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Journal of Loss Prevention in the Process Industries 23 (2010) 773e780

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Journal of Loss Prevention in the Process Industries

journal homepage: www.elsevier .com/locate/ j lp

Computational fluid dynamics simulation of fog clouds due toambient air vaporizers

Filippo Gavelli*

Exponent, Inc., 17000 Science Dr., Suite 200, Bowie, MD 20715, USA

a r t i c l e i n f o

Article history:Received 23 February 2010Received in revised form19 July 2010Accepted 30 July 2010

Keywords:CFDFogAtmospheric dispersionAmbient air vaporizerLNG

* Current address: GexCon US, Inc., 7735 Old GBethesda, MD 20814, USA. Tel.: þ1 301 915 9925.

E-mail address: fgavelli@gexcon.com.

0950-4230/$ e see front matter � 2010 Published bydoi:10.1016/j.jlp.2010.07.009

a b s t r a c t

Ambient air vaporizers (AAVs) are widely used to regasify liquefied industrial gases, which are liquefiedfor transport and storage. Depending on the conditions (temperature and relative humidity) of ambientair and AAV effluent, the potential exists for the formation of fog as the two fluids mix with each other.This has raised some regulatory and environmental concerns that the fog cloud may impact humanactivities in the vicinity of the AAV arrays.

This paper describes a CFD-based modeling approach to predict the formation, dispersion and dissi-pation of a fog cloud due to AAV operation. The model uses the psychrometrics equations to determinewhen saturated air conditions are reached and to calculate mass and energy transfer between the moistair and the fog cloud. A parametric study is presented, based on an array of 6 AAVs, to demonstrate theeffects of wind speed and AAV discharge elevation on the behavior of the fog cloud.

� 2010 Published by Elsevier Ltd.

1. Background

Ambient air vaporizers (AAVs) are widely used to regasify liq-uefied industrial gases, which are liquefied for transport andstorage. Examples of AAV use include the regasification of liquidoxygen in hospitals and liquid nitrogen or argon in metal workingfacilities. More recently, large scale applications of AAVs have beenproposed for liquefied natural gas (LNG) import terminals.

AAVs use ambient air as the source of energy to regasify thecryogenic liquid. Air flows by natural or forced draft on the outsideof long, vertical finned tubes and transfers heat to the cryogenicliquid within the tube (see Fig. 1). The use of heat from ambient airresults in lower operating costs and lower environmental impactthan other regasification methods based on fossil fuel combustionor open loop water circulation. Nonetheless, regulatory and envi-ronmental concerns have been raised about the potential impact ofAAVs used in LNG import terminals, due to the large number ofvaporizers involved in those applications (approximately onehundred or more units, covering a footprint on the order ofa thousand square meters or more). Of particular interest is theformation of fog as the cold air discharge from these large AAVarraysmixes with warm and humid air, and the potential for the fog

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cloud to affect human activities (e.g., transportation) in proximityof the LNG terminals.

This paper will review the physics of fog formation and willpresent a method to quantify, using computational fluid dynamics(CFD), the formation and dispersion of fog from the operation of anarray of AAVs.

2. Principle of operation of AAVs

Ambient air vaporizers are long, single-pass heat exchangerswith the cold fluid (the cryogenic liquid) flowing inside verticaltubes and the warm fluid (ambient air) flowing on the outside(see Fig. 1). The AAV tubes are finned on the outside to increase theheat transfer surface on the air side. The tubes are aligned verticallyto take advantage of the buoyancy-driven downward air flow that isestablished as ambient air cools down between the finned tubes. Inorder to increase the buoyancy-driven flow, as well as the heattransfer surface, AAV towers are generally tall and slender(approximately 3 m by 3 m footprint and 12 m tall, in many LNGapplications). The discharge end (at the bottom of the towers) iselevated above ground to reduce the overall flow resistance and toallow the cold discharge (the “effluent”) to be dispersed (see Fig. 2).

