injector study via vof: emphasis on vapor condensation due to

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Injector Study via VOF: Emphasis on Vapor Condensation

due to Spray

W. Kalata*, K. J. Brown, and R. J. SchickSpray Analysis and Research Services

Spraying Systems Co.Wheaton, IL 60187 USA

Abstract

Condensation and absorption are used in gas scrubbing applications and industrial scale production of chemicals. Various processes that depend on condensation techniques require the usage of liquid injection such as jets and sprays. The mass transfer efficiency of these techniques depends on ability of liquid to disperse into vapor and interact in a controlled manner. Computation Fluid Dynamics (CFD) can be used to aid or verify a design of certain class of spray injectors within condensing processes.

Volume of Fluid (VOF) technique was used to investigate condensing steam due to cooling by atomized liquid. Two

types of hollow cone injectors varying by design and size were investigated at moderate delivery pressure conditions. Initially, both injectors’ spray angles were validated empirically at standard conditions. In this study, the VOF model approaches condensation and evaporation via the Hertz-Knudsen relation. The CFD results revealed a trend that the spray angle decreases as the rate of condensation increases. The increase of the condensation rate was partially dependent on the inverse of characteristic diameter which further was accounted in the VOF mass transfer model.

As presented at: ILASS–Americas, 23rd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA, May 2011

*Corresponding author

2 www.sprayconsultants.com

Injector Study via VOF: Emphasis on Vapor Condensation due to Spray

Introduction

Mass transfer of dispersed liquid has proven to be extremely useful in many industrial applications starting with evaporative flue gas conditioning inside high temperature flow conduits ending with condensing and absorptive systems for production of chemicals. In today’s world, many industrial systems are designed or upgraded to optimize production efficiency with beneficial operating costs. In mass transfer, spray technology provides solutions to many complex problems.

Presently, Computational Fluid Dynamics (CFD) has been widely adopted in many disciplines that involve critical assessment of fluids in motion. As technological advancements in numerical simulation have developed, fluid motion is often coupled with complex heat and mass transfer. Currently, simulation tools are becoming more available and cost effective in engineering applications. The computational sciences have become an integral part of engineering research and design.

Compared with empirical testing, numerical simulation is becoming more cost effective and

more environmentally friendly. While experiments usually can only provide focused point information reliably, CFD can give detailed information of the full computational domain, especially in environments that are difficult to reproduce experimentally.

The focus of this study was to investigate spray condensation properties of two differently sized hollow cone nozzles (shown in Figure 1) spraying liquid into condensing vapor. Only a single fluid in its liquid and vapor states were investigated.

Figure 1. Spraying Systems Co. pressure swirl type spray nozzles (small capacity – left, large capacity – right).

Swirling Nozzle Simulations

The CFD simulations were performed with ANSYS FLUENT version 12.1. The CFD models were reproduced according to the internal geometry inside swirling chambers and orifices for two injectors that are shown in Figure 1. The biggest difference was the spray nozzle capacity. The orifice of the large capacity injector was two orders of magnitude larger than the small capacity nozzle. In some instances, geometry was simplified to reduce geometrical complexities in 3D CAD model (Figure 2).

Meshing was performed within ANSYS Workbench 13. Initially each unstructured grid was composed of about 4.0–4.5 million of mixed cells which employed boundary layer type inflation at all walls. Inside FLUENT, each mesh was converted into polyhedral grid while the boundary layer mesh remained. The grids were reduced to 0.8–1.2 million polyhedral cells. Dense mesh was incorporated in vicinity of orifices.

Size functions were used to focus smaller grid sizes on geometries such as whirling chambers or orifices.

Each CFD model was set up with liquid velocity or mass flow inlet boundary condition (BC) with temperature at 20ºC. The outlet pressure BC was setup as constant zero pressure with standard 1 bar operating pressure. The backflow temperature for

METHODS

Figure 2. Swirling injector chambers used in CFD.



METHODS

the outlets was set as slightly above saturation temperature (Tsat) (105ºC) with only vapor passing through, which means that the liquid volume fraction backflow (LVFBF) was set to zero. Injector and other walls were set as rigid, with no-slip and adiabatic conditions. All vapor material properties were dependent on temperature. The density of the vapor was solved through incompressible ideal gas law, where pressure term is an operating pressure. Throughout all simulations the following models were included: k-e Realizable Turbulence Model, energy enabled and Volume of Fluid (VOF) with inclusion of mass transfer and temperature dependent surface tension of liquid. The simulations were performed in steady state mode. Table 1 shows the BC summary for both injectors used in this study.

