International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Cavitation reduction of a flapper-nozzle pilot valve using continuous
microjets
He Yang ⇑, Wen Wang, Keqing Lu, Zhanfeng Chen
School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou, China
a r t i c l e
i n f o
Article history:
Received 9 September 2018
Received in revised form 25 December 2018
Accepted 2 January 2019
Keywords:
Cavitation suppression
Flapper-nozzle valve
Hydraulic valve
Microjets
a b s t r a c t
The flow cavitation in the flapper-nozzle stage is one of the main factors that produce the flapper vibration and thus deteriorate the performance of the flapper-nozzle servo valves. This work proposes a novel
method, deploying two continuous microjets around the main jet of each nozzle, to suppress the cavitation. The cavitation reduction using continuous microjets is numerically examined in detail by comparing
the vapor fraction with and without the microjets at different inlet pressure, housing diameter and the
null clearance. The mass flow rate measurements and the flow visualization are conducted to validate
the numerical simulation. It is found that the cavitation in the flapper-nozzle stage is significantly
reduced under the effect of the continuous microjets. And the flow cavitation exhibits a great dependence
on the inlet pressure, housing diameter and the null clearance. In the traditional flapper-nozzle structure,
the cavitation is strongly enhanced at high inlet pressure, small housing diameter or large null clearance.
Nevertheless, the cavitation in the flapper-nozzle structure with the microjets is still remarkably suppressed at the same condition. This indicates that the continuous microjets are highly effective in reducing the cavitation of the flapper-nozzle valve.
Ó 2019 Published by Elsevier Ltd.
1. Introduction
Electrohydraulic servo-valves are the key components of highprecision hydraulic power systems in many engineering applications, such as rocket, airplane, ship, and hydraulic robot. Recent
review [1] provides an excellent compendium of the state of the
art of the electrohydraulic servo-valves. Due to the advantages of
high precision, good linearity and fast dynamic response, the
flapper-nozzle servo-valve is widely used over the past few decades, which mainly consists of the flapper-nozzle pilot stage and
the main spool stage. The flapper-nozzle pilot stage acts as an electromechanical converter and is crucial for managing the accurate
movement of the main spool valve [2]. The flow characteristics in
the flapper-nozzle stage directly affect the flow force on the flapper
and the hydraulic output of the servo valve [3]. Thus, understanding and improving the flow characteristics in the flapper-nozzle
stage is of great importance to the vibration suppression of the
flapper and the performance improvement of the servo valve.
Considerable interest has been given to study the flow characteristics of the hydraulic valves. In the solenoid operated directional control valve, the increase of flow forces caused by the
⇑ Corresponding author at: No. 1158, No. 2 Street, Jianggan District, Hangzhou
310018, China.
E-mail address: yanghe@hdu.edu.cn (H. Yang).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.008
0017-9310/Ó 2019 Published by Elsevier Ltd.
change of the flow characteristics may disturb the force balance
on the spool and affect the valve operation. Lisowski et al. [4]
deployed additional internal channels to reduce the flow forces
on the spool and achieved an increase of about 45% in the flow
range. In the study of a hydraulic spool valve, Ye et al. [5] demonstrated that the groove shape of notches has a vital impact on the
flow characteristics of the spool valve, e.g. discharge characteristic,
flow area, throttling stiffness and steady flow force. In the numerical investigation of a servo valve, Mchenya [6] explored the velocity distribution in the flapper-nozzle stage and found a large
pressure drop around the nozzle. Pan et al. [7] investigated the discharge characteristics of the spool stage of a servo-valve using the
CFD method and found that the relation of the discharge coefficient
and the square root Reynolds number is consistent for spool valve
orifices with different size and numbers. Lisowski and Filo [8] conducted a numerical investigation on the flow characteristics of a
proportional flow control valve and found that the modification
of the openings shape in the spool could result in more precise
adjustment of the flow rate. Due to the high pressure drop and sudden velocity change, cavitation may occur in the flow field of the
hydraulic proportional directional valves, which also has a great
effect on the flow rate and driving forces of the spool [9].
The cavitation phenomenon in hydraulic valves and its reduction have been extensive studied. Zou et al. [10] investigated the
1100
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
cavitation in spool valve with U-grooves and found that the
increase in groove depth may enhance the cavitation. In the study
of the water hydraulic poppet valves, Liang et al. [11] demonstrated that the existence of a groove at valve port and the increase
in the frequency of the inlet pressure fluctuations could reduce the
intensity of the cavitation. Han et al. [12] found that a large cone
angle in a water hydraulic poppet valve may result in more serious
cavitation while the backpressure could reduce the intensity of
cavitation. In the investigation of cavitation phenomenon in
mechanical heart valves, Lim et al. [13] pointed out that the drop
of contact area and squeeze flow velocity may suppress the cavitation, and the temporal acceleration of fluid also has a great effect
on cavitation inception.
