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A model for assessing fuel jettisoning effects
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Pergamon
Atmospheric Environment Vol. 28, No. 16, pp. 2751 2759, 1994 Copyright © 1994 Elsevier Sclence Ltd Printed in Great Britain. All rights reserved 1352-2310/94 $7.00+0.00
1352-2310 (94) E0076-V
A MODEL FOR ASSESSING FUEL JETTISONING EFFECTS TODD R. QUACKENBUSH a n d MILTON E. TESKE Continuum Dynamics, Inc., P.O. Box 3073, Princeton, NJ 08543, U.S.A. and CONSTANTINE E. POLYMEROPOULOS Rutgers University, Department of Mechanical and Aerospace Engineering, P.O. Box 909, Piscataway, NJ 08855, U.S.A. (First received t0 August 1993 and in final form 5 January 1994)
Ahstrac~The present effort addresses the technical issues associated with hydrocarbon fuel jettisoning from aircraft, including the adaptation of an existing aerial application model for pesticide deposition. The analysis produces qualitatively and quantitatively reasonable results both in multicomponent evaporation calculations for isolated droplets, as well as in fully coupled calculations of airborne fuel jettisoning. Both classes of computations confirm earlier conclusions that the likely groundfall of JP-8 jet fuel is substantially higher than the more volatile JP-4 jet fuel, and reiterate the need for a careful assessment of the environmental impact of fuel jettisoning events involving JP-8. The preliminary model appears to be a suitable starting point for full-scale development of a flexible, practical fuel jettisoning simulation code. Key word index: Modeling, spray behavior, multicomponent evaporation, fuel jettisoning.
INTRODUCTION Fuel jettisoning has always been an option for the U.S. Air Force and the commercial airline industry, in response to an in-flight emergency, unforeseen operational requirement, or in preparation for a carrier landing. It is typically performed to reduce the weight of the aircraft and increase the likelihood of a safe landing. In most cases this operation occurs above the mixing layer height but below the top of the troposphere (1-12 km altitude). Previous work in this area has dealt mostly with the jettisoning of JP-4 jet fuel and its impact on the environment, including simplified preliminary analyses (Lowell, 1959a, b), in situ studies in the atmosphere (Good et al., 1978; Good and Clewell, 1980; Clewell~ 1980a, b), and measured ground contamination (Clewell, 1983; Cross and Picknett, 1973). These references conclude that if JP-4 jet fuel were jettisoned above a certain altitude, the ultimate groundfall would be insignificant and the corresponding environmental impact minimal. Recently, however, JP-8 jet fuel has been replacing JP-4 jet fuel, with still wider use projected for the years ahead. JP-8 (like commercial Jet A) exhibits significantly lower volatility than JP-4, and it is therefore anticipated that a significant portion of JP-8 jettisoned from any position in the troposphere will reach the surface. Pioneering work on the analysis of fuel jettisoning was conducted in the United States by Lowell and
Clewell, and in the United Kingdom by Cross and Picknett. The first flight experiments involved lowlevel (15 m altitude) passes with fuel jettisoned perpendicular to the oncoming airstream. Collection of the jettisoned droplets on sample paper provided early estimates of the droplet size distribution during jettisoning events. Efforts with JP-4 fuel involved several interrelated tasks: a data gathering effort, summarizing over three years of operational experience with fuel jettisoning scenarios in worldwide USAF operations; experimental studies, including in-flight measurements of drop size and laboratory tests of evaporation; and development of a preliminary computational model. The gathered data provided a valuable profile of jettisoning events and indicated that both tactical aircraft (e.g. F-4, F-111) and strategic aircraft (e.g. KC135, RC-135, FB-111) generated a significant number of events. It was found that among strategic aircraft, roughly 60% of jettisoning events were caused by emergency situations, with the remainder being due to operational requirements or aborted missions. Tactical aircraft accounted for the largest number of events, with the weight of fuel jettisoned averaging 2-4 metric tons (roughly 17.8-35.6 kN). Jettisoning events by strategic aircraft (predominantly tankers) averaged 15-20 metric tons (roughly 133.5-177.9 kN) and accounted for the majority of the total fuel jettisoned despite the smaller number of events. Sites were also surveyed and it was found, not surprisingly, that the
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T.R. QUACKENBUSHet al.
