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Dynamic simulation of swing check valve
Article · January 2012
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Dynamic simulation of swing check valve
F Selimovic, M Polster, M Stähle
TUV NORD Sweden AB
NOMENCLATURE
a
Adisk
Ator
Ats
C
Cv
CHS
CHR
Fn
Feff
Ff
K
Kloc
LX
pdyn
ploc
Re
Re
T
Tf
v
vdisk
vrel
vRmax
v0
Yeff
We
Speed of sound [m/s]
Disk area [m2]
Total surface area of torus Ator=2 _LDk [m2]
Surface torus section Ats= Ator *( - min)/360 [m2]
Discharge coefficient [-]
Flow coefficient [-]
Non-dimensional factor for static torque [-]
Non-dimensional factor for dynamic (rotational)
Torque [-]
Normal force Fn = Fhyd * cos( )
Effective force [N]
Force factor [-]
Total pressure loss factor [-]
Local pressure loss factor [-]
Calculated lever arm LX = T/Fnormal [m]
Dynamic pressure [Pa]
Local pressure loss (across the disk) [Pa]
Reynolds number [-]
Reynolds number [-]
Torque (total torque) [Nm]
Non-dimensional torque coefficient [-]
Fluid velocity (usually related to seat velocity) [m/s]
Disk velocity vdisk=L* *cos( ) [m/s]
Relative velocity vrel = v-vdisk [m/s]
Maximum reverse velocity [m/s]
Critical flow velocity [m/s]
Specific energy loss [m2/s2]
Weight of the disk [kg m/s2]
Flow factor [-]
Offset , distance of hydraulic force acting point tothe center of the disk,
LX-L [m]
Density of water [kg/m3]
Angular velocity of disk w=d /dt [rad]
© BHR Group 2012 Pressure Surges 11
=
381
1
INTRODUCTION
Water hammer is an important load in many pipe systems, for example, in the process
industry, district heating and power generation plants. It is a pressure surge or wave
resulting when a fluid in motion is forced to stop or change direction. If pressure surge
are induced by check valve they could result in pressure peaks and oscillations causing
fatigue damages and could lead to pipe break and support deformation. Check valves
should close so that the amount of fluid flowing to wrong direction is as small as
possible.
There are different types of check valves: swing, lift, tilting disk, duo/double disk, stop
and nozzle. But most common because of its simple design, low pressure drop, price and
wide range of sizes are Swing Check Valves (SCV). Unfortunately, information about
the SCV:s characteristic is usually limited. This makes it difficult to perform precise
calculations of the pressure and forces caused by the water hammer. Hence, safety factors
should be used if the valve characteristic is not known which can lead to oversize of the
entire system.
One difficulty with describing check valves lies in the fact that the characteristics depend
on the circumstances as the pressure drop across the disk is depending on its speed. It is
relatively easy to produce a loss characteristic for a stationary disk, but because of the
fact that the disk movement is dependent on the pressure loss across it, there is no
definition for a general loss characteristic. Sometimes a process engineer could face the
fact that there is not any specification given of the loss characteristics regarding
stationary disk. Instead, a curve from a similar valve is used. When there is no
sufficiently similarity between valves with known and unknown characteristic two
alternatives could be the solution. One is to perform experiments with a fixed disk, which
is quite expensive and often difficult. The second is using three-dimensional flow
calculations, Computational Fluid Dynamics (CFD), producing a curve for a stationary
disk. This is also a quite expensive alternative, but quite common today in industry.
In this work a CFD tool was applied to analyse the flow field with the objective of
investigating the pressure drop over the disk and calculating the hydraulic force acting on
the disk. These investigations were performed for both stationary and moving disk.
Moving disk simulations give better understanding of the closing sequence which when
transferred to a one dimensional model can predict forces more close to reality.
The goal of this work is to perform three-dimensional flow calculations with CFD tool
FLUENT, Ref [7] for both a stationary and movable disk. A one dimensional pressure
surge tool (in house coded) has been applied for water hammer calculations with more
than 30 years of experience and verifications by field tests. The results of this work
expect to give improvements for a SCV model when integrated into in house code. The
results are also compared with measured and calculated results from the literature.
