Evaluation of Air/Cavitation Interaction Inside a Vane … · Evaluation of Air/Cavitation Interaction Inside a Vane Pump Federico Brusiani, Ph.D, Eng, Gian Marco Bianchi, Ph.D, Associate

Evaluation of Air/Cavitation Interaction Inside a Vane Pump Federico Brusiani, Ph.D, Eng, Gian Marco Bianchi, Ph.D, Associate Professor, Marco Costa, Eng DIEM Department University of Bologna, Italy Raffaele Squarcini, Ph.D. Eng., Matteo Gasperini Eng. Pierburg S.p.A. Livorno, Itay ABSTRACT Generally, in a positive displacement pump, cavitation can occur when the fluid pressure falls under the vapour pressure at the operating conditions. This phenomena leads to the generation of vapour bubble dispersed inside the flow. In fluid power application, cavitation is mostly detrimental because the vapour bubbles could be transported by the fluid toward the high pressure zones inside the pump causing their implosion and hence shock waves. When these shock waves are sufficiently close to the pump walls their physical action on the walls appears as a surface mechanic erosion. Direct detection of cavitation is quite impossible because of the difficulties in positioning experimental sensors inside the fluid power components. To overcome this problem a valid alternative approach could be represented by the Computational Fluid Dynamic (CFD) tools. In this paper the CFD analysis of a vane pump is presented. All the 3D simulations were performed using Fluent V12. In particular, the pump analysis was focused on the generation and evolution of the cavitation phenomena inside the machine to identify the locations where this phenomena can occur. Moreover, the influence of incondensable gas dissolved inside the fluid operator on both pump performance and cavitation evolution was evaluated. Significant results were obtained about the influence of expansion/compression of non-condensable gas on the cavitation evolution. The adopted approach is generic in nature, and the obtained results can be easily use to optimise other pump designs as well. 1. INTRODUCTION Two different processes in liquid flow can promote the nucleation of vapor bubble: cavitation and boiling [1,2]. Cavitation is the process of nucleation in a liquid that occurs when the liquid pressure falls below the vapor pressure, while boiling is the process of nucleation that occurs when the liquid temperature is raised above the saturated liquid/vapor temperature with heat addition [3,4,5]. In this paper, only the cavitation phenomena was examined. In fluid power system, cavitation is an ordinary and undesirable problem because it degrades the machine flow rate and produce physical damages on the machine case [6,7], and produce undesirable noise [8]. For these reasons, it is important to verify the existence of cavitation and its location inside fluid power systems. In particular, the evaluation of

EASC 20094th European Automotive Simulation Conference

Munich, Germany6-7 July 2009

Copyright ANSYS, Inc.

dissolved gas influence on cavitation evolution could be very important because, virtually, all liquids contain some dissolved gases. Indeed, it is virtually impossible to eliminate these gases from any substantial liquid volume. For example, water contains about 15ppm of dissolved air (saturation at atmospheric pressure) and it takes more than a week to reduce the air amount dissolved in water to 3ppm [3]. When voids are generated inside a liquid flow containing dispersed gas, the void filling process could be subdivided into two steps [3]:

• Firstly, when the local pressure of a liquid is reduced sufficiently, dissolved gas starts to come out of solution and it is diffused through void wall into the void;

• Secondly, when pressure in the liquid is further reduced, evaporation pressure of the liquid is achieved and the liquid starts to evaporate filling with vapor the cavity;

Also from the cavitation evolution point of view, dissolved gas concentration has an influence on the bubble dynamic evolution. It could be described considering the equilibrium equation of a generic bubble having radius R and pressure pB, surrounded by a liquid at pressure p:

2B

Sp pR

− = − (1)

where S is the surface tension. If the nucleated bubble contains a gas, the bubble pressure pB can be expressed as the sum of the partial pressure of this gas, pg, and the vapor pressure pv. Eq.(1) can be rewritten as:

2( )v gSp p p

R− + = − (2)

or 2

v g

SRp p p

=+ −

(3)

