Design of Choking Cavitator and Its Feasibility Study in Wastewater Treatment

Zhang Fenghua1, a, Li Nian2,b and Tang Chuanlin3,c

1 Hunan University of Technology, China

2 Hunan University of Technology, China

3 Hunan University of Technology, China

afenghua387@126.com, bxiangnian354@163.com, ctcl5608@126.com

Keywords: cavitation; choking; gas-liquid mixed flow;choking cavitator; cavitation noise.

Abstract.A new cavitator-choking cavitator is designed on the basis of analyzing the choking

cavitation phenomena that occurs in gas-liquid mixed flow of straight pipe ，in jet pump under

operating limits and in steady adiabatic flashing flow of stepped circular tube as well as in a

cylindrical pipe with a sharp edged-corner for the steady and unsteady flows. The feasibility

preliminary research of choking cavitator is carried out with analysis the signals of cavitation noise

and treating simulated wastewater (phenol solution). The results offers a new approach in cavitator

development field at home and abroad because of the effect that treating simulated wastewater with

choking cavitator is preferable，and the cavitation per energy produced by choking cavitator is

higher than that by self-oscillated chamber nozzle．

Introduction

Cavitation is a dynamic phenomenon liquid particular owned that can in general be defined as

the combined phenomena of the formation, growth and subsequent collapse of microbubbles or

cavities containing vapor, gas or volatile organic compounds occurring in liquid or liquid-solid

interface when the local pressure of liquid reduces to a certain degree. With a tremendous amount

of scientific work about cavitation mechanism, researchers discovering high pressures (in the range

of 100-5000bar) and temperatures (in the range of 1000-10000K) is produced in local district when

the bubbles collapse (milliseconds), so as well as strong shock waves and high speed micro jet[1-2]

,

those extreme conditions can result in the intensification of various physical/chemical operations

that almost cannot obtain in general condition. Full use of the special physical/chemical condition

and a large magnitude of energy obtained by bubbles collapse can effectively degrade organic

contaminant in liquid[3]

. In recent, the major parts of application researches of cavitation in waste

water treatment district were ultrasonic cavitation and hydrodynamic cavitaion. The ultrasonic

cavitation was restricted in industry application due to low energy utilization efficiency and poor

amplification effect of its cavitator. And hydrodynamic cavitation becomes a new technology in

food sterilization, microbial cell disruption and water disinfect district[4]

. But until now

hydrodynamic cavitation still have some limits in it industry application which are the low

cavitation scales in liquid and the low effective collapse ability (it cannot rapidly collapse and

release a large magnitude of energy.).

Choking flow phenomenon is used to represent the condition occurring in liquid system when

the flow rate doesn’t increase with the downstream pressure decrease based on the premise that

maintaining the upstream pressure constant. Choking flow is a special condition occurs when

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gas-liquid mixed flow reaches a critical point that the current velocity attained the local sonic

velocity, in another words, the Mach number[5-6]

is 1.

Cavitation and choking will happen simultaneously at a certain condition that cavitation

phenomenon occurs in pipeline flow and the cavitation degree is enough to form gas-liquid

two-phase mixed flow. At present, there are few research literatures in home and abroad researching

the combine of cavitation and choking. Thus, this paper propose a new type cavitator i.e. choking

cavitator glanced at the needs in wastewater treatment district with hydrodynamic cavitation

technology according to hydrodynamic cavitation principle and the gas-liquid two-phase mixed

critical flow theory based on analyzing and researching the production about choking cavitation

phenomenon obtained by researchers in home and abroad, and then preliminarily study the

feasibility of choking cavitator used in organic liquid pollutant treatment.

Researches on choking cavitation

Choking cavitation occurs in gas-liquid two-phase mixed flow of straight tube. J.H. Witte et

al.[5]

adopting thermostatic theory model testify the appearance of choking cavitation flow when

they research gas-liquid two-phase mixed flow in straight tube. When the Mach number of one

interface is equal to 1, the choking cavitation occurs in the straight tube. The flow state suddenly

changes from jet flow to bubble flow, accompany with energy consumption and pressure increases,

and J.H. Witte et al. call this phenomenon mixing shock. Fig1 is the experimental setup of their

research.

