Evaluation of Cavitation in a Liquid-Liquid Ejector · 2017-10-19 · Figure 3. Fluid inverse of ejector pump including inlet and exit flow boundaries. Table 1 summarizes the analyzed

ILASS Americas, 24th Annual Conference on Liquid Atomization and Spray Systems, San Antonio, TX, May 2012

Evaluation of Cavitation in a Liquid-Liquid Ejector

Carsten Mehring* Central Engineering, Parker Aerospace

16666 Von Karman Avenue Irvine, CA 92606-4917 USA

Abstract

This paper summarizes the numerical analysis of a liquid-liquid ejector pump with focus on the accuracy of the em-ployed cavitation model and in view of its potential application as a dual- or multi-liquid mixing and injection sys-tem. While the use of gas-phase or gas/liquid-phase ejection systems has found wide application in gas/hybrid burners and scrubbers for air pollution control; the use of liquid-phase ejectors for the mixing and preparation of different liquids and additives prior to atomization or other processing steps is not common place. As a metered-delivery and mixing device, the ejector system has to be properly designed in order to omit onset of cavitation within the em-ployed working fluids and across the system operating range. Cavitation would not only impact ejector perfor-mance, it could also affect steady-state flow conditions and result in poor mixing of the liquid phases which can af-fect the quality of the subsequent processing steps. In order to utilize CFD analysis as part of the design process for the prescribed system, it is important that the em-ployed cavitation model accurately predicts onset and extend of cavitation within the system. As a first step, the pre-sent work focuses on the numerical analysis of a liquid fuel ejector pump over a range of operating conditions and including onset of cavitation. The analysis is carried out by employing ANSYS/CFX v13.0 with its implementation of the Rayleigh-Plesset cavitation model. Comparison with empirical data shows that, the numerical analysis accurately tracks ejector performance and the employed cavitation model accurately predicts the onset of cavitation within the ejector. The relevance of dissolved gases and viscous stresses on the cavitating ejector flow is discussed.

*Corresponding author: [email protected]

ILASS Americas, 24th Annual Conference on Liquid Atomization and Spray Systems, San Antonio, TX, May 2012

Introduction Ejector or jet pumps are commonly used to pump

fuel within an aircraft fuel system. One application in-cludes scavenging fuel from remote corners or the bot-tom of fuel tanks and discharge that fuel at the inlet to the main fuel feed pump(s). See Figs. 1 and 2.

In an ejector or jet pump, a driving fluid is expand-

ed through a nozzle (motive flow), converting its pres-sure energy into kinetic energy thereby reducing its static pressure according to Bernoulli’s Principle. The low pressure high-speed fluid zone downstream of the motive nozzle draws in and entrains the surrounding suction fluid fed from a separate inlet. Motive and suc-tion fluids mix as the static pressure of the mixture in-creases further downstream when kinetic head is trans-formed back into pressure head. The suction fluid can be of the same type as the motive flow or it can be a different fluid. The fact that an ejector pump does not have any moving parts allows the pumping of suction fluids that cannot be delivered by other pumps, e.g., due to impurities such as particle loading, for example.

Figure 1. Schematic of aircraft fuel system includ-

ing ejector pump for fuel scavenging [1].

Figure 2. Two typical ejector pumps out of the

Parker product line.

In the fuel scavenging application described above,

the fuel scavenged from the bottom of fuel tanks is of-ten contaminated with considerable amounts of water (originally dissolved within the fuel or entering the fuel tank via condensation through vent lines); consequent-ly, an important function of ejector pumps in this appli-cation is to disperse any water present within the scav-enged liquid volume (i.e., suction fluid) into fine drops, so that the fuel with its finely dispersed water droplets can be safely consumed by the engine without any per-formance impact. Since traditional ejector pumps do not have any moving parts, they are highly reliable if used within their operating range, latter being limited by the onset of cavitation.

