Using Computational Fluid Dynamics to
Predict the Onset of Cavitation (xFz)
Presenter:
Alan H. Glenn
Academic Education and Degrees:
1987 Doctoral Thesis on Eliminating Screech in Control Valves,
Brigham Young University, Provo, Utah
Present Position: Principal Engineer at Flowserve Corporation—
Flow Control Division
Associate Author:
Gifford Decker
Academic Education and Degrees:
2006 Masters Degree in Mechanical Engineering,
Brigham Young University, Provo, Utah
Present Position: Staff Engineer at Flowserve Corporation—
Flow Control Division
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
Using Computational Fluid Dynamics to
Predict the Onset of Cavitation (xFz)
Alan H. Glenn, Gifford Z. Decker, FLOWSERVE FCD Valtek Control Products
Keywords: cavitation, computational fluid dynamics, CFD, xFz, vapor pressure,
shear zone, vortices
1 Abstract
Computational Fluid Dynamics (CFD) has been used extensively to
successfully model fluid flow in other fields, such as aerospace and pump design.
It has not been used as much to model the very complex flow through valves. In
this study, however, a high end CFD tool was used to numerically predict the
point of incipient cavitation in several complex valve configurations.
Flow conditions at the point of incipient cavitation are used to determine
the characteristic pressure ratio, xFz, a parameter necessary for predicting
hydrodynamic noise in control valves using the international hydrodynamic noise
prediction standard, IEC60534-8-4. In the past, accurate values for xFz could
only be found from expensive and time consuming tests, which were often not
feasible, especially for large valves. Using CFD analysis to accurately predict the
flow conditions where cavitation begins could greatly decrease the cost of
obtaining accurate values for xFz.
In this study, values for xFz were found using several separate geometries
and conditions where cavitation would be present. The value of xFz was taken as
the value of the ratio (p1-p2)/(p1-pv), where p1 and p2 are the valve upstream and
downstream pressures respectively and pv is the fluid vapor pressure, at the
conditions where the lowest value for static pressure minus dynamic pressure,
anywhere in the flow field, equaled the vapor pressure, pv. The CFD analyses
predicted values for xFz, using this method, which agreed with the values
determined from testing.
This paper briefly explains cavitation and its effect on hydrodynamic noise,
the approach used to predict xFz using CFD methods, and the results obtained
using these numerical methods. Finally, it shows the comparison between the
CFD and test results, from tests performed on the same valve geometries, to
validate the CFD predictions.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
2 Introduction
Cavitation in liquid flow through control valves is a serious problem; it can
cause severe damage to the valve and make it unusable and it can be the source
of unacceptably-high sound pressure levels. Cavitation results from a two step
process that can occur in a control valve if the pressure drop is high enough
relative to the difference between the upstream pressure and the vapor pressure.
First, the pressure in the liquid drops to a value below the vapor pressure and
vapor bubbles form in localized regions near or downstream of a restriction in the
valve. Then, further downstream, the fluid pressure recovers or increases to a
pressure above the vapor pressure and the vapor bubbles suddenly collapse.
The violent collapse of the bubbles creates pressure pulses that result in
significant noise and, if close to a material surface, can cause damage to the
material.
Cavitation is a very complex phenomenon that has defied precise
prediction by analytical methods. However, with more advanced computer
systems and better fluid analytical models, progress has been made to the point
where computational fluid dynamics (CFD) can be used to predict some useful
information relative to cavitation. This may reduce the amount of testing needed
to find the parameters required to predict the noise and, perhaps, to determine
the conditions where cavitation can be damaging. This paper discusses CFD
analysis methods recently developed that were used to determine the
approximate characteristic pressure ratio, xFZ, (the point of incipient cavitation) a
key parameter needed to accurately calculate the sound pressure level of a
control valve in liquid service. The methods are described and compared with
results from testing.
