15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

Prediction of cavitation erosion occurring in a control valve using
computational fluid dynamics (CFD)
Kenji Saito1, *, Youn Chongho1
1

Department of valve product development, Azbil Corporation, Kanagawa, Japan*corresponding author: k.saito.ht@azbil.com

Abstract Control valves are used to control the flow of fluid through piping systems in plants and factories. If
the fluid is a liquid, cavitation may occur due to vortices or increase in local flow velocity. In this study, we
visualize and validate the cavitation flow using computational fluid dynamics (CFD). A 1.5” valve with a flowto-open direction was used to compare the experimental results with those of Yuzawa et al. A homogeneous flow
model was used to represent a cavitation flow, and a turbulent calculation model using large-eddy simulation
was used to express the state of the vortex directly. The visual result of the CFD modelling of cavitation flows
showed that the appearance of cavitation is similar to experimental results and agrees well with the flow
coefficient 𝐶𝐶𝑣𝑣 . Cavitation modelling was also used to evaluate erosion indexes under an upstream pressure 𝑃𝑃𝑈𝑈 =20 MPa and cavitation coefficient 𝜎𝜎 = 1.005. The results prove that the erosion index is effective for theprediction of the points where the cavitation erosion occurs.
Keywords: control valve, erosion, CFD, cavitation

1 Introduction
Control valves are used to control the flow of fluid through piping systems in a variety of plants andfactories. They are required to operate reliably for a long time and must guarantee accurate flow
characteristics. These requirements need to be fulfilled for all types of fluids.
The degree to which the valve is open is controlled by the control valve and if the fluid is a liquid,cavitation may occur due to vortices or increase in local flow velocity. Cavitation is a phenomenon in whichbubbles are formed when the pressure of the liquid drops below the saturated vapor pressure. When thepressure rises above the saturated steam pressure again, the bubbles collapse and eject high pressure micro
jets. A collapsing bubble in close proximity will exert high stress to the pipe wall and cause erosion.
Cavitation erosion occurs in various fluid machines such as pumps and ship propellers. It often occurs near
the plug of a control valve resulting in flow deterioration, difficulties in shutting off the valve and can evenlead to plant shutdown.
Cavitation erosion research has therefore been conducted for a long time. Kuiper visualized the generationof vortex cavitation occurring in ship propellers, and proposed a blade shape with a low risk of cavitation
erosion [1] while Yuzawa visualized cavitation erosion in control valves caused by high-pressure angle valve[2]. Other studies have proposed using erosion indexes to predict cavitation erosion using CFD, and haveapplied these indexes to propellers for efficiency verification [3][4]. However, there are limited studies using
erosion indexes for internal flows such as control valves, and it is unclear which indexes are the mosteffective.
Nomenclature:flow coefficient
𝐶𝐶𝑣𝑣:pressure𝑃𝑃:volume flow rate
𝑄𝑄
𝑚𝑚̇+ , 𝑚𝑚̇− :mass transfer rates:void fraction
𝛼𝛼:cavitation coefficient𝜎𝜎:mixture density
𝜌𝜌
Subscripts:downstream𝐷𝐷:upstream
𝑈𝑈:liquid phase𝑙𝑙:vapor phase𝑣𝑣
Paper ID:133

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

The purpose of this study is to predict cavitation erosion occurrences in control valves by performing CFD
modelling of unsteady cavitation flows. We applied the currently proposed 4-type erosion index to predicterosion
2 CFD analysis of the angle valve
2.1 CFD model
The contoured type angle valve to be analyzed is as shown in Fig.1. A 1.5” valve with a flow-to-open
direction was used in order to compare the experimental results with those of Yuzawa et al. With diameter D,
the upstream and downstream pipe lengths were modelled at 2D and 6D, respectively. CFD analysis was
conducted with valve openings of 90% and 100%.

