressure decreases below the local vapor pressure and cavities are formed. Due to formation of vena contracta, liquid is separated from the wall and formed a jet at the centre. On the other hand, near the wall low pressure recirculation zone is formed. The cavities are formed in this area of low pressure, resulting in a thin vapor film at the circumference. After the pressure recovered they diffuse into liquid bulk stream. As a result, it can be observed that with increasing the distance from the plane of area change, the intense vapor layer at the wall disappear gradually to form a liquid-vapor mixture. The higher pressure noticed at the up and downstream of the contraction is in agreement with existing literature. Higher operating pressure ( in the range of 10 MPa) was also reported by Cioncolini et al. (2016) for a 10 mm pipe fitted with a orifices in the range of 0.3 mm to 0.15 mm. Kumar et al. (2000) also reported an operating pressure of 69kPa to 345 kPa for orifice plate of hole size 2 mm fitted on a 38 mm pipe.
In their experimental paper Yan and Thorpe (1990) identified different regimes of cavitation. According to them, the regime where the water jet is completely surrounded by vapor phase is termed as super cavitation. From Fig. 6, it can be evident that at the vena contracta the super cavitation is occurring for the given U s of 2 m/s and corresponding velocity of throat U th is 50 m/s. However, on moving further downstream a mixture of vapor and water is present. 5.2 Effect of liquid velocity Next, an interest is felt to study the effect of liquid (water) velocities on the cavitation. Hence, for this purpose U s of water are varied from 0.5 m/s to 16 m/s. Fig.7 depicts the cross sectional phase contours for water at 0.3 sec for different upstream velocities with β 0.6 at distance of 0.5 mm 12
from the plane of area change. It can be seen from the figure, that the vapor volume fraction is very less at the cross sectional area for U s 0.5 m/s and entrance or throat U th velocity of 12.5 m/s. However, as the magnitude of U s increases to 2 m/s, the amount of vapor at the inner side of the outer wall also increases. Increasing the U s beyond 2 m/s does not have a prominent effect on increasing the vapor content. Hence, it can be said that for this particular geometry initiation of cavitation begins at a lower water velocity. However, there is no effect of increasing U s , on phase distribution is observed beyond a critical value of U s 2 m/s. To understand the relationship of vapor layer from the plane of area change, radial average value of volume fraction ( avg ) is plotted with axial distance from plane of area change in Fig. 8. It can be seen from the figure, that avg is maximum closer to the plane of area change. The magnitude of avg decreases as the flow moves towards the outlet. It can also be noted, that with increases of U s the magnitude of avg over the length increases. A closer observation reveals, that there is distinct characteristics of avg for U s 1 m/s and U s 2 m/s. For U s 1 m/s, as seen from the inset of Figure 8 that the avg reaches a maximum just after the contraction and decreases to zero over a very short span of 0.25 L/D. On the other hand, avg corresponds to U s 2 m/s, decreases gradually over the length. If the magnitude of U s is further increases to 4 m/s and 6 m/s then there is very marginal increases of magnitude of avg over the length. From this figure, it can be estimated that maximum value of avg lies in the range of 0.3 to 0.37, just after the plane of area change. In order to understand, if the pressure drop just after the plane of area change could be the sole driving force to fulfill the energy requirement of water to produce 0.3 vapor fraction, pressure profiles are examined. The pressure profiles corresponding to water 13
superficial velocities of 0.5 m/s-16 m/s are investigated. Fig. 9 shows the variation of radial average of total pressure (Pavg) with L/D for the same set of velocities. It can be seen that there is a sharp drop in magnitude of total pressure just after the plane of area change. The drop is in order of 1.2 MPa for U s 2 m/s. This pressure drop is alone sufficient to produce cavities as shown in appendix A. The pressure later recovered along the downstream. The fluctuations in total pressure can also observed at downstream. These fluctuations indicate presence of vapor bubbles and their subsequent collapse. Degassing occurs due to pressure reduction just after the plane of area change at the smallest tube. However, as the dissolution rate is lower the magnitude of pressure fluctuations are not high and gradually decay down over length. Further, a closer observation of the pressure profiles reveals that Pavg increases by 2.5 times if U s increases from 2 m/s to 4 m/s. However, the avg does not increases much as indicated in Fig. 8. Hence, it can be said that U s 2 m/s or U th 50 m/s is the optimum velocity to get the hydrodynamic cavitation for water in a 6 mm downstream pipe. It can be concluded that there exist a threshold or critical velocity for a specific geometry and liquid to initiate cavitation. It is not economical to operate the reactor at higher superficial velocities as this increases the extent of cavitation insignificantly while increasing the pressure abnormally. 5.3 Effect of geometry Further, attempts are made to estimate effect of geometry, typically the diameter of the smallest tube on cavitation. For this, β is varied from 0.2 to 0.6, keeping all other parameter same. As the diameter of the third pipe is getting changed so the velocity at the smallest cross section would be different despite of having same U s . Hence, in order to compare the effect of geometries on cavitation, they are compared at the same throat velocity U th instead of U s . As mentioned earlier, 14
vapor layer is present at 25 m/s ( U s =1 m/s), however, it is not present entirely at the cross section, as shown in Fig 7. However, at 50 m/s super caviation condition establishes for β 0.6. In order to investigate and compare the super caviation condition at other geometries, U th of 50 m/s is also simulated at β 0.2 and 0.4. Fig.10 shows the longitudinal phase contour at U th of 50 m/s for different geometries. Fig. 11 depicts avg for all the geometry at the same U th of 50 m/s as a function of L/D ratio. It can be seen from the figure, that the value of avg is not the same for all geometries. It is maximum for β 0.6. and gradually decreases for others. In order to find out the reason, variation of total pressure with L/D for different geometries, is shown in Fig.12. It can be seen that, for the same throat velocity the pressure is very high for smaller downstream pipe as expected. Pressure drop just after the second constriction is 1.2 MPa for β=0.6 while that for β=0.2 is 4.1 MPa for the same throat velocity. In the present case the diameter of the last pipe is being changed from 6 mm to 2 mm , keeping all other parameters same. Hence, it can be estimated that
to maintain
same
throat velocity at smaller downstream pipe, its
corresponding upstream velocity at 10 mm pipe would be much lower. This decreases the dynamic pressure head at the upstream pipe. . Hence, as can be estimated from Bernoulli’s equation the pressure head will be high at 10 mm pipe corresponding to these smaller pipes. As the water is at higher pressure, hence, it is difficult to cavitate despite the fact that smaller pipe causes larger pressure drop at constriction. Therefore, for the same throat velocity the smaller pipe diameter are unable to cavitate. 5.4 Effect of liquid vapor pressure Next, an interest is felt to study the effect of liquid characteristics namely vapor pressure on the cavitation. Apart from water two other liquids are also considered for the study in same geometry 15
with β=0.6. They are ethyl alcohol and fuel oil. Among these three, ethyl alcohol (density=780 kg/m3) is the most volatile with maximum vapor pressure of 5950 Pa at 200C and fuel oil (density=960 kg/m3) is least volatile with lowest vapor pressure of 1329 Pa at a temperature of 200C. Fig.13 shows the cross-sectional as well as longitudinal phase contours of the three liquid for U s 2 m/s. It can be seen from the contours, that the fuel oil and water have comparable radial vapor thickness. Fig. 14 shows avg for all the three liquids at the same U s of 2 m/s . It can be noted, that the trend of avg for ethyl alcohol, is similar to that of water corresponds to a U s of 1 m/s (Fig.9). To find out the reason, variations of radial average of total pressure (Pavg) with L/D of three liquids at same U s are compared in Fig.15. A close observation of Fig 15 reveals, that the pressure drop is larger in case of water. The magnitude of ∆P in case of water is about 1.2 MPa while for ethyl alcohol is 0.99 MPa. Hence, the energy available for sustaining the cavitations is lesser for ethyl alcohol, in comparison to that of water. On the other hand, as the latent heat of vaporization is larger for ethyl alcohol, this energy is sufficient to produce 0.37 radial average volume fraction of vapor just after the plane of area change, at L/D 0.083. However, as this energy is lesser, it cannot support much vapor formation along length (Fig.13). On the other hand, avg is negligible for fuel oil at the same condition. Fig. 16 depicts, the variation of avg with different U s for fuel oil. It can be seen, from the figure that, the fuel oil shows a very different characteristic all together. The magnitude of avg , changes significantly with increase of
U s in case of fuel oil. However, the cavitating zone length lies within 2 mm from plane of area change. It can be seen from the Fig.15, that Pavg is highest for fuel oil followed by water and ethyl alcohol. The trend of Pavg is again different from the other two liquid. It can also be noted, that the pressure in the downstream decreases continuously with axial length. The reason can be attributed 16
to high viscosity of fuel oil. The fuel oil has a very high viscosity, 48 cP while that of water is 1 cP. As a result, the inlet Reynolds number with U s 2 m/s is falling under laminar zone for fuel oil, while that of water with same velocity is highly turbulent. This in turn, results in higher pressure drop for the former case. As the liquid velocity of the liquids are specified at inlet, the solver back calculated the pressure require to sustain such velocity throughout the domain. As a result, the pressure in case of fuel oil is order of magnitude higher than that of water at same velocity.