Here, two types of cavitation are to be distinguished; i.e., gaseous cavitation and vapor cavitation both of which are very different in nature. The formation and ‘collapse’ of gaseous cavitation bubbles is a gas diffu-sion process taking place across the bubble interface. This is in contrast to vapor cavitation, where bubble formation and collapse is the result of a phase change of the liquid from liquid-phase to gas-phase, i.e., a very rapid process taking place in microseconds. This rapid phase-change causes the release of considerable amounts of energy when vapor bubbles collapse, which can result in cavitation damage if the bubble collapse occurs close to walls. Gaseous cavitation, on the other hand, will not cause any material damage; however, just like vapor cavitation, it can be the performance limiting factor in ejector pumps.

The present paper investigates a fuel ejector pump

whose performance limit is determined by the onset of vapor cavitation. Accordingly, comparison of the sub-sequently presented CFD results with actual test or em-pirical data provides a means to evaluate the perfor-mance of the cavitation sub-model employed within the analysis. Problem Set-Up and Operating Conditions

Figure 3 shows a cut-away of the fluid inverse gen-erated from the ejector pump geometry considered for this study. The suction flow is fed from a side inlet into a plenum chamber where the suction fluid interacts with the motive flow which enters the cylindrical plenum axially. Geometric dimensions of motive nozzle, ple-num, mixing section and diffuser section are fixed. Various operating points of the ejector pump are ana-lyzed governed by motive and suction flow static inlet pressures and mixture flow static pressure at the dif-fuser outlet.

Figure 3. Fluid inverse of ejector pump including

inlet and exit flow boundaries. Table 1 summarizes the analyzed operating points,

identified by flow ratio Φ = Wi/ Wm with Wi and Wm representing the induced/suction flow and motive flow, respectively; and the non-dimensional total pressure ratio formed by the differences of total downstream and suction pressures (Pt,d - Pt,s), and total motive and down-stream pressures (Pt,m - Pt,d), respectively.

Case Flow Ratio  Φ= W

i/W

m

Pressure Ratio  (P

t,d–P

t,s)/(P

t,m–P

t,d)

1 8.4 0.0094

2 11.6 0.0086

3 13.6 0.0079

4 13.7 0.0075

Table 1. Analyzed ejector pump operating condi-

tions..

Each analysis was carried out by specifying mo-tive, suction and downstream static pressures at the respective boundaries. Motive and suction static pres-sures were held constant. The outlet static pressure was adjusted producing the total pressure ratios and flow rates summarized in Table 1. Reference pressure was 2.5924 psia corresponding to an altitude of 41,000 feet. Pumping fluid was Jet A with a vapor pressure of 0.294 psia corresponding to a fuel temperature of at 140°F.

The analysis was carried out by employing ANSYS

CFX v13.0 using constant fluid properties and the SST (Shear Stress Transport) turbulence model of Menter. Cavitation was modeled by employing the homogene-

ous multiphase model together with the Rayleigh-Plesset Cavitation Model assuming a nucleation site diameter of 2μm. No changes have been made to the other cavitation model parameters, i.e., cavitation con-densation/vaporization coefficients = 0.01 and 50, re-spectively; and nuclei volume fraction of 0.0005. Planar symmetry conditions were employed, i.e., only one half of the ejector was analyzed (see Fig. 3). Total mesh count was 3.1 million and care was taken in order to properly resolve wall shear layers and free shear lay-ers of the discharging motive jet (see Figure 4).

Figure 4: Hexahedral mesh (3.1 million nodes). Top: mesh in symmetry plane. Bottom: Mesh near motive nozzle in symmetry plane. Results Figures 5 and 6 illustrate the flowfield within the prescribed fuel ejector pump under design operating conditions at flow ratio Φ = 8.4 and pressure ratio (Pt,d -

Pt,s)/(Pt,m - Pt,d) = 0.0094 (Case 1 in Table 1). As the suction flow is entrained by the discharging motive jet, its static pressure drops while being accelerated through the throat of the pump (i.e., the interface between ple-num and mixing section in Fig. 3). Note that, suction flow directly entrained from the suction side inlet and not entering the inner plenum volume accelerates around the tight bend connecting suction and mixing

tubes resulting in lower static pressure in the throat re-gion adjacent to the suction inlet tube. As suction and motive flow mix downstream of the throat and as motive flow kinetic energy is converted back into pressure head, the overall static pressure of the mixture increases in the mixing and diffuser section. As seen in Fig. 5, pressure recovery occurs early in the mixing section and is only enhance further downstream in the short diffusing section.