Eq.(3) shows the influence of dispersed gas on bubble radius [9] at equilibrium condition. When the bubbles generated inside the fluid flow are subjected to a pressure rise, their growth is stopped and bubbles start to collapse due to dissolution of air and condensation of vapor. If bubble implosions are violent enough and take place near enough to the solid material, mechanic degradation (cavitation erosion) on the machine internal walls can be observed. Despite its importance, the mechanism of cavitation erosion is still not fully clear. At present, there are two possible ways to explain mechanic cavitation erosion [10,11,12]:

• When a cavity collapses within the body of liquid, the collapse is symmetrical. The symmetrical collapse of a cavity emits a shock wave to the surrounding liquid (Figure 1-a);

• When a cavity is in contact with or very close to the solid boundary, the collapse is asymmetrical and the cavity is perturbed from the side away from the solid boundary. Finally the fluid is penetrating through the cavity and a micro-jet is formed (Figure 1-b);

(a) (b) Figure 1: Cavitation erosion mechanisms.

As stated in [13,14], each of this mechanism does not give a full explanation to the observed cavitation erosion phenomena: in both cases the perturbations (shock waves or micro-jets)




produced inside the liquid phase are dumped too rapidly to allow a mechanic degradation of a solid material. To justify the cavitation erosion is necessary to consider each bubble not only like a single bubble dispersed in the liquid but like a bubble who belongs to a bubble cluster. When a bubble in a cluster is collapsing, it triggers each other’s collapse, producing a cluster collapse effect who can produce the cavitation erosion. From what stated above, clearly appear the importance to evaluate the cavitation presence inside a fluid power machine. Experimentally, this goal could be fulfilled performing acoustic analysis based on energy emission due to the bubble dimension fluctuations (bubble growth or collapse [15,16]. However, performing only an acoustic energy analysis, it is quite impossible to identify the cavitation inception point inside the machine. Due to experimental restrictions about direct cavity detections, indirect cavity detection methods have to be adopted. CFD approach can be considered as a good alternative to experimental approach [17,18]. Today, CFD approach is widely used for performance optimization of fluid machinery working with viscous, turbulent flows, also in presence of cavitation, however the numerical reproduction of cavitation phenomena remains a non-trivial problem. This paper presents the CFD numerical analysis of the cavitation phenomena inside a rotary vane pump used in lubrication circuits for heavy duty applications. All the presented simulations were performed by Fluent v12 (Beta version) CFD code. In particular, the main goal of this analysis was to clarify the reasons of localized mechanic erosion (compatible with cavitation phenomena) observed on internal pump walls. Moreover, the influence of air percentage dissolved in the pump working fluid was evaluated on both cavitation evolution and mechanic erosion. 2. PAPER OUTLINE This paper was organized in three main areas. In the first part, an overview about CFD multiphase simulation was presented focusing the attention on cavitation numerical model adopted for these analysis. In the second part, the rotary vane pump geometry was presented together with the adopted simulation set-up and pump boundary conditions. In the last part, numerical results were presented underling the interaction between cavitation phenomena and mechanic surface erosion. 3. FLOW GOVERNING EQUATIONS AND CAVITATION MODEL To perform a multiphase CFD simulation, it is necessary to adopt numerical model able to manage, simultaneously, different fluid phases and their interactions. The mixture model is a multipurpose multiphase model that can model n phases by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities (if the phases are moving at different velocities). The authors refered to [19] for a complete description of the multiphase model implemented in Fluent V12. Additionally to a generic multiphase model, to numerically reproduce cavitation phenomena, an addition transport equation for the vapor phase has to be solved:

( ) ( )v v v e cV R Rtαρ αρ

∂+∇ ⋅ = −

∂

uur (4)

where α is the vapor volume fraction, ρv is the vapor density, vVuur is the vapor phase velocity,