The energy extracted from the air stream consists of both sensibleand latent heat losses. The sensible heat loss results in cooling of theair stream. The latent heat loss is associatedwith the condensation ofpart of the water vapor (moisture) in the air, once the air has beencooled down below its dew point temperature. The condensedmoisture is depositedon thefinnedwalls of the vaporizer tubes. If the

Fig. 1. Ambient air vaporizer with finned tubes gasifying liquid natural gas.

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780774

finned wall temperature is below freezing, the condensed moisturewill freeze on the walls, forming a soft, snow-like frost blanket thatgrows during operation from the base of the AAV towards the top(see Fig. 3). The frost blanket creates thermal insulation between thecryogen and the air, and therefore decreases the heat transfer effi-ciency of the vaporizer. When the cryogen flow is interrupted, thefinned tube walls warm up and the ice falls off, returning the AAV toits original heat transfer efficiency.

Different types of ambient air vaporizers are available. Adistinction exists between “natural draft” and “forced-draft” AAVs.Natural draft AAVs rely solely upon buoyancy to drive ambient airflow through the units. As such, they have no moving parts andresult in the lowest operating cost. However, their performance isstrongly dependent upon ambient air conditions and very sensitiveto flow obstructions created by ice formation. Forced-draft AAVsinstead utilize a set of fans to supplement the buoyancy-driven flowof ambient air through the unit. Therefore, forced-draft AAVstypically have higher air flow rate (i.e., higher regasificationcapacity per unit) and are less sensitive to ambient air conditions.However, operating costs are increased by the presence of the fans.Another distinction exists between “direct” and “indirect” vapor-izers. Direct vaporizers transfer the heat extracted from ambient airdirectly to the cryogenic liquid, which is flowing inside the AAVtubes. Indirect vaporizers, instead, utilize an intermediate fluid thatflows through the AAV tubes to absorb heat from ambient air andthen transfers it to the cryogenic liquid in a separate heatexchanger. For a discussion of the pros and cons of either system,the reader is directed to Shah, Wong, and Minton (2008).

3. Fog formation

The effluent discharged from an ambient air vaporizer is typi-cally at temperatures near or below freezing. It is also at saturation,

as the effluent temperature is by design well below the dew pointof ambient air. As the effluent mixes with ambient air, which iswarmer and has higher moisture content, both the temperatureand the moisture content of the mixture change. Under theassumption of negligible heat transfer to/from the environment(i.e., “adiabatic mixing”), the mixing of cold air effluent andambient air can be traced graphically on a psychrometric chart(see Fig. 4). The psychrometric chart allows the properties of themixed state (e.g., enthalpy, humidity ratio, etc.) to be determined byknowing the conditions of the mixing streams (i.e., ambient air andeffluent) as well as their respective mass fractions, as follows(McQuiston, Parker, & Spitler, 2000):

um ¼ xAuA þ xEuE (1)

hm ¼ xAhA þ xEhE (2)

where:

� A denotes the ambient air;� E denotes the effluent air;� m denotes the mixed air;� u is the humidity ratio (mass of moisture per mass of dry air);� h is the enthalpy (kJ/kg).� x is the mass fraction of the fluid (effluent or ambient air) in themixture.

For any given temperature and pressure, the maximum amountof moisture that can be in the vapor phase is given by the saturationhumidity ratio:

us ¼ 0:622Ps

Pa � Ps(3)

where Pa is the local pressure and Ps is the vapor pressure of watervapor at saturation. Ps can be calculated from the MagnuseTetensformula (Barenbrug, 1974) as a function of local temperature (indegrees Celsius):

Ps ¼ 0:6105 exp�

17:27T237:7þ T

�½kPa� (4)

If the mixture humidity ratio is greater than us, the mixture issupersaturated and the excess moisture (um�us) will condenseinto water droplets e commonly known as “fog” (see point “M” inFig. 4). The fog concentration F will then be given by:

F ¼ rmðum � usÞ�kgm3

�(5)

where:

� rm is the density of the mixed air stream (kg/m3);� us is the saturation humidity ratio at the saturation tempera-ture for the enthalpy hm of the mixed stream.