Nozzle TX-2 CRC-250Dorifice mm 0.71 82.6Prated* barg 3.79 2.07Inlet BCVIN m/s 5.24 6.48AIN m2 4.7054E-07 0.004927QIN m3/s 2.4656E-06 0.03193QIN lpm 0.1479 1915.7ṁIN kg/s 0.002461 31.871Dh m 0.0007740 0.07921Re – 3.30E+04 4.18E+06TIN °C 20 20Outlet BCType Constant PressurePOUT bara 1 1TBF °C 105 150LVFBF barg 0 0Mass TransferL kJ/kg 2257 2270Tsat °C 100 100βqp** - 0.01 0.01Dq (SMD)* μm 1620 78B - 48.2 1002*laboratory measurement **Hagen et al. [7]

Table 1. Boundary conditions summary

The VOF model used implicit scheme for volume fraction in equation below (1) with modified version of High Resolution Interface Capturing (HRIC) discretization scheme [1].

(1) 𝛼𝛼𝑞𝑞𝑛𝑛+1𝜌𝜌𝑞𝑞𝑛𝑛+1− 𝛼𝛼𝑞𝑞𝑛𝑛𝜌𝜌𝑞𝑞𝑛𝑛

𝛥𝛥𝛥𝛥 + 𝜌𝜌𝑞𝑞𝑛𝑛+1𝑈𝑈𝑓𝑓𝑛𝑛+1 𝛼𝛼𝑞𝑞,𝑓𝑓𝑛𝑛+1 𝑓𝑓 =

= 𝑆𝑆𝛼𝛼 + 𝑚𝑚 𝑝𝑝𝑞𝑞 − 𝑚𝑚 𝑞𝑞𝑝𝑝 𝑛𝑛𝑝𝑝=1

In VOF scheme equation (1) above, ṁqp is the mass transfer from phase q to phase p and ṁpq is the mass transfer from phase p to phase q. By default, the mass source term on the right-hand side of Equation (1) Sα, is zero, but you can specify a constant or user-defined mass source for each phase. Uf, ρq, ρp, αq,f , Δt, V, f, and n are volume flux through face, density of phase q and p fluid, face value of phase volume fraction, time step (or iteration step if steady), volume of cell, cell face index, and computational stepping index [1].

In this study, right side from equation (1) was employed to assess mainly condensation effects within the vicinity of sprayed liquid phase. The mass transfer was conditional with respect to the saturation temperature (Tsat) that was an input by a user. In most cases, for water liquid and vapor, Tsat was set at 100°C since operating pressure was set at standard conditions. In higher pressure applications, Tsat would have to be determined based operating pressure for particular fluid that is being analyzed. Additionally, volumetric heat source (Sh) was included in energy computations. It was computed based on calculated mass transfer for a particular phase (ṁpq) and fluid’s latent heat (L) as shown in equation (2) below.

(2) ̇



Mass Transfer Considerations

The mass transfer model (MTM) used in VOF simulations was based on supplying evaporation and condensation constants (A and B respectively) in mass transfer equations shown in (3) and (4) [1]. These equations represent mass rate per volume (kg/s•m3) transferred through gas-liquid interface. When setting p to be gas phase and q liquid phase, ṁqp becomes mass rate from liquid to vapor (evaporation), ṁpq represents mass rate from gas to liquid (condensation), αp and αq are volume fractions for gas and liquid, and ρp and ρq are densities for gas and liquid.

(3) ̇

(4) ̇

As ANSYS FLUENT documentation points out, A and B need to be fine-tuned accordingly to fluids’ properties while Hertz-Knudsen relation (5) is considered. This formula gives evaporation-condensation flux (F) based on kinetic theory [2-5].

(5) √

( )

β, M, R, Tsat, Psat, and P* are accommodation coefficient, molecular weight, universal gas constant, saturation temperature and pressure, and partial pressure at the interface, respectively. When assuming that pressure and temperature (P* and T*) are close to saturation condition, a combination of (5) with Clasius Clapeyron relation (6) and accommodation for interfacial area within cell volume (7), resulted with derivation for equations (3) or (4), where A or B coefficients take form of equations (8) and (9).