5.5 Cavitation number Cavitations number is a dimensionless number. It is utilized to characterize the flow behavior and degree of cavitations in the cavitation reactors. In the present study, super cavitations is observed. As suggested by Yan and Thrope (1990) super cavitations is observed when the flow is choked in an orifice. In order to check if the flow is choked or not, the outlet pressure is gradually reduced from 101325 Pa to 30 kPa for U s of 2 m/s numerically. However, no effect of it is noticed on the outlet mass flow rate. Cavitations number of a choked cavitations is given as
Pd Pv 1 U th2 2
(17)
where, Pd , Pv ρ are recovered downstream pressure, vapor pressure of the liquid and density of the liquid. Fig. 17 shows the cavitation number as a function of U s for different diameters of the smaller pipe for water. It can be seen that the cavitation number decreases with the increases in U s then becomes constant for each geometry. As indicated by Yan and Thrope (1990), that choked 17
cavitation number is independent of U th . Hence, it can be said that in the present case the choked cavitation occurs for 1.2 to 1.8 for 0.2 0.6. Yan and Thrope (1990) reported the choked cavitation number in the range of 0.5 to 0.9 for orifice plates of similar hole to pipe diameter ratios. However, Sarc et al (2017) reported a choked cavitation number in the range of 0.1 to 0.35 in venturi. The present value of choked cavitation number is thus higher from both these studies. Therefore, it can be concluded that due to abrupt change in diameter the flow in sudden contraction chocks easily at higher cavitation number. Fig. 18 shows the choked cavitations number for all the liquids together at 0.6. It can be seen from the figure, that all the liquid shows similar trend of decreasing cavitation number with increase in U s . However, the value of cavitation number of fuel oil is much higher than other two liquids. The range of cavitation numbers for fuel oil lies in between 2-3.3 with caviation noticed to occur at a value of 2.47. For water caviation inception is noticed at 2.26 and that of ethyl alcohol is 1.98. Therefore, it can be inferred the critical value of caviation number at which choked caviation occur lies in the range of 2-2.5 for present study. This is in agreement with the value of inception of cavitation number reported by Yan and Thrope (1990) as 2-3. 6. Conclusion Hydrodynamic cavitation through sudden contraction has been simulated in the present study. A 3D model has been developed by using CFD software ANSYS FLUENT 16. Model is validated against experiments at lower phase velocities of water. Validation with experiments indicates a good agreement for numerical model. The following conclusions can be made from the present study: Cavitaion is influenced by liquid velocity, diameter ratio and liquid vapor pressure.
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Super cavitation is observed for a threshold velocity which is unique for a given geometry and liquid. Once the super cavitation is established the flow is choked and cavitation number and downstream pressure remain constant with increasing the liquid velocity. As the water velocity increases beyond 2m/s, for β 0.6 the drop in pressure after the constriction as well as the average pressure at downstream increases as much as 2.5 times while avg increases insignificantly. Caviation would not occur for same throat velocity with pipes having smaller diameter. To design such a hydrodynamic cavitation basedreactor one should know about the geometric and operating condition which optimize the production of cavities. Hence, the liquid properties, velocity and geometry are all important input parameter to design the reactor for optimum cavity generation. The analysis further shows that computational fluid dynamics model can be used to
model such a reactor
satisfactorily. Acknowledgement: This work is supported by Faculty Initiation Grant of IIT Roorkee, India
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Appendix: Energy calculation The energy available for cavitation just after the second constriction will be as follows:
Ea PAcUth =1.69kJ /s
(A1)
where , Ac is the area at the plane of contraction and U th is the throat velocity at entrance. Corresponding to vapor volume fraction of 0.3 the mass of the vapor is as follows: mg =0.3*Q* g =2.54E-4 kg/s
(A2)
The energy required to form this vapor will be ER mg
(A3)
where , is the latent heat of vaporization at 250C The sensible heat in this case is not considered as the global temperature of the liquid before and after the hydrodynamic cavitation remain same. The value of ER is 0.65 kJ/s which is less than that of Ea . Hence the pressure drop is the sole driving force to vaporize the water.