Whether fog is formed by themixing of effluent and ambient airdepends on the physical states (e.g., temperature and relativehumidity) of the mixing masses. In general, fog will be more likelyto form in higher ambient air temperature and relative humidity.The effect of ambient moisture is shown in Fig. 5: if the effluent(0 �C, 100% RH) mixes with ambient air at 30 �C, 80% RH fog isformed (red line), while if the same effluent mixes with air at 30 �C,40% RH fog is not formed (blue line). For a given effluent state, therange of ambient conditions that will generate fog can be identifiedgraphically as those ambient conditions that fall in the shaded areaabove the line passing through the effluent state and tangent to the

Fig. 2. Array of natural draft ambient air vaporizers.

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780 775

saturation line. The lower boundary of the fog region is graphicallyshown as the green line in Fig. 5.

Fig. 6 shows the variation of relative humidity as a function ofthe degree of mixing (DoM) of the effluent and ambient air in themixed air stream, for the same two cases shown in Fig. 5. The DoMin Fig. 6 ranges from 0 (pure effluent) to 1 (pure ambient air), so theevolution of a mass of effluent as it moves away from the AAV andmixes with ambient air can be visualized by moving from left toright on the plot. The red curve shows that RH> 100% (i.e., fogforms) as soon as mixing occurs, and fog persists until theDoM> 0.74, that is, until the effluent is diluted to a ratio ofapproximately 1e2.8 with ambient air. The blue curve in Fig. 6,instead, never crosses into the fog region (i.e., the relative humidityalways remains below saturation or RH< 100%).

4. Fog dispersion modeling

The cold air effluent from ambient air vaporizers for LNG rega-sification is approximately 25e45 �C colder than the ambient air.Therefore, the density of the effluent is approximately 15e35%higher than the density of ambient air. Before the dispersion of a fogcloud from AAV operation can be modeled, it is important tounderstand whether the fog cloud behaves as a “passive” gas (i.e., itis advected by the existing air flow distribution) or a “dense” gas(i.e., it stratifies near the ground and affects the pre-existing airflow patterns).

A criterion to determinewhen an atmospheric release should betreated as a dense gas release is provided by Britter (1989) in termsof a modified Richardson number. According to Britter’s formula-tion, an atmospheric release behaves as a dense gas release when:

�gr� rara

Q0D

�

U

13

� 0:15 (6)

where:

� g is the acceleration due to gravity [m/s2];� r is the density of the effluent [kg/m3];� ra is the density of ambient air [kg/m3];� Q0 is the total effluent volumetric flow rate [m3/s];� D is the characteristic dimension of the source [m];� U is the ambient air velocity [m/s].

The modified Richardson number is found to be greater than0.15 for most LNG-specific applications of AAVs. Therefore, thebehavior of a fog cloud from an array of AAVs can be expected to besimilar to that of other dense gas clouds (e.g., LNG vapor clouds):the fog cloud will tend to remain close to the ground, and mixingwith ambient air will occur primarily by shear-induced turbulenceat the interface between the two fluids.

This paper presents a method to perform quantitative analysesof AAV-induced fog dispersion using commercially available CFDmodels. The work presented in this paper was performed using

Fig. 3. Active AAV with frost blanket due to condensed moisture (left) and inactiveAAV (right).

Fig. 4. Adiabatic mixing of effluent (E: 0 �C, 100% RH) and ambient air (A: 30 �C, 80%RH). Mixed state (M) corresponds to 50% dilution of the effluent.

Fig. 5. Mixing of effluent (0 �C, 100% RH) with ambient air. The red line (with ambientair at 30 �C, 80% RH) crosses the fog region; the blue line (with ambient air at 30 �C,40% RH) does not. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780776

Star-CCMþ, version 4.02 (www.cd-adapco.com); however, a similarmethod may be implemented with other CFD models.

