numerical study of cavitating flow inside a flush valve

Conference on Modelling Fluid Flow (CMFF’09) The 14th International Conference on Fluid Flow Technologies

Budapest, Hungary, September 9-12, 2009

NUMERICAL STUDY OF CAVITATING FLOW INSIDE A FLUSH VALVE

Annie-Claude BAYEUL-LAINẺ1, Sohie SIMONET2, Guy CAIGNAERT3

1 Arts et Metiers PARISTECH, LML, UMA CNRS 8107, 8, boulevard Louis XIV 59046 LILLE Cedex Tel.: +33 20 62 39 04, Fax: +33 20 53 55 93, E-mail: [email protected] 2 Arts et Metiers PARISTECH, LML, UMA CNRS 8107, E-mail: [email protected] 3 Arts et Metiers PARISTECH, LML, UMA CNRS 8107, E-mail: [email protected]

ABSTRACT In water supply installations, noise pollution

often occurs. As a basic component of a system, a flush valve may frequently be a source of noise and vibration, of which cavitation can be the problem, especially during valve closing or valve opening.

The aim of this paper is to show how a numerical industrial code can point out a cavitation problem even if this code doesn’t use a cavitation model. This approach shows a good agreement with one using a cavitation model. The numerically obtained contours of the volume fraction of water vapor show cavitation inception distribution behind the poppet of the valve.

Computational Fluid Dynamics (CFD) simulations of cavitating flow through water hydraulic industrial flush valve were performed using the Reynolds averaged Navier-Stokes (RANS) equations with a near-wall turbulence model. The flow was turbulent, incompressible and steady. The studied flush valve is a real one. The structure of this flush valve was simplified due symmetry considerations. The model used is three dimensional. Flow field vizualization was numerically achieved.

The effects of outlet pressure as well as mesh size and mesh type on cavitation intensity (evaluated by pressure intensity) in the flush valve were numerically investigated thanks to two commercial code : FLUENT 6.3 and STAR CCM+ 3.04.009.

Keywords: Cavitation, Noise, Numerical simulation, Water supply systems

NOMENCLATURE αv [-] Vapor volume fraction Nbub [-] Number of vapor bubbles in a control volume Vv [m3] Volume of vapor in a control volume Vl [m3] Volume of liquid in a control volume

R [m] micro bubble radius

1. INTRODUCTION We must not ignore the effects of borough’s

improvement on our working and living environment. These can include air pollution, noise and vibration, contamination of land and water.

One of the most important parameters in buildings construction is noise control. Cavitation noise generated by installations such as water supply systems like valve noise has frequently posed serious problems. In each country, there are legal code of practice and today new builds and major construction projects are well controlled. Taps and valves can, therefore, be classified on the basis of their acoustic behaviour, in accordance with the ISO 3822 and NF EN 12541 standards ([1, 2]).

In order to determine the sources of noise and the best design methods to minimize noise generation, experimental and numerical analyzes were carried out in our laboratory. The aim of this paper is to present some numerical results.

0 2 4 6 8 10 12 14 16 18

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Figure 1. Flow rate in a flush valve during a cycle

Figures 1 and 2 describe respectively flow rate (fig. 1) and upstream static pressure (fig. 2)

evolutions during one operating cycle, from opening to closure. The main aim of such a valve is to deliver a fixed volume of liquid (6 or 9 l, for example) with a high enough momentum. It is clear, from these two figures, that the operation of such a valve is unsteady and transitional. Nevertheless, the cycle duration (about 10s) allows to consider the flow inside the valve as a succession of quasi-steady operating conditions. This is the main hypothesis that has been made in the present study, because CFD codes are not really still able to describe accurately such a transitional behaviour with a control of the opening and closure of the valve by the flow itself.

0 2 4 6 8 10 12 14 16 181

1.5

2

2.5

3

3.5x 105

Figure 2. Upstream static pressure in a flush valve during a cycle

This work deals with the problem of noise generated by a flush valve in water supply systems with conditions of valve opening or closing especially when cavitation occurs. This is the case when pressure in the liquid drops below the vaporization pressure. Vapor bubbles are formed, but rapidly collapse with increase of pressure. That collapse of bubbles is clearly associated to noise generation ([3,]).