Re is the mass transfer source term connected to the vapor bubble growth, and Rc is the mass transfer source term connected to the vapor bubble collapse. This additional transport equation describes the liquid-vapor mass transfer and it has to be solved together with the continuity and Navier-Stokes equations previously presented for the mixture model. To solve Eq. (4) it is necessary to model the mass transfer terms, Re and Rc




by the cavitation model. Different cavitation models adopt different methodologies to model the mass transfer terms. In this paper, the cavitation model proposed by Zwart-Gerber-Belamri (ZGB) [20,21] was used. ZGB cavitation model is based on the Rayleigh-Plesset equation (RP) [3] that describes the dynamic growth of a gas bubble nucleated inside a liquid. The general form of RP equation is:

22

243 2

2lB B B

B Bl B l B

VD R DR p p SR RDt R RDt ρ ρ

⎛ ⎞−⎛ ⎞+ = − ⋅ −⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(5)

where RB is the bubble radius, S is the liquid surface tension, ρl is the liquid density, pB is the bubble surface pressure, and p is the local far-field pressure. Usually, within an Eulerian-Eulerian frameworks for multiphase flow, a first order approximation of Eq. (5) is adopted neglecting also the surface tension force. By these reductions, the Eq. (5) becomes:

23

B B

l

DR p pDt ρ

⎛ ⎞−= ⋅⎜ ⎟⎜ ⎟

⎝ ⎠ (6)

The basic assumptions that ZGB adopted to develop a source term form for the total interphase mass transfer rate per unit volume (R) were:

• Bubble growth and collapse follows the simplified version of the RP equation; • Bubbles are assumed to grow from an initial average radius of RB and return (when

condensing) to bubbles of the same size; • All the bubbles in a system have the same size; • The are no thermal barriers to the droplet growth;

On the basis of these assumptions, ZGB defined R as: 24 BB v

DRR n RDt

π ρ= (7)

where n is the number of bubbles per unit volume of the mixture, available as nucleation sites. Substituting Eq. (6) into Eq. (7):

2 24 sgn( )3

vB v v

l

p pR n R p pπ ρ

ρ−

= − (8)

where n is given by:

33

4d

mb

nR

αα

π= (9)

during bubble vaporization, and:

33

4v

bn

R

α

π= (10)

during bubble condensation. αm, αv, and αd represent respectively the volume fractions of the mixture, the vapor, and the dispersed phases. n is not the only parameter who changes depending on the direction of the phase change (vaporization/condensation). In fact, the vaporization and condensation processes are also characterized by different time scales: the condensation process is typically slower than the evaporation process. To take into account this difference, an empirical constant factor F has to be introduced in Eq. (8). All in all, the final equations for Re and Rc source terms are:

( )3 1 23

nuc v v ve vap

B l

p pR F

Rα α ρ

ρ− −

= ⋅ ⋅ (11)

if vp p≤ (vaporization) and:




3 23

v v vc cond

B l

p pR F

Rα ρ

ρ−

= ⋅ ⋅ (12)

if vp p> (condensation). Typical values for F are: 50 when vaporization occurs and 0.001 when condensation occurs. These values were obtained by experimental testing performed by [22] and [23]. To use the presented cavitation model is also necessary to define two other parameters: the volume fraction of nucleation sites αnuc (correlated to the mass fraction of non-condensable gas) and an estimation of the bubble radius RB. Typical values for these parameters are equal to 10e-6 m for RB and 5e-4 for αnuc . 4. ROTARY VANE PUMP CFD SIMULATION 4.1 Pump Design and Boundary Conditions As previously introduced, this paper presents the fluid dynamic analysis of a rotary vane pump. In particular, the pump considered in the present analysis was designed to work as re-circulation pump on lubrication circuit for heavy duty applications. The considered computational domain was made by three main parts (Figure 2-a): Pump inlet plenum, Pump outlet plenum, and Rotor ring having nine vanes generating nine chambers. Each vane rotates off-centre with respect to the housing guaranteeing the expansion of the volumes during the suction phase and the contraction of the volumes during the discharge phase (Figure 3). This expansion/contraction of the volumes generates the pumping action. As boundary conditions, a total pressure boundary condition was placed on the inlet section and a static pressure boundary condition was placed on the outlet section (Figure 2-a). Table 1 summarizes the main fluid dynamic conditions imposed on the inlet/outlet boundaries. Sliding interfaces were placed between rotor and inlet/outlet plenums to allow the fluid dynamic connection between the volumes (Figure 2-b). Table 1: Boundary fluid dynamic conditions.