(6) ( ) ( ⁄ ⁄ ) (

)

(7)

(8) ( ) ( )√

(

)

(9) ( ) ( )√

(

)

L, Ai, Dp and Dq are latent heat, interfacial area density, volume fraction of fluid, and representative diameters for both condensation and evaporation, respectively. By quick examination, it can be noticed that density term can make A larger than B by 2 or 3 orders of magnitude, depending on fluid and operating conditions which may vary saturation temperature. Also Dp and Dq could be assumed based on Sauter-Mean Diameter (SMD, D32) measured at that specific flow rate at standard laboratory conditions. As it can be noticed in equations (8) and (9), A and B are proportional to an inverse of SMD.

In various scientific literatures, theoretical and experimental values for evaporation or condensation accommodation coefficients (βqp and βpq respectively) can be found. There, accommodation coefficients are further modified to equations (10) and (11) shown below where Ke and Kc are known as evaporation and condensation constants [4-7].

(10)

(11)

In studies with whirling injectors, water and steam were used to determine injector’s performance when condensation effects are involved. Condensation and evaporation constants for water were available in literature where these constants were obtained through various experimentally and theoretically [4-7]. The value for condensation accommodation coefficient was 0.01 which was chosen based on Hagen et al. [7].

The simulations were performed first without and then with MTM to capture effects of condensation with respect to non-condensing environment. A comparative study was performed indicating spray performance differences.

METHODS



Swirling Nozzle Simulations

The summary of results for low capacity injector simulation with mass transfer is shown in Figure 5 below. The results show partial collapse of the spray plume as compared to the simulation performed without MTM (see Figure 6). Initially, in the case without condensation, the simulation resulted with ~66 degrees. When condensation was included, the temperature of vapor advancing up from the bottom towards the orifice had a temperature drop over a longer span, therefore cooling it earlier (Figure 6 top). The spray angle resulted in ~47 degrees (Figure 7 bottom).

The summary of results for high capacity injector simulation with MTM is shown in Figure 7 below. The results show no collapse of the spray plume with respect to the simulation performed without mass exchange (see Figure 8). Slight variations in temperature were noticed in the swirling core inside the nozzle chamber and in the bottom portion of the spray. Temperature profiles of fluid mixture were slightly higher with MTM where condensing process added heat to the mixture via latent heat. The spray

angle resulted in ~90 degrees for both cases with and without MTM.

Backflow Study

At gas velocity approaching a spray at 4 m/s, the spray collapsed at backflow LVF value of 0.05 (Figure 9 top). With gas velocity at 8 m/s, the spray collapsed partially at LVFBF value of 0.04 (Figure 9 bottom).

Discussion

In low capacity injector study, an inlet BC and injector geometry was set up according to work by Bade et. al. The difference between the reported study by Bade et al. and current study without condensation was the gaseous phase which was water vapor instead of air at laboratory conditions and thermal effects were added with vapor properties varying with temperature. The case without condensation showed some differences in dynamics as compared to Bade et al. work. The spray angle was 66 degrees as compared to 77 degrees reported by Bade et al. Taking account that injector is spraying into less dense gas and with higher viscosity, it experienced

RESULTS & DISCUSSION

METHODS

Backflow Study

Large capacity pressure swirl type of nozzle (see Figures 1 and 2) was used in studying an injector outflow in various liquid volume fraction backflow conditions ranging from 0.0 to 0.05. This backflow was a part of constant pressure outlet BC setup. Overall schematic of the flow problem is shown in Figure 3. In this study, the level of liquid volume fraction (LVF) that advances into swirling core inside the nozzle chamber was varied until the spray collapse. The advancement is due to negative pressure caused by swirling fluid inside and below the nozzle. A toxic fluid mainly composed of trioxin (Metaformaldehye) ~50%, water ~25% and additional toxic chemicals was used in cases with inlet gas velocity BC of 4 and 8 m/s. Mass exchange model described above was enabled.

Figure 3. CFD setup schematic for LVF backflow study.



RESULTS & DISCUSSION

a resistance which posed a result that is somewhat counter intuitive (density and dynamic viscosity of steam at 105°C is 0.58 kg/m3 and 1.25e-5 N·s/m3 respectively and air density and viscosity at 20°C is and 1.21 kg/m3 and 1.79e-5 N·s/m3 respectively).

A quick study was performed where steam temperature was increased consequently decreasing the steam density but increasing the dynamic viscosity and further causing reduction of spray angle. The plot below (Figure 4) shows that the spray angle decrease and corresponding vapor/air kinematic viscosity increase with increasing temperature.

Figure 4. Spray angle and kinematic viscosity with varying temperature.