In this type of valve, in conditions of closing or opening position, static pressure remain relatively constant before and behind the singularity formed by piston and seat (called narrow zone in the next text : detail (a) on fig. 4) where quite all the part of the head drop occurs.

GAO H., FU X., YANG H. and TSUKIJI T. ([4]) showed the importance of predicting cavitation in water hydraulic valve and the necessity of continuing investigation.

Cavitation model in commercial CFD codes, designed for two interpenetrating fluids (generally liquid and vapor phases of a same fluid: water in the case of this paper), describes the formation of bubbles when the local pressure becomes less than the vapor pressure. The cavitation model solves a single set of momentum equations shared by the two fluids, a continuity equation for the liquid (primary phase) and a volume fraction equation for the secondary phase. It is assumed that all vapor bubbles in a control volume have the same radius R

and an homogenous distribution. This assumption leads to describe the bubble distribution by a single scalar field, the vapor volume fraction αv.

(1)

Assuming that only one liquid phase (volume Vl) and the corresponding liquid-vapor phase (volume Vv) can occupy a control volume V where cavitation takes place, the mass of produced vapor depends on the vapor density, the anticipated average size (radius R) and vapor bubbles density. Cavitation model includes also mass transfer between the fluids. Models in commercial codes can predict the inception of cavitation but few can predict the collapse of the bubbles.

Cavitation is a complex process influenced by a lot of factors. The formation of bubbles followed by their collapse make this problem highly unsteady. So we have to choose between steady or unsteady approaches for cavitation. In the two cases, simulation takes a lot of time. The steady approach is sufficient to confirm that cavitation occurs.

In this paper, we intend to show how a commercial CFD code can point out a cavitation problem with a classical model without use of a cavitation model.

Two commercial code were used : FLUENT 6.3 and STAR CCM+ 3.04.009.

In a first time, we show a comparison between the two models (no cavitation and cavitation with steady approach) thanks of code FLUENT for a relatively fine mesh.

In a second time, we made a comparison between the two codes.

In a third time, we study the influence of the mesh (size and type).

2. DESCRIPTION OF THE VALVE The geometry of the flush valve, used for the

present study, is showed in figure 3. The main path of water stream is represented by white arrows.

Figure 4 presents details on position between piston and valve seat (a) and the narrow passage for the fluid between piston and seat. The high of this zone is 0.8 mm. Simulations show that cavitation can occur in this narrow passage.

The associated fluid zone is presented in figure 5. Only one half of geometry is modelised due to the symmetry of the valve.

3. COMPARISON BETWEEN NO CAVITATION MODEL AND CAVITATION MODEL

In this paragraph, flush valve is studied using first a no cavitation model and then a cavitation model.

The first geometric model, showed in figures 6 and 7 is a tetrahedral mesh with 607 210 cells. The grid of the fluid domain has been created in preprocessor GAMBIT. The mesh size depends on position. In order to well represent the flow field in narrow zone, refined mesh is used. Small size lies near narrow zone and is about 0.1 mm and this size growths until 1mm far away from narrow zone (at the inlet and at the outlet). So we have about 8 cells in the passage height of the narrow zone.

Figure 3. Flush valve geometry (cut ¾ view)

Figure 4. Flush valve geometry (zoom on narrow passage)

Figure 5. Flush valve geometry : fluid zone

The boundaries of the valve are relative pressure inlet (0,12 MPa), relative pressure outlet (0 MPa), and wall boundaries. That pressure inlet is the lower pressure usually used in such valve ([1]). The fluid is water (density=998.2 kg/m3, viscosity=1.003 10-3 Pa.s) for non cavitating model and mixture between water liquid and water vapor (density constant equal to 0.02558 kg/m3, viscosity=1.26 10-6 Pa.s). The density ratio between water and vapor is about 39000. The flow is assumed incompressible (the two phases are treated as incompressible fluids), steady and turbulent. The Reynolds number based on height of narrow passage is 19000 for water and 400 for water vapor (for a maximum velocity of 25 m/s). So flows occur at low rather Reynolds number. The standard k-omega turbulence model is used in the two cases. The cavitation model used is the Rayleigh model.

