Two Step Throttle

8/11/2019 Two Step Throttle

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pressure characteristics etc. In this paper, cavitationindex of two-step throttle is analyzed. For throttles withdifferent structure, experiments are conducted for the

research of flow and pressure characteristics, and flowcoefficient. Test results indicate that the anti-cavitationability of two-step throttle is higher than the single-stepone which makes the former, and the flow coefficient of a throttle using water as pressure medium is lager thanthat of one using oil as working medium.

CAVITATION CHARACTERISTICSANALYSIS

Usually cavitation index is used to describe the trend of cavitation occurrence. It is defined as:

v p p p pk

−−=

1

31 (1)

If the cavitation index of a throttle or orifice takes smallvalue, there is less trend of cavitation occurrence in it.

Fig.1 shows the structure of a two-step throttle. Itconsists of two orifices or two throttles, throttle 1 andthrottle 2. Suppose the cavitation indexes of the twothrottles are k 1 and k 2 respectively. They can be

presented as:

v p p p p

k −−

=1

211 (2)

v p p p p

k −−

=2

322 (3)

For a single-step throttle, i.e. one consisting of only oneorifice, if the pressure drop across it is the same as in thetwo-step throttle, i.e. Ä p=(p 1-p3), its cavitation index isgiven by Equation (1).Because p1 p 2 p3, then k 1 k and k 2 k. That means the

cavitation index at each orifice of a two-step throttle is

smaller than that of a single-step throttle. Therefore, atwo-step throttle has lower possibility of cavitationoccurrence than a single-step one.

If p 3 is considered as atmosphere pressure, p2 can beexpressed as:

121

22

12

+=

A

A

p p (4)

Substituting (4) into (2) and (3) yields:

1

2

1

2

1

1

1)(

11

p

p A A

k v−

+−

= (5)

1

2

1

2

1

2

1

2

2

1)(1

11)(1

p p

A A

p A A

k v+−

+−= (6)

Equation (5) and (6) show that the cavitation indexes of two throttles are the function of the ratio of their flowarea A 2/A 1. Fig. 2 shows the relationship between k 1, k 2and A 2/A1. When k 1 increases with the increase of A 2/A1,k 2 decreases. So in the designing of a two-step throttle, itis very important to select proper value of A 2/A 1 to keep

both k 1 and k 2 at relative small value for the purpose of preventing cavitation occurrence.

k

A2/A1

k 1

k 2

Fig. 2 Diagram of cavitation index

Fig. 1 A type of two-step throttle

0 1 2 3 4 5 6 7 8 9 10-1.5

-1

-0.5

0

0.5

1

Inlet p1, Q

Throttle 2

p2

p3

Outlet

Throttle 1



EXPERIMENT RESULT

(1) Test ApparatusIn order to find out the differences of flow and pressurecharacteristics between single- and two-step throttles,experiments were carried out in two forms of two-stepthrottles and a single-step one. Test apparatus for this

purpose is shown in Fig. 3. In the test, p 1 and p 3 weremeasured respectively by two pressure transducersinstalled at the upstream and downstream of the testassembly. Flow rate Q was measured by a flow-ratemeter or a measuring cup or a scale, poppet lift x wasmeasured by a displacement transducer attached at theend of the poppet.In this research two kinds of two-step throttle, Assembly

A and B, were tested. Assembly A, as shown in Fig. 4consists of a poppet of 30 °cone angle and a seat withstep shape bore. Assembly B, as shown in Fig. 5 ,consists of a poppet of 30 °cone angle and a chamferedseat with a groove in it. A single–step throttle, referred asAssembly C (see Fig. 3) , which has a poppet of 30-

degree cone angle and a sharp edged seat in this paper,was also used in the test. The inlet diameter, d, is 16 mm.For each assembly, test was conducted by varyingupstream and downstream pressure while holding poppetlift x constant at a time. There were several poppet liftsused in the test. Pressure, flow rate and the poppetdisplacement were recorded.

(2) Flow and Pressure CharacteristicsFig. 6 and Fig. 7 show the Q-dp relationship of the threeassemblies at poppet lift x=0.1mm and x=0.7mm,respectively. At small lift (x=0.1mm) Assembly A and

Assembly C have larger flow gain than Assembly B. Inthis case, although Assembly C is a single-step throttle, it

has larger flow-pressure gain than Assembly A. At largelift (x=0.7mm), Assembly A and Assembly C still havelarger flow gain than Assembly B. But this timeAssembly A has larger flow gain than Assembly C,which is an inverted result with in the case of x=0.1mm.According to our test and previous documents[3]cavitation is easier to occur when poppet lift is large. Atsmall lift, there is no cavitation observed in both single-and twothrottles. Because the former has less flowrestriction than the latter its flow gain is larger than thatof the latter. At large lift, cavitation choke is more likelyto occur because under this condition cavitation has hightendence to occur. Assembly C has lower flow gain

because the increasing of pressure drop can not increasethe flow rate through throttle due to the cavitation choke.Larger flow gain means less possibility of flowsaturation and cavitation occurrence. Experimentalresults show that Assembly A has lower cavitationsensitivity than Assembly B and C.