Fig. 1 Diagram of the experimental setup

Thermostatic theory model includes some basic assumptions, including the gas phase of

upstream mixing shock and liquid phase of downstream mixing shock are continuous phase,

ignoring the influence of vapor pressure, gas and liquid viscosity, and assuming liquid

incompressible, ideal gas, irrespective of gas mass flow and wall surface friction, the flow state is

gas-liquid homogenous two-phase mixed flow, ignoring velocity slip after mixing shock.

Based on these assumptions, gas-liquid volume flow rate ratioθof upstream mixing shock can

be obtained by combining mass continuity equation, momentum equation, mixing state equation,

and energy equation.

2= 1/ ) 1 (F 1)a a （ (1)

In the equation (1) above, αis the Euler number before mixing shock,εis the pressure ratio

before and after mixing shock, F is the throat-to nozzle section area ratio .

Applied Mechanics and Materials Vol. 535 299

The Mach number M2 of downstream mixing shock can be calculated by adiabatic sonic

expression, viz. 1

22 1 2/ ( ) /m mM U c a (2)

In the equation (2) above, Cm2 is the local sonic velocity of downstream gas-liquid two-phase

mixing flow.

From equation (1) we can see that when =0 the pressure ratio reaches its maximum value

( max ).

max 1 ( 1)a F (3)

The equation (1) can be seen as a parabolic equation explains the relationship between and .

By taking the box vertex of equation (1) into equation (2), we can obtain that the Mach number

(M2) of downstream mixing shock is equal to 1. Thus, the trajectory of box vertex on and is a

certain line M2=1. From this we can infer that in the downstream of straight tube the Mach number

is equal to 1 on an interface, the velocity of mixed flow is equivalent to local sonic velocity of

gas-liquid two-phase flow, and then choking cavitation occurs in tube.

A special pattern mixing shock can be obtained after simple sealing gas valve of injector,

which is called cavitation shock phenomenon that there is only vapor in spraying jet before mixing

shock and bubbles natural collapse at mixing shock stage, and only liquid phase remained in virtue

of the local pressure is higher than the saturated vapor pressure of liquid. The maximum pressure

ratio max passing through the mixing shock can be expressed by expression (3) or expression (4),

and it is obtained when =0 in equation (1). The equation (4) calculates the maximum pressure

ratio thinking of there is only liquid phase in flow after mixing shock and the local pressure of

upstream of shock is equal to saturated vapor pressure.

max 2 / vp p (4)

The liquid superficial velocity of mixed tube is calculated by expression (5).

u 4 / ( 2)l lW D (5)

Where lW is the mass flow rate, D is the throat diameter and l is the liquid density.

Substituting the equation (5) and 2 /l va u p into equation (3), the maximum pressure ratio

can be indicated as another form. 2

max 2 4

16 ( 1)=1+ l

l v

W F

D p

(6)

The maximum pressure ratio max=197 calculated by equation (6) is obtained

when 11.1 / , 3.106, 0.03 ,lW kg s F D m 3 21000 / , 2650 /l vkg m p N m . It demonstrate that

300 Energy Engineering and Environment Engineering

the pressure of upstream and downstream of choking section (before and after mixing shock) is

relatively large when choking cavitation occurs, in another words, the recovery degree of static

pressure of straight tube is relatively significant when choking cavitation occurs, the static pressure

is far greater than saturated vapor pressure.

The Fig.2 is the mixing shock when the liquid mass flow rate is 11.1kg/s

and 23.5, 78,a 3.44, 4F , we can discover that choking cavitation flow emerge a large

magnitude of cavities.

Fig. 2 Mixing shocks

The Fig.3 is the mixing shock when the liquid mass flow rate is 12.5kg/s and

118, 270,a 0, 3.106F , we can see from it that cavities almost all collapse at the choking

interface.

Fig. 3 Cavitation shocks

From the analysis above, we can obtain that the relatively grate pressure ratio rate 2 v=p /p of

upstream and downstream of choking section is achieved when choking cavitation occurs in straight

pipe. The bubbles produced in upstream of the choking section (before mixing shocks) almost all

collapse under the action of the pressure of downstream of the choking interface (after mixing

shocks) far great than liquid saturated vapor pressure, and then, choking is able to produce a large

magnitude of bubbles and effectively collapse.