Cavitation in flapper-nozzle valves can lead to the deleterious
effects of noise, flapper vibration and cavitation erosion, reducing
the reliability and performance of the servo-valves [3,14]. Thus,
understanding and suppression of the cavitation in flappernozzle pilot stage is of great importance to the performance
improvement of the servo-valves. Aung et al. [2] pointed out that
the curved edge of the traditionally used flapper may be responsible for the occurrence of the cavitation and thus they proposed a
method of using a rectangular flapper to reduce the cavitation.
Yang et al. [15] conducted a detail investigation on cavitation suppression using two innovative flappers, that is, rectangular and
square flappers. Due to the absence of the curved surface, the cavitation is suppressed for both innovative flappers. Moreover, the
rectangular flapper is more effective because the longer flat land
could greatly reduce the strength and the growth of the jet flow.
It should be noted that the cavitation suppression for two innovative flappers is weakened at high inlet pressure and large flappernozzle null clearance. Thus, further effort should be made to
reduce cavitation in servo valves.
Previous investigations have shown that the cavitation in the
flapper-nozzle pilot valve could be suppressed through reducing
the strength of the jet flow. On the other hand, the rapid decay
of the jet flow could be achieved by using microjets [16,17]. Considering these facts, this work aims to numerically investigate
the cavitation reduction in the flapper-nozzle stage using continuous microjets. Focus is given to the detail comparison of cavitation
phenomenon with and without continuous microjets under different inlet pressure, chamber size and flapper-nozzle null clearance.
The working principle of the flapper-nozzle stage is briefly introduced in Section 2. The details of numerical modelling and experimental validation are described in Section 3 and Section 4,
respectively. Section 5 presents the numerical results and discussions. The conclusions drawn are shown in Section 6.
2. Working principle and flow structures of the flapper-nozzle
stage
A typical two-stage servo-valve with the flapper-nozzle pilot
structure consists of a spool, a flapper-nozzle structure and an electrical torque motor, as schematically shown in Fig. 1. Without the
input current, the flapper keeps the equivalent distance from the
two nozzles separated azimuthally by 180 degrees. And the
hydraulic oil with the same flow rates from the two nozzles
impinges upon the two opposite surfaces of the flapper. As a result,
a pressure balance is achieved in the two nozzles and thus at both
sides of the main spool. Once the working current is input into the
coils, a rotating torque is produced on the armature under the
magnetic field. The flapper fixed on the armature exhibits a clockwise or anti-clockwise rotation, approaching to one of two nozzles.
This asymmetric structure disrupts the pressure balance between
the both sides of the main spool and thus forces the main spool
to move. Then, under the combined effect of feedback rod, spring
tube, magnetic torque and flow force, the flapper returns to the
null position, recovering the equilibrium between pressures on
both sides of the main spool. As a result, the main spool operates
at a certain opening that is proportional to the input working
current.
The flow structures in the flapper-nozzle stage mainly consist of
impinging jets and radial jets [18], as described in Fig. 2. Initially,
the flow issuing from each nozzle impinges upon the flapper surface, forming an impinging jet. From the stagnation region, the
flow spreads along the radial direction in the slot between the nozzle and the flapper, and subsequently impinges upon the housing
wall. Then the flow reattaches to the surfaces of the nozzle and
the flapper, forming swirling regions. Due to the high pressure
drops, the cavitation initially occurs in the slot between the flapper
and the nozzle. Then, the cavitation bubbles travel downstream,
forming cavitation at the curved surface of the flapper and in the
swirling regions. The cavitation in the flapper-nozzle stage may
result in pressure fluctuations, noise and cavitation erosion, reducing the working performance of the servo valve.
3. Numerical modelling
3.1. Geometry details
The three-dimensional model of the flapper-nozzle stage and
corresponding computational domain are shown in Fig. 3. A quarter section of the symmetrical flow model is chosen as the computational domain to save computational resources. The
computational domain is built in GAMBIT 2.4.6 and calculated with
FLUENT 17.0. Two microjets are separated azimuthally around
each main jet, as presented in Fig. 3(b). The diameters of the main
jet and the microjet in the nozzle are of 0.5 mm and 0.1 mm,
respectively. The distance between the centerlines of the main
jet and the microjet is of 0.4 mm. To explore the effect of the chamber size on the cavitation, three values of the housing diameter Dc
are chosen, i.e., 3.5 mm, 3.8 mm and 4 mm. The detailed dimensions of the flappers and the null clearances for different configurations are described in Table 1.
3.2. Governing equations
Previous investigations [11,12] have demonstrated that there is
little variation on the simulation of cavitating flows in hydraulic
valves among different turbulence models. Thus, in this work, the
standard k-e model is used for solving turbulent characteristics
and the Singhal et al. model is chosen for calculating cavitation
phenomenon, as used in Refs. [2,3,15,18,19]. The governing equations of a two-phase mixture model consists of continuity equation, momentum equation, turbulence kinetic energy equation,
turbulent dissipation rate equation and vapor transport equation.
Continuity equation:
@ qm
!