Outlet 𝑃𝑃𝐷𝐷

Inlet 𝑃𝑃𝑈𝑈

Fig.1 Angle valve（1.5 ”）
2.2 CFD conditions
The conditions of the CFD analysis are shown in Table.1. The solver used Advance/Frontflow/Red Ver5.4,
a general-purpose fluid analysis code. The cavitation model used the homogeneous flow model proposed by
Ikohagi et al. [5] with the following equations:𝑚𝑚̇ = �𝑚𝑚̇+ 𝑖𝑖𝑖𝑖 𝑃𝑃 < 𝑃𝑃𝑣𝑣∗
𝑚𝑚̇− 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

𝑃𝑃𝑣𝑣∗ − 𝑃𝑃

(1)

𝜌𝜌𝑙𝑙
,
𝑚𝑚̇ + = 𝐶𝐶𝑒𝑒 𝐴𝐴𝐴𝐴(1 − 𝛼𝛼) � �𝜌𝜌𝑣𝑣 �2𝜋𝜋𝜋𝜋𝑇𝑇𝑠𝑠
𝑃𝑃𝑣𝑣∗ − 𝑃𝑃,
𝑚𝑚̇ − = 𝐶𝐶𝑐𝑐 𝐴𝐴𝐴𝐴(1 − 𝛼𝛼)�2𝜋𝜋𝜋𝜋𝑇𝑇𝑠𝑠
𝐴𝐴 = 𝐶𝐶𝑎𝑎 𝛼𝛼(1 − 𝛼𝛼)(4)Paper ID:133

2

(2)

(3)

where 𝑇𝑇𝑠𝑠 is the saturation temperature and 𝐶𝐶1∗ = 𝐶𝐶𝑒𝑒 𝐶𝐶𝑎𝑎 and 𝐶𝐶2∗ = 𝐶𝐶𝑐𝑐 𝐶𝐶𝑎𝑎 are the empirical model constants. In
the contoured control valve, the separation generated at the point of constriction causes a wide range of 3D
vortices and swirling flows [6]. Since this is an unsteady flow pattern, it is difficult to express accurately in
Reynolds Averaged Navier-Stokes (RANS). We initially calculated the vortex appearance with a larger thanmesh resolution in large-eddy simulation (LES) due to the close relationship between cavitation behavior andvortexes.
The static pressure boundary was given to inlet and outlet, and wall boundaries are given as Spalding-law.
Cavitation generation and collapse were expected to occur repeatedly in the area of vena contracta (point of
maximum constriction) and hence the mesh resolution was defined around the plug high.

15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

Table.1 CFD analysis settings
SoftwareAdvance/FrontFlow/Red Ver5.4
Turbulent model
Large Eddy Simulation (LES)
Fluid
Water (25℃, compressible)
Travel 100 %
6,723,867
Number of cells
Travel 90 %7,899,316
Momentum2nd order upwind
Advection term
discrete scheme
Energy1st order upwind
Low of the wall
Spalding’s low
Simulation time step Δt [s]2 × 10−6 ～1 × 10−5
Number of parallels
288
2.3 Simulation results
Validation of the cavitation analysis was done using CFD with the conditions listed in Table.1 and the
CFD analysis and experimental conditions are given in Table.2. These are the same conditions in which
Yuzawa et al visualized the occurrence of cavitation. Verification was done by comparing the CFD resultswith those of the experimental results. Cavitation coefficient 𝜎𝜎 is used to represent the extent of cavitationand is defined as𝜎𝜎 =𝑃𝑃𝑈𝑈 − 𝑃𝑃𝑉𝑉𝑃𝑃𝑈𝑈 − 𝑃𝑃𝐷𝐷

(5)

The analytical and experimental 𝐶𝐶𝑣𝑣 are given in Table.3 and Fig.2, and the cavitation visualization results
are shown in Fig.3. The range of void fraction contour is visualized with a value of 0.05. A value comparison
between the CFD analysis and the experiment shows 2% error of 𝐶𝐶𝑣𝑣 converted from the volume flow and acomparable occurrence of cavitation.
Cavitation number 𝜎𝜎
1.13

Table.2 Experimental and CFD conditions
𝑃𝑃𝑈𝑈 [kPa (abs)]
𝑃𝑃𝐷𝐷 [kPa (abs)]
1100
128.7

Travel [%]100

Table.3 CFD analysis results
Flow rate 𝑄𝑄 [m3/h]
𝐶𝐶𝑣𝑣
2.889
1.07

Table.1 Exp.