Figure 5: Normalized static pressure for Case 1 (see Table 1) in symmetry plane (top) and in various axial cross-sections (bottom). Scale does not apply to motive nozzle; normalized motive pressure Ps,m/Ps,d = 55.58).

Figure 6: Top: Suction flow streamlines for Case 1 (see Table 1) colored by normalized velocity magnitude (range 0-6.59). Bottom: Velocity contour lines in ejec-tor symmetry plane (range 0 – 24.31). Normalization w.r.t. average exit flow velocity. The suction flow streamline plot shown in Fig. 6 illus-trates that, as static pressure recovers after the throat, the adverse pressure gradient causes local flow separa-tion on both sides of the entrance to the mixing section.

The prescribed flow characteristics do not change as the ratio of induced flow to suction flow Φ = Wi/ Wm in-creases with decreasing diffuser exit static pressure. As the exit static pressure decreases, the depressed suction pressure in the throat also decreases until it drops below the fuel vapor pressure leading to the onset of vapor cavitation. CFD analysis indicates that the operating condition at which this first occurs in the pre-sent ejector pump is at flow ratio Φ = 13.6 and pressure ratio (Pt,d - Pt,s)/(Pt,m - Pt,d) = 0.0079, i.e., Case 3 in Ta-ble 1.

Figure 7: Suction flow streamlines for Case 3 (Table 1) colored by normalized static pressure. Also shown cavitation bubble (i.e., iso-surface of vapor-phase vol-ume fraction 0.5. Pressure normalization w.r.t. absolute static exit pressure Ps,d. Figure 7 illustrates suction streamlines for this case colored by normalized static pressure. The cavitation region is identified by and iso-surface of vapor-phase volume fraction with value 0.5. Cavitation is pro-nounced on the lower section (suction-inlet side) of the mixing tube, with no cavitation on the opposed side and only limited cavitation on the side walls in the entry section of the mixing tube. In addition, there is a very small toroidal cavitation pocket located at the wall of the motive nozzle in the nozzle exit plane. While the overall flow characteristics have not changed, the flow recirculation regions described for Case 1 (see Fig. 6) have considerably decreased in size and shifted downstream. Note that, the flow recircula-tion zone on the cavitating side of the mixing tube is limited to the cavitation zone located farthest down-stream in the mixing tube. The extend of the cavitation region for Case 3 is also illustrated in Fig. 9. As the downstream static pressure is further reduced (Case 4 in Table 1), the cavitation region significantly expands downstream into the mixing section (see Fig. 8) resulting in no further increase in flow ratio (see Fig. 9). The ejector pump has reached its performance limit

and in the present case, the limiting factor is fuel vapor cavitation.

Figure 8: Contour lines of vapor-phase volume frac-tion in various axial cross sections of the ejector pump for Case 4 of Table 1.

Figure 9: Top: Comparison of empirical ejector pump performance data including performance limit and cal-culated performance for Cases 1-4 summarized in Table 1. Flow Ratio Φ = Wi/ Wm, Pressure Ratio = (Pt,d -

Pt,s)/(Pt,m - Pt,d). Also shown, iso-surfaces of vapor-phase volume fraction (= 0.5) for cases with fluid cavitation, i.e., Case 3 (middle) and Case 4 (bottom).