þ r qm u m ¼ 0
@t
ð1Þ
where qm is the mixture density, given by qm ¼ aqv þ ð1 aÞql , a is
the vapor volume fraction, qv and ql are the vapor and liquid den!
sity, respectively. u m is the mixture velocity.
Momentum equation:
h i
@ ! !
!
!
qm u m þ r qm !
u m u m ¼ rp þ r lm r u m þ r u Tm
@t
!
n
X
! !
!
ð2Þ
ak qk !
u dr;k u dr;k
þ qm g þ F þ r k¼1
1101
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
Fig. 1. Schematic of a two-stage servo-valve with the flapper-nozzle pilot structure.
where C1e, C2e, Cl, rk and re are the constants for the standard k-e
model, C1e = 1.44, C2e = 1.92, Cl = 0.09, rk = 1 and re = 1.3.
The vapor mass fraction is governed by the vapor transport
equation [20]:
@
!
ðqm f v Þ þ r qm u v f v ¼ rðcrf v Þ þ Re Rc
@t
ð6Þ
where fv is the vapor mass fraction, the relation between the fv and
a can be expressed as: qm f v ¼ aqv , c is the diffusion coefficient, Re
and Rc represent the vapor generation and condensation rate,
respectively. In the Singhal et al. model, they can be expressed as
follows [21]:
Re ¼ C e
Rc ¼ C c
Fig. 2. Typical flow structures in the flapper-nozzle pilot stage.
!
!
where p is the pressure, F is the body force, g is the gravity, n is the
phase number, lm is the mixture viscosity, given by
lm ¼ alv þ ð1 aÞll , lv and ll are the vapor and liquid kinetic vis!
cosity, respectively, u dr;k is the drift velocity.
Turbulence kinetic energy equation and dissipation rate equation are listed as follows:
lt;m @
!
ðqm kÞ þ r qm u m k ¼ r l þ
rk þ Gk;m qm e
@t
rk
lt;m
@
e
!
ðqm eÞ þ r qm u m e ¼ r l þ
re þ
@t
re
k
C 1e Gk;m C 2e qm e
ð3Þ
k
ð4Þ
2
e
r
pffiffiffi
k
r
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ðpv pÞ
ql qv
1 fv fg
3ql
ql qv
if p 6 pv
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ðp pv Þ
ð1 f v Þ if p > pv
3ql
ð7Þ
ð8Þ
where fg = 1.5 105 is the non-condensable gas fraction, Ce = 0.02
and Cc = 0.01 are the vaporization and condensation rate coefficients, respectively. Considering the effect of turbulence, the
phase-change threshold pressure pv is rearranged by [12]
1
pv ¼ psat þ pt
2
ð9Þ
where psat is the saturation pressure of vapor, pt = 0.39qk is the turbulent pressure fluctuation.
3.3. Boundary conditions and solving strategies
where the turbulent viscosity of the mixture lt,m is presented by the
following:
lt;m ¼ C l qm
pffiffiffi
k
ð5Þ
Four types of boundary conditions are defined in the computational domain. The pressure-inlet condition is set at the inlets of
the main jet and the microjet. The outlet is defined as the
pressure-outlet with the value of zero, i.e., gauge pressure. The
symmetry-type boundary condition is applied for the symmetry
planes. Other surfaces are set as wall-type boundary. No slip stationary condition is selected for the wall condition and the standard wall functions are chosen for near-wall treatment. The
1102
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
Fig. 3. Flow model and dimensional size of the flapper-nozzle stage (a) without microjet (b) with four microjets.
Table 2
The properties of the hydraulic fluid and cavitation parameters.
Table 1
Detailed structural dimensions for various configurations.
Configuration
Xf0 (mm)
L (mm)
Dc (mm)
C1
C2
C3
C4
C5
0.1
0.1
0.1
0.08
0.05
1.7
1.7
1.7
1.74
1.8
4
3.8
3.5
3.5
3.5
Parameters
Values
Liquid density
Liquid dynamic viscosity
Vapor density
Vapor dynamic viscosity
Surface tension coefficient
Vaporization pressure
Non-condensable gas mass fraction
850 kg/m3
0.0085 Pas
0.025 kg/m3
1 105 Pas
0.0273 N/m
3000 Pa
1.5 105
3.4. Mesh generation and grid independence test
fraction of the vapor phase is defined as zero at the inlets and outlet. The properties of the hydraulic fluid and cavitation parameters
are presented in Table 2, as used in previous investigations
[3,14,19].
The governing equations mentioned above are solved by FLUENT 17.0 using pressure-based solver. The SIMLEC algorithm is
chosen for the pressure-velocity coupling and the body PRESTO!
scheme is used for pressure discretization. In multiphase calculation, the QUICK scheme is chosen for calculating the vapor fraction
while the first order upwind is used for solving the momentum,
turbulent kinetic energy and turbulent dissipation equations. To
ensure the convergence of the iterations, the residual value of each
parameter is under 1 103 and the deviation between the total
mass flow rates at inlets and outlet is less than 1 105.
