Numerical Optimization and Experimental Validation

Numerical Optimization and Experimental Validation of Hydrodynamic Cavitating Device Gaurav G. Dastane, Mandar P. Badve, Virendra Kumar Saharan & A. B. Pandit* Chemical Engineering Division, Institute of Chemical Technology, Matunga, Mumbai - 400 019. INDIA

Introduction: Cavitation is phenomenon of sequential formation, growth and collapse of millions of microscopic vapour bubbles (voids) in the liquid.The collapse of these cavities creates high localized temperature and pressure or results into short-lived, localized hot spot in cold liquid, thus serving as a means of concentrating the diffusedenergy, and can be used as an intensification tool for chemical processes that require stringent operating conditions. Hydrodynamic cavitation is generated by passing the liquid througha constriction such as orifice plates, venturietc[1].When the liquid passes through a constriction, the kinetic energy of the liquid increases at the expense of the pressure. If the throttling is sufficient to cause the pressure around thepoint of vena contracta to fall below vapour pressure of the liquid, millions of cavities are generated. Subsequently, as the liquid jet expands, pressure recovers and this results incollapse of the cavities. During the passage of the liquid through the constriction, boundary layer separation occursand substantial amount of energy is lost in the form of turbulence and permanent pressure drop. This work will present numerical and experimental study of non-circular venturis as a cavitating device. The special interest in noncircular geometry is based on the hypothesis that cavitation is a function of perimeter/flow area ratio of the constriction. Cavitation is attributed to the shear forces acting on the liquid at the periphery of the constriction, and hence a higher perimeter/flow area ratio will lead to increased efficacy of cavitational

effects. This hypothesis is already verified by comparison of numerical simulations of rectangular slit venturi, annular slit venturi and 2 annular slits venturi against the parameter of perimeter/flow area by Bashir et al(2011) [2]. The cavitational efficacy, estimated numerically, was found to be highest in case of 2 annular slits venturi, followed by annular slit venturi, slit venturi and standard circular venturi. It was found that non-circular venturis show higher cavitational intensity as compared to circular venturi. This hypothesis is also validated experimentally showing at least 50% increase in cavitation. This work contains a comparison of numerical simulations of elliptical venturi, rectangular slit venturi and standard circular venturi on the basis of cavitational efficacy. To measure the Cavitational efficacy parameters such as cavitational zone, the fluid density variation across the geometry and the pressure recovery curves are used. Geometries selected for Simulation: CFD simulations were carried out for standard circular venturi geometry, elliptical venturi and slit venturi geometry, by varying parameters like inlet pressure, perimeter to area ratio etc. Simulations on Circular venturi were carried out to find the optimum values of parameters such asinlet pressure, to get maximum cavitational yield. The inlet diameter (D) for the venturi was taken 17 mm, the convergent angle was taken as 23.5° i.e. the length of convergent section was taken as 18mm., the length of the throat section was taken as 1mm and the throat diameter was

Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) Edited by Claus-Dieter OHL, Evert KLASEBOER, Siew Wan OHL, Shi Wei GONG and Boo Cheong KHOO. c 2012 Research Publishing Services. All rights reserved. Copyright ISBN: 978-981-07-2826-7 :: doi:10.3850/978-981-07-2826-7 204

508

Proceedings of the Eighth International Symposium on Cavitation (CAV 2012)

taken as 2mm. The values of design parameters were decided based on the results reported by Bashir et al. (2011) [2].

The value of perimeter to cross sectional area ratio was varied by varying the major axis to minor axis ratio in case of elliptical venturi, whereas in case of slit venturi length to width ratio was varied to get different perimeter to cross sectional area ratios. The ratio of major axis to minor axis was varied from 1:0.2 to 1:0.8 for the elliptical venturi, and the length to width ratio was varied from 1:0.2 to 1:1. The details of elliptical and slit venturigeometries used are given in Table 1 (a) and (b) respectively. The length of inlet, outlet, throat, convergent section and divergent section were kept same as that of standard circular venturi to make the geometries comparable.