Figure 9 identifies ejector pump performance based on pressure ratio (Pt,d - Pt,s)/(Pt,m - Pt,d) delivered at a given flow ratio Φ = Wi/ Wm as predicted by the prescribed CFD analyses (red dots). Also shown is the perfor-mance curve for the investigated pump based on empir-ical data. As indicated by the 2D-plot, the employed CFD analy-sis accurately tracks pump performance within its oper-ating range. In addition, the employed Rayleigh-Plesset Cavitation Model only slightly overpredicts the onset of vapor cavitation and hence the performance limit for this pump, i.e., (ΦCFD- Φemp)/Φemp= 0.07. Note that, at the performance limit of the investigated pump, i.e., where the performance curve ends in the 2D-plot of Fig. 9, test data shows that the pressure ratio drops sharply to zero. The same behavior is observed when comparing the CFD results for Case 3 and Case 4 described previously and illustrated in Figs. 7 through 9. At the performance limit, any decrease in pressure ratio leads to a rapid expansion of the cavitation region from the throat of the pump downstream into the mix-ing region. While onset of cavitation is found near the pump throat on the suction-inlet side, full blockage of the pump by fuel vapor will take place near the mid-section of the mixing region. Additional Considerations The analysis results presented above were produced using ANSYS/CFX v13.0 with cavitation modeled based on the Rayleigh-Plesset equation for bubble dy-namics [2,3]. Input parameters for this cavitation mod-el are: Liquid saturation pressure, mean diameter of nucleation sites, nuclei volume fraction, two empirical coefficients (Cavitation Condensation/Vaporization Coeff.), and two computational model parameters (max. density ratio, cavitation rate under-relaxation factor). The prescribed cavitation model and the underling equation describing bubble dynamics do not include the effect of viscous stress on cavitation as described in Refs. [4-6] and as reviewed in Ref. [7] nor the effect of gases dissolved within the liquid phase and diffusing into the bubble [8-10]. Effect of Dissolved Gases The influence of the gas content within a nucleus on cavitation inception has been described in Refs. [2,8]. For larger gas-contents, as a consequence of larger amounts of dissolved gases within the fluid, cavitation inception occurs at larger nuclei sizes and at larger fluid pressures. Also, bubbles or nuclei with higher gas con-tent can become visible at pressures above the vapor pressure without leading to vapor cavitation. Their growth or decay is dominated by gas diffusion through the bubble interface and is governed by the amount of gas which can be kept in solution within the surround-

ing liquid. This phenomenon is referred to as gaseous cavitation [9]. It is worthwhile to note that, the performance of ejector pumps can be limited by both, vapor cavitation (as in the present case) or by gaseous cavitation. However, cavitation wear or damage of material walls as a conse-quence of bubble collapse near walls is solely a result of vapor cavitation, i.e., the rapid collapse of vapor bubbles and the associated energy release as a conse-quence of a rapid phase-change process. Gaseous cavi-tation, i.e., the growth and dissolution of gas bubbles within a liquid (driven by a ‘slow’ diffusion process) does not cause material damage. Moreover, the energy released during vapor bubble collapse or vapor cavita-tion (measured in terms of implosion pressure and tem-perature) is significantly reduced with increasing gas-phase content within the vapor bubble [10]. In context with the influence of dissolved gases on va-por cavitation, an improved cavitation model, has been proposed by Singhal et al. [3]. Effect of Viscous Stress Vapor cavitation occurs when the liquid pressure drops below the critical pressure or critical stress also identified as the breaking strength of the liquid. In an idealized case this critical pressure is the vapor pressure of the liquid at the given temperature [6]. Within the present analysis the prescribed criterion for cavitation onset has been employed. However, as proposed and discussed by Joseph [4,5], viscous stresses might have to be considered when ana-lyzing cavitation. In consideration of the prescribed work, the critical pressure formulation of Martynov et al. [7] has been reviewed. According to Ref. [7], cavita-tion occurs when the fluid pressure drops below the critical pressure defined by 2 1 where pv denotes the liquid vapor pressure, μ the dy-namic viscosity of the liquid, μt turbulent/eddy viscosity and Sij

max the maximum principal component of the strain-rate tensor. Within the present CFD analysis, Sij

max is obtained by a user-defined expression transforming the local strain-rate tensor into principal coordinates. For the consid-ered operating conditions, the fuel vapor pressure is pv = 0.294 psia and the dynamic viscosity μ = 8.23· 10-4 Pa s. Figures 10 and 11 show contour lines of turbulent eddy viscosity and maximum principal strain rate in the symmetry plane of the ejector under Case 3 operating conditions (see Table 1).