The computational domain is meshed with GAMBIT 2.4.6. The
combination of the tetrahedron and hexahedron elements is
applied for meshing. Specifically, the structured hexahedron elements are deployed in the regions of microjet, main jet and the slot
between the flapper and the nozzle tip while the tetrahedron and
unstructured hexahedron meshes are applied for other regions
(Fig. 4). To ensure the accuracy, ten grid layers are meshed in the
slot for all the cases. A fixed-type size function is used for generating the tetrahedron and unstructured hexahedron meshes. The
skewness values of the meshes are under 0.74 and thus the mesh
qualities are acceptable [19].
In the flapper-nozzle stage, the cavitation shedding mainly
occurs in the region between the housing wall and the flapper
1103
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
[22]. Therefore, the mesh effect on the flow characteristics in this
region is the main concern. Four types of meshes for each configuration are examined by comparing the mass flow rate Mf at the
rated inlet pressure of Pin = 7 MPa (Table 3). At large housing diameter (C1, Dc = 4 mm), the variation of mass flow rate in four meshes
is less than 0.2%, and the mass flow rate remains the same as the
maximum cell size is refined from 0.08 mm to 0.06 mm. At small
housing diameter (C3, Dc = 3.5 mm), the variation of mass flow rate
in four meshes is under 0.04%, and the mass flow rate remains
unchanged as the maximum cell size is refined from 0.06 mm to
0.04 mm. Thus, the maximum cell size adopted is of 0.08 mm at
large housing diameter (C1) and 0.06 mm at medium and small
housing diameters (C2, C3, C4 and C5).
4. Experimental details
To validate the simulation setup, the flow characteristics in the
flapper-nozzle structures are experimentally investigated and
compared with numerical results. The flow rate measurements
and flow visualization are conducted under different inlet
pressures.
The hydraulic circuit consists of hydraulic pump, pressure relief
valve, throttle valve, pressure gauge, flapper-nozzle assembly,
flowmeter and one-way throttle valve (Fig. 5a and b). The pump
has a delivery flowrate of 2.9 L/min at rated pressure of 21 MPa.
The throttle valves are employed for the pressure adjustments
and the pressure gauges with an accuracy of ±1.6% are used for
the pressure measurements. The pressure gauges at the upstream
and downstream of the flapper-nozzle assembly have a measuring
range of 0–16 MPa and 0–1 MPa, respectively. The inlet pressure
Table 3
Mass flow rate of the outlet under various meshes.
Configuration
Number of
elements
Maximum cell
size (mm)
Mf (kg/s)
C1
C1
C1
C1
C3
C3
C3
C3
192,331
342,204
506,230
972,840
286,054
390,919
700,688
2,003,999
0.12
0.10
0.08
0.06
0.10
0.08
0.06
0.04
0.0203252
0.0203632
0.0203252
0.0203252
0.0203312
0.0203244
0.0203252
0.0203252
Pin for the flapper-nozzle assembly is increased from 0 MPa to
11 MPa, while the outlet pressure remains to be zero. The flow rate
is measured by the flowmeter installed at the downstream of the
flapper-nozzle assembly. The flowmeter is calibrated by the manufacturer to work for hydraulic fluids with a density of 850 kg/
m3 and the measurement accuracy of the flowmeter is of ±1.5%.
The flapper-nozzle structure includes flapper, two nozzles, flapper
holder, nozzle holder, front cover and back cover (Fig. 5c). The flapper and nozzles are manufactured by Computer Numerical Control
machines and the maximum fabrication error in the dimensions of
the flapper and nozzles is within ±0.02 mm. The slot between the
flapper and the nozzles are adjusted under the vision of a digital
microscope, which is also used to capture the flow field in the
flapper-nozzle structure.
Fig. 6 qualitatively compares the numerical and experimental
observations of the flow fields in the flapper-nozzle structure with
and without microjets (C1). It can be observed from the experimental results that the radial jets are formed after impingement
Fig. 4. The boundary conditions and mesh details of the computational domain (a) without microjet (b) with microjet.
1104
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
1 – One-way throttle valve, 2 – Flowmeter, 3 – Pressure gauge, 4 – Flapper-nozzle assembly, 5 –
Throttle valve, 6 – Hydraulic pump, 7 – Oil tank, 8 – Pressure relief valve, 9 – Digital microscope,
10 – Flapper holder, 11 – Back cover, 12 – Front cover, 13 – Nozzle holder, 14 – Nozzle without
minijets, 15 – Flapper, 16 – Nozzle with minijets
Fig. 5. Experimental setup (a) hydraulic circuit, (b) photograph of the test rig, (c) mechanical components of the flapper-nozzle assembly, (d) dimensions of the nozzle with
two minijets.
upon the flapper and then they move towards the housing wall in
case of the traditional nozzles without microjets. The numerical
results without the cavitation model show an obvious disagreement with the experimental photographs, while the numerical
results with the cavitation model exhibit a relatively good agreement with the experimental results. This indicates that the cavitation model should be considered in numerical modelling of the
flapper-nozzle valve. Moreover, both the CFD and experimental
results show that the radial jets are greatly suppressed under the
effect of the microjets. It should be pointed out that the experimental observations are affected by imperfectness in the fabrication, low visibility of the hydraulic oil and overlap effect of the
three-dimensional flow.