Figure 6. Mesh of fluid zone

Figure 7. Mesh detail in narrow zone

A steady state solution was calculated in the cavitation model to simulate the formation of vapor in the narrow passage. This steady solution needed about 1500 iterations. It’s obvious that a more computationaly intensive unsteady calculation should be necessary to simulate the formation and the growth of bubbles but it wasn’t the aim of this work.

(a)

(a)

(a)

The question of the possible use of a laminar model arises, due to the low Reynolds numbers. In fact, it must be pointed out that a liquid-vapor mixture occurs in cavitating conditions and laminar conditions are really questionable in such situations. Nevertheless a calculation with laminar hypothesis has been made in non cavitating hypothesis. The results are discussed in paragraph 5, even if convergence problems appeared.

Figure 8. Contours of absolute static pressure with no cavitation model (FLUENT)

Figure 9. Contours of volume fraction of water with a cavitation model (FLUENT)

Figure 10. Contours of absolute static pressure with a cavitation model (FLUENT)

Simulation with the model with no cavitation shows that absolute pressure becomes negative in the narrow zone (Fig. 8), which has no physical sense. So it can be supposed that cavitation occurs in this zone.

A simulation with a cavitation model shows effectively that there is cavitation in this zone (Figs. 9, 10, table 1). In case of cavitation model, it can be seen on fig. 10 that pressure is generally higher than vaporization pressure and that cavitation area is so limited to the narrow zone.

It can be seen on fig. 9 that the volume fraction of waper drops to 31 % in this zone.

Table 1 presents number of iterations, flow rate and minimum absolute pressure obtained with each model.

Table 1. results with the two models with Fluent

No cavitation

cavitation

Number of iterations

600 1500

Flow rate (kg/s) 0.374 0.366

Minimum absolute static pressure

(MPa)

-0.16 0

4. COMPARISON BETWEEN TWO CODES

4-1 Model with no cavitation. For the same mesh model (tetrahedral mesh

with 607 210 cells), with the same boundary conditions, the same turbulent model (k-ω), results between FLUENT and STAR CCM+ codes are compared.

Overall results are given in table 2. Minimum absolute pressure and maximum velocity are given for cell centroid base values.

Table 2. results with the two CFD simulation, no model cavitation

Fluent Star CCM+

Number of iterations 600 500

Flow rate (kg/s) 0.374 0.540

Minimum absolute static pressure (MPa)

-0.16 -0.343

Maximum velocity in narrow passage (m/s)

25 32.15

The two CFD codes give the same type of

results : cavitation occurs in the narrow passage. But there is a rather high difference between flow rate and minimum absolute pressure (See table 2).

These differences can be explained by the fact that Star CCM+ is known to give better results with polyhedral mesh and that there is a low Reynolds

problem and, perhaps, a low Reynolds mesh should be used.

Figure 11. contours of absolute static pressure with no cavitation model (k-ω turbulent model) (STAR CCM+ x_z plane view)

Figure 12. contours of static pressure with no cavitation model (k-ω turbulent model) (STAR CCM+ x_y plane view)

Figure 13. contours of static pressure with no cavitation model (k-ω turbulent model): zones where pressure is lower than vapor pressure (STAR CCM+ )

Figures 11 and 12 present contours of absolute pressure (in case of no cavitation model) in two planes for the narrow zone cavitation.

It can be seen on fig. 13 contours of static absolute pressure for pressure only lower than vapor pressure. This can be used to locate cavitating zones (area in the circle).