The overall approach to a fog dispersion simulation using CFD issimilar to that followed for other dense gas releases (Gavelli,Bullister, & Kytomaa, 2008; Luketa-Hanlin, Koopman, & Ermak,2007):

� The simulation domain must be defined, including allgeometrical features that will affect the dispersion of the fogcloud. In this case, the presence of the AAV towers must beaccounted for, as it is likely to have a strong effect on the flowfield and turbulent mixing near the effluent discharge;

� The simulation domain needs to be discretized using a meshthat can accurately resolve the areas where fog is present. Thisis particularly important near the ground, where the stratifi-cation induced by the dense cloud typically requires a high gridresolution in the vertical direction. A grid independence studyor a Richardson extrapolation (Carey, 1997) should be per-formed to ensure that the results are not affected by themeshing choices;

� Initial and boundary conditions must be imposed for velocity,temperature, and turbulence, as well as, for the ambientconcentration of air and water vapor. Boundary conditionsconsistent with the PasquilleGifford stability classes (Turner,1964) should be imposed, unless sufficient data is availablefrom local weather stations.

Fig. 6. Variation of RH with degree of mixing of effluent air (0 �C, 100% RH) withambient air (red curve: 30 �C, 80% RH; blue curve: 30 �C, 40% RH). (For interpretationof the references to colour in this figure legend, the reader is referred to the webversion of this article.)

Table 1Fog dispersion distance for the different scenarios.

Scenario Wind speed(m/s)

PasquilleGiffordclass

Dischargeelevation

Max. fogdispersiondistance

X2F05 2 m/s F 1.5 m 58 mX2F10 2 m/s F 3.0 m 55 mX2F20 2 m/s F 6.0 m 34 mX5D05 5 m/s D 1.5 m 44 mX5D10 5 m/s D 3.0 m 41 m

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780 777

The main difference between modeling a fog cloud and otherdense gas releases is the phase change that occurs when fog isformed or dissipated. Fog formation reduces the amount of excessmoisture by forming water droplets; it is also an exothermicprocess. Conversely, fog dissipation converts water droplets backinto water vapor, while absorbing heat.

A built-in model for moisture condensation/evaporation in thebulk flow, that can track the liquid phase (fog) mass, is not availablein most current commercial CFD codes. Therefore, the methodpresented in this paper applies user defined functions to imple-ment the phase change between water vapor and fog droplets, asdefined by the psychrometric model equations.

When the conditions for fog formation (i.e., RH> 100%) are pre-dicted by the gas dispersion model, condensation of water vaporoccurs andmass is transferred fromwater vapor to fog. However, fogismodeled as a gas-phase component (not as a liquid phase)with thesame thermophysical properties as liquidwater.When conditions forfog dissipation are predicted by the dispersionmodel (i.e., RH< 100%and F> 0), the reverse process occurs: fog droplets evaporate andmass is transferred from fog to water vapor. In both scenarios, latent

Fig. 7. Detail of the computational mesh for the 6-AAV a

heat of vaporization is also released or absorbed according to thedirection of mass transfer. This approach is computationally moreefficient thana “true”multiphase (gaseliquid) simulation. In fact, thismodel allows the convective- and turbulent diffusion-driven motionof the fog to be accurately simulated, while neglecting the gravita-tional drift of the small fog droplets.

The practical reason for concern with AAV-induced fog forma-tion is the impact of fog on visibility, both in proximity of thevaporizers (e.g., for personnel operations) and farther away (e.g., forimpact on road or maritime traffic). In fact, fog consists of a largenumber of minute water droplets suspended in air (ranging in sizefrom approximately 0.3 to over 10 mm). As light passes through fog,it is scattered by the water droplets so that both the intensity of thelight and the contrast of objects are reduced. An object is no longervisible when its contrast with the background can no longer bedetected. Correlating fog density to visibility reduction is quitecomplicated, given the large number of droplets, the stochasticdroplet size distribution and its dynamic variation due to conden-sation, evaporation and coalescence of droplets. Under theassumptions of this model (where droplet size distribution isassumed constant and equal to that of “typical” fog), the effect offog concentration on visibility can be expressed according to thecorrelation by Arnulf, Bricard, Curé, and Veret (1957):

V ¼ 0:024f�0:65 (7)

where f is the fog density (g/m3) and V is the visibility (km).