To quantitatively compare the numerical and experimental
results, Fig. 7 presents the mass flow rates of the outlet at various
inlet pressure Pin (C1). The experimental data in Ref. [19] is also
included for comparison. It can be observed that all the curves
exhibit a similar trend. For the traditional nozzles without microjets, present CFD results exhibit an averaged relative derivation
of 1.6% from present experimental results and of 5.4% from experimental results in Ref. [19]. For the nozzles with microjets, the relative departure between the present CFD and experimental results
is less than 8.5%. The small deviations suggest a relatively good
agreement between the CFD and experimental results for the nozzles with and without minijets. Thus, the present CFD setup is reasonable for numerical modelling of the flapper-nozzle pilot valve.
As one of the important flow characteristics, null leakage is
denoted by the mass flow rate at the outlet. As shown in Fig. 7,
the mass flow rate under the effect of the microjets exhibits an
averaged increase of 9.4% and 14.7% for CFD and experimental
results, respectively. This indicates that the deployment of the
microjets may require more power consumption. To cope with this
drawback, a possible solution could be to reduce the diameter of
the nozzles to maintain the value of the null leakage constant.
5. Results and discussions
In this section, cavitation reduction of the flapper-nozzle stage
using continuous microjets is explored in detail using CFD simulation. Cavitation characteristics with and without microjets are
compared at different inlet pressure, chamber size and null
clearance.
5.1. Effect of the inlet pressure on the cavitation
The inlet pressure has a great effect on cavitation characteristics. Previous investigations (e.g. [22]) have shown that the
increase of inlet pressure may intensify the cavitation in the
flapper-nozzle servo-valves. Thus, it is necessary to examine the
cavitation characteristics with and without microjets at high inlet
pressure. In this work, three values beyond the rated inlet pressure
of the flapper-nozzle stage are chosen, i.e., 8 MPa, 10 MPa and
11 MPa.
Fig. 8 presents the velocity contours of the flapper-nozzle stage
in case of Dc = 4 mm and Xf0 = 0.1 mm. In the traditional flappernozzle stage, i.e., without the microjet, the radial jet from the stagnation region moves out of the slot between the flapper and the
nozzle, and then impinges upon the housing wall. After that, the
jet deflects along the wall, forming wall jets further downstream
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
1105
Fig. 6. Qualitative comparison of CFD and experimental observations on the flow field (a) numerical results without cavitation model, (b) numerical results with cavitation
model, (c) experimental observation (Dc = 4 mm, Xf0 = 0.1 mm).
Fig. 7. CFD and experimental results of mass flow rate at different inlet pressure Pin.
(Dc = 4 mm, Xf0 = 0.1 mm).
[23]. As Pin increases from 8 MPa to 11 MPa, the radial jet velocity
becomes higher and thus the impingement on the housing wall is
strengthened. As a result, the jet flow moves back to the flapper
surface and nozzle wall, forming flow structures with anticlockwise swirling on the left side and clockwise swirling on the
right side, respectively. This is consistent with previous findings
by Aung et al. [2]. Once the microjet is introduced, the velocity of
the radial jet exhibits a remarkable drop, especially in the annulus
region between the flapper surface and the housing wall. The jet
impingement upon the housing wall and subsequently the swirling
flow structures are absent even at Pin = 11 MPa. This indicates that
the microjet could greatly reduce the velocity of the radial jet.
Fig. 9 shows the vapor fraction contours of the flapper-nozzle
stage in case of Dc = 4 mm and Xf0 = 0.1 mm. Without the microjet,
the cavitation occurs at three regions, i.e., flapper surface, nozzle
tip and the annulus between the flapper and the housing wall. As
the jet flow propagates downstream, the cavitation initially
emerges at the nozzle tip and then the curved surface of the flapper, due to the high pressure drop in the slot. After that, cavitation
bubbles may travel downstream with the radial jet, forming cavitation on the right part of the annulus. This is probably due to that
the confined space is more beneficial to the concentration of the
cavitation bubbles. As Pin rises from 8 MPa to 11 MPa, the vapor
fraction exhibits a substantial increase, almost covering the right
half of the annulus. This suggests that the cavitation in the annulus
is strongly intensified. In the study of the diesel nozzle, Qiu et al.
[24] also confirmed the enhancement of the cavitation by the
increase of the inlet pressure. With the microjet, the cavitation
attached to the nozzle tip and the flapper surface are suppressed,
but not eliminated at Pin = 8 MPa. Interestingly, the cavitation in
the annulus is absent. This may result from the remarkable suppression of the radial jet (Fig. 8). In fact, the flow velocity has a
great effect on the cavitation occurrence [25,26]. In the study of
the flapper-nozzle valves with rectangle-shaped flappers, Yang
et al. [15] demonstrated that the suppression of the radial jet
velocity caused by the rectangle-shaped flappers is responsible
for the cavitation reduction in the flapper-nozzle stage. As the Pin
goes up to 11 MPa, the cavitation attached to the flapper surface
and the nozzle tip is enhanced while the cavitation in the annulus
is negligible. This suggests that the microjet is still effective in
reducing the cavitation even at high inlet pressure. Thus, the
1106
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
Fig. 8. Velocity contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different inlet pressure (Dc = 4 mm, Xf0 = 0.1 mm).