4-2 Model with cavitation Results are compared for the same mesh model

(tetrahedral mesh with 607 210 cells), the same boundary conditions, with turbulent model (k-ω) for

FLUENT and turbulent model (k-ε) for STAR CCM+. Turbulent model (k-ω) leads to some convergence problem with this mesh for STAR CCM+, this is the reason why turbulent model (k-ε) was used with STAR CCM+. RAYLEIGH cavitation model ([5]) is used for FLUENT and RAYLEIGH-PLASSET cavitation model ([6]) for STAR CCM+

Table 3. results with the two CFD simulation, model cavitation

Fluent Star CCM+

Turbulence model k-ω k- ε

Number of iterations 1500 1000

Flow rate (kg/s) 0.366 0.409

Minimum absolute static pressure (MPa)

0 -0.028

Maximum velocity in narrow passage (m/s)

25 20.9

Minimum contours of volume fraction for

water (%)

31 41,4

Figure 14. Contours of volume fraction of water with cavitation model with STAR CCM+ (x_z plane)

Table 3 summarizes results for cavitation simulation with the two codes. The two simulations show cavitation and results are in better agreement than those obtained with the simulation with no cavitation, especially for the flow rate.

In Star CMM+ code, negative absolute pressure still exists.

Figure 14 shows cavitation zone thanks of volume fraction of water.

5. INFLUENCE OF TURBULENCE MODEL

For the same mesh model (tetrahedral mesh with 607 210 cells) and the same boundary conditions, results for STAR CCM+ using different turbulent models are given for calculation with no

cavitation model. A laminar flow was also simulated. This model leads to some convergence problem, so a turbulent model was used for initial conditions.

In each case, cavitation was detected thanks of negative absolute pressure (table 4).

Table 4. results with different turbulent models, no model cavitation

Star CCM+

Star CCM+

Star CCM+

Turbulence model

k-ω k- ε laminar

Flow rate (kg/s)

0.540 0.541 0.531

Minimum absolute pressure (MPa)

-0.359 -0.343 -0.300

Maximum velocity in

narrow passage

(m/s)

32.15 31.62 31.39

6. INFLUENCE OF MESH SIZE STAR CCM+ has been used to analyse the

results sensitivity to the mesh size. In each case, tetrahedral cells has been used with the same boundary conditions, the same turbulence model ((k-ε) model with realizable (k-ε) two layer), and no cavitation model. The difference in mesh size is mainly near narrow zone as it can be observed in figures 15 to 17.

Table 5. results with different number of cells, no model cavitation and tetrahedral mesh

Star CCM+

Star CCM+

Star CCM+

case T1 T2 T3

Number of cells

166 842 239 771 832 211

Flow rate (kg/s)

0.464 0.474 0.474


-0.201 -0.218 -0.218

Maximum velocity in

narrow passage

(m/s)

26.08 25.59 25.6

Results, given in table 5, show few influence for cavitation area, minimum absolute pressure and maximum velocity in narrow zone.

Figure 15. case T1 : 166842 tetrahedral cells



7. INFLUENCE OF MESH TYPE

7-1 polyhedral mesh without prism layer

STAR CCM+ has been used to analyse the influence of mesh type, using polyhedral cells. In each case, (k-ε) model with realizable (k-ε) two layer has been used with no cavitation model. Different meshes can be observed in figures 18 to 20.

In STAR CCM+, volume mesh are built thanks of surface mesh. A same surface mesh with triangular cells can generate tetrahedral mesh or polyhedral with or without prism layer. The basic tetrahedral model used in this paper (607210 cells, fig. 7) and the Case P0 (fig 18), have the same surface mesh, so they have the same size reference.

Table 6. results with different number of cells, no cavitation model and polyhedral mesh

Star CCM+

Star CCM+

Star CCM+

case P0 P1 P2

Number of cells

167988 79006 142684

Flow rate (kg/s)

0.538 0.512 0.532


-0.222 -0.199 -0.207

Maximum velocity in

narrow passage

(m/s)

27,5 26.26 27,94

Results given in table 6 show no great influence

of mesh size between different polyhedral calculations. So the use of a coarse grid can allow a gain of calculation time.

These polyhedral meshes give results that are well comparable to those obtained with tetrahedral mesh thanks of FLUENT (minimum absolute pressure and maximum velocity in narrow passage). The main advantage is, for a same quality (in size), that polyhedral mesh needs less cells (607 210 cells for a tetrahedral mesh and 167 988 for a polyhedral). Flow rate remains quite greater with STAR CCM+ than with FLUENT which is not yet explained.