Based on the optimum values found from circular venturi simulations, elliptical and slitventuri geometries were simulated. The values of perimeter to cross sectional area ratio for these geometries were varied to see its effect on cavitational yield. The cross sectional area at the inlet and at the throat was kept constant and equal to that in case of circular venturi. Cross sectional area at the inlet was taken as 226.865 mm2and the cross sectional area at the throat was taken as 3.14 mm2.

D1/D2

D1

D2

P

A

P/A

d1

d2

P

a

p/a

1:0.2

38.01

7.6

79.81

226.86

0.351

4.47

0.89

9.39

3.14

2.99

1:0.5

24.04

12.02

58.201

226.86

0.2566

2.828

1.414

6.847

3.14

2.1806

1:0.8

19.01

15.205

53.878

226.86

0.2375

2.236

1.789

6.338

3.14

2.018

Table 1(a): Elliptical Venturi Designs. L/W

L

W

P

A

P/A

L

w

P

a

p/a

1:0.2

33.68

6.74

80.83

226.86

0.36

3.96

0.79

9.51

3.14

3.03

1:0.5

21.3

10.65

63.9

226.86

0.28

2.51

1.255

7.52

3.14

2.39

1:1

15.06

15.06

60.25

226.87

0.27

1.77

1.77

7.09

3.14

2.26

Table 1(b): Slit Venturi Designs. 550,000 and that for slit geometry was around 200,000.

Softwares Used in Simulation: Gambit 2.2.30 was used to build the venturi geometries.2D geometry was sufficient for circular venturi because of the symmetry. The meshing used was QUAD type meshing, and the mesh number was approximately240,000.

Ansys Fluent 6.30 was used to carry out the CFD simulations on the geometry. For the CFD simulations, various turbulence models like k-ȦPRGHON-Ȧ667PRGHOVLPSOH k-İPRGHODQGN-İUHDOL]DEOHPRGHOZHUHWULHG It was observed that k-İUHDOL]DEOHPRGHOJLYHV better convergence as compared to the other models. The simulations were carried out till the residual values dropped below 10-5.

For elliptical and slit venturi 3D geometries were made with HEX/WEDGE type of meshing for elliptical venturi and HEX type of meshing for slit venturi. The mesh number for elliptical geometry was around

The Numerical model developed by Mahulkar et. al. (2008)[3] for finding the

509


cavity radius, the collapse pressure and temperature of the collapsed cavity, the maximum pressure reached inside the cavity, the nature of the cavity dynamics (transient or oscillating) and the number of cavities generated (taking the reference of a standard venturi as 40) was used.

Effect of inlet pressure was studied by varying the inlet pressure from 0.2 MPa to 0.5 MPa for standard circular venturi. The outlet pressure was maintained equal to atmospheric pressure. It was observed that as the inlet pressure was increased from 0.2 MPa to 0.5MPa, the length of cavitational zone increased from 15mm to 50mm.The cavitational zone is defined as a region where the pressure of the liquid flowing through the geometry falls below and remains at its vapour pressure, a zone where pressure recovers, this entire zone is termed as the cavitation zone. The cavities collapse in this region generating shockwaves which are vital for most reactions to proceed and complete.

Conditions for Simulations: The boundary conditions used for the simulations were pressure inlet and pressure outlet. The inlet pressure was varied from 0.2MPa to 0.5MPa, and the outlet pressure was kept equal to atmospheric pressure. Results and Discussion: Effect of Inlet Pressure: 600000

Pressure (Pa)

500000

0.2 MPa 0.3 MPa 0.4 MPa 0.5 MPa

400000

300000 200000 100000 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Axial Distance (m)

0.08

0.09

0.1

0.11

0.12

Figure 1.Effect of Inlet Pressure on Pressure Recovery in Standard circular Venturi Simulations were carried out on slit as well as elliptical venturi with boundary conditions of inlet pressure equal to 0.5 MPa and outlet at atmospheric pressure. The pressure and density contours obtained for elliptical venturis are shown in Fig. 3, and those for slit venturi are shown in Fig, 4.