Abs. Pressure [Pa] Temperature [K] Inlet 1.013e+5 393

Outlet 8.38e+5 393

(a) (b) Figure 2: Vane pump computational domain.




Figure 3: Pump rotor ring section.

4.2 Mesh Generation and Moving Mesh To perform the CFD simulations, a fully unstructured hexahedral/tetrahedral mesh was generated by using Gambit mesh generator. Inlet/outlet plenums were discretized by tetrahedral elements while rotating chambers were discretized by hexahedral elements (Figure 4). The total number of cells was near 530000. To simulate change-in-time shape of the rotor chambers the Fluent v12 dynamic mesh capability was used. In particular, the motion was described by the definition of an user define function (UDF). On the basis of this UDF, the displacement of each mesh node of the rotor was defined as the sum of two motions: a solid body rotation and a radial translation. Node displacements were a function of chamber eccentricity, revolution speed, and the rotor/case shapes. Based on these inputs, Fluent automatically updated the rotor mesh at each time step. The use of this UDF to manage the vane motion instead of a classic smoothing/re-meshing approach was very useful to reduce the computational cost and to improve the numerical stability of the simulation. Moreover, using the defined UDF no addition/subtraction of cells was necessary during the mesh motion.

(a) (b) Figure 4: Mesh structures inside the inlet plenum (a) and the rotor chambers (b).

4.3 General Numerics All the CFD simulations of the rotary vane pump were performed by using Fluent v12 (Beta version) adopting a segregated flow solver together with a fully implicit first-order transient scheme [19]. In particular, to simulate the cavitation phenomena, the mixture model was adopted together with the Zwart-Gerber-Belamri (ZGB) cavitation model.




In all the simulations a flow with two-phase three-component was considered, assuming no interphase slip and thermal equilibrium between any of the phases/components (Homogeneous Equilibrium Model). As flow components were assumed: lubricant oil in fluid state (primary phase), lubricant oil in gaseous state (secondary phase), and air as non-condensable gas (dissolved phase). The liquid compressibility was considered supposing isentropic condition for the fluid. Under this hypothesis, the liquid compressibility was expressed as:

1

ref

P

ρρ

β

=⎛ ⎞Δ−⎜ ⎟

⎝ ⎠

(23)

where β is the bulk modulus. Under the same hypothesis, the liquid sound velocity assumed this form:

a βρ

= (24)

The vapor density was assumed as a constant, evaluated at the vapor pressure and nominal fluid temperature. The air density was evaluated by the ideal gas equation of state using local pressure and temperature information from the solution. Table 2 summarizes the physical characteristics of the three fluid components. Diffusive and convective fluxes were discretized adopting first-order upwind scheme while turbulence was simulated by a standard k-ε turbulence model [17,18]. The pump was tested at a rotation velocity of 5000 rpm, the same rotation velocity at which the experimental tests were performed. For each pump simulation, at least five complete rotor revolutions were simulated. This was necessary to avoid the influence of initial fluid dynamic conditions on the simulation results. Table 2: Fluid physical characteristics.

Oil Fluid Oil Vapor Air Density [kg/m^3] 801 0.0137 Ideal Gas

Bulk modulus [Pa] 1e+9 - -

Viscosity [kg/m⋅s] 0.008 7e-4 1.78e-5

Sat. pressure [Pa] - 1545 -

4.4 Simulation Results Next, the numerical results related to the fifth rotor revolution are presented. In particular, to evaluate the influence of non-condensable gas on cavitation evolution, an air volume fraction equal to 0.8 % was considered. This air concentration value was the closest to the real pump operating condition. The mean outlet volume flow rate was available as experimental data. Under the imposed operating conditions (Table 1), the inlet/outlet volume flow rates reported in Figure 7 were recorded during the pump simulation. The inlet volume flow rate was almost constant during the rotor revolution while the outlet volume flow rate was fluctuating with a specific frequency. The mean numerical outlet volume flow rate was equal to 119 lt/min while its experimental value was equal to 113,8 lt/min. It shows that the overall pump performance was well predicted by numeric simulation.