Fig.2 𝐶𝐶𝑣𝑣 by experiment at 𝑃𝑃𝑈𝑈 =1[MPa][2]Paper ID:133

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy■:ΔT = 0■:ΔT = 5[ms]■:ΔT = 12.5[ms]3 Simulation of erosion indexes

Fig.3 Cavitation features at 𝑃𝑃𝑈𝑈 =1[MPa]3.1 Erosion indexes
Erosion indexes are physical models that use bubble and pressure values to predict erosion risk. Thesemodels compute the magnitude of cavitation erosion as a modulus of change of void fraction and pressure on
surfaces. The following erosion indexes are proposed by Nohmi et al [4][7].
1 𝑇𝑇𝑐𝑐𝜕𝜕𝜕𝜕� 𝛼𝛼 ∙ 𝑚𝑚𝑚𝑚𝑚𝑚 � , 0� 𝑑𝑑𝑑𝑑
𝑇𝑇𝑐𝑐 0𝜕𝜕𝜕𝜕
1 𝑇𝑇𝑐𝑐� 𝛼𝛼 ∙ 𝑚𝑚𝑚𝑚𝑚𝑚[𝑃𝑃 − 𝑃𝑃𝑣𝑣 , 0]𝑑𝑑𝑑𝑑
Index2 ∶𝑇𝑇𝑐𝑐 0𝜕𝜕𝜕𝜕
1 𝑇𝑇𝑐𝑐� 𝑚𝑚𝑚𝑚𝑚𝑚 �−, 0� 𝑑𝑑𝑑𝑑
Index3 ∶𝜕𝜕𝜕𝜕
𝑇𝑇𝑐𝑐 0𝜕𝜕𝜕𝜕
1 𝑇𝑇𝑐𝑐� 𝑚𝑚𝑚𝑚𝑚𝑚[𝑃𝑃 − 𝑃𝑃𝑣𝑣 , 0] ∙ 𝑚𝑚𝑚𝑚𝑚𝑚 �−, 0� 𝑑𝑑𝑑𝑑
Index4 ∶𝜕𝜕𝜕𝜕𝑇𝑇𝑐𝑐 0
Where 𝑇𝑇𝑐𝑐 is the period of the cavitation.
Index1 ∶

(6)

(7)

(8)

(9)

3.2 Comparison of erosion indexes and experimental results
The erosion indexes from section 3.1 were compared with the experimental results to examine thesuperiority of each one. Specifying trim material of SUS316 and a time period of 30 hours, the CFD analysis
and experimental test parameters are given in Table.4 and the results shown in Figs.4 and 5.
Erosion mainly occurs at the seat, taper, and end of taper surfaces (See Fig.7), however this was notreflected in the results where different points of cavitation erosion occurred. In the experimental result ofcase 1, the plug sheet surface displays the highest erosion while case 2 displays erosion at the taper surfaceof the plug.
The erosion index results at Index 3 for case 1 show a higher cavitation erosion value at the plug tip thanat the seat surface which contradicts the results of the experiment.
The other indexes did not show much difference, and effectively identified the risk of erosion location.
Table.4 Erosion test conditions and flow rate results

Case 1Case 2

Cavitation number
𝜎𝜎Paper ID:133

1.058
1.041

𝑃𝑃𝑈𝑈 [MPa (abs)]
20
20

𝑃𝑃𝐷𝐷 [MPa (abs)]
1
0.8

Travel [%]90

Flow rate 𝑄𝑄[m3/h]

Simulation
8.53
8.63

Experiment
8.75
8.82

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

ErosionIndex 1

Index 2

Experiment [2]Index 3

Index 4
Fig.4 Erosion test results (Case 1)

ErosionIndex 1

Index 2

Experiment [2]Index 3

Index 4

Fig.5 Erosion test results (Case 2)
4 Discussion of erosion indexes
4.1 Erosion by cavitation flow
To explain the relationship between the CFD results and cavitation erosion, Fig 6 depicts the void fraction
contour when the simulation time step is passed by ∆𝑇𝑇 and indicates that cavitation erosion occurs at vena
contracta. In case 1, cavitation bubble flows are observed from upstream to downstream along the surface ofthe plug and collapse. These bubbles, as shown in Fig.3, have an annular shape and are considered to be
Paper ID:133

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

cloud cavitation generated by vortices detached from the plug and seat ring boundary layer.
On the other hand, the plug characteristic portion is covered by a layer of cavitation which is allegedly due
to developed sheet cavitation. Sheet cavitation composes a relatively stable vapor phase in front of the plug,and then separates it downstream. A separated cavitation becomes a crowd cavitation and collapses thetapered surface. In the context of this research, cloud cavitation greatly affects erosion and the collapse
position of cavitation by the CFD analysis agrees with the experimental erosion results. The theoretical
relationship between cavitation and erosion generated on the plug surface was confirmed by the CFD
modelling of cavitation flows performed in this research.