highest concentratiori of jettisoning events occurred close to U.S. Air Force bases, with some sites recording over 200 events per year; however, scattered events were recorded across much of the continental United States and Europe. Jettisoning events took place in a wide variety of seasonal and climatic conditions, circumstances that can strongly affect total groundfall. Clewell's work included reports on flight tests using chase aircraft equipped with impact droplet measurement devices. These tests produced estimates of the droplet size distribution roughly 90 s after the passage of a KC-135. This information was used as input into a computational model that produced estimates of the groundfall for JP-4 released from various altitudes. The capsule recommendations that emerged from this study were that a critical altitude of 1500m was identified for tactical aircraft, above which dumps of JP-4 could be made with minimal chance for significant groundfall; the corresponding critical altitude for fuel jettisoning by strategic aircraft, given the larger average volume dumped by these aircraft, was estimated to be 6000 m. Recent events have made it desirable to revisit this issue. As noted by Martel (1987), introduction of JP-8 by the U.S. Air Force will save money due to reduced evaporation losses in stored fuel; however, this reduced volatility will inevitably increase groundfall of jettisoned fuel. The issue of JP-8 evaporation was not addressed in detail by Clewell, but it was suggested that groundfall of JP-8 would increase substantially. The predictive model used by ClewelI neglected aircraft wake effects on the jettisoned fuel; the experience of previous investigations into aerial spray events indicates that wake effects are in general quite important (Tennaukore et al., 1980). Moreover, in recent years mo.e advanced experimental techniques have arisen and have made it both possible and desirable to re-examine the issue of droplet size in the jettisoned fuel stream, especially since droplet size distribution is a particularly critical feature of any evaporation model. Also, community awareness of environmental impact of military activities is if anything higher than at the time of the original work on this topic, a circumstance that makes continuous updating of procedures used to study it very important.
AERIAL SPRAY M O D E L I N G
Over the last 20 years the USDA Forest Service and the U.S. Army have been developing computer models to predict the deposition distribution of aerially released material. The USDA Forest Service selectively uses aerial spray applications to control forest pests, while the U.S. Army is interested in assessing the effectiveness of chemical and biological materials released to the atmosphere in military applications. Both agencies have been interested in achieving a more complete understanding of the behavior of spray
material from the time the spray is released from an aircraft until it has deposited or, in the case of spray drift, diffused to levels below some threshold toxicity. Because mathematical spray dispersion models are useful in determining the interactions of the many factors affecting spray operations, these agencies have supported the continued development and application of these models. The two operational models are A G D I S P (for AGricultural DISPersal) and FSCBG (for Forest Service, Cramer, Barry and Grim, its developers). A G D I S P (Bilanin and Teske, 1984; Bilanin et al., 1989) is based on a Lagrangian approach to the solution of the equations of motion, and includes simplified models for aircraft wake and ambient turbulence effects (including wing-tip vortices, jet engines and propellers, crosswind, vortex decay and material evaporation). FSCBG is a Gaussian line-source model that takes the near-wake results of A G D I S P and predicts downwind dispersion. FSCBG operates on personal computers, with a menu-driven user interface and extensive graphics capability. An overview of its operation, and details on the equations in the model, may be found in Teske et al. (1993). The fuel jettisoning model discussed here retains a substantial portion of the near-wake A G D I S P and downwind dispersion FSCBG working code. The principal modification here is the replacement of the original water-based droplet evaporation model with a multicomponent evaporation model able to predict the evaporation of hydrocarbon fuels. Appendices A and B summarize the Lagrangian and Gaussian formulations in the fuel jettisoning model.