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References 1. P. R. Gogate, Cavitational reactors for process intensification of chemical processing applications: A critical review, Chem. Eng. Process. Process Intensif. 47(2008) 515–527. 2. Z. L. Wu, B. Ondruschka, and P. Bräutigam, Degradation of chlorocarbons driven by hydrodynamic cavitation,Chem. Eng. Technol. 30(2007) 642–648. 3. P. Braeutigam, Z. L. Wu, A. Stark, and B. Ondruschka, Degradation of BTEX in aqueous solution by hydrodynamic cavitation, Chem. Eng. Technol. 32(2009)745–753. 4. R. K. Joshi and P. R. Gogate, Degradation of dichlorvos using hydrodynamic cavitation based treatment strategies, Ultrason. Sonochem.19(2012) 532–539. 5. P. N. Patil and P. R. Gogate, Degradation of methyl parathion using hydrodynamic cavitation: Effect of operating parameters and intensification using additives, Sep. Purif. Technol. 95(2012)172–179. 6. M. A. Kelkar, P. R. Gogate, and A. B. Pandit, Intensification of esterification of acids for synthesis of biodiesel using acoustic and hydrodynamic cavitation, Ultrason.Sonochem.15 (2008) 188–194. 7. A. Pal, A. Verma, S. S. Kachhwaha, and S. Maji, Biodiesel production through hydrodynamic cavitation and performance testing,Renew. Energy 35 (2010) 619–624. 8. D. Ghayal, A. B. Pandit, and V. K. Rathod, Optimization of biodiesel production in a hydrodynamic cavitation reactor using used frying oil, Ultrason. Sonochem.20 (2013) 322–328. 9. V. L. Gole, K. R. Naveen, and P. R. Gogate, Hydrodynamic cavitation as an efficient approach for intensification of synthesis of methyl esters from sustainable feedstock, Chem. Eng. Process. Process Intensif. 71(2013) 70–76. 10. M. M. Gore, V. K. Saharan, D. V. Pinjari, P. V. Chavan, and A. B. Pandit, Degradation of reactive orange 4 dye using hydrodynamic cavitation based hybrid techniques, Ultrason. Sonochem. 21(2014) 1075–1082. 11. J. Ji, J. Wang, Y. Li, Y. Yu, and Z. Xu, Preparation of biodiesel with the help of ultrasonic and hydrodynamic cavitation, Ultrasonics 44 (2006). 12. M.P.Badve, M.N.Bhagat, A.B. Pandit, Microbial disinfection of seawater using hydrodynamic cavitation, Separation and Purification Technology 151 (2015a) 31–38. 13. M.P.Badve, T.Alpar, A.B. Pandit, P.R. Gogate, L. Csoka, Modeling the shear rate and pressure drop in a hydrodynamic cavitation reactor with experimental validation based on KI decomposition studies, Ultrasonics Sonochemistry 22 (2015b) 272–277 14. M.Dular, T.G. Bulc, I. G.Aguirre, E. Heath, T.Kosjek, A.K., Klemencˇic, M. Oder, M. Petkovšek, N. Racˇki, M. Ravinkar, A.Šarc, , B. Širok, M. Zupanc, M. Zitnik, B. Kompare, M. , Strazˇar, Use of hydrodynamic cavitation in (waste) water treatment, Ultrason. Sonochem. 21(2016)577-588 15. V.S. Moholkar, A.B. Pandit, Bubble behavior in hydrodynamic cavitation: effect of turbulence, AIChE J. 43 (1997) 1641. 21
16. S. Arrojo, Y. Benito, A theoretical study of hydrodynamic cavitation, Ultrason. Sonochem. 15 (2008) 203–211. 17. A. Sharma, P. R. Gogate, A. Mahulkar, and A. B. Pandit, Modeling of hydrodynamic cavitation reactors based on orifice plates considering hydrodynamics and chemical reactions occurring in bubble,Chem. Eng. J. 143(2008) 201–209. 18. X. Zhang, Y. Fu, Z. Li, and Z. Zhao, The Collapse Intensity of Cavities and the Concentration of Free Hydroxyl Radical Released in Cavitation Flow, Chinese J. Chem. Engg.16(2008) 547–551. 19. R.P.Gogate,S.Shaha,L.Csoka, Intensification of cavitational activity in the sonochemical reactors using gaseous additives, Chemical Engineering Journal 239 (2014) 364–372 20. R.P.Gogate,S.Shaha,L.Csoka, Intensification of cavitational activity using gases in different types of sonochemical reactors, Chemical Engineering Journal 262 (2015) 1033– 1042 21. T. Qiu, X. Song, Y. Lei, X. Liu, X. An, M. Lai, Influence of inlet pressure on cavitation flow in diesel nozzle Applied Thermal Engineering 109 (2016) 364–372 22. F.J. Salvador, D. Jaramillo, J.-V. Romero, M.-D. Roselló, Using a homogeneous equilibrium model for the study of the inner nozzle flow and cavitation pattern in convergent–divergent nozzles of diesel injectors, Journal of Computational and Applied Mathematics 309 (2017) 630–641 23. E. Roohi, A. P. Zahiri, M. P. Fard, Numerical simulation of cavitation around a twodimensional hydrofoil using VOF method and LES turbulence model, Applied Mathematical Modelling 37 (2013) 6469–6488 24. Vedanth Srinivasan , Abraham J. Salazar, Kozo Saito, Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach, Applied Mathematical Modelling 33 (2009) 1529–1559 25. A. Šarc, T. Stepišnik-Perdih, M. Petkovšek, and M. Dular,The issue of cavitation number value in studies of water treatment by hydrodynamic cavitation, Ultrason. Sonochem.34(2017) 51–59. 26. ANSYS FLUENT Theory guide, 2013. ANSYS Inc., Canonsburg, USA. 27. G. H. Schnerr and J. Sauer. Physical and Numerical Modeling of Unsteady Cavitation Dynamics. In Fourth International Conference on Multiphase Flow, New Orleans, USA. 2001. 28. S.V., Patankar, Numerical Heat Transfer and Fluid Flow, 1980,Hemisphere, Washington, DC. 29. R.I. Issa, Solution of the implicitly discretized fluid flow equations by operator splitting. J. Comput. Phys. 62(1986) 40-65. 30. A. Cioncolini, F. Scenini, J. Duff, M. Szolcek, M. Curioni, Choked cavitation in microorifices: An experimental study, Experimental Thermal and Fluid Science 74 (2016) 49– 57.
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31. P.S. Kumar, M.S. Kumar, A.B. Pandit, Experimental quantification of chemical effects of hydrodynamic cavitation, Chem. Engg. Sci. 55 (2000) 1633-1639 32. Y. Yan and R. B. Thorpe, Flow regime transitions due to cavitation in the flow through an orifice, Int. J. Multiph. Flow 16(1990) 1023–1045.
23
Figure 1: Computational domain
a) Zoomed View
b) Complete domain Figure 2: Meshed geometry
24
Figure 3 Grid independency
25
a) Schematic
b) Photograph Figure 4: Experimental set up of hydrodynamic cavitation
26
Time
Phase contour
0.0001 s
0.1 s
0.2 s
0.3 s
a) Cross sectional phase contours at L/D=0.083 27
b) Longitudinal phase contours at 1 s Figure 5: Vapor formation with time for Us 2 m/s at β 0.6
a)Pressure profile 28
b) Longitudinal contour Figure 6: Pressure profile and corresponding phase contours at different axial locations at 0.3 seconds for β =0.6 and water superficial velocity of 2 m/s
Figure 7: Phase contours for different water superficial velocity at 0.3 seconds for β =0.6 and L/D=0.083
29
Figure 8: Radial averaged volume fraction of vapor as function of L/D ratio for different velocities of water
30
Figr-18
Figure 9: Radial averaged total pressure as function of L/D ratio for different velocities of water
Figure 10: Longitudinal phase contours for different geometry ratio at U th 50 m/s
31
Figr-3
Figure 11:Radial averaged volume fraction of vapor as function of L/D ratio for different geometries at throat velocity of 50 m/s
32
Figure 12: Radial averaged of total pressure as function of L/D ratio for different for different geometries at throat velocity of 50 m/s
33
Water
Ethyl alcohol
Fuel oil
a) Cross sectional contours at L/D=0.083
b) Longitudinal contours Figure 13: Phase contours of different liquids at 0.3 s with superficial velocity of 2 m/s for β =0.6
34
Figure 14: Radial averged volume fraction as a function of L/D for different liquids at 0.3 s with superficial velocity of 2 m/s for β =0.6
35
Figure 15: Radial averaged total pressure as function of L/D ratio for different liquids at 0.3 s with throat velocity of 50 m/s for β =0.6
36
Figure 16: Radial averged volume fraction as a function of L/D for fuel oil at 0.3 s with different superficial velocity for β =0.6
37
Figure 17: Cavitation number as a function of superficial velocity for different geometries
38
Figure 18: Cavitation number as function of superficial velocities for different liquids at same geometry (β 0.6)
39
Table1 Validation with experiments Superficial Downstream Average velocity Pressure (Experimental), m/s (Us) Pa (0.1m from plane of 2nd contraction) 0.1 0.15 0.2 0.24
151665 196139 252629 331092
Downstream Average Pressure (Numerical, Standard k-ɛ), Pa, (0.1m from plane of 2nd contraction) 158358 204895 268615 298769
40
Downstream Average Pressure (Numerical, RNG k-ɛ), Pa (0.1m from plane of 2nd contraction) 162524 205687 274589 301267