Figure 7: Vane pump inlet/outlet volume flow rates recorded during the fifth rotor revolution.

In particular, by CFD simulation an imbalance of about 11 lt/min between inlet/outlet volume flow rates was found. As detailed after, this was due to the expansion/compression of the air (dissolved in the liquid) during the charge/discharge phases of the rotor chambers. The first step of pump numeric analysis was to understand where and why cavitation structures could be generated inside the pump. To do that a detailed analysis of the pump fluid dynamic behaviour during chamber charge/discharge phases was mandatory. Rotor chamber discharge phase Generally, the volume flow outlet fluctuation could be considered linked to two main aspects: pump fluid dynamic operating conditions and pump mechanic operating principle. To clarify this statement, Figure 8-a-b-c can be considered. Figure 8-a shows the time instant when the generic pump chamber, named a’, was isolated from both inlet/outlet plenums. In this position the mean absolute pressure inside the a’ chamber was of the order of 5e+4 Pa. As expected, this pressure value was lower than the inlet pressure at pump inlet section because of the fluid dynamic losses encountered when the fluid moved from the inlet plenum to the rotary pump chamber through the suction passages. The main consequence of this fluid pressure reduction was the expansion, during the suction phase, of the air dispersed in the liquid. Figure 9 shows the air distribution inside the rotor chamber at the rotor position of Figure 8-a. As could be noted the air volume fraction reached concentration higher than 50% in extended zones inside the a’ chamber. Carrying on the rotor revolution, the a’ chamber was connected to the outlet plenum (Figure 8-b) where a mean absolute pressure value higher than 8e+5 Pa was available. At this time, the pressure difference drove the fluid from the outlet plenum to the a’ chamber causing the compression of the mixture contained inside the chamber itself. The fluid compression rate depended on the air concentration inside the main liquid phase (increasing the air percentage, the mixture bulk modulus was reduced). In the considered case, the compression of the fluid inside the a’ chamber produced a macroscopic reduction of the mean volume flow rate recorded on outlet system section (Figure 8-d). During the fluid compression inside the a’ chamber, its mean total pressure increased until the flow inverted its direction (from the a’ chamber to the outlet plenum) producing a macroscopic rise of the mean volume flow rate recorded on the outlet system section (Figure 8-d). Obviously, the volume flow rate fluctuation frequency was defined by the total chamber number and the velocity revolution.

-200

-150

-100

-50

0

50

100

150

200

1440 1530 1620 1710 1800

Inlet Volume Flow Rate Outlet Volume Flow Rate

Volu

me

Flow

Rat

e [lt

/min

]

Angle [°]