3 Cavitation noise
The noise produced by liquid flow is relatively low until the pressure drop
is high enough that cavitation begins. Fig. 1 below is a typical plot of the sound
pressure level, Lp, versus the differential pressure ratio, xF. The parameter xF is
a ratio of the pressure drop across the valve divided by the pressure difference
(p1 – pv) where p1 is the upstream pressure and pv is the vapor pressure of the
liquid at the upstream temperature. When the pressure drop is very low, and xF
is low, there is no cavitation and the sound pressure level is low. As xF
increases, Lp increases gradually until the point where cavitation just begins.
The value of xF at this point is called the characteristic pressure ratio and
designated as xFz. In the plot below, the region with no cavitation goes from xF =
0 to xF = xFz = 0.57. Once cavitation begins, the sound pressure level increases
very rapidly as xF increases. The international hydrodynamic noise prediction
standard IEC 60534-8-4, requires an accurate value of xFz to predict
hydrodynamic noise. It is one of the few parameters required by the standard
that cannot be easily determined by just knowing the valve geometry and service
conditions. In the past, it could only be determined experimentally but this paper
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
presents a method of calculating it by CFD analysis that was found to be
reasonably accurate for the rotary and linear valves and for the severe service
valve trims analyzed.
Lp vs. xF
Anti-cavitation Trim AC4
75
70
65
Lp (dB(A))
60
55
50
xFz = 0.57
45
40
35
30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
xF (=(p1-p2)/(p1-pv))
Fig. 1: Sound pressure level, Lp, versus xF for anti-cavitation trim tested,
designated as “AC4”, showing value of xFz (i.e. point of incipient cavitation).
4 CFD Analysis Setup and Assumptions
4.1 Introduction
The CFD analyses were set up by applying a constant pressure at the inlet of the
geometry and a time varying pressure at the outlet. The assumption of symmetry
was used to reduce the size of the models whenever possible. Fig. 2 below
shows a geometry (segmented ball valve) that was used in the CFD analyses to
illustrate how the boundary conditions were applied.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
Symmetry Applied
At Half Plane
Outlet Boundary
Time Variant Pressure
Inlet Boundary
Constant Pressure
Flow Direction
Fig. 2 Geometry of one of the valves used in the CFD analyses with the
boundary conditions illustrated.
The flow was modeled as turbulent flow using the Reynolds Averaged NavierStokes (RANS) k-ε turbulence model. Any boundary layers were modeled by
implementing a wall treatment. Traditional CFD turbulent flow models, like the kε model, implement wall treatments in the boundary layer, such as the log law,
which assume that the boundary layer effects (turbulent vortices) are represented
well enough by relationships from empirical data for averaged values of velocity
and pressure. Other models such as Large Eddy Simulation (LES) or Detached
Eddy Simulation (DES) attempt to model the actual vortices inside the boundary
layer, but require a very fine mesh in the boundary layer. The cost of
computation for LES and DES is still not practical for everyday engineering
problems. Two models for analyzing the pressure field for comparison to the
vapor pressure and the onset of cavitation were developed. It was anticipated
that the values for xFz predicted by these two models would encompass the true
xFz (found by testing). These models are described in more detail below.
4.2 Calculated Pressure Model
The calculated pressure model refers to the pressure calculation based on the
traditional pressure result obtained from solving the k-ε model. Therefore, the
model predicts cavitation when the pressure in a finite volume cell is less than
the vapor pressure: cavitation occurs if pcell < pv (where pcell is the volume cell
pressure, and pv is the vapor pressure of the fluid) [1]. This model works well
when the cavitation results from large flow effects in the free stream. However,
when the cavitation is mostly occurring due to localized low pressures in
individual vortices of highly turbulent flow generated in the shear zone (i.e. the
boundary layer or separated flow region) the calculated pressure field model is
inadequate, due to the inability to accurately and easily predict the physics of
such vortices using traditional CFD turbulent flow models.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
4.3 Fluctuating Pressure Model
The second method for predicting the onset of cavitation includes an
approximation for the pressure fluctuations that occur due to turbulent mixing in
the shear zone or boundary layer. The approximation assumes that the pressure
fluctuations will be on the order of the averaged velocity squared, V2, at any point
1
in flow field: p = ρV 2 , where p is the approximate fluctuating pressure, ρ is the
2
density of the fluid, and V is the velocity magnitude [2]. This fluctuating pressure
is then subtracted from the average pressure at the same point in the flow field.