5. Model validation

There is currently no available experimental data on fogdispersion that would allow a direct validation of the model pre-sented in this paper. However, confidence in the accuracy of the

rray fog dispersion scenario (three AAVs are visible).

Fig. 8. Temperature on a streamwise vertical plane through one row of AAVs, for 2 m/s wind speed: 1.5 m discharge elevation (top); 6 m discharge elevation (bottom).

Fig. 9. Fog isocontour with concentration 10�6 kg/m3 for dispersion from 1.5 m elevation discharge: 2 m/s wind speed (top); 5 m/s wind speed (bottom).

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780778

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780 779

model can be obtained by separately testing the two maincomponents of a fog dispersion model: the dispersion of a densegas release and the psychrometric model.

The dense gas dispersion capabilities of Star-CCMþ were testedby simulating the LNG vapor cloud dispersion experiment knownas Burro 8 (Koopman et al., 1980). The Burro 8 experiment consistedof a spill of LNG onto a water pond and dispersion of the resultingvapor cloud over mostly flat terrain, under low wind and a stableatmosphere. The CFD simulation of the Burro 8 scenario predicteda maximum distance to the lower flammable limit (LFL) withinapproximately 11% of the experimental value. Additionally, thepeak gas concentration at various downwind locations predicted bythe CFD model was well within a factor of 2 of the correspondingexperimental data.

The psychrometric model was tested by comparison with theadiabatic saturator theory (Moran & Shapiro, 2000). A CFDmodel ofa long tube (length/diameter ratio of approximately 100) withadiabatic walls was created and two moist air streams (a ‘cold’ anda ‘warm’ stream) were inserted concentrically at the inlet. Themassflow-averaged temperature, relative humidity and fog concentra-tion predicted by the CFD model at the outlet of the tube werecompared with the theoretical values obtained from the psychro-metric chart. A total of seven combinations of cold/warm streamvalues were tested. The CFD predictions were within less than 0.5%of the corresponding theoretical values for the non-saturatedmixtures and within approximately 12% of the correspondingtheoretical values for fog conditions.

Fig. 10. Streamlines for AAV effluent from 1.5 m elevation discharge: 2 m/s wind speed (top

Based on the results of the dense gas dispersion and of thepsychrometric model, the fog dispersion method presented in thispaper can be expected to provide acceptable estimates of the fogdispersion distances.

6. Examples of application of the fog dispersion model

The dispersion of the fog cloud generated by an array of sixforced-draft AAVs was simulated in order to demonstrate theapplication of the fog dispersion model. The AAVs were grouped intwo rows of three units each, in the direction of the wind. Thevaporizers measured approximately 3 m by 3 m by 12 m tall andwere spaced approximately 1.5 m apart. A total of five scenarioswere examined, in which the wind speed was varied from 2 to5 m/s (at 10 m elevation) and the elevation of the effluent dischargewas varied between approximately 1.5 and 6.0 m, to evaluate theeffect of both parameters on fog dispersion.

The vaporizers were assumed to be shrouded, as is typical forforced-draft units. Each vaporizer was assumed to generate an airflow rate of approximately 45 kg/s, with the effluent being atsaturation at 0 �C. Ambient air was assumed to be at 30 �Ctemperature and 80% relative humidity. The five scenarios were setup as follows:

� Wind speed of 5 m/s at 10 m elevation and neutral atmosphericstability (PasquilleGifford ‘D’ class). Two scenarios were run,with AAV discharge elevations of 1.5 and 3 m, respectively;

); 5 m/s wind speed (bottom). Streamlines are colour-coded according to temperature.

F. Gavelli / Journal of Loss Prevention in the Process Industries 23 (2010) 773e780780

� Wind speed of 2 m/s at 10 m elevation and stable atmosphere(PasquilleGifford ‘F’ class). Three scenarios were run, with AAVdischarge elevations of 1.5, 3, and 6 m, respectively.