Rotor chamber charge phase About the rotor chamber charge phase, its fluid dynamic behaviour was quite different to the rotor chamber discharge phase previously presented. To understand why, the rotor chamber coming from the discharge side and isolated from the inlet/outlet plenums was considered. In this angular position, the chamber mean absolute pressure was about 8e+5 Pa, i.e. the mean absolute discharge pressure. It meant that, when the rotor chamber engaged the inlet plenum, the pressure difference between the two connected volumes was the same as during the discharge phase (obviously, now the volume of fluid at 8e+5 Pa was much lower than during the discharge phase). Nevertheless, the inlet volume flow rate fluctuations were quite lower than the outlet volume flow rate fluctuations. This was possible because of the different air distribution inside the rotor chambers before their connection with inlet/outlet plenums. Figure 10 shows the air volume fraction distribution inside the rotor chamber just before its connection to the inlet plenum: no zones with an air volume fraction concentration higher than 0.1% were identified, therefore no significant air expansion could be expected after the engagement between the rotor chamber and the inlet plenum. From the previous analysis it could be stated that during the pump working cycle the highest fluid dynamic gradients could be expected during the chamber discharge phase and, in particular, only just the connection between the a’ chamber and the outlet plenum (Figure 11-a). At this time the highest pressure difference was concentrated across the smallest cross section (Figure 11-b). Numerical simulation showed as such fluid dynamic conditions could promote the generation of voids inside the flow that, due to their sudden growth, could not be covered only by the expansion of the air dissolved in the main fluid flow. In such void zones it was found as the pressure fell below the liquid vaporization pressure promoting its vaporization especially in the lower part of the rotor volumes (Figure 11-c). CFD simulations detected cavitation zones also along the upper rotor interface but more attention was focused on the lower rotor discharge side because here the vapor bubbles were generate very close to the pump case: from the cavitation damage point of view it meant that the risk of mechanic erosion was the highest in such zone. Experimental tests confirmed the detection of cavitation erosion closer to the lower rotor outlet interface near the side where the pump chambers engaged the outlet plenum (Figure 12). To perform a detailed fluid dynamic analysis of the lower outlet plenum, two probe points, named I and H, were placed on the lower wall of the outlet plenum part (Figure 13). The probe point I was placed inside the zone where cavitation erosion was experimentally detected. Moreover, two additional probe points, named J and K, (symmetric to the previous ones) were placed on the upper wall of the outlet plenum part. For each probe point the pressure and the vapor volume fraction were recorded during a complete rotor revolution.

(a) (b) (c) (d) Figure 8: Discharge phase.




Figure 9: Distribution of the air volume fraction inside the a’ chamber just before its connection with the outlet plenum (Red colour = 58% of air volume fraction; Blue colour = 0% of air volume fraction).

Figure 10: Distribution of the air volume fraction inside the a’ chamber just before its connection with the inlet plenum (White = Red colour = 0.8% of air volume fraction; Blue colour = 0% of air volume fraction).

(a) (b) (c) Figure 11: Velocity vector distribution and void generation only just the connection between the a’ chamber and the outlet plenum.

Figure 12: Cavitation damaged experimentally observed.

Figure 13: Probe point positions.




Figures 14 and 15 show pressure and vapor volume fraction evolutions recorded at the probe point position I along the first part of the fifth rotor revolution. As expected, the pressure was oscillating neighbourhood the value of 8e+5 Pa: this was due to the previously described fluid dynamic behaviour of the generic a’ chamber during the discharge phase. Comparing Figures 8-d and 14 it was possible to observe as the pressure value recorded at I location was the lowest just after the engagement between the a’ chamber and the outlet plenum. After this instant the pressure at I location rapidly increased reaching the highest value. As could be noted, the pressure at I location never fell under the vaporization pressure value, however a vapor volume fraction different from zero was here recorded (Figure 15). It was possible because, thanks to the fluid flow configuration, vapor bubbles were transported by the flow at I location just after the engagement between the a’ chamber and the outlet plenum. In particular, analysing the phasing between pressure and vapor volume fraction profiles (Figure 16) it could be observed as the vapor bubble residence time at I location was very small, just 6-7 degrees of revolution. This was due to the pressure profile that promoted the sudden collapse of vapor bubbles. Simulations identified the zone around I location as a vapor condensation zone and not as a vapor generation zone. Thus the relation between the vapor generation timing and the pressure profile was the key about the cavitation erosion. In fact, the very fast pressure increment recorded at I location just after the vapor cluster migration in this zone, forced the bubbles to collapse very fast and, due to geometry configuration, close to the wall. This behaviour promoted the generation of an intense instantaneous load on the solid surface, therefore the cavitation erosion as experimentally observed. Figure 17 shows the condensation rate at I location: according to the previous analysis its value, defined by Eq. (12), was the highest just near the lower outlet plenum edge. To understand why only at I location cavitation erosion was detected, its pressure and vapor volume fraction profiles were compared with the profiles recorded at J, H, and K locations. Figures 18 and 19 show the comparison between the recorded profiles at I and H locations. As can be noted, in terms of maximum pressure value the pressure profile recorded at H location was very close the pressure profile recorded at I location (Figure 14). The main difference between the two pressure profiles resided in the minimum pressure value. As previously discussed, at I location vapor was not generated but condensed, in fact minimum pressure value did not fall below the vaporization pressure. Differently, at H location the minimum pressure value fell below the vaporization pressure: also this location was a generation point of vapor bubbles but these bubbles were carried away from the main fluid flow, therefore the bubble condensation rate at H location was very low in comparison with the value recorded at I location. Moreover, the vapor volume fraction at H location was of one order of magnitude lower than at I location. From these considerations mechanic erosion could not be expected at H location as experimentally confirmed (Figure 17). Similar considerations could be made at J and K locations. Here, the minimum and maximum pressure values were of the same order of magnitude that at I location (Figure 20), therefore cavitation structures could not be generated in these locations. However, vapor volume fraction values different from zero were recorded in both J and K locations (Figure 21) because vapor bubbles were transported here by the main fluid flow. Anyway, differently from I location, J and K locations could not be considered as condensation points for the vapor bubbles because, due to the different geometric configuration with respect to the lower discharge part, these vapor bubbles were not forced to collapse near the pump internal walls, therefore, as experimentally confirmed, also in these locations mechanic erosion could not be expected. 4.5 CONCLUSION The aim of this paper was to study the fluid dynamic conditions inside a rotary vane pump designed for lubricant system system of heavy duty engines. In particular, the analysis was focused on the cavitation detection and on the evaluation of cavitation erosion risk.