The result is a measure of the approximate effect of the individual vortices in the
shear zone on the pressure drop. This method is most effective for flows where
there is large flow separation wherein the boundary layer is highly turbulent and
large compared to the flow area, such as valve trims with small holes and
channels designed to reduce cavitation.
To implement the fluctuating pressure model, a user defined function was
created in the CFD program that took the pressure in the volume cell and
subtracted ½ times the density times the velocity squared of the volume cell:
1
2
pBL = pcell − ρ cell * Vcell . Where pBL is the predicted minimum pressure in the
2
flow field, pcell is the pressure in the volume cell, ρ is the density of the volume
cell, and Vcell is the velocity in the volume cell.
5 Results
5.1 Introduction
Several different types of geometries were analyzed including nine anti-cavitation
trims, and three standard valve configurations: a segmented ball valve (SBV), a
rotary butterfly disk valve (BDV), and a standard globe style valve (SGV). Each
of the geometries that were analyzed using CFD, were also physically tested to
determine the onset of cavitation for validation of the cavitation prediction
methods. In all the tables and figures in the results section the data referred to as
CFD1 represents the xFz predictions using the fluctuating pressure model, and
the data referred to as CFD2 represents the xFz predictions using the calculated
pressure model.
5.2 Anti-Cavitation Trims
The results for the anti-cavitation trims are presented below in Table 1 and in
Fig. 3.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
Table 1: Tabulated results for anti-cavitation trims including test results
Fluctuating
Calculated
No
Pressure
Test Pressure
Model
Model
AC1
0.508
0.478
0.628
AC2
0.501
0.500
0.601
AC3
0.544
0.540
0.609
AC4
0.578
0.570
0.617
AC5
0.485
0.580
0.586
AC6
0.355
0.475
0.474
AC7
0.510
0.610
0.632
AC8
0.578
0.610
0.711
AC9
0.554
0.738
0.745
0.8
0.7
0.6
xFz
0.5
CFD1
Test
CFD2
0.4
0.3
0.2
0.1
0
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
Fig. 3: Bar graph with CFD results compared to test results CFD1 represents
fluctuating pressure model, and CFD2 represents calculated pressure model
(data from Table 1).
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
In the above bar graph, the blue columns represent the values of xFz predicted
using the CFD fluctuating pressure model (approximation of the shear zone
pressure fluctuations), the red columns represent the values of xFz from the
testing, and the beige columns represent the value of xFz using the CFD
calculated pressure model. From the above plot it can be seen that the results of
the cavitation prediction were very good for the anti-cavitation trims. All but one
of the trims (AC4) are within 6% of either the fluctuating pressure model or the
calculated pressure model, and AC4 is within 9%.
Most of the test data is closer to the fluctuating pressure model prediction (AC1,
AC2, AC3, AC4, and AC8); the reason for this can be seen by further
investigation of the flow area where the cavitation is predicted to occur. For the
trims AC1, AC2, AC3, AC4, and AC8 the cavitation was predicted to happen in
an area where large flow separation occurred and the boundary layer was very
large and turbulent. Fig. 4 shows an example of this cavitation region for AC2.
Diameter of Hole
Width of Channel
Boundary layer
Boundary layer
due to flow
due to flow
separation, where
separation where
cavitation was
cavitation was
predicted to begin.
predicted to begin.
Fig. 4: Vector plot for AC2 showing where cavitation was predicted to occur, in
the region of large flow separation.
The above figure shows flow coming from a rectangular channel into a circular
hole. As shown, the flow separates from the wall as it turns the corner from the
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
channel into the hole; which results in a very large region of separated flow. In
the above example the separated flow area is greater than half the diameter of
the hole, which would suggest that turbulent mixing and vortices in the shear
zone will have a large effect on the minimum pressure.
For the other trims the test data was closer to the calculated pressure model
predicted value (AC5, AC6, AC7, AC9); for these trims the cavitation was
predicted to occur in regions where there was little or no flow separation, but very
high velocity gradients resulting in low pressure drops. Fig. 5 shows an example
of this type of region for AC5.