2
SWING CHECK VALVE
The motion of the valve disk can be described by Newton’s second law, an angular
momentum conservation law. The momentum conservation equation can be traditionally
written as:
(1)
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Where represents disk angle positive counterclockwise, Fig 1. The torque components
in the right side of equation (1) summarizes all the torques involved and regarding the
flow direction as in Figure 1, can further be written as:
(2)
Where
is the hydrodynamic torque,
is the torque because of weight. The weight
of moved parts is corrected by the buoyancy force of steel mass in the fluid. Additionally
one should add a torque because of friction axis. The friction torque stands for the
friction of the lever arm at the axis of rotation. It is the sum of a steady friction and a
moving friction. Typically this value is negligible comparing the other values for the total
torque and we are not taking it into account here.
Fig. 1: Schematic of swing check valve
Left side of the Eq. (1) and (2) terms the total moment of inertia: I, the moment of inertia
of the disk assembly with respect to the valve shaft axis. If an external weight is applied
on a valve then additional term for torque and inertia in Eq. (2) should be added. This
was not subject in this work. In the dynamic CFD simulation the hydraulic torque
comprises also an acceleration part which is object of the added mass model. Therefore
no added mass must be introduced into the moment of inertia in CFD simulation. Further
the hydraulic torque is defined by:
(3)
The difference in the pressure
is given by:
(4)
The relative velocity vrel , Fig. 1, follows from:
(5)
where
. We introduced the relative velocity on the bases of a field test of pump
stops during 1980.
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383
During valve closure the velocity of the disk is negative, see Figure 1. Therefore the
relative velocity in a closing swing check valve is always greater than the fluid velocity
in the seat, Eq. 5. Near the end of the valve closure the disk velocity becomes really high.
Therefore in some cases backflow exists but in most applications the flow in the gap is
positive. Consequently loss factors for backflow are not evaluated here. Reliable K
values as function of the valve angle were in the past difficult to find in the literature
but nowadays measured values over the complete valve are available. Because of the lack
of local loss factors at the disk the published values are applied conservatively to
calculate the pressure loss over it.
It is quite common to refer to the velocity to the seat area. Sometimes the velocity is
referred to the gap area, e.g. DRAKO- Ref [8], and RELAP5, Ref [9], models.
The impingement of the flow jet on the valve disk may result in an inclination of the
resulting force acting on the disk. Here the total hydraulic force acting on the disk is:
(6)
Where Fx and Fy act in x-and y-direction, Fig.2
Fig. 2: Geometrical definitions for some parameters used in modelling
In Figure 2, following parameters are listed:
Deviation angle of hydraulic force from the normal,
Offset , The distance of hydraulic forces acting point to the centre of the disk,
= LX-L.
Calculated lever arm LX, is calculated by LX = Thyd/Fn , where Fn is given by:
3
SIMULATION AND RESULTS
KSB swing check valve Staal40 AKKS DN400 PN40 has been selected in such purpose
that large diameter makes it easier to perform grid generation and also increase reverse
velocity at higher velocity gradients, Ref [1]. Valve data for simulations can be found in
Table 1.
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Tab 1: Valve data used for the simulations, (see Fig. 1)
Parameter
Geometrical lever arm L or e1
Excentricity e2
Radius to center of gravity, Rg
Angle of Rg to lever arm
Minimal valve angle o
Maximal valve ange max
Diameter of disk, Dd
Inner diameter of pipe, Di
Moved mass of disk
Moment of inertia
Disk area Adisk
Seat area As
Total surface Area of torus, Ator
Value [unit]
266.26[mm]
17.280 [mm]
247.3 [mm]
4.0 [°]
2.51 [°]
60.0 [°]
410.0 [mm]
378.0 [mm]
46.66 [kg]
2.987 [kgm²]
0.1322832 [m²]
0.11222083 [m²]
2.1569646 [m²]
3.1
Simulation and results of stationary disk
The simulation has been performed for the opening angels from 8° to 60°. The geometry
is based on the KSB valve and consists of a halve model of the valve and the pipes. The
diameter of the pipes is 0.378 m and the length is 4.7 m in front and behind the valve.
Further measures could be taken from the drawings by KSB.