Choking cavitation occurs in jet pump under operating limits. When study the cavitation flow

of jet pump under operation limits, Long Xinping etc.[6-7]

discover that stability shape cavitation

cloud is formed in throat when jet pump is at the cavitation developing stage. Along with the further

developing of cavitation, cavitation cloud expands to the exit of the throat. And cavitation flow

changes to well mixing froth flow when the jet pump is under operating limits, then the bubbles

collapse rapidly in the exit of throat or diverging pipe. The discharge rate of jet pump doesn’t

change as the outlet pressure under operating limits.

The governing equations build based on the characteristics of jet pump, the assumption of

constant, isothermy and horizontal flow , and Wood sonic expression, it is about the

one-dimensional homogeneous bubbly flow of throat from the middle to bottom when jet pump

under operating limits. The equations are listed as follows.

Applied Mechanics and Materials Vol. 535 301

2

2

2

12

2

2 2 2

12

dp (1 )-

(1 )

1 1

f

l

v l

v l l v

WCA d a

Mdz

a a a a Wv v M

c c v v A

(7)

Where dp

dzis pressure gradient of throat from the middle to bottom, fC is friction coefficient

of gas –liquid two-phase flow, A is cross area of pipe, W is mass flow rate, d is diameter of pipe,

l is liquid-phase density, a is vapor rate of section, M is the Mach number, vc is local gas-phase

sonic velocity, lc is local liquid-phase sonic velocity, vv is gas-phase specific volume, and vv is

liquid-phase specific volume.

Mach number of gas-liquid two-phase flow from the middle to the bottom of throat is

calculated on the basis of governing equations and the friction pressure test result of the jet pump

surface. From the middle of the throat to the bottom, the Mach number of gas –liquid two-phase

flow gradually increase, and it is equal to 0.94 around the minimum pressure point, close to 1.Thus

there must contain a section around the minimum pressure point that Mach number is 1 from the

middle of throat to the bottom, then the mixed velocity of gas –liquid two-phase flow run up to

local sonic velocity, choking cavitation flow occurs in tube. It was shown in Fig. below.

Fig. 4 Choking cavitation in jet pump under the operating limits

The density of the bubbles decrease when the vapors flow pass through the obvious interface

that occurs in throat as the exit pressure increase under the operating limits ,it indicate that a large

magnitude of bubbles collapse on the interface, this is similarly to cavitation shock this paper just

talked in upper segment. Further observation finds out that the section changes in the throat along

with operation conditions changes, moves to forth or towards to bottom, shown as Fig. 5. The Fig.

5d doesn’t observe the interface because it moves to diffusion tube. It can be obtained that the

interface observed in experiment must be the interface Mach number is equal to 1 based on the

analysis above.

a) Choking section A-A emerge in the middle of throat

b) Choking section A-A emerge in the bottom of throat

302 Energy Engineering and Environment Engineering

c) Choking section A-A emerge in the head of throat

d) Choking section A-A not emerge in the middle of throat

Fig. 5 The movement of interface in the throat pipe

The jet pump shapes choking cavitation flow in throat under operating limits, and the interface

M=1 changes along with operation condition, moves to forth or towards to bottom. Thus we can

control the position of the interface M=1 by changing relevant operation parameters.

Choking cavitation occurs in cylindrical choke pipe with a sharp edged-corner.

Japanese researchers Aoyama Yuri etc.[8-11]

adopting flow visualization technique have

experimental studied the cavitation performance of cylindrical choke pipe with a sharp

edged-corner under steady and unsteady flows. The choke pipe engenders cavitation phenomenon

under steady and unsteady flows by remaining the downstream pressure and changing the upstream

pressure or by remaining the upstream pressure and changing the downstream pressure. Then using

high speed camera makes photos of cavitation bubbles test plot under different values of three

parameters, viz. four choke pipe diameters d, two choke pipe lengths l , two chamfering lengths s.