Figure 10: Contour lines of turbulent eddy viscosity for Case 3 (Table 1) in ejector symmetry plane.

Figure 11: Contour lines of maximum principal strain rate for Case 3 (Table 1) in ejector symmetry plane. While maximum principal strain rates are highest in the motive nozzle, they will not impact cavitation due to high motive operating pressures. However, considera-tion of viscous stress does impact the extend of the cav-itation region present under Case 3 operating condi-tions. Considering an average value of (μ Sij

max)av = 1646 Pa as laminar stress contribution in the vicinity of the cavitation region in Fig. 7, the critical pressure for cavitation to occur increases from the vapor pressure value of 0.294 psia to 0.7716 psia. Figure 12 shows the corresponding pressure iso-surface for Case 3, illustrat-ing a significant increase in the cavitation region under consideration of the laminar viscous stress term in Eqn. (1). Note that, with eddy viscosities averaging 0.2 Pa s in the cavitation region currently predicted for Case 3 (see Figs. 7 and 10), consideration of the turbulent viscous stress term in Eqn. (1) would result in unrealistically high critical pressures and cavitation onset not con-sistent with the experimentally observed performance limit of the investigated ejector pump.

Figure 12: Iso-surface of vapor-phase volume fraction 0.5 (blue) and static pressure iso-surface ps= pv+μ (Sij

max)av = 0.7716 psi (orange) for Case 3 (Table 1).

Summary A liquid fuel ejector pump has been analyzed at various operating conditions including operation at its performance limit induced by vapor cavitation. The analysis was carried out by using ANSYS/CFX v13.0 and its implementation of the Rayleigh-Plesset cavita-tion model. Performance predictions for the pump agreed well with empirical data. Onset of cavitation was shown to be accurately predicted by the employed cavitation model and without considering the effect of dissolved gases within the liquid fuel. Consideration of laminar viscous stress was demon-strated to expand the cavitation region predicted with the current model, indicating an improvement in the prediction of cavitation onset and ejector pump perfor-mance limit. Consideration of turbulent viscous stress based on eddy-viscosity resulted in excessive critical pressure predictions and cavitation onset not in line with empirical ejector pump data. References 1. Langton, R., Clark C., Hewitt, M., and Richards,

L., Aircraft Fuel Systems, Wiley & Sons, 2009. 2. Brennen, C.E., Cavitation and Bubble Dynamics,

Oxford Univ. Press, 1995. 3. Leighton, T.G., “Derivation of the Rayleigh-Plesset

Equation in Terms of Volume,” ISVR Technical Report No 308, Institute for Sound and Vibration Research, University of Southampton, 2007.

4. Joseph, D.D., Phys. Review, E., 51 (3): 1649-1650 (1995).

5. Joseph, D.D., J. Fluid Mech., 366:367-378 (1998) 6. Dabiri, S., Sirigniano, W.A., and Joseph, D.D.,

Phys. Fluids 19: 072112 (2007). 7. Martynov, S.B., Mason, D.J., and Heikal, M.R.,

“Effect of Viscous Stress on Cavitation Flow in Nozzles,” Engineering Research Center, School of Engineering, Univ. Brighton, UK, 2006.

8. Baur, T., et al., Third International Symp. On Cavi-tation, Grenoble, France, April 1998.

9. Holl, J.W., J. Basic Eng., Trans. ASME 82: 941-946. 10. “Cavitation in Control Valves,” Samson Technical

Information Report, Samson AG, V74/Training, Frankfurt, Germany.

11. Singhal, A.K., Althavale, M.M., Li, H., Jiang, Y., J. Fluids Engineering 124: 617-624 (2002).