Discussion

In low capacity injector study, an inlet BC and in-

jector geometry was set up according to work by Bade

et. al. The difference between the reported study by

Bade et al. and current study without condensation was

the gaseous phase which was water vapor instead of air

at laboratory conditions and thermal effects were added

with vapor properties varying with temperature. The

case without condensation showed some differences in

dynamics as compared to Bade et al. work. The spray

angle was 66 degrees as compared to 77 degrees re-

ported by Bade et al. Taking account that injector is

spraying into less dense gas and with higher viscosity, it

experienced a resistance which posed a result that is

somewhat counter intuitive (density and dynamic vis-

cosity of steam at 105°C is 0.58 kg/m3

and 1.25e-5

N·s/m3 respectively and air density and viscosity at

20°C is and 1.21 kg/m3and 1.79e-5 N·s/m

3 respective-

ly).

A quick study was performed where steam temper-

ature was increased consequently decreasing the steam

density but increasing the dynamic viscosity and further

causing reduction of spray angle. The plot below (Fig-

ure 4) shows that the spray angle decrease and corres-

ponding vapor/air kinematic viscosity increase with

increasing temperature.

Figure 4. Spray angle and kinematic viscosity with

varying temperature.

MTM was not included. Steam density was calcu-

lated with ideal gas law shown in equation (12).

(12)

As condensation was included the spray angle col-

lapsed even further as shown in Figure 5. When kine-

matic viscosity of the mixture was investigated around

the orifice, local kinematic viscosity was lower due to

condensed vapor. This is a reversed situation as com-

pared to non-condensing scenario. It poses non-

intuitive scenario where nozzle performance depends

on both heat and mass transfer which are directly

coupled.

In the large capacity injector case, interaction dy-

namics are significantly different. There is a significant

swirling core inside the nozzle chamber and its size has

remained the same when comparing cases with or with-

out MTM. There were slight temperature effects due to

condensation heat sources but the overall dynamics

remained almost identical.

The additional study showed that liquid volume

fraction would have to be higher than 0.04 or 0.05 in-

side the core to decrease the spray angle or even col-

lapse the spray plume. For this to occur, there needs to

be either a high condensation rate inside the core, which

is rather unlikely due to the nature of the spray, or high

enough LVF advanced due to suction of the swirling

action.

There is room for improvement in this model. The

MTM at some point relies on characteristic diameter as

shown in equations (8) and (9) . In this study SMD was

used for the characteristic diameter. It was based on

laboratory measurement of the spray at the same flow

rate but in standard laboratory conditions. The SMD

changes spatially and throughout the temporal evolution

of the spray. Also droplet growth is not accounted for

in MTM. It is likely that mass and heat sources will

decrease as droplets experience growth.

Conclusions

In this study, the performance of pressure swirl

atomizers in condensing fluid were investigated. Two

hollow cone spray nozzles with significant variations in

size (and capacity) were simulated and compared with

non-condensing scenarios.

The small capacity nozzle was affected by the con-

densation where its spray angle partially collapsed

(Figures 6 and 10). The large capacity spray was not

affected directly by condensation (Figures 8 and 10).

However when liquid volume fraction was introduced

into swirling core inside the nozzle chamber, the spray

plume was affected and even collapsed at LVF of 0.05

(Figure 9).

The mass transfer model relied on fluid properties

and on the characteristic diameter that was based on

SMD values. The coefficient for the condensation was

proportional to the inverse of the characteristic diame-

ter; therefore theoretically the smaller the drop size, the

better the condensation rate.

Nomenclature

f cell face index

n computational stepping index inlet mass transfer flow rate mass transfer from phase q to phase p

MTM was not included. Steam density was calculated with ideal gas law shown in equation (12).

(12)

As condensation was included the spray angle collapsed even further as shown in Figure 5. When kinematic viscosity of the mixture was investigated around the orifice, local kinematic viscosity was lower due to condensed vapor. This is a reversed situation as compared to non-condensing scenario. It poses nonintuitive scenario where nozzle performance depends on both heat and mass transfer which are directly coupled.

In the large capacity injector case, interaction dynamics are significantly different. There is a significant swirling core inside the nozzle chamber and its size has remained the same when comparing

cases with or without MTM. There were slight temperature effects due to condensation heat sources but the overall dynamics remained almost identical.