Fig. 9. Vapor fraction contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different inlet pressure (Dc = 4 mm, Xf0 = 0.1 mm).
microjet is very suitable for the cavitation reduction of the flappernozzle valves that may work at a relatively wide range of inlet
pressure.
5.2. Effect of the housing diameter on the cavitation
The housing diameter determines the size of the annulus
between the housing wall and the flapper surface and thus may
have a great effect on the cavitation characteristics of the
flapper-nozzle stage. In this work, three values of the housing
diameter are examined, i.e., 4 mm, 3.8 mm and 3.5 mm.
Fig. 10 presents the velocity contours of the flapper-nozzle
stage in case of Pin = 9 MPa and Xf0 = 0.1 mm. In the traditional
flapper-nozzle stage, with the decrease of the housing diameter,
the radial jet in the annulus becomes thicker and the velocity
decays more slowly. The swirling structures become visible at
Dc = 3.8 mm and 3.5 mm. This is apparently due to the reduced distance between the flapper surface and the housing wall. In the
impinging jet, a drop in the nozzle-to-plate distance could increase
the axial velocity and radial velocity near the plate [27,28]. In the
flapper-nozzle stage with the microjet, the radial jet is suppressed
and thus the impingement upon the housing wall vanishes at
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
1107
Fig. 10. Velocity contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different housing diameter (Pin = 9 MPa, Xf0 = 0.1 mm).
Dc = 4 mm. As Dc decreases to 3.5 mm, the radial jet velocity
remains unchanged in the slot, but rises in the annulus. However,
the jet impingement upon the housing wall is still absent.
The vapor fraction contours of the flapper-nozzle stage in case
of Pin = 9 MPa and Xf0 = 0.1 mm are shown in Fig. 11. Without the
microjet, cavitation forms in three regions at Dc = 4 mm. The cavitation in the annulus dominates the vapor fraction in the flappernozzle stage. As Dc reduces to 3.8 mm, the cavitation in the annulus
is enlarged and three cavitation regions are connected with each
other. At Dc = 3.5 mm, the cavitation is further enhanced. The right
half of the annulus is almost filled with the vapor. In the flappernozzle stage with the microjet, the area of the cavitation attached
to the flapper surface and the nozzle tip is reduced and the cavita-
tion in the annulus disappears at Dc = 4 mm. As the housing diameter decreases, the attached cavitation becomes more intensified,
and a weak cavitation is formed in the annulus from Dc = 3.8 mm.
In spite of this, the cavitation in the annulus is greatly reduced in
comparison with that of the traditional flapper-nozzle structure,
suggesting the effectiveness of the microjet on cavitation suppression in small housing diameter.
5.3. Effect of the null clearance on the cavitation
As the null clearance increases, mass flow rate of the radial jet
becomes larger, which may enhance flow cavitation in the
flapper-nozzle valve [15]. Thus, cavitation reduction by the micro-
Fig. 11. Vapor fraction contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different housing diameter (Pin = 9 MPa, Xf0 = 0.1 mm).
1108
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
Fig. 12. Velocity contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different null clearance (Pin = 10 MPa, Dc = 3.5 mm).
Fig. 13. Vapor fraction contours of the flapper-nozzle stage (a) without microjet and (b) with microjet at different null clearance (Pin = 10 MPa, Dc = 3.5 mm).
jet is required to be investigated under different null clearance. In
practical applications, the null clearance of the flapper-nozzle
structure is in the range of 0.03–0.13 mm [15,29]. In this work,
three values of the null clearance Xf0 examined are 0.05 mm,
0.08 mm and 0.1 mm.
Fig. 12 presents the velocity contours of the flapper-nozzle
stage in case of Pin = 10 MPa and Dc = 3.5 mm. In the traditional
flapper-nozzle stage, as Xf0 goes up, the radial jet velocity exhibits
a substantial growth, due to the increased mass flow rate. As a
result, the impingement upon the housing wall is enhanced and
the swirling structure is evident from Xf0 = 0.08 mm. Under the
effect of the microjet, the radial jet in the annulus is greatly suppressed, compared with that of the traditional flapper-nozzle
stage. At Xf0 = 0.05 mm, the radial jet is only discernable on the
flapper surface after moving out of the slot. As Xf0 rises to
0.1 mm, the radial jet in the annulus grows, but still not enough
to impinge upon the housing wall. This may benefit for the reduction of the impinging erosion on the housing wall.