Also the minimum density observed in the flow was 220 kg/m3 at 0.2 MPa inlet pressure, which reduced to 130 kg/m3for inlet pressure of 0.5MPa, indicating that the vapour fraction in the flow was highest when inlet pressure was kept at 0.5MPa. The maximum vapour volume fraction observed for inlet pressure of 0.2 MPa was 75% and it increased to approximately 90%for inlet pressure of 0.5 MPa. The contours of pressure and vapour volume fraction for inlet pressure of 0.5 MPa are as shown in Figure 2 (a) and (b) respectively.

It can be seen that as the perimeter to cross sectional area ratio is increased, the length of cavitational zone is in fact decreasing. Fig. 2(a) shows the pressure variation across elliptical venturi with p/a ratio of 3:1 (with d1/d2ratio of 1:0.2), and the length of cavitational zone for this venturi is less than 5 mmas shown in Fig. 3. The maximum vapour volume fraction observed in this geometry is 40%. And as the ratio decreases

Effect of Perimeter/Cross Sectional Area:

510


the length of the cavitational zone increases to 20mm (for p/a ratio equal to 2:1, i.e. d1/d2 ratio of 1:0.8). The maximum vapour volume fraction observed in this case is approximately 85%.

decreases. This means that the packing density of cavities is lower, and the fraction of liquid surrounding the cavities is higher. Hence cavities tend to behave as single transient cavity instead of a cluster of cavities, and hence collapse more violently and over a shorter length due to faster pressure recovery. Therefore even though the length of pressure recovery zone is shorter for higher p/a ratio, the cavitational intensity is higher than other geometries. This is validated using experiments carried out using circular as well as non-circular venturi.

In case of slit venturi, when the p/a ratio is maximum (p/a = 3:1, for l/w ratio of 1:0.2) the length of cavitational zone is 25 mm as shown in fig. 4. The vapour volume fraction observed for this geometry is 40%. And as the p/a ratio decreases to 2.25:1, the cavitational zone length remains 25 mm,however the maximum vapour volume fraction observed in this case increases to approximately 70%.

Experimental Results:

These results indicate that the cavities produced at the throat of the venturi, collapseover a shorter lengthie faster and more violently. The cavitational intensity will depend upon what fraction of cavities collapse violently, what fraction dissolves slowly and what fraction will implode with neighboring cavities as a cluster. If the fraction of cavities collapsing violently is higher, then the cavitational activity will be maximum. [4]

Experiments were carried out on industrial effluent with initial COD in the range of 600650 ppm using standard circular venturi as well as slit venture of same flow area. Reduction in COD of the sample was used as the criteria to compare the cavitational efficacy. Samples were collected at regular interval (10 passes) till 50 passes were completed for each device and COD values were measured. It was found that most of the degradation was completed in first 20 passes and afterward there is only a small decrease in COD. There was 25% decrease in COD value for the circular venturi whereas the COD value reducedby 46% when the experiments were carried out on slit venturi for equal number of passes

Since in this case the operating conditions and the cross sectional area is kept constant, the value of Cavitation Number (C v) remains constant. The value of cavitation number is maintained at approximately 0.21. The cavities are generated at the expense of pressure energy lost by the flowing liquid at the venturi throat. The number of cavities formed in a particular geometry can be calculated theoretically using Weber Number (We) criteria. Weber number criteria suggests that for a bubble (or in this case cavity) to grow to a highest size in a flow, its Weber Number value can not exceed 1. The theoretical number of cavities for various geometries is calculated using the simulation data and are given in Table 2. It can be seen that as perimeter to cross sectional area ratio increases, the theoretical number of cavities produced also increases, indicating that more number of cavitational events occur as the perimeter is increasing.

Conclusions: The hypothesis regarding dependence of cavitational intensity on perimeter to cross sectional area ratio is verified using CFD simulations as well as experimental results, and it is proved that non circular venturis with a higher perimeter to cross sectional area ratio give higher cavitational yields. However,there is a further scope of study to determine the optimum geometry which gives highest cavitational yields. Also further research needs to be carried out to determine and validate the bubble dynamics in case of non-circular venturi.