S0255-2701(17)30598-6 https://doi.org/10.1016/j.cep.2017.10.008 CEP 7092
To appear in:
Chemical Engineering and Processing
Received date: Revised date: Accepted date:
22-6-2017 6-10-2017 8-10-2017
Please cite this article as: Narotam Jangir, Prateek Diwedi, Sumana Ghosh, Design of a Hydrodynamic Cavitating Reactor, Chemical Engineering and Processing https://doi.org/10.1016/j.cep.2017.10.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Design of a Hydrodynamic Cavitating Reactor Narotam Jangir, Prateek Diwedi and Sumana Ghosh* Department of Chemical Engineering, IIT Roorkee, Roorkee 247667, India Email: [email protected] *Corresponding author: Tel.: +91-01332-284803
Graphical Abstract
Water, Us= 2 m/s
Ethyl alcohol, Us= 2 m/s Cavitation of different liquid
Fuel oil, Us= 2 m/s
Us= 0.5 m/s
Us= 1 m/s Caviation with water at different velocities
Us= 2 m/s
Research Highlights:
CFD simulation of hydrodynamic cavitation in horizontal pipe fitted with sudden contractions Three different liquids of different vapor pressure are considered Phase velocity of the liquids varied from 0.5 to 16 m/s Diameter ratio varied from 0.2 to 0.6 Radial averaged volume fraction and pressure are compared for different situations
Abstract In the present work, a computational fluid dynamic simulation has been performed to investigate hydrodynamic cavitation in sudden contraction. Hydrodynamic cavition of water, ethyl alcohol and fuel oil have been simulated using commercial CFD soft ware package ANSYS FLUENT 1
16.A satisfactory match between the simulated data and experimental results have been obtained. A detailed study has been performed to obtain the influence of liquid velocity, diameter ratio and liquid properties on average vapor volume fraction. A critical condition is identified for a specific geometry and liquid vapor pressure with respect to average volume fraction. Keywords: Hydrodynamic cavitation; sudden contraction; choking; CFD 1. Introduction Hydrodynamic cavitation is a tool of process intensification. In case of hydrodynamic cavitation the bubbles formed when the liquid pressure decreases due to a change in area of its flow path. Bubbles collapse during recovery of pressure. Collapses of cavities or bubbles in liquid results in very high local temperature and pressure. However, the total temperature and pressure of the liquid remain unaffected. At the same time free radicals are released from the collapse of bubbles. It also produces local turbulence and micro-circulation in the reactor. All these factors enhances the rate of any chemical reaction (Gogate 2008). As a result, hydrodynamic cavitation has been found to be efficient in producing the desired chemical changes in different applications i.e. biomedical, waste water treatment (Wu et al. 2007, Brauetigam et al. 2009, Joshi and Gogate 2012, Patil and Gogate 2012) and production of biodiesel (Gogate 2008, Kelker et al. 2008, Pal et al. 2010, Ghayal et al. 2013, Gole et al. 2013) etc. It is reported in literature that hydrodynamic cavitation is more energy efficient than acoustic cavitation (Gore et al. 2014, Ji et al. 2006). A review of past literature, shows that hydrodynamic cavitation has a potential to enhance chemical reactions. Also it can handle larger volumes of reactants. As a result, it could be easily scaled up for industrial purposes than acoustic cavitation. The intensity of cavitation in this case, majorly depends on the pressure drop at plane of area change as well as the liquid characteristics. The design of the reactor plays an important role in cavitation intensity. In most of the past 2
literature, the hydrodynamic cavitation is investigated by using either an orifice plate or venturi in the test rig. Recently some innovative designs are suggested for establishing hydrodynamic cavitation. Badve et al. (2015a) used a slit venturi along with circular venturi. Further, Badve et al. (2015b) also used rotor stator assembly to establish hydrodynamic cavitation. Dular et al.(2016) used a shear induced hydrodynamic cavitation reactor, which consists of two rotor with grooves. The major challenge in this field is to identify and control the parameters those influence cavitation. Inlet pressure, geometry of orifice plate and venturi are identified as controlling parameters. Although search of literature reveals that majority of the numerical study carried out in past are focused on bubble dynamics. In some initial studies, Rayleigh Plasset equation is solved without a consideration of heat and mass transfer ( Moholkar and Pandit 1997). Later effect of heat transfer (Arrojo and Benito 2008) is included. Sharma et al. (2008) modeled an orifice based hydrodynamic reactor based on bubble dynamics and reaction occurring in air water interface. They concluded that inlet pressure, initial bubble radius and orifice to pipe diameter ratio influence the final radius achieve before collision and the collapse pressure. Similar study also reported by Zhang et al.(2008) on venturi based hydrodynamic cavitation reactor. Gogate et al.(2014, 2015) effectively modeled and showed that presence of a gaseous species and its type influences cavitational yield of a chemical reaction in a sonochemical reactors. Badve et al.(2015b) modeled the rotor-stator hydrodynamic caviation reactor. They concluded the shear rate and pressure distribution, have a strong dependence on speed of rotation. These studies, effectively show the cavitation yield with various input parameters. Howeve,r the phase distribution inside the reactor is not discussed. Recently few studies on hydrodynamic cavitation in diesel injection( Qiu et al 2016, Salvador et al. 2017) and hydrofoil (Roohi et al 2013, Srinivasan et al. 2009) use commercial CFD software to simulate phase distribution inside these devices.
3
In the present study, an interest is felt to investigate if hydrodynamic cavitations can be initiated in a horizontal pipe fitted with sudden contraction, which is very common pipe fitting. For this purpose, an experimental set up is designed fitted with two successive sudden contractions. Initial experiments are carried at lower water velocities. However it is difficult to find an optimum operating condition at which cavitation is occurring and the corresponding inner flow field hydrodynamics. Therefore, a numerical 3D model is developed. As discussed by Sarc et al.(2017) that caviation number cannot be sole criteria to define cavitation. They also pointed out that there is a huge importance of geometry, liquid and liquid velocities on the extent of cavitation. Hence, the present work tried to investigate the influence of all these parameters to design a hydrodynamic cavition reactor.
2. Modeling: Fig.1 depicts the geometry of the flow passage considered for computational modeling. The geometry consists of three tubes. The diameters of larger tubes are of 0.03 m and 0.01 m respectively. Hence, the first contraction diameter ratio is fixed for all cases i.e. 0.33. The diameter of the smallest pipe is varied from 0.002 m to 0.006 m. The diameter ratio for the second contraction, defined as β, is varied from 0.2, 0.3, 0.4 and 0.6. The total length of the computational domain is 0.5 m. This ensures enough axial length needed for the development of flow. Finite volume based commercial CFD software ANSYS FLUENT 16 (2013) has been used for the simulation. Finite volume
technique is used to discretize the governing equations. After
discretization, the governing equations are solved by using segregated solver. The computation has been performed for unsteady flow to investigate the initiation of cavitation in sudden contraction. The assumptions include unsteady flow, homogenous mixture of liquid and vapor, constant liquid properties etc. 4
2.1. Governing equations A 3D homogenous model, is used for modeling the phenomenon. In this technique, a single set of momentum equation is shared by both the liquid and its vapor. It assumes no slip between the phases. In the present study, three different liquids are used namely water, ethyl alcohol and fuel oil in order to find out the effect of vapor pressure of liquid on cavitation characteristics.
The governing equations are:
Continuity:
m t
.( mU m ) 0
(1)
where, m , U m ,t, are mixture density, velocity and time respectively.