The simulation with an initial
mesh which then was refined in
several steps until the values for
the pressure, the forces and
moments at the disk are not
changed The areas where the
grid
was
refined
were
characterized by high velocity
gradients or pressure gradients.
The initial mesh has 651373
cells, the final mesh for this case
has 2 285200 cells. In both cases
the mesh consists of tetraeder
Fig. 3: Geometry of the valve
and hexaeder cells. Around the
disk a special layer with hexaeder cells was applied. This layer has a thickness of 0.007
m and contains in the initial mesh two layers of hexaeders. The cell height is about
0.0035 m the spatial resolution is about 0.006 m.
Stationary simulation set-up:
Density: 995.71 kg/m³, Viscosity: 0.000797022 kg/m
Inlet mass flow-rate: 110 kg/s (~1.97m/s), Pressure-outlet: 135000 Pa
Wall: no slip, Turbulence model: k-e realizable with Standard Wall Functions
The pressure at the position 5D (five diameters), is applied for pressure loss evaluation.
The direction of hydraulic force deviates from the normal to the disk by an angle .The
calculated or actual lever arm of the hydraulic force is represented by Lx which is
displaced to the centre of the disk and is calculated by:
(7)
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385
Deviation Angle
of the Hydraulic Force Fhyd to the Normal of the Flap
10
20
12
Deviation Angle (°)
10
8
6
4
2
0
0
30
40
50
60
Valve Angle (°)
Fig. 4: The deviation angle delta of the hydraulic force of the opened valve deviates
from the normal to the disk by about 12° and decreases to negligible values for
less than 30°
In the partly opened valve, 30° to 60°, the actual lever arm of the hydraulic force exceeds
the geometrical lever arm up to 8,5%. The negative offset between about 15° and 30 °
means that the actual lever arm of the hydraulic force becomes shorter than the
geometrical lever arm.
Offset
, Distance of the Acting Point of the Hydraulic Force to the Centre of Flap
25
20
Offset (mm)
15
10
5
0
0
10
20
30
40
-5
Valve Angle (°)
Fig 5: The offset of the hydraulic force
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50
60
Static Hydraulic Torque Trq (Nm)
10000
Torque (Nm)
1000
100
10
0
10
20
30
40
50
60
Valve Angle (°)
Fig 6: Hydraulic torque at different valve angles
The fluid velocity in the seat is kept constant to 1.97 m/s in the simulation and is lower
than the critical velocity, which is needed to fully open the SCV which in the actual
application is about 2.45 m/s.
The hydraulic torque results from the local pressure loss at the disk:
(8)
Inversely the local pressure loss is calculated with the knowledge of the hydraulic torque
as result of FLUENT simulation and herewith the local loss factor referred to the fluid
velocity in the seat can be evaluated:
(9)
For general use the pressure loss factor K is often transformed to the flow coefficient Cv
which is unlimited for low K therefore it seems preferable to transfer K to the so called
flow factor alpha defined by:
(10)
which is limited between 0.0 and 1.0.
The force normal to the disk Fn differs slightly from the value of the hydraulic force Fhyd,
Fig. 7 which is a result of the simulation. Following to Ref [2] and [5], an effective force
Feff acting normal to the disk center was introduced:
(11)
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387
A nondimensional force factor Ff is defined by:
(12)
with
(13)
Forces: Hydraulic , Normal and Effectiv
Fhyd
Fnormal
Feff
700
600
500
400
300
200
100
0
30
35
40
45
50
55
60
Valve Angle (°)
Fig 7: Hydraulic force, normal force and effective force as function
of the valve angle
With the knowledge of the force factor Ff , Fig. 8, and the local loss factor Kloc the static
hydraulic torque for some other swing check valves follows in static simulations from:
(14)
With this definition the effects of the offset of the acting point as well the deviation from
the normal direction of the hydraulic force are included.