Figure 18. case P0 : 167988 hexahedral cells



7-2 polyhedral mesh with prism layer (Low Reynolds mesh)

Prismatic near wall layers has be included for the above mesh P0 by using the prism meshing model in the volume meshing process. A prism layer mesh is composed of orthogonal prismatic cells that usually reside next to wall boundaries in the volume mesh.

Table 7. results with different number of cells, no model cavitation, polyhedral mesh and prism layer

Star CCM+

Star CCM+

Star CCM+

case P0 PL1 PL2

Number of cells

167988 259669 308066

Flow rate (kg/s)

0.538 0.394 0.404


-0.222 -0.053 -0.079

Maximum velocity in

narrow passage

(m/s)

27,5 22.04 22,7

Number of prism

layer

0 2 3

Table 7 presents the influence of the use of a

low Reynolds mesh (prism layer). Polyhedral cells with the same boundary conditions and no cavitation model have been used. PL1 and PL2 calculations used a k- ω turbulence model with a first prism layer thickness equal to 10 μm and a prism layer strechting of 1.5

Polyhedral mesh with prism layer thickness (Fig. 21) shows hardly cavitation and calculations needs to decrease under-relaxation parameters to obtain good convergences.

But flow rate is near the one obtained with FLUENT that are well correlated to experimental data.

Figure 21. case PL2 : 308066 hexahedral cells

8. INFLUENCE OF PRESSURE INLET For the first mesh (607210 cells) simulation

with relative inlet total pressure equal to 0.25 MPa (conditions of normalized tests ([4]) was performed.

Simulations lead to a minimum absolute pressure of -1 MPa, a flow rate of 0.786 kg/s and a maximum velocity of 42,59 m/s.

We can see on figure 21 that area of cavitation is much greater than those in the case of pressure inlet of 0.12 MPa, which is quite normal and can be associated to the large increase of flow velocities in narrow zone.

Figure 22. isopression for inlet pressure=0.25 MPa

9. CONCLUSIONS Simulations of a flush valve in case of opening

or closing conditions have been performed using classical models in FLUENT and in STAR CCM+ and cavitation model in the same CFD with steady state conditions.

Results of the pressure field with classical models (with no cavitation) indicate areas where cavitation occurs : regions where the pressure is negative and also regions where the pressure is near to the vapor pressure value specified in the problem set up.

Examination of water vapor fraction with cavitation model in FLUENT (and in STAR CCM+) confirms that cavitation indeed occurs in these regions.

The influence of turbulent model, mesh size, mesh type and the value of total inlet pressure have been studied. Even with coarse mesh, cavitation was showed with classical model (with no cavitation), with no particular parameters unless in case of prism layer. On the contrary, cavitation models need some precautions to give available results (low under_relaxation parameters, good meshes…).

Using classical model is an economical method for testing trial flush valve and for detecting cavitation, source of noise through a large range of operating conditions. It is an economical tool for engineers to estimate the design of valve avoiding cavitation.

REFERENCES [1] NF EN 12541, 2003, norme européenne

“Robinetterie sanitaire, robinets de chasse d’eau et d’urinoirs à fermeture hydraulique automatique PN 10 »

[2] ISO 3822, 1997, Mesurage du bruit émis par les robinetteries et les équipements hydrauliques utilisés dans les installations de distribution d’eau

[3] Lecoffre Yves, « Cavitation Bubbles Trackers », Balkema, 1999. 399 pp. ISBN 90 5410 783 9. 75 Hfl.

[4] Gao, H, Fu, X, Yang, H , Tsukiji, T, 2002, “Numerical investigation of cavitating flow behind a poppet valve in water hydraulic system”, Journal of Zheijang University Science V3,No. 4, pp 395-400.

[5] FLUENT documentation user’s guide

[6] STAR CCM+ documentation

[7] Romeu, J, Jiménez, S, Capdevilla R., 2004, “Noise emitted by water supply installations”, Applied Acoustics 65, pp 401-419.

numerical study of cavitating flow inside a flush valve

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