The experiment results shows there are three kind cavitation districts viz. laminar cavitation, bubbly

cavitation and cloud cavitation in long choke pipe. Even the cavitation number is identical, the area

of each kind cavitation type changes by the change of d and s in the long choke pipe. Fig. 6 is the

cavitation phenomenon of cylindrical choke pipe when K=0.194, s=0, d=3mm, l =20mm for steady

flow, and the parameter K is the cavitation number.

Fig. 6 Cavitation phenomenon for steady flow in the cylindrical choke pipe

Choking cavitation occurs in steady-state adiabatic flashing flow in a stepped circular tube.

Belgian Auttou etc.[12-13]

discover a funny thing when study steady-state adiabatic flashing flow in a

stepped circular tube that two choking cavitation phenomena occurs, this is based on two

fundamental conditions including downstream pressure condition and entropy increase condition.

The downstream pressure condition is that backpressure is less than or equal to the critical pressure

of the critical point in the downstream of stepped circular pipe. The entropy increase pressure

condition is that head loss coefficient of downstream flow is less than or equal to maximum head

loss coefficient. Two critical interfaces (interface 1 and s in Fig. 7) were appeared in stepped

circular tube with appropriate geometry structure and operation parameters. The maximum critical

flow rate is only affected by the previous interface, not affected by the rear one.

Applied Mechanics and Materials Vol. 535 303

Fig. 7 Multiple choking cavitation of steady-state adiabatic flashing flow in a stepped circular tube

According to the multiple choking cavitation of steady-state adiabatic flashing flow in a

stepped circular tube, it is likely to obtain multiple choking interfaces by specially designated

cavitator structure and proper operation parameters. The bubbles effective collapse multiple, and

then it is likely to improve its cavitation effect. But there is still a long way for improving the

application effect of the stepped circular in water treatment under single choking cavitation with

specially designated cavitator structure and proper operation parameter.

Choking cavitator design and its noise signals

Zhang fenghua et al. full using of the special flow characteristic produced by choking

phenomenon designs a new type cavitator viz. choking cavitator[14]

combined gas-liquid two-phase

critical flow theories and hydrodynamic cavitation mechanization.

The diagram of choking cavitator principle is shown as Fig. 8. Liquid burst into choke pipe

through annular slot, forming low pressure zone in the downstream of choke pipe, and then a large

magnitude of bubbles occurs. After the flow with a large magnitude of bubbles flows to the choke

pipe, the gas –phase content increase quickly and the local sonic velocity of gas-liquid two-phase

flow sharply decline. When the Mach number of one interface (choking interface) is equal to 1 in

the downstream of choke pipe, the choking cavitation occurs. According to the gas-liquid two-phase

critical flow theory, and dividing the flow field into two parts by choking interface, the local

pressure change (below critical pressure) of the downstream field has no effect on the pressure of

the upstream field. If steady choking cavitation flow is built in choking cavitator by adjusting the

geometry of choking cavitator, the flow field in fact is divided into two parts by choking interface

as a natural gate. The upstream field (low pressure zone) is the formation and development district,

the downstream field (high pressure zone) is the subsequent collapse district, the pressure gradient

between the high pressure zone and low pressure zone is relatively high. Appropriately increasing

the downstream pressure of the choking interface under prerequisite that the flow performance of

throat keeps choking flow, the bubbles can be mostly collapse as through the interface. Thus, the

different pressure request for bubbles formation and subsequent collapse is fulfilled by the choking

cavitator, and it makes the bubbles cavitation produced almost effectively collapse.

Fig. 8 Diagram of choking cavitator principle

Experiment results of reference 14 about cavitation noise power spectra of plain nozzle,

oscillation cavity nozzle and choking cavitator show that the cavitation noise power density of plain

nozzle decreases quickly as the frequency increases, and it hasn’t energy saving phenomenon at

high band (50-120KHz), the oscillation cavity nozzle has energy saving phenomenon at high band

304 Energy Engineering and Environment Engineering

(50-120KHz), though it has a platform at 50~120KHz, its power density amplitude is quite low,

choking cavitator has a high energy platform at 50~120KHz, and it has nice energy saving

phenomenon all the platform. The platform feature of choking cavitator is particularly contributed

to the application of choking cavitator in water treatment zones.