This definition differs to the non-dimensional torque coefficient introduced by Ref [2]
and [5]:
(15)
A different non-dimensional factor for the static torque was introduced by Ref [3] with:
(16)
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Static Force Factor Ffac
1
0.9
Force Factor (_)
0.8
0.7
0.6
0.5
0.4
0
10
20
30
40
50
60
50
60
Valve Angle (°)
Fig 8: Force factor at different valve angles
Flow Number Alfa local at Disc and total at 5D / Static Simulation
alfa-5D
alfa-loc
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
Valve Angle (°)
Fig 9: Local and total flow number alpha ( ) for different valve angles, (K=1/ ²-1)
The effect of higher losses in the partly opened valve can be seen in the growing gap of
the alpha numbers for local and total losses.
Tuerk, Ref [4] performed static measurement of pressure loss at a variety of swing check
valves of different diameter including reverse flow. The presented characteristic is made
up of mean values, Fig.10. Remarkable in work of Tuerk is the lower pressure loss
(higher alpha number) for low valve opening.
The simulated KSB valve differs in its design constructively to the Westark, Ref [6]
valve at the outlet. The difference between both valves is reduced for low valve angles,
Fig. 10.
© BHR Group 2012 Pressure Surges 11
389
Flow Number ALFA [=1/SQRT(1+K)]
Tuerk
alfa-loc_static
Westark
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Valve Lift normed (-)
Fig 10: Flow number alpha at normalized valve lift
3.2
Simulation and results for moving disk
The simulations with the moving disk have used the dynamic mesh functionality of
FLUENT. The initial mesh consists of 1535371 cells. It was not possible to keep the
hexaeder cells inside the layer around the disk. For the transitions from hexaeder cells to
tetraeder cells a layer of pyramids is needed. But unfortunately the dynamic mesh
functionality does not work with these pyramids. So the layer around the disk is meshed
with tetraeder cells (cell size: 0.0035m) as well. For a stationary case it was tested if
there is any influence of the cell type on the results for pressure, forces and moments on
the disk. It could be shown that for the used resolution the effect is negligible.
Transient simulation set-up:
Turbulence model: the same as for the stationary simulation.
Boundary conditions: inlet velocity decreasing linearly, Outlet: pressureat 135000 Pa fix.
Wall: no slip: Symmetry: half
A set of simulations was performed which differ in the inlet-velocity and the angularvelocity of the disk. The angular-velocity of the disk was kept constant respectively
depending on the acting forces and moments. The initial inlet-velocity was increased to
2.75 m/s compared to 2.0 m/s in the stationary simulations in purpose to start with a
stable disk position.
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Fig. 11: Mesh for the dynamic simulations after 1.48s (10.4°), 1228590 cells
Valve Angle and Angular Velocity
fi (°)
omega [1/s]
70
0
60
-0.2
50
-0.4
40
-0.6
30
-0.8
20
-1
10
-1.2
0
-1.4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time (s)
Fig. 12: Valve angle and angular velocity,
For the simulation of valve closure accelerated by own weight, a mean inlet velocity in
time was: v = 2.75 – 2*t m/s. The valve angle together with the angular velocity is shown
over time in Fig. 12. The simulation stopped at about 6 ° because of numerical grid
problems (the minimum valve angle is 2.51 °). The valve closure starts at a fluid velocity
of about 2.45 m/s when the weight torque exceeds the hydraulic torque. Remarkable is
the gradient of the angular velocity which shows acceleration at the begin and
deceleration near the end of the valve closure. The numerical derivation of the angular
velocity, Fig 13 shows two inflection points. The first inflection point at about 0.247 s
and nearly still 60 ° opening angle can probably be explained by an adjustment of the
growing dynamic friction. From Fig. 13 it could be seen that the added mass effect,
assumed as proportional to the acceleration, increases considerably at starting of the
© BHR Group 2012 Pressure Surges 11
391
valve closure and decreases remarkably towards the end of the valve closure. But in the
very last closure phase with a negative hydraulic torque a repeated increase of the added
mass effect is occurring.