Fig. 13 shows the vapor fraction contours of the flapper-nozzle
stage in case of Pin = 10 MPa and Dc = 3.5 mm. Without the microjet,
the cavitation occurs in the annulus, along with the curved surface
of the flapper and the nozzle tip. As Xf0 increases from 0.05 mm to
0.0.08 mm, the area of the vapor fraction in the annulus is extended,
suggesting an enhanced cavitation in this region. Further at
Xf0 = 0.1 mm, a weak cavitation can be observable in the left side
of the annulus. Thus, in the traditional flapper-nozzle stage, the
increasing null clearance mainly results in the enhancement of
the cavitation in the annulus. Once the microjet is deployed, the
attached cavitation on the nozzle tip is suppressed and the cavitation in the annulus is absent at Xf0 = 0.05 mm. With the increase
H. Yang et al. / International Journal of Heat and Mass Transfer 133 (2019) 1099–1109
of the null clearance, the attached cavitation is extended to the
inclined wall of the nozzle, probably due to the rising velocity in
this region (Fig. 12). Therefore, in contrast with the traditional
flapper-nozzle pilot stage, the rising null clearance in the pilot stage
with the microjet mainly contributes to the enlargement of the
attached cavitation, especially along the inclined wall of the nozzle.
Nevertheless, the total area of vapor fraction is still strongly
reduced by the microjet in the range of Xf0 = 0.05 0.1 mm.
6. Conclusions
In this work, a novel method is proposed to suppress the cavitation in the flapper-nozzle stage of a servo valve. Two microjets
are deployed symmetrically around the main jet of each nozzle.
Cavitation phenomenon with and without microjets are numerically compared in detail at different inlet pressure, chamber size
and null clearance. The flow visualization and mass flow rate measurements are carried out to validate the numerical simulation.
The following conclusions may be drawn from this work.
(1) The cavitation in the flapper-nozzle stage could be greatly
reduced under the effect of the microjets. The considerable
drop in the radial jet velocity leads to the suppression of
the impingement upon the housing wall and the swirling
structures in the annulus, which may be responsible for
the cavitation reduction.
(2) The inlet pressure has a substantial effect on the cavitation
in the traditional flapper-nozzle stage. The rising inlet pressure could lead to the remarkable enhancement of the flow
cavitation, due to the growth of the radial jet. Once the
microjet is introduced, with the increase of the inlet pressure, the cavitation on the flapper surface and nozzle wall
is slightly extended while the cavitation in the annulus
remains absent. This indicates that the continuous microjets
are still highly effective in reducing cavitation under high
inlet pressure.
(3) The cavitation exhibits a strong dependence on the housing
diameter. In the flapper-nozzle stage with and without the
microjets, the cavitation could be intensified by reducing
the housing diameter. This implies that the confined space
of the annulus is more beneficial for the generation of the
flow cavitation. In other words, increasing the housing diameter could contribute to the cavitation suppression.
(4) The null clearance exerts a distinct impact on the cavitation
behaviors in the flapper-nozzle stage with and without the
microjets. In the traditional flapper-nozzle stage, the
increased null clearance mainly results in the growth of
the cavitation in the annulus. In contrast, it mostly extends
the cavitation attached to the flapper surface and nozzle
tip for the flapper-nozzle stage with the microjets, especially
along the inclined wall of the nozzle. Nevertheless, cavitation reduction by the microjets is still notable at large null
clearance.
Acknowledgements
We wish to acknowledge the financial support for this work from
Zhejiang Provincial Natural Science Foundation of China under
grant No. LQ19E050013 and the Scientific Research Startup Fund
of Hangzhou Dianzi University under grant No. KYS015618005.
Conflict of interest
The authors declare no conflict of interest.
1109
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at https://doi.org/10.1016/j.ijheatmasstransfer.
2019.01.008.
References
[1] P. Tamburrano, A.R. Plummer, E. Distaso, R. Amirante, A review of electrohydraulic servovalve research and development, Int. J. Fluid Pow. (2018) 1–23.
[2] N.Z. Aung, S. Li, A numerical study of cavitation phenomenon in a flappernozzle pilot stage of an electrohydraulic servo-valve with an innovative flapper
shape, Energ. Convers. Manage. 77 (2014) 31–39.
[3] L. Li, H. Yan, H. Zhang, J. Li, Numerical simulation and experimental research of
the flow force and forced vibration in the nozzle-flapper valve, Mech. Syst.
Signal Pr. 99 (2018) 550–566.
_
[4] E. Lisowski, W. Czyzycki,
J. Rajda, Three dimensional CFD analysis and
experimental test of flow force acting on the spool of solenoid operated
directional control valve, Energ. Convers. Manage. 70 (2013) 220–229.
[5] Y. Ye, C. Yin, X. Li, W. Zhou, F. Yuan, Effects of groove shape of notch on the flow
characteristics of spool valve, Energ. Convers. Manage. 86 (2014) 1091–1101.
[6] J.M. Mchenya, S. Zhang, S. Li, A study of flow-field distribution between the
flapper and nozzle in a hydraulic servo-valve, in: Proc. 2011 Int. Conf. Fluid
Power Mechatronics, 2011, pp. 658–662.