However, as perimeter at the throat is increasing, the number density of cavities, i.e. number of cavities generated per unit length

511


Type of Venturi

p/a Ratio

P1 (Pa)

P2 (Pa)

Circular Venturi

2

500962

2340

Slit Venturi Elliptical Venturi

P3 (Pa)

U (m/s)

V (m/s)

Cavitation Number (Cv)

Theoretical Number of Cavities (x1019)

101325

0.36

30.83

0.21

5.09

500976 2340 101325 0.35 29.64 3.03 0.22 500931 2340 101325 0.37 30.46 2.39 0.21 500931 2678 101325 0.37 30.42 2.26 0.21 500919 2744 101325 0.4 29.47 2.99 0.22 500931 2340 101325 0.37 30.22 2.18 0.21 500931 2971 101325 0.37 30.44 2.01 0.21 Table 2: Theoretical number of Cavities for Various Venturi Geometries

8.12 5.58 5.62 8.45 6.44 5.56

Nomenclature:

ı6XUIDFHWHQVLRQRIZDWHU

A: Cross sectional area at the inlet of venturi

v: Velocity of water at the throat

a: Cross Sectional Area at the throat of venturi

db: Bubble Diameter

D: Inlet diameter of Standard circular Venturi

References:

d: Throat diameter of Standard circular Venturi

[1]

Gogate P.R., Pandit A.B., ³+\GURG\QDPLF FDYLWDWLRQ D VWDWHRIWKHDUWUHYLHZ´5HY&KHP Eng. 17(1), Page 1-85

[2]

Bashir T. A., Mahulkar A. V., Soni A. G., Pinjari D. V., Pandit A. B., 2011, ³*HRPHWULFDO 2SWLPL]DWLRQ RI Modified Venturi: Cavitational Approach´ 7KH &DQDGLDQ -RXUQDO RI Chemical Engineering, Vol. 89(6), Page 1366-1375.

[3]

Mahulkar A.V., Bapat P.S., Pandit $% /HZLV )0 ³6WHDP %XEEOH &DYLWDWLRQ´$,&KH -RXUQDO Vol. 54(7).

[4]

Kanthale P.M., Gogate P.R., Pandit A.B., Wilhelm A.M., 2005, ³'\QDPLFVRIFDYLWDWLRQDOEXEEOHVDQG design of a hydrodynamic cavitational UHDFWRU FOXVWHU DSSURDFK´ UltrasonicsSonochemistry, Vol. 12, Page 441-452.

D1: Inlet Major Axis of elliptical venturi d1: Throat Major Axis of elliptical venturi D2: Inlet Minor Axis of elliptical venturi d2: Throat Minor Axis of elliptical venturi L: Length of Inlet of Slit venturi l: Length of Throat ofSlitventuri pT: Perimeter at the throat of venturi PP: Perimeter at the inlet of venturi W: Inlet Width of Slit venturi w: Throat Width of Slit venturi Weber Number (We) ȡ'HQVLW\RIZDWHU

512

Proceedings of the Eighth International Symposium on Cavitation (CAV 2012) Figures:

Figure 2 (a) Contours of Static Pressure for standard circular venturi at Inlet Pressure of 0.5 MPa

Figure 2 (b) Contours of vapour volume fraction for standard circular venturi at Inlet Pressure of 0.5 MPa

600000 500000 Pressure (Pa)

d1/d2=0.2 400000 d1/d2=0.5 300000 d1/d2=0.8 200000 100000 0 0

0.02

0.04

0.06 Length (m)

0.08

0.1

0.12

Figure 3 Pressure Variation across elliptical venturi with d1/d2 ratio varying from 1:0.2 to1:0.8 600000

Pressure (Pa)

500000

L/w=0.2

400000

L/w=0.5

300000

L/W=1

200000 100000 0 0

0.02

0.04

0.06 Length (m)

0.08

0.1

0.12

Figure 4 Pressure Variation across slit venturi with l/w ratio varying from 1:0.2 to 1:1

513