Angular Velocity and Numerical Derivation together with Trendline
dom/dt
omega [1/s]
Polynomisch (dom/dt)
0
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
-1
-1.2
-1.2
-1.4
-1.4
-1.6
-1.6
time (s)
Fig. 13: Angular velocity and numerical its derivation together with trend line
Torque, Fluid Velocity in Seat and Relative Velocity between Flap and Fluid
V (m/s)
Vrel (m/s)
Torque
3
140
2.5
120
2
100
1.5
80
1
60
0.5
40
0
20
0
10
20
30
40
50
60
-0.5
0
Valve Angle (°)
Fig. 14: Hydraulic torque, fluid velocity in seat and relative velocity
The mean velocity in the seat becomes negative below 18°,Fig 14 but the hydraulic
torque is still positive. This effect is explained by the still positive relative velocity
between fluid and disc. The contour plot, Fig. 15 of the total pressure for a valve angle of
10.4° shows qualitatively a higher pressure backward than forward of the disk. The still
positive pressure difference over the disk is responsible for a positive torque for the
global back flow situation. The relative velocity comprises a mean velocity value of the
disk only i.e. the inner end of the disk (near the axle) moves slower than the outer end of
the disk. The definition of the relative velocity refers to the velocity of the centre of the
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© BHR Group 2012 Pressure Surges 11
disk. A more sophisticated definition is conceivable but the application of the relative
velocity as actually defined rendered good conformity with measured values in field tests
in the past.
Fig. 15: The contour plot of the total pressure for a valve angle of 10.4 °
(7.8 ° opening angle)
The loss factor at the disk, Fig. 16 demonstrates once more the relevance of usage of the
relative velocity definition. Beginning at about 18 ° the velocity in the seat becomes
negative whereas the relative velocity is still positive.
Local Loss Factor K as Function of the Velocity in the Seat and of the Relative Velocity
K-loc
Kloc_Vrel/dyn
100000
10000
Loss Factor (-)
1000
100
10
1
0
10
20
30
40
50
60
0.1
Valve Angle (°)
Fig. 16: Local loss factor and relative velocity as function of valve angle
© BHR Group 2012 Pressure Surges 11
393
The alpha-numbers of the static and dynamic local losses reveals a difference of both
values, Fig.17. Dynamic hydraulic effects are being responsible for the higher losses in
the dynamic case. For the fully opened valve at 60 ° the disc is at rest and the losses are
nearly conforming.
Flow number of Alfa / Static and Dynamic Simulation
alfa-loc_Vrel
alfa-loc_static
0.8
0.7
0.6
Alfa (-)
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
Valve Angle (°)
Fig. 17: Flow number (alpha) for static and dynamic simulations
Deviation of Hydraulic Force / Dynamic and Static Simulation Results
deviation (°)
deviation-static
11
9
7
Deviation (°)
5
3
1
-1 0
10
20
30
40
50
60
-3
-5
-7
Valve Angle (°)
Fig. 18: Deviation of hydraulic force to the normal of the disk
(dynamic vs. static simulations)
The deviation, Fig. 18 and deflection, Fig 19 of the hydraulic force become also modified
in the dynamic valve closure. The deviation of the hydraulic force falls fast down and
becomes negative below a valve angle of about 37 °. In the stationary disk case the
deviation tends to zero but does not become negative.
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Offset of Hydraulic Force / Static and Dynamic Simulation
Offset (mm)
offsetstatic
25
20
Offset (mm)
15
10
5
0
0
10
20
30
40
50
60
-5
-10
Valve Angle (°)
Fig. 19: Offset of hydraulic force (dynamic vs. static simulations)
In the dynamic case the offset is always positive and varies between 4 % and 8.7 %. The
offset falls down to a relative minimum at about 35 ° and grows versus 10 °. In the static
case the deviation starts for the open valve at the same value and becomes negative
beyond 31 °.
The force factor Ff differs for static and dynamic simulations. The difference reveals
once more the remarkable influence of the valve motion. The non-dimensional factors
derived from static analyses cannot be applied to dynamic analyses without
modifications. The increased drag and dynamic hydraulic torque together with the altered
deviation and offset of the forces also a variable added mass and possibly further other
effects are responsible for the non applicability of the force factor in the dynamic case as
demonstrated by Fig. 20.