Width of Channel
Minimal flow
separation
High velocity
gradient where
cavitation occurred
Fig. 5: Vector plot for AC5 showing where cavitation was predicted to occur, in
the region of high velocity gradient.
In the above vector plot, flow is exiting a hole and entering a channel with a much
smaller area than the hole. This decrease in flow area results in a large velocity
gradient as the flow must speed up to maintain the flow rate. However, unlike
the flow in Fig. 4, the boundary layer is much smaller (less than one third the
channel width) and reattaches quickly suggesting that the shear zone effects in
this flow are not as significant as in Fig. 4.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
5.3 Standard Valves
The results for the standard valves are presented in Table 2 and Fig. 6 below.
Table 2: Results for standard valves including test results
Fluctuating
Calculated
Valve
Pressure
Test
Pressure
Model
Model
Segmented
Ball Valve
0.115
0.208
0.198
(SBV)
Butterfly
0.276
Disk Valve
0.172
0.133
(BDV)
Standard
Globe
0.221
0.204
0.338
Valve
(SGV)
0.4
0.35
0.3
xFz
0.25
CFD1
Test
CFD2
0.2
0.15
0.1
0.05
0
SBV
BDV
SGV
Fig. 6: Bar graph with CFD results compared to test results CFD1 represents
fluctuating pressure model, and CFD2 represents calculated pressure model
Table 2).
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
The above results show a similar trend as seen in the results for the anticavitation trim results. In the above plot, the xFz values are plotted on the y-axis,
the CFD fluctuating pressure model results are represented by the blue columns
, the test results are represented by the red columns , and the CFD
calculated pressure model results are represented by the beige columns . All
the test results are within 5% of either the fluctuating pressure model or the
calculated pressure value. Each valve was investigated in more detail to
determine the type of flow regime that was prevalent when cavitation occurred.
5.3.1 Segmented Ball Valve (SBV)
The measured xFz for the SBV was very close to the CFD calculated pressure
value; this would suggest that the cavitation is mostly due to high velocity
gradients and or large pressure drops and not due to high turbulent mixing or
vortices in the shear zone. Fig. 7 and Fig. 8 show the velocity magnitude
contour plot through the half-plane of the SBV valve and a close up vector plot of
the cavitation region respectively.
See Fig. 6
Flow Direction
Fig. 7: Velocity contour plot for the Segmented Ball Valve (SBV) at 53.8% open.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
Very little shear
zone, as seen by the
relatively small
velocity in the
separated flow
regime
Cavitation
occurred here.
Fig. 8: Vector plot of the Segmented Ball Valve (SBV) analysis showing where
cavitation occurred.
In the above vector plot, the flow is passing through the port of the segmented
ball, the resulting flow is similar to a jet, as can be seen there is very little shear
near the point of maximum velocity because there is very little fluid flow in the
region of separation. This leads to the conclusion that there is very little shear
zone effect on the minimum pressure for this flow.
5.3.2 Butterfly Disk Valve (BDV)
The measured xFz for the BDV unlike the Segmented Ball Valve (SBV) was
closer to the CFD fluctuating pressure model value, suggesting that the cavitation
is mostly due to turbulent mixing in the shear zone. Fig. 9 and Fig. 10 show the
velocity magnitude contour plot through the half-plane of the BDV valve and a
close up vector plot of the cavitation region respectively.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
See Fig. 8
Flow Direction
Fig. 9: Velocity contour plot for the Butterfly Disk Valve (BDV) at 39.9% open.
Cavitation first
predicted here in
the region of
separated flow
Fig. 10: Vector plot of the Butterfly Disk Valve (BDV) analysis showing where
cavitation occurred.
In contrast to the Segmented Ball Valve (SBV), the BDV vector plot (see Fig. 10)
shows that there appears to be an area where there is greater probability for
turbulent mixing, as seen in the area where the flow is separating near the
leading edge. The velocities inside this mixing region are on the same order as
the free stream velocities suggesting that the shear zone effect will be significant.