CFD approach was used to reproduce the fluid dynamic pump behavior adopting a multiphase approach together with the Zwart-Gerber-Belamri cavitation model. By the analysis of the simulation results, it was possible to point out the main aspects driving the pump chamber discharge phase during which, as experimentally observed, cavitation erosion was generated. The risk of cavitation erosion was evaluated comparing the pressure and the vapor volume fraction profiles at different locations inside the outlet plenum: when vapor volume fraction and pressure peaks were phased, high condensation rate value was detected. A good match between experimental and numerical position of cavitation erosion zones was obtained. In conclusion, our findings suggest as today, adopting CFD approach, is possible to perform a qualitative analysis of the cavitation zones inside a rotary vane pump obtaining also information about cavitation erosion risk. On the basis of the presented results the considered rotary vane pump was modified finding a rotor/case configuration able to reduce the pump cavitation tendency, therefore the possibility of cavitation damage of the component.

Figure 14: Pressure profile recorded at the probe point position I.

Figure 15: Vapor volume fraction profile recorded at the probe point position I.

Figure 16: Vapor volume fraction and pressure profiles recorded at the probe point position I.

Figure 17: Condensation ratio at I and H locations (White colour means high condensation rate – Range 0-200).

0

5 105

1 106

1,5 106

2 106

1440 1485 1530 1575 1620

Probe I: Pressure

Pres

sure

[Pa]

Angle [°]

0

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

1440 1485 1530 1575 1620

Vapor Volume Fraction [-]

Vapo

r Vol

ume

Frac

tion

[-]

Angle [°]




Figure 18: Pressure profiles recorded at the probe point positions I and H.

Figure 19: Vapor volume fraction profiles recorded at the probe point positions I and H.

Figure 20: Pressure profiles recorded at the probe point positions J and K.

Figure 21: Vapor volume fraction profiles recorded at the probe point positions J and K.

REFERENCE 1 Frenkel, J. “Kinetic Theory of Liquid”, Dover, New York, 1955. 2 Skripov, V. P., “Metastable Liquids”, John Wiley and Sons, 1974. 3 Benner, C. E., “Cavitation and Bubble Dynamics”, Oxford University Press, 1995.