Force Factor Ffac / Static and Dynamic simulation
Ffac_Vr-dynamic
Ffac/static
30
40
1
Force factor Ffac (-)
0.9
0.8
0.7
0.6
0.5
0.4
0
10
20
50
60
Valve Angle (°)
Fig. 20: Force factor (static vs. dynamic simulations)
© BHR Group 2012 Pressure Surges 11
395
Li and Liou, 2003, Ref [3] have split up the hydraulic force into two parts: a static
hydraulic torque :
THS= CHS *Adisc*L*0.5* *V² (see Eq. 16) and a rotational hydraulic torque :
THR =CHR *Adisc*L* 0.5* *(L* )².
From the dynamic CFD simulation follows the total dynamic hydraulic torque. The
difference of the total hydraulic torque and the static hydraulic torque was formed to
evaluate the factor CHR. All three variables are shown in Fig. 21. The rotational
hydraulic coefficient CHR becomes really high for the starting closure of the disc and
tends to low values near the end of valve closure where the difference Tdiff tends to zero.
Rotational Hydraulic Torque Coefficient, Total Hydraulic Torque and Difference
to Static Hydraulic Torque
CHR
Torque-dyn
Tdiff
250
120
80
CHR (-)
150
60
100
40
50
Torque / Torq diff (Nm)
100
200
20
0
0
0
10
20
30
40
50
60
Valve Angle (°)
Fig 21: Rotational hydraulic coefficient CHR, total dynamic hydraulic torque
Torque-dyn and the difference Tdiff to the static hydraulic torque
CONCLUSIONS
The application of the CFD-simulation results to the simulation of a swing check valve in
1D flow simulation with finite difference methods is quite straight forward by solving the
equation of movement Eq.(1). The transient fluid velocity at the entry to the valve
follows from the fluid code. With the force factor Ff, Eq. (12) follows the effective force
Feff and further with Eq. (11) directly the hydraulic torque to the disk.
The force factor Ff as well the loss factor Kloc are evaluated by this CFD simulation for
steady flow and also for a transient flow with an gradient of 2.0 (m/s²) of the inlet
velocity. These results are transferable to other geometries as the parameters are nondimensional. Conclusions can further been summarized into following:
1. The known effects of deviation and offset of the hydraulic forces acting onto the
disc of a SCV valve are quantified for a static application. The modification of
these effects in the dynamic case is demonstrated.
2. A non dimensional force factor applicable to the static one dimensional simulation
of related SCV is quantified. On the bases of the force factor the critical velocity
which is needed to fully open the SCV can be worked out reliably.
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© BHR Group 2012 Pressure Surges 11
3. The static loss characteristic of a SCV can be evaluated by CFD in a reliable
manner. The characteristic becomes modified in dynamic case.
4. The dynamic simulation of a SCV requires counting of the relative motions of the
fluid and the disc. A simple model of the relative velocity is approved since
longtime. In the very last closure phase of the disc the applied model seem to
become inaccurate.
5. The acceleration of the angular velocity of the valve disc which counts for the
added mass revealed as nonlinear function. It grows rapidly to the start of the valve
movement and tends to damp out before the end of the closure.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Provoost, G. A. (1983). A Critical Analysis to Determine Dynamic Characteristics
of Non-Return Valves. 4th International Conference on Pressure Surges, (ss. 275286). University of Bath, England.
Gronenberg.
Untersuchung
des
dynamischen
Verhaltens
vun
Ruckflussverhinderern unterschiedlicher Bauart. Stuttgart: Institut fur
Hydraulische Strömungsmaschinen, 1990.
Liou, G. L. (2003 Vol.125). Swing Check Valve Characterization and Modeling
During Transients. Journal of Fluids Engineering , 1043-1050.
Tuerk, K, Stroemungstechnische Untersuchung an Rueckschlagklappen Technische
Information Armaturen Magdeburg 25, 1990
Csemniczky, J. Hydraulic Invetigations of the Check Valves and Butterfly Valves.
Proc. of the 4th Conf. on Fluid Mech., Budapest, 1972
Westark-GmbH Armaturenfabrik, D-4620 Castrop-Rauxel
FLUENT, CFD code ANSYS FLUENT, Release 13.0, ANSYS, Inc., 2010.
DRAKO Pressure Wave Calculation in Pipe Systems Software, KAE Kraftwerks& Anlagen- Engineering
RELAP5 Thermal-hydraulic safety analysis software developed by Idaho National
Engineering Laboratory
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