U 2
Um
1
1 1
1
m
(2)
and
m 1 11 2
(3)
Where 1 , 1 , U1 are the vapor phase fraction, density and velocity. Momentum: A single momentum equation is solved throughout the domain and the resulting velocity field is shared among the phases. Assuming turbulent flow, the momentum equation can be written as:
mU m t
.( mU m .U m ) P . m U m U m T ( m g ) F
(4)
where, P, g, F, μm are pressure in the flow field, acceleration due to gravity, body force acting on the system and viscosity of the flow system respectively. 2
m 11 1
2.2 Cavitation Model: 5
(5)
Unsteady cavitation phenomenon based on Schnerr and Sauer (2012) has been used for the present study. The governing equations are as follows: -
Vapour phase:
D1 ( 11 ) . 11U m 1 2 t m Dt
(6)
The net mass source term R is given as: R
12 d1 m dt
(7)
Vapor volume fraction 1 can be related to number of cavities in liquid as 4 nb RB3 3 1 4 1 nb RB3 3
(8)
where, RB is the bubble radius. It is can be calculated as
3 1 RB 1 1 1 4 n
(9)
The source term in equation (7) can be obtained as (ANSYS FLUENT user guide 2013)
R
1 2 3 1 (1 1 ) m RB
2(P1 P) 3 2
(10)
2.3. Turbulence model There are several turbulent models available however as an initial attempt to simulate such flow condition both standard and RNG k- models have been used. This model estimate the turbulent kinetic energy and viscous dissipation rates and they used to obtain the turbulent viscosity in the flow field. a) k- turbulence model
( k ) ( kU ) ( t .k ) 2t Eij . Eij . t k 6
(11)
( ) 2 ( U ) ( t . ) C1 2t Eij . Eij . C2 t k k
t C
k2
(12)
(13)
where, k, , t are the turbulent kinetic energy, dissipation rate and eddy viscosity respectively . Eij is defined as
1 U i U j Eij 2 X j X i
(14)
The constant are taken as C 0.09, k 1, 1.3, C1 1.44, C2 1.92 . b) RNG k-ɛ turbulence model ( k ) ( kU ) (k eff .k ) Gk Gb YM t
( ) 2 ( U ) ( eff . ) C1 Gk C3 Gb C2 R t k k
(15)
(16)
In the above equations, k and are the inverse effective Prandtl numbers for k and , respectively. 2.4. Initial and Boundary condition In all the cases the flow has been initialized from inlet. The boundary conditions are reported below: Inlet Boundary condition Velocity of liquid under consideration is specified at the inlet of the largest pipe. Wall Boundary conditions 7
A stationary, no-slip, no penetration boundary is imposed on the wall of the pipe. Uz = 0 (No slip) and Ur = 0 (No penetration) In addition, contact angle between water and pipe wall material is provided at the wall. The contact angle of liquid is measured with pipe wall material (stainless steel) using a contact angle goniometer (Kruss DSA258). For water it is found to be 720. This angle, is then provided as an input parameter while specifying the wall boundary. Outlet Boundary condition At the outlet, pressure is specified and the diffusion fluxes for the variables in exit direction are set to zero. The range of pressure at outlet is specified as 101 kPa to 30kPa. 3. Numerical simulation 3.1. Meshing of the model The meshing of the models has been done using a software GAMBIT. As a vapor film formation is expected just after the contraction near the wall, smaller adaptive meshes are generated near the wall of the smallest pipe. Fig.2 shows the zoomed meshed geometry for the up and downstr. To ensure the grid independence of the results, numerical time averaged pressure at downstream of the plane of area change for β 0.6 are estimated by varying number of meshes. Fig.3 depicts the grid independence result. Based on the optimum performance, in terms of accuracy and computational effort, 397649 hexahedral elements and 78708 nodes are chosen for the geometry for β=0.6. As β decreases from 0.6 to 0.2, the geometry changes so also the number of nodes. Hence the grid independence test is carried out for each of the geometry. For β=0.4, 0.3 and 0.2 respective values are 61465, 59067 and 57830 respectively.
8
3.2. Discretization method Due to the dynamic nature of cavitation phenomenon variation in both time and space has been considered. A transient simulation with a time step of 0.00001s is taken for computation. Simulations are carried out for 10E5 time steps. Equation of continuity has been discretized by PRESTO (Patankar (1980). On the other hand, momentum, turbulent kinetic energy and dissipation rate equations are discretized by first order upwind method. For pressure velocity coupling in the present model, PISO algorithm (Issa 1986) is used. 3.2. Convergence criterion The convergence criterion is chosen based on the residual value of the calculated variables, namely mass, velocity and volume fraction. For the present model, the numerical computation is said to be converged if the residuals of the different variables are lowered by three orders of magnitude. However in case of turbulent energy and dissipation rate, residuals should lowered by five order of magnitude. 4. Experimentation and Validation In order to validate the model performance, the numerical result is compared with that obtained from an existing experimental set up. This setup, is operated with water as test liquid. A schematic of the experimental setup, has been presented in Fig.4. It comprised off a test rig made up of three tubes of different cross-sectional area. Largest tube has an inner diameter of 0.03 m. It is followed by another tube with inner diameter of 0.01 m. The tube at the end has a smallest inner diameter of 0.006 m corresponds to β=0.6. Last two tubes are made up of stainless steel and each has a length of 1 m. Water is pumped from a tank (T) of 80 liter capacity by a centrifugal pump. The flow rate is measured using is rotameter (F). The range of the rotameter is from 0 to 30 LPM with
9
a least count of 1 LPM. As water encounters a change in area of its flow path, its pressure reduces drastically just downstream of second constriction. This reduction in pressure, produces the cavities. The cavities collapse as the pressure recovers along the length of the downstream pipe ( i.e. 0.006 m id ). After it flows through the test rig, water is collected in the same tank. The flow rate of water in test rig, is controlled by the help of two valves. One is present on the bypass line and other one is present on the main line just before the rotameter. Two pressure sensors (Range 0 to 6 bar) are used to measure the downstream pressure for first and second contraction. Both sensors, are placed at a distance of 0.1 m at the downstream of first and second contraction respectively. Signals from pressure sensors are transferred to the data acquisition. From data acquisition, voltage signals are generated and recorded in PC. In order to validate the simulation, the results are compared with the experimental data obtained with water. Experimental superficial velocity of liquid ( U s ), is estimated from the volumetric flow rate and cross sectional area of the largest pipe (i.d 0.03 m). Experiments are performed at lower
U s ranges from 0.05 m/s to 0.25 m/s. For this range of U s , the simulated data on time averaged downstream pressure are compared with experiments in Table 1. In numerical simulations, cavitation is noticed only after the second contraction. Hence, in Table 1, numerical pressure data, corresponds to experimental data obtained from the sensor at the downstream of the second constriction is provided. It is a checking for two phase flow pressure drop which validates the multiphase model used in the present study. Table 1 shows the pressure data comparison both for standard and RNG k-ɛ model. It is noticed that both the model predict the experimental data within ± 10%. Hence the standard k-ɛ model is used for the further simulation as discussed in the next section. 5. Results and Discussion: 10
After the validation, simulations are carried out at higher superficial velocities and different geometries as well as with different liquids to explore the effect of all these parameters on cavitation characteristics. As like the experiments, the liquid velocity specified at the largest pipe is termed as superficial velocities ( U s ). On the other hand, average velocity with which the liquid is flowing at the smallest pipe (0.006 m i.d) is defined as the throat velocity U th . The up and downstream distance after the second contraction is expressed in terms of positive and negative L/D ratios where, D is the diameter of the smallest pipe. Simulations are carried out for the entire length as shown in Fig.1. However, as mentioned earlier cavitation is noticed only after second constriction. Hence, the results are shown for second constriction in the following section. 5.1 Development of caviation in flow field In Fig.5a, the picture sequence depicts the formation of vapor film at L/D 0.083 with time during flow of water in geometry with β 0.6 at a U s of 2 m/s. Fig 5b shows the longitudinal profile for the same flow situation at 1 s. A gradual development of vapor zone with time can be noted from this figure. The red color indicates presence of only vapor and blue is the water. It can be seen from the figures, that with time vapor layers are present at the inner wall of the smallest pipe while the liquid remains at the centre core. Next, the cross sectional contours of phase distribution at different axial locations at 0.3 s for U s 2 m/s along with the corresponding pressure profile is depicted in Fig.6a. Fig.6b shows the longitudinal pressure contour. It can be seen from the figure, that at the plane of area change there is no significant formation of vapor layers. However just after the plane of area change at 0.5 mm, an intense vapor layer is observed at the inner wall. It can be resulted from the formation of vena contracta at this location. At this point, (0.5 mm from the
11
plane of second contraction) the U th increases to 50 m/s and the pressure drop of 1.2 MPa are noticed. As a result, the local static pressure decreases below the local vapor pressure and cavities are formed. Due to formation of vena contracta, liquid is separated from the wall and formed a jet at the centre. On the other hand, near the wall low pressure recirculation zone is formed. The cavities are formed in this area of low pressure, resulting in a thin vapor film at the circumference. After the pressure recovered they diffuse into liquid bulk stream. As a result, it can be observed that with increasing the distance from the plane of area change, the intense vapor layer at the wall disappear gradually to form a liquid-vapor mixture. The higher pressure noticed at the up and downstream of the contraction is in agreement with existing literature. Higher operating pressure ( in the range of 10 MPa) was also reported by Cioncolini et al. (2016) for a 10 mm pipe fitted with a orifices in the range of 0.3 mm to 0.15 mm. Kumar et al. (2000) also reported an operating pressure of 69kPa to 345 kPa for orifice plate of hole size 2 mm fitted on a 38 mm pipe.