(3) Flow CoefficientThe relationship between the flow rate through a valveand the pressure drop across it is frequently described bythe discharge coefficient, C d, according to theequation[4]

20

1

)(1[

)(2

AaC

p paC Q

c

cd

−

−= (7)

In practice, the pressure at the vena contracta can be verydifficult to measure, so it is difficult to calculate C d. Flowcoefficient C q, which is based on the difference betweenthe upstream and downstream pressures after the vena

Fig. 3 Test assembly of valve characteristics

Fig. 4 Assembly A

Fig. 5 Assembly B

d

Inlet

Outlet

d

Outlet

Inlet



contracta, is then taken as an alternative measure todescribe valve characteristics. Using flow coefficient,flow rate can by described as:

ρ

)(2 310

p p AC Q q−= (8)

From Eq. (8), C q can be calculated with measured p 1, p3

and Q.Fig. 8 shows the C q-dp relationship of the threeassemblies. In the test, pressure drop was kept at 2.0Mpaand poppet lift was changed from small to large value.Fig. 8 reveals that the C q of the throttles, which is

between 0.82 and 0.95, does not change significantlywith the increasing of lift x, that means the flow is inturbulent state even with small lift and low pressuredrop. At small lift, Assembly C has larger coefficient

than Assembly A and B because of its flow restriction issmaller than those of Assembly A and B. At large lift,the situation is inverted because of cavitation. With thevariation of poppet lift, C q of Assembly C experiences afluctuation a little larger than those of Assembly A andB. That means flow rate through a two-step throttlevaries less than that of a single-step throttle when themagnitude of pressure differential fluctuation is thesame.Fig. 9 is the C q-Re relationship of the three assemblieswhen poppet lift was kept at 0.5mm. It shows thatAssembly A and C have larger C q than Assembly B andthis trend becomes more clearer when Re is larger than20,000. It can be judged that there is no cavitationoccuring in Assembly A and C at this lift. The C q of Assembly B begins to decrease when Re reaches 20,000,which may be due to cavitation. So although Assembly Bis a two-step throttle, its anti-cavitation capacity is lower than Assembly C, a single-step throttle. That means notany two-step throttle has higher anti-cavitation abilitythan all single-step ones. Therefore, it is very importantto select suitable structure of two-step throttle for the

purpose of anti-cavitation.

CONCLUSI ONS

A. The flow coefficient of two-step throttle usingwater as pressure medium is between 0.82~0.95;B. If properly designed, a two-step throttle can have

better anti-cavitation capacity than single step throttle.C. Under non-cavitation condition, two-step throttlehas lower flow coefficient because of its large flowrestriction compared with single-step throttle.D. As for the three assemblies used in the test, the anti-cavitation ability of them is in the order of Assembly B,C and A, from low to high.E. Assembly A is a kind of suitable two-step throttlethat can be applied in water hydraulic elments.

REFERENCES

[1]. Li Zhuangyun, Yu Zuyao, He Xiaofeng, et al The

Development and Perspective of Water Hydraulics, (Keynote Lecture ) 4th JHPS International Symposiumon Fluid Power, Tokyo ’99, Nov. 15~17, 1999: 335~342[2]. Li, Zhuangyun. Cavitation in Fire Resistant FluidPower Systems. Proceedings of 38th national Conferenceon Fluid Power, USA, Nov. 16-18, 1982: 213-224[3]. P. Kenny, E. D. Yardley, A. R. Eedy et al. A Studyof Erosion and Corrosion of Materials Used in HydraulicEquipment with Fire-resistant Fluids. The MiningEngineer, 9/1979:235~243.[4]. D N Johnston et al., Experimental investigation of flow and force characteristics of hydraulic poppet anddisc Valves. Pro Instn Mech Engrs Vol 211 Part A,1991:161~171.



0

10

20

3040

50

0 1 2 3 4 5dp( MPa )

Q ( L / m i n )

x =0. 7 mm( As s e m. A)x =0. 7mm( Ass e m. C)x =0. 7mm( As s e m. B)

Fig. 7 Q-dp curves at x=0.7mm

Fig. 8 Cq-x/d curves

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07

x /d

C q

dp=2. 0 MPa( Ass em. A)dp=2. 0 Mpa( Ass em. C)dp=2. 0 MPa( Ass em. B)

Fig. 6 Q-dp curves at x=0.1mm

012345678

0 1 2 3 4 5

dp ( MPa )

Q ( L / m i n )

x =0. 1 mm( As s e m. A )x =0. 1 mm( As s e m. C )x =0. 1 mm( As s e m. B )

Fig. 9 Cq-Re curves

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

0 10000 20000 30000 40000 50000 60000

Re

C q

x=0. 5 mm( As se m. C)x=0. 5 mm( As se m. B)x=0. 5 mm( As se m. A)

Two Step Throttle

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