The computational domainmeasured approximately 300 mwideby 400 m long by 30 m high and was discretized using a hexahedralmesh with prismatic boundary layer cells at the walls. As shown inFig. 7, a fine mesh with minimum cell size of approximately 0.15 mwas applied to a volume between the ground and approximately0.6 m above the AAV discharge, enveloping the region where fog isexpected. A variable sizemeshwas used to fill the rest of the domain,with cell size growing progressively up to approximately 9.2 m. Atotal of approximately 530,000 cells were used in the simulation.

The realizable keepsilonmodel (Shih, Liou, Shabbir, Yang, & Zhu,1994)was used for turbulence closure and the simulationswere runusing the steady solver. The inlet boundary condition profiles forvelocity, temperature, turbulent kinetic energy and dissipation ratewere obtained from theMonineObukhov theory (Golder,1972). Theground was assumed to be at a constant temperature of 30 �C.

Themaximumdownwind distance reached by the fog cloudwasused as the quantitative term of comparison between the fivescenarios. As shown in Table 1, higher wind speed and higherdischarge elevation tend to accelerate the dissipation of the fogcloud. The effect of discharge elevation is particularly strong oncethe discharge elevation is raised above 3 m (scenario X2F20).

The effect of discharge elevation is also evident in Fig. 8, whichshows the air temperature on a streamwise vertical plane througha row of AAVs for lowwind speed scenarios. In the top image (1.5 mdischarge elevation), the cold temperature effluent fills the gapbetween the AAVs and the ground, creating a “cold” core shieldedfrom the warmer ambient air. In the bottom image (6 m dischargeelevation), the warm ambient air penetrates the region below theAAV discharge, increasing the mixing surface between the twofluids and resulting in faster dissipation of the fog cloud.

Fig. 9 shows the fog cloud isocontours (at a fog concentration of10�6 kg/m3) for the low and high wind speed scenarios (top andbottom image, respectively) and an AAV discharge elevation of1.5 m. The behavior of the fog cloud in the two cases is noticeablydifferent. In the low wind case, the fog cloud extends approxi-mately 50 m laterally (crosswind) on both sides of the AAV array, aswell as approximately 10 m upwind; the cloud remains close to theground, never stretching more than approximately 3 m above theground. The streamlines plot in Fig. 10 (top) shows how the AAVeffluent impinges on the ground and initially spreads radially; thewind affects the effluent jet dispersion only farther away from theAAV towers. In the high wind speed case, instead, the wind isaffecting the AAV effluent even in the region directly beneath thetowers: the jet streamlines (Fig. 10, bottom) are immediatelydeflected and impinge on the ground farther downwind. As shownin Fig. 9 (bottom), there is minimal crosswind spread and noupwind dispersion of the fog cloud. The stronger wake formeddownwind of the AAV array lifts up the fog cloud, which reaches

a maximum thickness of approximately 9 m immediately down-wind of the towers, before dissipating a short distance away.

7. Conclusions

Ambient air vaporizers (AAVs) are widely used to regasify liq-uefied industrial gases, which are liquefied for transport andstorage. Depending on the conditions (temperature and relativehumidity) of ambient air and AAV effluent, the potential exists forthe formation of fog as the two fluids mix with each other. Thispossibility has raised some regulatory and environmental concernsthat the fog cloudmay impact human activities in the vicinity of theAAV arrays. A method to quantitatively predict the formation,advection and dissipation of the AAV-induced fog usinga commercial CFD model was developed and applied to an array ofsix forced-draft AAVs.

The discharge from an array of six forced-draft AAVswas used asan example to demonstrate the application of the fog dispersionsimulation method. The example evaluated the effects on fogdispersion of AAV discharge elevation and of wind speed. Consis-tent with the experience gathered from other dense gas releases,higher wind speed was shown to accelerate the dissipation of thefog cloud. An increase in the elevation of the AAV discharge resultedin faster mixing of the effluent with ambient air and, as a result,shorter fog dispersion distances.

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