In their experimental paper Yan and Thorpe (1990) identified different regimes of cavitation. According to them, the regime where the water jet is completely surrounded by vapor phase is termed as super cavitation. From Fig. 6, it can be evident that at the vena contracta the super cavitation is occurring for the given U s of 2 m/s and corresponding velocity of throat U th is 50 m/s. However, on moving further downstream a mixture of vapor and water is present. 5.2 Effect of liquid velocity Next, an interest is felt to study the effect of liquid (water) velocities on the cavitation. Hence, for this purpose U s of water are varied from 0.5 m/s to 16 m/s. Fig.7 depicts the cross sectional phase contours for water at 0.3 sec for different upstream velocities with β 0.6 at distance of 0.5 mm 12
from the plane of area change. It can be seen from the figure, that the vapor volume fraction is very less at the cross sectional area for U s 0.5 m/s and entrance or throat U th velocity of 12.5 m/s. However, as the magnitude of U s increases to 2 m/s, the amount of vapor at the inner side of the outer wall also increases. Increasing the U s beyond 2 m/s does not have a prominent effect on increasing the vapor content. Hence, it can be said that for this particular geometry initiation of cavitation begins at a lower water velocity. However, there is no effect of increasing U s , on phase distribution is observed beyond a critical value of U s 2 m/s. To understand the relationship of vapor layer from the plane of area change, radial average value of volume fraction ( avg ) is plotted with axial distance from plane of area change in Fig. 8. It can be seen from the figure, that avg is maximum closer to the plane of area change. The magnitude of avg decreases as the flow moves towards the outlet. It can also be noted, that with increases of U s the magnitude of avg over the length increases. A closer observation reveals, that there is distinct characteristics of avg for U s 1 m/s and U s 2 m/s. For U s 1 m/s, as seen from the inset of Figure 8 that the avg reaches a maximum just after the contraction and decreases to zero over a very short span of 0.25 L/D. On the other hand, avg corresponds to U s 2 m/s, decreases gradually over the length. If the magnitude of U s is further increases to 4 m/s and 6 m/s then there is very marginal increases of magnitude of avg over the length. From this figure, it can be estimated that maximum value of avg lies in the range of 0.3 to 0.37, just after the plane of area change. In order to understand, if the pressure drop just after the plane of area change could be the sole driving force to fulfill the energy requirement of water to produce 0.3 vapor fraction, pressure profiles are examined. The pressure profiles corresponding to water 13
superficial velocities of 0.5 m/s-16 m/s are investigated. Fig. 9 shows the variation of radial average of total pressure (Pavg) with L/D for the same set of velocities. It can be seen that there is a sharp drop in magnitude of total pressure just after the plane of area change. The drop is in order of 1.2 MPa for U s 2 m/s. This pressure drop is alone sufficient to produce cavities as shown in appendix A. The pressure later recovered along the downstream. The fluctuations in total pressure can also observed at downstream. These fluctuations indicate presence of vapor bubbles and their subsequent collapse. Degassing occurs due to pressure reduction just after the plane of area change at the smallest tube. However, as the dissolution rate is lower the magnitude of pressure fluctuations are not high and gradually decay down over length. Further, a closer observation of the pressure profiles reveals that Pavg increases by 2.5 times if U s increases from 2 m/s to 4 m/s. However, the avg does not increases much as indicated in Fig. 8. Hence, it can be said that U s 2 m/s or U th 50 m/s is the optimum velocity to get the hydrodynamic cavitation for water in a 6 mm downstream pipe. It can be concluded that there exist a threshold or critical velocity for a specific geometry and liquid to initiate cavitation. It is not economical to operate the reactor at higher superficial velocities as this increases the extent of cavitation insignificantly while increasing the pressure abnormally. 5.3 Effect of geometry Further, attempts are made to estimate effect of geometry, typically the diameter of the smallest tube on cavitation. For this, β is varied from 0.2 to 0.6, keeping all other parameter same. As the diameter of the third pipe is getting changed so the velocity at the smallest cross section would be different despite of having same U s . Hence, in order to compare the effect of geometries on cavitation, they are compared at the same throat velocity U th instead of U s . As mentioned earlier, 14
vapor layer is present at 25 m/s ( U s =1 m/s), however, it is not present entirely at the cross section, as shown in Fig 7. However, at 50 m/s super caviation condition establishes for β 0.6. In order to investigate and compare the super caviation condition at other geometries, U th of 50 m/s is also simulated at β 0.2 and 0.4. Fig.10 shows the longitudinal phase contour at U th of 50 m/s for different geometries. Fig. 11 depicts avg for all the geometry at the same U th of 50 m/s as a function of L/D ratio. It can be seen from the figure, that the value of avg is not the same for all geometries. It is maximum for β 0.6. and gradually decreases for others. In order to find out the reason, variation of total pressure with L/D for different geometries, is shown in Fig.12. It can be seen that, for the same throat velocity the pressure is very high for smaller downstream pipe as expected. Pressure drop just after the second constriction is 1.2 MPa for β=0.6 while that for β=0.2 is 4.1 MPa for the same throat velocity. In the present case the diameter of the last pipe is being changed from 6 mm to 2 mm , keeping all other parameters same. Hence, it can be estimated that
to maintain
same
throat velocity at smaller downstream pipe, its
corresponding upstream velocity at 10 mm pipe would be much lower. This decreases the dynamic pressure head at the upstream pipe. . Hence, as can be estimated from Bernoulli’s equation the pressure head will be high at 10 mm pipe corresponding to these smaller pipes. As the water is at higher pressure, hence, it is difficult to cavitate despite the fact that smaller pipe causes larger pressure drop at constriction. Therefore, for the same throat velocity the smaller pipe diameter are unable to cavitate. 5.4 Effect of liquid vapor pressure Next, an interest is felt to study the effect of liquid characteristics namely vapor pressure on the cavitation. Apart from water two other liquids are also considered for the study in same geometry 15
with β=0.6. They are ethyl alcohol and fuel oil. Among these three, ethyl alcohol (density=780 kg/m3) is the most volatile with maximum vapor pressure of 5950 Pa at 200C and fuel oil (density=960 kg/m3) is least volatile with lowest vapor pressure of 1329 Pa at a temperature of 200C. Fig.13 shows the cross-sectional as well as longitudinal phase contours of the three liquid for U s 2 m/s. It can be seen from the contours, that the fuel oil and water have comparable radial vapor thickness. Fig. 14 shows avg for all the three liquids at the same U s of 2 m/s . It can be noted, that the trend of avg for ethyl alcohol, is similar to that of water corresponds to a U s of 1 m/s (Fig.9). To find out the reason, variations of radial average of total pressure (Pavg) with L/D of three liquids at same U s are compared in Fig.15. A close observation of Fig 15 reveals, that the pressure drop is larger in case of water. The magnitude of ∆P in case of water is about 1.2 MPa while for ethyl alcohol is 0.99 MPa. Hence, the energy available for sustaining the cavitations is lesser for ethyl alcohol, in comparison to that of water. On the other hand, as the latent heat of vaporization is larger for ethyl alcohol, this energy is sufficient to produce 0.37 radial average volume fraction of vapor just after the plane of area change, at L/D 0.083. However, as this energy is lesser, it cannot support much vapor formation along length (Fig.13). On the other hand, avg is negligible for fuel oil at the same condition. Fig. 16 depicts, the variation of avg with different U s for fuel oil. It can be seen, from the figure that, the fuel oil shows a very different characteristic all together. The magnitude of avg , changes significantly with increase of
U s in case of fuel oil. However, the cavitating zone length lies within 2 mm from plane of area change. It can be seen from the Fig.15, that Pavg is highest for fuel oil followed by water and ethyl alcohol. The trend of Pavg is again different from the other two liquid. It can also be noted, that the pressure in the downstream decreases continuously with axial length. The reason can be attributed 16
to high viscosity of fuel oil. The fuel oil has a very high viscosity, 48 cP while that of water is 1 cP. As a result, the inlet Reynolds number with U s 2 m/s is falling under laminar zone for fuel oil, while that of water with same velocity is highly turbulent. This in turn, results in higher pressure drop for the former case. As the liquid velocity of the liquids are specified at inlet, the solver back calculated the pressure require to sustain such velocity throughout the domain. As a result, the pressure in case of fuel oil is order of magnitude higher than that of water at same velocity.