The additional study showed that liquid volume fraction would have to be higher than 0.04 or 0.05 inside the core to decrease the spray angle or even collapse the spray plume. For this to occur, there needs to be either a high condensation rate inside the core, which is rather unlikely due to the nature of the spray, or high enough LVF advanced due to suction of the swirling action.

There is room for improvement in this model. The MTM at some point relies on characteristic diameter as shown in equations (8) and (9). In this study SMD was used for the characteristic diameter. It was based on laboratory measurement of the spray at the same flow rate but in standard laboratory conditions. The SMD changes spatially and throughout the temporal evolution of the spray. Also droplet growth is not accounted for in MTM. It is likely that mass and heat sources will decrease as droplets experience growth.

Conclusions

In this study, the performance of pressure swirl atomizers in condensing fluid were investigated. Two hollow cone spray nozzles with significant variations in size (and capacity) were simulated and compared with non-condensing scenarios.

The small capacity nozzle was affected by the condensation where its spray angle partially collapsed (Figures 6 and 10). The large capacity spray was not affected directly by condensation (Figures 8 and 10). However when liquid volume fraction was introduced into swirling core inside the nozzle chamber, the spray plume was affected and even collapsed at LVF of 0.05 (Figure 9).

The mass transfer model relied on fluid properties and on the characteristic diameter that was based on SMD values. The coefficient for the condensation was proportional to the inverse of the characteristic diameter; therefore theoretically the smaller the drop size, the better the condensation rate.



References

1. ANSYS FLUENT 12.0 - Theory Guide, ANSYS, Inc., Canonsburg, PA, 2009.

2. Ythehus, T. and Ostmo, S., International Journal of Multiphase Flow, 22-1:133-155 (1996).

3. Wang, Z.-J., Chen, M. and Guo, Z.-Y., International Conference “Passive and LowEnergy Cooling for the Built Environment:, Santorini, Greece, May 2005, pp. 543-547.

4. Tamir, A. and Hasson, D., The Chemical Engineering Journal, 2: 200-211 (1971).

5. Marek, R and Straub, J., International Journal of Heat and Mass Transfer, 44: 39-53 (2001).

6. Mills, A.F. and Seban, R.A., International Journal of Heat and Mass Transfer, 10: 1815-1827 (1967).

7. Hagen, D.E., Schmitt, J., Trueblood, M., Carstens, J., White, D.R. and Alofs, D.J., Journal of the Atmospheric Sciences, 46-6:803-816 (1989).

8. Bade, K.M., Kalata, W. and Schick, R.J., ILASS Americas, 22nd Annual Conference on Liquid Atomization and Spray Systems, Cincinnati, OH, May 2010.

Nomenclaturef cell face indexn computational stepping indexṁIN inlet mass transfer flow rateṁqp mass transfer from phase q to phase pṁpq mass transfer from phase p to phase qp first phase (gas)q second phase (liquid)

A evaporation constantAi interfacial area densityAIN inlet BC cross-sectional areaB condensation constantD32 Sauter-Mean DiameterDh hydraulic diameterDorifice orifice diameterDp representative diameter in phase pDq representative diameter in phase qF evaporation-condensation fluxKc condensation constantKe evaporation constantL fluid latent heat of vaporizationLVFBF backflow liquid volume fractionM molecular weightP* partial pressure at the phase interfacePOUT outlet pressure

Prated pressure rated at certain flow ratePsat fluid saturation pressureQIN inlet volumetric flow rateR universal gas constantRe Reynolds numberSα mass source for energy equationSh volumetric heat source for energy equationT temperatureT* partial temperature at the phase interfaceTBF backflow temperatureTIN inlet temperatureTsat fluid saturation temperatureUf volume flux through faceV volume of cellVIN velocity for inlet BC

αq,f face value of phase volume fractionαp volume fraction of phase pαq volume fraction of phase qβ accommodation coefficientβpq accommodation coefficient for condensationβqp accommodation coefficient for evaporationΔt time step (or iteration step if steady)ρp density of phase pρq density of phase q



Figure 5. Summary of CFD results for the small capacity injector.



Figure 6. Main differences between cases with and without mass transfer in the small capacity injector.



Figure 7. Summary of CFD results for a large capacity injector.



Figure 8. Noticeable differences between cases with and without mass transfer in a large capacity injector.

Figure 9. VOF results for backflow study. Effect of LVF backflow on the large whirling nozzle with two gas velocity modes.



Figure 10. Streamlines indicating swirling liquid motion inside and outside the nozzles.

injector study via vof: emphasis on vapor condensation due to

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