MULTICOMPONENT EVAPORATION The literature on multicomponent evaporation of hydrocarbon droplets is drawn in large part from combustion research, the motivation for this work typically being the combustion of droplet sprays in hot atmospheres. For a given droplet size distribution and composition of the droplet, several critical features of the evaporation process must be modeled if the evolution of the drop size and the ultimate composition of the groundfall are adequately captured. First, because the various components of the droplet will not in general evaporate at a uniform rate, the composition of the droplet will change over time as evaporation proceeds; hence, the time history of the individual evaporating components must be tracked. Second, the energy exchange due to the change of phase of the various components from liquid to vapor must be addressed, and the subsequent transport of the vapor into the ambient atmosphere must be modeled using suitable assumptions about mass and energy flows within the droplet and near its surface. Several different approximations have been used to address this problem. First, a particularly simple
Fuel jettisoning effects formulation can be developed by assuming what is typically called the d2-1aw of evaporation
2
2
ds, o - d~ = 2t
where ds,o is the initial drop diameter, t is time, and 2 is the evaporation constant (Lefebvre, 1989). The model assumes uniformly mixed spherical drops and negligible radiation heat transfer (Godsave, 1953; Spalding, 1953). Initial efforts to apply this model were centered on experimentally determining an appropriate evaporation constant. The simplicity of this approach found its way into other simple evaporation approaches (Trayford and Welch, 1977) where 2 is replaced by the inverse of an evaporation relaxation time t e that includes the wet-bulb temperature depression and a series dependence on the Reynolds number based on relative air speed. Simple numerical models using this approach (Chin and Lefebvre, 1983; Chin e t a l . , 1984) have been developed to examine the evaporation characteristics of JP-4 and JP-5 jet fuel sprays prior to combustion. Another possible approach to multicomponent evaporation is a detailed solution of the partial differential equations governing heat and mass transfer within and surrounding the drop. Typical detailed numerical models (Megaridis and Sirignano, 1990) include equations for the gas and liquid phases (species, energy, state, vorticity, and stream function) and gas-liquid interface conditions at the surface of the drop. Approaches of this type were judged to be too complex for the quick solution desired here. However, using the same governing differential equations and invoking reasonable simplifications regarding the internal structure of the droplet can provide a basis for developing an appropriate model. Combustion researchers in general focus on a hot ambient environment, while the troposphere does not generally fit this description. Sirignano (1983) suggests that low ambient temperatures permit the researcher to discard many of the driving assumptions in the more complicated models, since droplet lifetime is so long that mass concentration of particular components in the droplet may be assumed uniform but time vaiying. In his discussion of such simplified evaporation models, Law (1976) expands on this point by identifying two useful limiting cases that illustrate the major assumptions involved in analyzing droplet evaporation: the first is the case of a very viscous fluid in which diffusion is the dominant transport mechanism; the second is that of a less viscous fluid in which internal convection dominates. In the latter case, internal mixing in the droplet can be assumed to be so fast that at any instant in time the mass fraction of each component within the droplet is approximately spatially uniform (an assumption similar to that later suggested by Sirignano). This is an especially helpful assumption near the surface, since the mixture properties at the surface dominate the evaporation rate for the various components.
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The evaporation model implemented in the present effort is drawn from the work of Law. This model treats the computation of evaporation from an isolated droplet composed of an arbitrary number of hydrocarbon compounds. Implementation of this model, and comparisons with two-component mixtures of hexane and octane, are in agreement with those predicted by Law, and are not reproduced here, but may be found in Quackenbush et al. (1993). Appendix C summarizes the model formulation.
FUELEVAPORATIONDIFFERENCES JP-4 and JP-8 may be represented by 33 and 27 major components, respectively (Clewell, 1980a, 1983). Before addressing the airborne evaporation of jettisoned fuels, it is instructive to compare the evaporation histories of representative droplets of JP-4 and JP-8 to scale the relative evaporation time of the two substances, and point out the volatility problem. For each fuel, evaporation calculations were undertaken for stationary droplets in a constant temperature atmosphere at 253, 273 and 293 K ( - 2 0 , 0, and 20°C), and one atmosphere pressure. The normalization of the calculation is such that the evaporation time history for a given initial droplet diameter can be easily generalized to those from any other initial diameter by rescaling the solution time step. For definiteness, we assume that the droplet has an initial diameter of 300/~m, near the center of the previously determined experimental distribution for JP-4 droplet sizes. The results of these calculations are shown in Figs 1 and 2. The JP-4 computation in Fig. 1 indicates that at 20°C, evaporation (here defined as the time to lose 99.7% of the initial droplet mass) proceeds very rapidly. The normalization of the time step is such that each nondimensional time unit is equivalent to 0.75 s;
~'Btl e.E
\\ ....
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'\, , a ~ 0° C ~ . . . . .
~ONDiMEHSIOHAL TIME E+03
Fig. 1. Temporal variation of total mass of a JP-4 droplet undergoing evaporation at one atmosphere and three different ambient temperatures.
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T.R. QUACKENBUSHet al. change the conclusions regarding the long droplet life of jettisoned JP-8 compared to JP-4, since similar corrections would apply in both cases.