5.5 Cavitation number Cavitations number is a dimensionless number. It is utilized to characterize the flow behavior and degree of cavitations in the cavitation reactors. In the present study, super cavitations is observed. As suggested by Yan and Thrope (1990) super cavitations is observed when the flow is choked in an orifice. In order to check if the flow is choked or not, the outlet pressure is gradually reduced from 101325 Pa to 30 kPa for U s of 2 m/s numerically. However, no effect of it is noticed on the outlet mass flow rate. Cavitations number of a choked cavitations is given as
Pd Pv 1 U th2 2
(17)
where, Pd , Pv ρ are recovered downstream pressure, vapor pressure of the liquid and density of the liquid. Fig. 17 shows the cavitation number as a function of U s for different diameters of the smaller pipe for water. It can be seen that the cavitation number decreases with the increases in U s then becomes constant for each geometry. As indicated by Yan and Thrope (1990), that choked 17
cavitation number is independent of U th . Hence, it can be said that in the present case the choked cavitation occurs for 1.2 to 1.8 for 0.2 0.6. Yan and Thrope (1990) reported the choked cavitation number in the range of 0.5 to 0.9 for orifice plates of similar hole to pipe diameter ratios. However, Sarc et al (2017) reported a choked cavitation number in the range of 0.1 to 0.35 in venturi. The present value of choked cavitation number is thus higher from both these studies. Therefore, it can be concluded that due to abrupt change in diameter the flow in sudden contraction chocks easily at higher cavitation number. Fig. 18 shows the choked cavitations number for all the liquids together at 0.6. It can be seen from the figure, that all the liquid shows similar trend of decreasing cavitation number with increase in U s . However, the value of cavitation number of fuel oil is much higher than other two liquids. The range of cavitation numbers for fuel oil lies in between 2-3.3 with caviation noticed to occur at a value of 2.47. For water caviation inception is noticed at 2.26 and that of ethyl alcohol is 1.98. Therefore, it can be inferred the critical value of caviation number at which choked caviation occur lies in the range of 2-2.5 for present study. This is in agreement with the value of inception of cavitation number reported by Yan and Thrope (1990) as 2-3. 6. Conclusion Hydrodynamic cavitation through sudden contraction has been simulated in the present study. A 3D model has been developed by using CFD software ANSYS FLUENT 16. Model is validated against experiments at lower phase velocities of water. Validation with experiments indicates a good agreement for numerical model. The following conclusions can be made from the present study: Cavitaion is influenced by liquid velocity, diameter ratio and liquid vapor pressure.
18
Super cavitation is observed for a threshold velocity which is unique for a given geometry and liquid. Once the super cavitation is established the flow is choked and cavitation number and downstream pressure remain constant with increasing the liquid velocity. As the water velocity increases beyond 2m/s, for β 0.6 the drop in pressure after the constriction as well as the average pressure at downstream increases as much as 2.5 times while avg increases insignificantly. Caviation would not occur for same throat velocity with pipes having smaller diameter. To design such a hydrodynamic cavitation basedreactor one should know about the geometric and operating condition which optimize the production of cavities. Hence, the liquid properties, velocity and geometry are all important input parameter to design the reactor for optimum cavity generation. The analysis further shows that computational fluid dynamics model can be used to
model such a reactor
satisfactorily. Acknowledgement: This work is supported by Faculty Initiation Grant of IIT Roorkee, India
19
Appendix: Energy calculation The energy available for cavitation just after the second constriction will be as follows:
Ea PAcUth =1.69kJ /s
(A1)
where , Ac is the area at the plane of contraction and U th is the throat velocity at entrance. Corresponding to vapor volume fraction of 0.3 the mass of the vapor is as follows: mg =0.3*Q* g =2.54E-4 kg/s
(A2)
The energy required to form this vapor will be ER mg
(A3)
where , is the latent heat of vaporization at 250C The sensible heat in this case is not considered as the global temperature of the liquid before and after the hydrodynamic cavitation remain same. The value of ER is 0.65 kJ/s which is less than that of Ea . Hence the pressure drop is the sole driving force to vaporize the water.