Case.1

Collapse

Separated

Case.2
Collapse

Fig.6 Void fraction contour on plug surface
4.2 Prediction of erosion using erosion indexes
As stated in section 3.2, the experimental results from cases 1 and 2 show that the erosion position is
dictated by and changes according to the pressure conditions. The evaluation of the erosion indexes istherefore conducted on the plug surface within a specific area as shown in Fig.7. The evaluation range,
calculated from the results in Chapter 3, is given in Table.5 and subsequently divides the sum of the erosion
indexes by area.

Paper ID:133

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy(Seat) (Taper)

Fig.7 Evaluation surface of erosion index
Table.5 Evaluation position of erosion index
Evaluation surface
A (Seat) [mm] B (Taper) [mm]Displacement x[mm]144±2
155±2.5
The erosion index results are shown in Fig 8. Although the values in the vicinity of the plug seat are lower
in case 1 compared to case 2, Index 2 hardly changes. However, a significant difference can be observed
between Index 1 and Index 4 and for taper surfaces, all erosion indexes are higher in case 2. These results arevalid from the result of cavitation erosion. Simulations with Index 1 and Index 4 appear to agree strongly
with experimental results, however, when comparing to the index values of the seat where erosion does notoccur, the taper index value tends to be lower. Therefore, further research is needed in order to use cavitationindexes as thresholds.

Index 1

2.00E+08
1.80E+08
1.60E+08
1.40E+08
1.20E+08
1.00E+08
8.00E+07
6.00E+07
4.00E+07
2.00E+07
0.00E+00

Index 2

8.00E+04
7.00E+04
Case.1

Case.2

Case.1

6.00E+04

Case.2

5.00E+04
4.00E+04
3.00E+04
2.00E+04
1.00E+04
0.00E+00

A(Seat)A(Seat)B(Taper)Index 3

1.20E+03
1.00E+03

Case.1

8.00E+02
6.00E+02
4.00E+02
2.00E+02
0.00E+00

A(Seat)

Case.2

Index 4

1.80E+08
1.60E+08
1.40E+08
1.20E+08
1.00E+08
8.00E+07
6.00E+07
4.00E+07
2.00E+07
0.00E+00

B(Taper)B(Taper)Case.1A(Seat)

Case.2B(Taper)Fig.8 Value of erosion indexes

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15th International Conference on Fluid Control, Measurements and Visualization
27-30 May 2019, Naples, Italy

5 Conclusion
In this study, in order to predict the erosion location in an angle type control valve, the effectiveness of the
proposed four erosion index from CFD and experimental results was evaluated and produced the following
results:
1. The erosion indexes 1, 2 and 4 were effective in the prediction of the location of erosion
2. Void ratio change was analyzed and clarified the generation mechanism of erosion on the plug surface
3. It proved difficult to judge the occurrence of erosion from the value of each erosion index
References[1] G.Kuiper (2001) NEW DEVELOPMENTS AROUND SHEET AND TIP VORTEX CAVITATION ON
SHIPS'PROPELLERS, Fourth International Symposium on Cavitation (CAV2001), CA USA.
[2] S.Yuzawa (2003) Cavitation and Erosion in Control Valves by Pressure Reduction and Flow Regulationof High Pressure Liquid (in Japanese), Doctoral Dissertation of Waseda University.
[3] Onur Usta, Batuhan Aktas et al.(2017) A study on the numerical prediction of cavitation erosion forpropellers, Fifth International Symposium on Marine Propulsion, Finland.
[4] N.Hasuike, S.Yamasaki et al.(2011) Numerical Study on Cavitation Erosion Risk of Marine Propellers
Operating in Wake Flow, Journal of the JIME, Vol. 46, No.3, pp 79-87[5] Y.Saito, T.Ikohagi et al.(2003) NUMERICAL ANALYSIS OF UNSTEADY VAPOROUS
CAVITATING FLOW AROUND A HYDROFOIL, Fifth International Symposium on Cavitation(CAV2003), Osaka, Japan.
[6] F.Inoue, E.Outa et al.(1991) An Experimental Study on Control Valve Cavitation (2nd Report, String
Bubble Cavitation in Contoured-plug Valve), Transactions of the Japan Society of MechanicalEngineers, Series B,Vol. 57,No 544[7] M.Nohmi, T.Ikohagi et al.(2008) Numerical Prediction Method of Cavitation Erosion, ASME Fluids
Engineering Division Summer Conference, FL, USA.

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