Feasibility study of choking cavitator in water treatment district

Cavitation noise test and analysis on choking cavitator. Experimental setup refers to reference

14. This chapter explains the cavitation noise test results of the three cavitation devices under the

distance 10-40mm, and analyzes experiment results by logarithmic of cavitation noise energy ratio.

Eb is background noise energy, E is cavitation noise energy. To ensure the Treated

experimental data reliable, this paper choose the noise collected by opening tap water as

Environmental noise. Because of a small amount of cavitation already occurs as opening tap water,

this paper take as the superficial characterization of obvious cavitation phenomenon.

Because the data after calculated is still large, there use analyze the data. When the

logarithm is larger than zero, it demonstrates obvious cavitation occurs.

The computational formula of energy ratio logarithmic is shown as follows.

20

12 2

' 20

1

= log log

( )

n

i i

i

n

i i

i

p fE

Ebp f

(8)

Where Pi is instantaneous sound pressure of cavitation noise collected on the corresponding

frequency (fi), and p 'i is instantaneous sound pressure of background noise collected on the

corresponding frequency (fi).

The energy ratio logarithms experimental result of choking cavitator, oscillation cavity nozzle

and plain nozzle is shown in Fig. 9.

Fig. 9 Comparison of energy ratio logarithms of the three kinds of cavitator

From the Fig. 9 above, we can conclude that choking cavitator has maximum energy ratio

logarithm (the maximum value is 49) when the distance is 20mm, and oscillation cavity nozzle has

maximum energy ratio logarithm (the maximum value is 9.8) when the distance is 30mm, plain

nozzle has maximum energy ratio logarithm (the maximum value is 1.7) when the distance is

30mm. The maximum energy ratio logarithm of choking cavitator is 5 times of oscillation cavity

nozzle, and almost 29 times of plain nozzle. The analytic results of energy ratio logarithms coincide

Applied Mechanics and Materials Vol. 535 305

with the analytic results of cavitation noise spectrum, it demonstrate that the cavitation effect of

choking cavitator is superior to the oscillation cavity nozzle.

The organism combination of cavitation mechanization and choking theory enlarge bubbles

formation area and make the bubbles almost effective collapse, this is plain nozzle and oscillation

cavity nozzle never owned.

Treat phenol solution by choking cavitator.

Experiment setup and experiment approach. Experiment setup is shown in Fig. 10, the liquid

system is consist of a vortex pump, a cavitator, a water tank, and a cooling system, the closed loop

is begin with water pumped to pipe from water tank, and end with water jetting into tank via

cavitator.

Fig. 10 Diagram of experiment setup

The cavitator was washed with large volumes of tap water to remove any residue and

chemicals in the setup before each experiment. The total volume of phenol solution used for the

experiment was 10L, the concentration of phenol was 100mg/L with a PH value of 6.5. The

operation parameter of the system was as follow: the inlet pressure was 0.95MPa, operation

temperature was 38℃ with a ambient temperature 23℃, treating time of the three cavitation setup

were 20, 30, 40, 50, 60min.

According to GB7490-87, Samples collected every 10min, were analysed using visible

spectrophotometer (Shanghai Youke Instrument Ltd.)

Experimental results and analysis. Phenol removal rate R is defined as follows.

0

0

(%) 100%tC CR

C

(9)

Where C0 is the concentration of phenol solution untreated, and Ct is the concentration of

phenol solution treated. The removal rate with the three kinds of cavitator is shown as Fig. 11

follows.

Fig. 11 Comprision of phenol removal rate with the three kinds of cavitator

306 Energy Engineering and Environment Engineering

From the Fig. 11, we can conclude that the removal rate of choking cavitator reaches 41.59%

by treating 60min, the oscillation cavity nozzle is 9.21% and the plain nozzle is 6.27%, the removal

rate of choking cavitator is 4.5times of the oscillation cavity nozzle’s and 6.6 times of the plain

nozzle’s. The reason for the phenomenon is the cavitation zone of plain nozzle and oscillation

cavity nozzle is lower than choking cavitator, and water cushion effect occurs when water jet

impact the target disc decreases pressure gradient of the regions beyond the stagnation point, then

some bubbles cannot effective collapse, this contributed to lower cavitating intensity and less

hydroxyl radical production, the concentration of hydroxyl radical is lower, all of those lead to the

lower phenol removal rate. Owning to the special geometrical structure of choking cavitator, a large

magnitude of bubbles was produced in the low pressure region of choke tube, there provide a stable

environment for the formation and development of bubbles in the upstream of choking interface,

and almost all the bubbles subsequent collapse effectively when the gas-liquid two-phase flow

containing a large magnitude of bubbles pass through the choking interface reached the high

pressure regions, it produces much more hydroxyl radical in the local district, thus the concentration

of hydroxyl radical is much higher than other two cavitator, all of those raise the phenol removal

rate.