20
References 1. P. R. Gogate, Cavitational reactors for process intensification of chemical processing applications: A critical review, Chem. Eng. Process. Process Intensif. 47(2008) 515–527. 2. Z. L. Wu, B. Ondruschka, and P. Bräutigam, Degradation of chlorocarbons driven by hydrodynamic cavitation,Chem. Eng. Technol. 30(2007) 642–648. 3. P. Braeutigam, Z. L. Wu, A. Stark, and B. Ondruschka, Degradation of BTEX in aqueous solution by hydrodynamic cavitation, Chem. Eng. Technol. 32(2009)745–753. 4. R. K. Joshi and P. R. Gogate, Degradation of dichlorvos using hydrodynamic cavitation based treatment strategies, Ultrason. Sonochem.19(2012) 532–539. 5. P. N. Patil and P. R. Gogate, Degradation of methyl parathion using hydrodynamic cavitation: Effect of operating parameters and intensification using additives, Sep. Purif. Technol. 95(2012)172–179. 6. M. A. Kelkar, P. R. Gogate, and A. B. Pandit, Intensification of esterification of acids for synthesis of biodiesel using acoustic and hydrodynamic cavitation, Ultrason.Sonochem.15 (2008) 188–194. 7. A. Pal, A. Verma, S. S. Kachhwaha, and S. Maji, Biodiesel production through hydrodynamic cavitation and performance testing,Renew. Energy 35 (2010) 619–624. 8. D. Ghayal, A. B. Pandit, and V. K. Rathod, Optimization of biodiesel production in a hydrodynamic cavitation reactor using used frying oil, Ultrason. Sonochem.20 (2013) 322–328. 9. V. L. Gole, K. R. Naveen, and P. R. Gogate, Hydrodynamic cavitation as an efficient approach for intensification of synthesis of methyl esters from sustainable feedstock, Chem. Eng. Process. Process Intensif. 71(2013) 70–76. 10. M. M. Gore, V. K. Saharan, D. V. Pinjari, P. V. Chavan, and A. B. Pandit, Degradation of reactive orange 4 dye using hydrodynamic cavitation based hybrid techniques, Ultrason. Sonochem. 21(2014) 1075–1082. 11. J. Ji, J. Wang, Y. Li, Y. Yu, and Z. Xu, Preparation of biodiesel with the help of ultrasonic and hydrodynamic cavitation, Ultrasonics 44 (2006). 12. M.P.Badve, M.N.Bhagat, A.B. Pandit, Microbial disinfection of seawater using hydrodynamic cavitation, Separation and Purification Technology 151 (2015a) 31–38. 13. M.P.Badve, T.Alpar, A.B. Pandit, P.R. Gogate, L. Csoka, Modeling the shear rate and pressure drop in a hydrodynamic cavitation reactor with experimental validation based on KI decomposition studies, Ultrasonics Sonochemistry 22 (2015b) 272–277 14. M.Dular, T.G. Bulc, I. G.Aguirre, E. Heath, T.Kosjek, A.K., Klemencˇic, M. Oder, M. Petkovšek, N. Racˇki, M. Ravinkar, A.Šarc, , B. Širok, M. Zupanc, M. Zitnik, B. Kompare, M. , Strazˇar, Use of hydrodynamic cavitation in (waste) water treatment, Ultrason. Sonochem. 21(2016)577-588 15. V.S. Moholkar, A.B. Pandit, Bubble behavior in hydrodynamic cavitation: effect of turbulence, AIChE J. 43 (1997) 1641. 21
16. S. Arrojo, Y. Benito, A theoretical study of hydrodynamic cavitation, Ultrason. Sonochem. 15 (2008) 203–211. 17. A. Sharma, P. R. Gogate, A. Mahulkar, and A. B. Pandit, Modeling of hydrodynamic cavitation reactors based on orifice plates considering hydrodynamics and chemical reactions occurring in bubble,Chem. Eng. J. 143(2008) 201–209. 18. X. Zhang, Y. Fu, Z. Li, and Z. Zhao, The Collapse Intensity of Cavities and the Concentration of Free Hydroxyl Radical Released in Cavitation Flow, Chinese J. Chem. Engg.16(2008) 547–551. 19. R.P.Gogate,S.Shaha,L.Csoka, Intensification of cavitational activity in the sonochemical reactors using gaseous additives, Chemical Engineering Journal 239 (2014) 364–372 20. R.P.Gogate,S.Shaha,L.Csoka, Intensification of cavitational activity using gases in different types of sonochemical reactors, Chemical Engineering Journal 262 (2015) 1033– 1042 21. T. Qiu, X. Song, Y. Lei, X. Liu, X. An, M. Lai, Influence of inlet pressure on cavitation flow in diesel nozzle Applied Thermal Engineering 109 (2016) 364–372 22. F.J. Salvador, D. Jaramillo, J.-V. Romero, M.-D. Roselló, Using a homogeneous equilibrium model for the study of the inner nozzle flow and cavitation pattern in convergent–divergent nozzles of diesel injectors, Journal of Computational and Applied Mathematics 309 (2017) 630–641 23. E. Roohi, A. P. Zahiri, M. P. Fard, Numerical simulation of cavitation around a twodimensional hydrofoil using VOF method and LES turbulence model, Applied Mathematical Modelling 37 (2013) 6469–6488 24. Vedanth Srinivasan , Abraham J. Salazar, Kozo Saito, Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach, Applied Mathematical Modelling 33 (2009) 1529–1559 25. A. Šarc, T. Stepišnik-Perdih, M. Petkovšek, and M. Dular,The issue of cavitation number value in studies of water treatment by hydrodynamic cavitation, Ultrason. Sonochem.34(2017) 51–59. 26. ANSYS FLUENT Theory guide, 2013. ANSYS Inc., Canonsburg, USA. 27. G. H. Schnerr and J. Sauer. Physical and Numerical Modeling of Unsteady Cavitation Dynamics. In Fourth International Conference on Multiphase Flow, New Orleans, USA. 2001. 28. S.V., Patankar, Numerical Heat Transfer and Fluid Flow, 1980,Hemisphere, Washington, DC. 29. R.I. Issa, Solution of the implicitly discretized fluid flow equations by operator splitting. J. Comput. Phys. 62(1986) 40-65. 30. A. Cioncolini, F. Scenini, J. Duff, M. Szolcek, M. Curioni, Choked cavitation in microorifices: An experimental study, Experimental Thermal and Fluid Science 74 (2016) 49– 57.
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31. P.S. Kumar, M.S. Kumar, A.B. Pandit, Experimental quantification of chemical effects of hydrodynamic cavitation, Chem. Engg. Sci. 55 (2000) 1633-1639 32. Y. Yan and R. B. Thorpe, Flow regime transitions due to cavitation in the flow through an orifice, Int. J. Multiph. Flow 16(1990) 1023–1045.
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Figure 1: Computational domain
a) Zoomed View
b) Complete domain Figure 2: Meshed geometry
24
Figure 3 Grid independency
25
a) Schematic
b) Photograph Figure 4: Experimental set up of hydrodynamic cavitation
26
Time
Phase contour
0.0001 s
0.1 s
0.2 s
0.3 s
a) Cross sectional phase contours at L/D=0.083 27
b) Longitudinal phase contours at 1 s Figure 5: Vapor formation with time for Us 2 m/s at β 0.6
a)Pressure profile 28
b) Longitudinal contour Figure 6: Pressure profile and corresponding phase contours at different axial locations at 0.3 seconds for β =0.6 and water superficial velocity of 2 m/s
Figure 7: Phase contours for different water superficial velocity at 0.3 seconds for β =0.6 and L/D=0.083
29
Figure 8: Radial averaged volume fraction of vapor as function of L/D ratio for different velocities of water
30
Figr-18
Figure 9: Radial averaged total pressure as function of L/D ratio for different velocities of water
Figure 10: Longitudinal phase contours for different geometry ratio at U th 50 m/s
31
Figr-3
Figure 11:Radial averaged volume fraction of vapor as function of L/D ratio for different geometries at throat velocity of 50 m/s
32
Figure 12: Radial averaged of total pressure as function of L/D ratio for different for different geometries at throat velocity of 50 m/s
33
Water
Ethyl alcohol
Fuel oil
a) Cross sectional contours at L/D=0.083
b) Longitudinal contours Figure 13: Phase contours of different liquids at 0.3 s with superficial velocity of 2 m/s for β =0.6
34
Figure 14: Radial averged volume fraction as a function of L/D for different liquids at 0.3 s with superficial velocity of 2 m/s for β =0.6
35
Figure 15: Radial averaged total pressure as function of L/D ratio for different liquids at 0.3 s with throat velocity of 50 m/s for β =0.6
36
Figure 16: Radial averged volume fraction as a function of L/D for fuel oil at 0.3 s with different superficial velocity for β =0.6
37
Figure 17: Cavitation number as a function of superficial velocity for different geometries
38
Figure 18: Cavitation number as function of superficial velocities for different liquids at same geometry (β 0.6)
39
Table1 Validation with experiments Superficial Downstream Average velocity Pressure (Experimental), m/s (Us) Pa (0.1m from plane of 2nd contraction) 0.1 0.15 0.2 0.24
151665 196139 252629 331092
Downstream Average Pressure (Numerical, Standard k-ɛ), Pa, (0.1m from plane of 2nd contraction) 158358 204895 268615 298769
40
Downstream Average Pressure (Numerical, RNG k-ɛ), Pa (0.1m from plane of 2nd contraction) 162524 205687 274589 301267