0

5 105

1 106

1,5 106

2 106

1440 1485 1530 1575 1620

Probe I: PressureProbe H: Pressure

Pres

sure

[Pa]

Angle [°]

0

5 105

1 106

1,5 106

2 106

1440 1485 1530 1575 1620

Probe J: PressureProbe K: Pressure

Pres

sure

[Pa]

Angle [°]

0

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

1440 1485 1530 1575 1620

Probe J: Vapor Volume FractionProbe K: Vapor Volume Fraction

Vapo

r Vol

ume

Frac

tion

[-]

Angle [°]




4 Acosta, A. J., “Cavitation and Fluid Machinery”, Proc. Of Cavitation Conference, Heriot-Watt Univ. of Edinburgh, Scotland, pp. 383-396, 1974.

5 Arndt, R. E. A., “Cavitation in Fluid Machinery and Hydraulic Structures”, Ann. Rev. of Fluid Mechanic, 13, 273-328, 1981.

6 Nguyen-Schafer, H., Sprafke, P., “Numerical Study on Interaction Effects of the Bubbles Induced by Air-Release and Cavitation in Hydraulic System”, 10th Bath International Fluid Power Workshop, Bath, UK, 1997.

7 Wang, Y. C., Brenner, C. E., “Shock Wave Development in the Collapse of a Cloud of Bubbles”, ASME-FED., 194, 15-18, 1994.

8 Soyama, H., Ito, Y., Ichioka, T., Oba, R., “Observation of Rapid Cavitation Erosion Arising in a Typical Centrifugal Pump”, ASME-FED., Vol. 10.

9 Baur, T., Kongeter, J., Leucker, R “Effects of Dissolved Gas on Cavitation Inception in Free Surface Flows”, Third International Symposium on Cavitation, Grenoble, France, 1998.

10 Knapp, R., Daily, W., Hammitt, F., “Cavitation”, McGraw-Hill, 578 p, 1970. 11 Koivula, T. K., “On Cavitation in Fluid Power”, Institute of Hydraulics and Automation

(IHA) / Tampere University of Technology, Tampere, Finland. 12 Lamb, W. S., “Cavitation and Aeration in Hydraulic Systems”, Bedfordshire,

BHRGroup, 114p., UK, 2000. 13 Hansson, C. M., Hansson, I. L. K., “Friction, Lubrication and Wear Technology”, ASM

Handbook, Vol. 18 p. 214-220, 1992. 14 Preece, C. M., “Treatise on Materials Science and Technology”, Academic Press Inc.,

New York, Vol. 16, Erosion, p. 249-308, 1979. 15 Grenié, M., “Acoustic Detection of Propeller Cavitation”, Université de Provence.,

U4.19. 16 Flynn, H. G., “Physics of Acoustic Cavitation in Liquid”, Physical Acoustic, Academic

Press, 1964. 17 Ferziger, J. H., Peric, M., “Computational Methods for Fluid Dynamics”, Springer, 2001. 18 Versteeg, H. K., Malalasekera, W., “An Introduction to Computational Fluid Dynamics”,

Longman, 2007. 19 Fluent v12 User Manual, Fluent Inc. 20 Zwart, P. J., Gerber, A. G., Belamri, T., “A Two-Phase Flow Model for Predicting

Cavitation Dynamics”, Fifth International Conference on Multiphase Flow, Yokohama, Japan, 2004.

21 Bakir, F., Rey, R., Gerber, A. G., Belamri, T., Hutchinson, B., “Numerical and Experimental Investigations of the Cavitating Behavior of an Inducer”, International Journal of Rotating Machine, 10: 15-25, 2004.

22 Gerber, A. G., “A CFD Model for Devices Operating Under Extensive Cavitation Condition”, IMEC, New Orleans, USA, IMECE 2002-39315, 2002.

23 Shen, Y., Dimotakis, P., “A The Influence of Surface Cavitation on Hydrodynamic Forces”, Proc. 22nd ATTC, St. Hohns, pp. 44-53, 1989.




Documents

Evaluation of Air/Cavitation Interaction Inside a Vane … · Evaluation of Air/Cavitation Interaction Inside a Vane Pump Federico Brusiani, Ph.D, Eng, Gian Marco Bianchi, Ph.D, Associate