[7] X. Pan, G. Wang, Z. Lu, Flow field simulation and a flow model of servo-valve
spool valve orifice, Energ. Convers. Manage. 52 (10) (2011) 3249–3256.
[8] E. Lisowski, G. Filo, CFD analysis of the characteristics of a proportional flow
control valve with an innovative opening shape, Energ. Convers. Manage. 123
(2016) 15–28.
[9] R. Amirante, E. Distaso, P. Tamburrano, Experimental and numerical analysis of
cavitation in hydraulic proportional directional valves, Energ. Convers.
Manage. 87 (2014) 208–219.
[10] J. Zou, X. Fu, X.W. Du, X.D. Ruan, H. Ji, S. Ryu, M. Ochiai, Cavitation in a noncircular opening spool valve with U-grooves, P. I. Mech. Eng. A J. Pow. Energ.
222 (4) (2008) 413–420.
[11] J. Liang, X. Luo, Y. Liu, X. Li, T. Shi, A numerical investigation in effects of inlet
pressure fluctuations on the flow and cavitation characteristics inside water
hydraulic poppet valves, Int. J. Heat Mass Tran. 103 (2016) 684–700.
[12] M. Han, Y. Liu, D. Wu, X. Zhao, H. Tan, A numerical investigation in
characteristics of flow force under cavitation state inside the water
hydraulic poppet valves, Int. J. Heat Mass Tran. 111 (2017) 1–16.
[13] W.L. Lim, Y.T. Chew, H.T. Low, W.L. Foo, Cavitation phenomena in mechanical
heart valves: the role of squeeze flow velocity and contact area on cavitation
initiation between two impinging rods, J. Biomech. 36 (9) (2003) 1269–1280.
[14] S. Li, N.Z. Aung, S. Zhang, J. Cao, X. Xue, Experimental and numerical
investigation of cavitation phenomenon in flapper-nozzle pilot stage of an
electrohydraulic servo-valve, Comput. Fluids 88 (2013) 590–598.
[15] Q. Yang, N.Z. Aung, S. Li, Confirmation on the effectiveness of rectangle-shaped
flapper in reducing cavitation in flapper-nozzle pilot valve, Energ. Convers.
Manage. 98 (2015) 184–198.
[16] H. Yang, Y. Zhou, Axisymmetric jet manipulated using two unsteady minijets,
J. Fluid Mech. 808 (2016) 362–396.
[17] L.N. Cattafesta, M. Sheplak, Actuators for active flow control, Annu. Rev. Fluid
Mech. 43 (1) (2011) 247–272.
[18] N.Z. Aung, Q. Yang, M. Chen, S. Li, CFD analysis of flow forces and energy loss
characteristics in a flapper-nozzle pilot valve with different null clearances,
Energ. Convers. Manage. 83 (2014) 284–295.
[19] S. Zhang, N.Z. Aung, S. Li, Reduction of undesired lateral forces acting on the
flapper of a flapper-nozzle pilot valve by using an innovative flapper shape,
Energ. Convers. Manage. 106 (2015) 835–848.
[20] T. Du, Y. Wang, L. Liao, C. Huang, A numerical model for the evolution of
internal structure of cavitation cloud, Phys. Fluids 28 (7) (2016) 77103.
[21] A.K. Singhal, M.M. Athavale, H. Li, Y. Jiang, Mathematical basis and validation
of the full cavitation model, J. Fluids Eng. 124 (3) (2002) 617–624.
[22] S. Zhang, S. Li, Cavity shedding dynamics in a flapper-nozzle pilot stage of an
electro-hydraulic servo-valve: experiments and numerical study, Energ.
Convers. Manage. 100 (2015) 370–379.
[23] K. Jambunathan, E. Lai, M.A. Moss, B.L. Button, A review of heat transfer data
for single circular jet impingement, Int. J. Heat Fluid Fl. 13 (2) (1992) 106–115.
[24] T. Qiu, X. Song, Y. Lei, X. Liu, X. An, M. Lai, Influence of inlet pressure on
cavitation flow in diesel nozzle, Appl. Therm. Eng. 109 (2016) 364–372.
[25] P.A. Brandner, B.W. Pearce, K.L. de Graaf, Cavitation about a jet in crossflow, J.
Fluid Mech. 768 (2015) 141–174.
[26] R.E.A. Arndt, Cavitation in Fluid Machinery and Hydraulic Structures, Annu.
Rev. Fluid Mech. 13 (1) (1981) 273–326.
[27] T.S. O’Donovan, D.B. Murray, Jet impingement heat transfer-Part I: mean and
root-mean-square heat transfer and velocity distributions, Int. J. Heat Mass
Tran. 50 (17) (2007) 3291–3301.
[28] J.A. Fitzgerald, S.V. Garimella, A study of the flow field of a confined and
submerged impinging jet, Int. J. Heat Mass Tran. 41 (8) (1998) 1025–1034.
[29] J. Watton, Fundamentals of fluid power control, Cambridge University Press,
New York, 2009.