5.3.3 Standard Globe Valve (SGV)
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
The analysis of the SGV appeared to be like the Butterfly Disk Valve (BDV), with
the test xFz being closer to the CFD fluctuating pressure value. Fig. 11 and Fig.
12 show the velocity magnitude contour plot through the half-plane of the SGV
and a close up vector plot of the cavitation region respectively.
See Fig. 10
Flow Direction
Fig. 11: Velocity contour plot for the Standard Globe Valve (SGV) at 99.6%
open.
Cavitation first
predicted here.
Fig. 12: Vector plot of the Standard Globe Valve (SGV) analysis showing where
cavitation occurred.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
The above vector plot shows that the cavitation in the SGV initiated in the region
where the flow had separated. In the separated region, the velocity again
appears to be significant and acting in a direction opposite to the free stream,
indicating that the shear zone effects are more likely to be causing cavitation
(see Fig. 12).
5.4 Refined Application of the Fluctuating Pressure
Model to Boundary Layer Flow Only
The above application of the two proposed models is sufficient for obtaining a
bracketed value of the xFz for the valves and trims analyzed. However, further
investigations of the application of the fluctuating pressure model showed that for
the valve and trims for which cavitation occurred in the regions where there was
very little flow separation or apparent boundary layer effects (AC5, 6, 7, and 9
and the segmented ball valve) the fluctuating pressure initially dropped below the
vapor pressure outside the boundary layer in the free stream. It was thus
proposed that the fluctuating pressure model be applied only in the boundary
layer (including regions of flow separation shear mixing zones etc.) Therefore, an
additional analysis was done on AC9 (following the same procedures as all other
analyses) that ignored the calculated CFD fluctuating pressure model values in
the free stream, while monitoring the results of the fluctuating pressure model in
the boundary layer. Fig. 13 below shows the results of the additional analysis
compared to the original results.
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
0.8
0.7
0.6
xFz
0.5
CFD1
Test
CFD2
0.4
0.3
0.2
0.1
0
AC9
AC9_2
Fig. 13 : Bar graph with CFD results compared to test results where AC9
represents the original analysis and AC9_2 represents the analysis done using
only boundary layer fluctuating pressure results. CFD1 represents CFD
fluctuating pressure model, and CFD2 represents the CFD calculated pressure
model.
The above results suggest that applying the CFD fluctuating pressure model in
the entire region can lead to a much smaller xFz (see Table 1: Tabulated results
for anti-cavitation trims including test results, Fig. 3, Table 2: Results for
standard valves including test results, and Fig. 6) than what is really happening.
However, if the method is applied only in the region of the boundary layer or
separated flow as seen in Fig. 13 the results are much closer to the test values.
6 Conclusions
The CFD predictions for xFz compared to test values have shown that it is
possible to predict the onset of cavitation in control valves whether it is due to
large scale flow effects, or turbulent mixing in the shear zone. Further more, an
investigation of the flow region where cavitation is likely lead to the conclusion
that the CFD fluctuating pressure model should be applied throughout the entire
flow region, because this can lead to much lower values for the predicted xFz than
the test values. However, if the results of the fluctuating pressure model are
monitored only in the boundary layer the result appears to be much closer to the
test value. This was shown for the one case of AC9 and it is recommended that
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
the same type of analysis be done for AC5, 6, 7, and the Segmented Ball Valve
to further validate this conclusion.
7 References
[1]
User Guide; Star-CCM+ Version 3.04.007; CD-adapco; 2008
[2]
Bernard, P.S.; Wallace J.M.: “Turbulent Flow Analysis, Measurement, and
Prediction”; John Wiley & Sons Inc.; 2002; Hoboken, New Jersey, USA
[3]
IEC 60534-8-4, Second edition, 2005-08, “Industrial-process control
valves – Part 8-4: Noise considerations – Prediction of noise generated by
hydrodynamic flow”, International Electrotechnical Commission, Geneva,
Switzerland
Originally presented at the Valve World 2008 Conference, Maastricht, the Netherlands