Conclusion

Choking cavitation is a special gas-liquid two-phase flow phenomenon. When choking

cavitation occurs in straight pipe, a relative pressure ratio can be obtained at the choking interface,

and static pressure of the pipe has a large gradient increase, then the downstream pressure of

choking interface is higher than the pressure on the choking interface. And then the bubbles

produced in the upstream of the interface almost collapse under the effect of downstream pressure.

Thus, choking cavitation is able to produce a large magnitude of bubbles and make the bubbles

effective collapse. Even there maybe obtain multiple choking interfaces by proper geometry

structure and homologous operation.

Choking cavitator has a large cavitation zones. Under the foundation of stable choking

cavitation flow, by appropriate increase the downstream pressure, we can achieve the goal that most

of the bubbles effectively collapse without affecting the upstream pressure of the interface and the

production of bubble in the upstream of the choking interface. The choking cavitator can solve the

problems that increasing the volume ratio cavitating region to water district and making the bubbles

effectively collapse, thus it is superior in hydrodynamic cavitation district.

In the analysis experiment about cavitation noise, the maximum energy ratio logarithm of

choking cavitator is 5 times of oscillation cavity nozzle, and almost 29 times of plain nozzle. And in

the water treatment experiment, the removal rate of choking cavitator reaches 41.59%, 4.5times of

the oscillation cavity nozzle and 6.6 times of the plain nozzle. Thus, it can be concluded that

choking cavitator is feasible in water treatment processes.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant

No.51374101), the Natural Science Foundation of Hunan Province (Grant No. 13JJ9013) and the

Projects of Hunan province science and Technology Department (Grant No. 2013SK3165).

Applied Mechanics and Materials Vol. 535 307

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Energy Engineering and Environment Engineering 10.4028/www.scientific.net/AMM.535 Design of Choking Cavitator and its Feasibility Study in Wastewater Treatment 10.4028/www.scientific.net/AMM.535.298

DOI References

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http://dx.doi.org/10.1126/science.247.4949.1439 [2] Flint E B, Suslick K S. The Temperature of Cavitation[J]. Science, 1991, 253(5026): 1397-1399.

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Engineerinng Journal, 2001, 7(3): 201-212.

http://dx.doi.org/10.1016/S1369-703X(00)00128-5 [4] Gogate Parag R. Hydrodynamic Cavitation for Food and Water Processing[J]. Food and Bioprocess

Technology, 2011, 4(6): 996-1011.

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Cylindrical Choke [J]. Transaction of the Japan Society of Mechanical Engineers, 1996, 62(601): 3243-3249.

http://dx.doi.org/10.1299/kikaib.62.3243 [10] Yamamoto Masao, Matsuoka Yoshihiro, Aoyama Yuri, et al. An Experimental Investigation of the Flow

in a Curved Diffuser: 2nd Report Effects of the Existence of a Guide Vane and the Variation in Logarithmic

Spiral Angle on the Diffuser Performance[J]. Transaction of the Japan Society of Mechanical Engineers,

1996, 62(598): 2296-2302.

http://dx.doi.org/10.1299/kikaib.62.2296 [11] Aoyama Yuri, Watanabe Naoto, Yamamoto Masao, et a1. Cavitation Performance of Cylindrical Choke

for Unsteady Flow: 2nd Report Comparison of Difference in Inlet Shape of Choke[J]. Transaction of the

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Choking Phenomenon[J]. Journal of Loss Prevention in the Process Industries, 1999, 12(5): 335-359.

http://dx.doi.org/10.1016/S0950-4230(98)00017-5