6.8\\ '\
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Fig. 2. Temporal variation of total mass of a JP-8 droplet undergoing evaporation at one atmosphere and three different ambient temperatures. thus, the 5000 time units in Fig. 1 correspond to 60 min of physical time. Reducing the temperature to 0°C slows the evaporation substantially, stretching the time to go to completion to beyond 60 rain; even in this case, however, the particle loses all but 10% of its mass in roughly 10min. Reducing the temperature still further to - 2 0 °C leaves a residual mass of nearly 20% of the original particle even after a full hour has elapsed. To put this time into context, a rough estimate for the time for a 300/~m droplet to fall from 1500 m altitude is approximately 20 min. Although detailed calculations of groundfall (taking into account drift, dispersion, a range of particle sizes, and extreme temperature conditions) would have to be taken into account, Clewell's estimate of 1500 m as a safe release altitude for small scale fuel jettisoning events is seen to be reasonable. Since temperatures in the first 1500 m of the troposphere will, under most conditions, be in the range 0-20 °C, it may indeed be concluded that in most cases only a small fraction of the initial mass of JP-4 will appear as groundfall. The situation changes dramatically when JP-8 is introduced in place of JP-4, as shown in Fig. 2. A similar qualitative progression of results is evident here as the temperature is decreased, although the time scale of the evaporation process increases dramatically. Even at 20°C, the droplet evaporation requires roughly 45 min; at the low end of the temperature range, nearly 40% of the droplet mass still remains after 10 h have elapsed. These results clearly confirm the observation by Clewell that use of JP-8 will lead to substantially increased groundfall of jettisoned fuel. Other effects not included in these calculations, such as free stream convection, can also affect the evaporation rate. For the flow rates and droplet sizes of interest here, this effect will produce an increase in evaporation rate that is by no means negligible, and can be as high as 60-70%. However, this effect will not
SCENARIO
The following calculations use published information on the planform and engine characteristics of the F-15 to define the wing wake and engine exhaust interaction with the jettisoned fuel. Discussions with U.S. Air Force personnel indicated that the fuel jettisoning port on the F-15 is a rectangular orifice 1.0 in (2.54 cm) by 3.5 in (8.8 cm) located 5.0 in (12.7 cm) inboard of the right wingtip. A typical fuel jettisoning rate is 140 gpm (530 f min- 1). One of the most disadvantageous jettisoning scenarios from the point of view of fuel groundfall is a system failure immediately after takeoff. In such conditions the aircraft will in general be unable to climb to altitude to jettison fuel. Assuming the failure to be serious but not catastrophic, the aircraft would enter its landing pattern and jettison its fuel at a relatively low speed of roughly 200 kts (100 m s - l ) . For the present, a jettisoning altitude of 300 m is assumed. For consistency a uniform wind of 1.0 m s - 1 will be assumed at all altitudes, although the model can accommodate wind profiles of an essentially arbitrary character. However, these inputs are adequate for illustrating the capability of the present analysis. Fuel jettisoning is assumed to take place over a finite length flight path of 1400 m. The flight path length could be easily extended, but the assumed length was judged convenient for presenting the results that follow. The ambient temperature was assumed to be 0°C. Finally, for these cases the fuel stream was assumed to consist entirely of 300 pm droplets; other droplet distributions can be easily specified, but are not done so here. A direct comparison of the deposition of JP-4 and JP-8 may be seen in Figs 3 and 4. Deposition is predicted over a 17 x 25 grid of receptors, forming a 1.1 km x 2.0 km measurement grid. Isopleths of deposition (in drops m -2) enable a quick comparison between the two cases. Replacing JP-4 by JP-8 greatly increases the groundfall at this temperature. The more rapid evaporation of JP-4 droplets is the clear cause of the reduced deposition area shown in Fig. 3. The fuel that survives to reach the ground has undergone a substantial shift in its composition, with the less volatile components surviving to become part of the groundfall. Figures 5 and 6 show the initial and final mass fractions for the deposition of JP-4 and JP-8, respectively, from 300 m altitude and at 0°C. These graphs number the components in order of increasing molecular weight, and show the mass fraction (expressed as the mass taken up by a particular component of a droplet as a fraction of the initial droplet mass) at the start of the calculation and at the time of groundfall. Clearly, the mass of the heavier, less
Fuel jettisoning effects
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Fig. 3. Isopleths of deposition of 300/~m droplets from an F- 15 aircraft at 300 m altitude jettisoning JP-4 fuel; ambient temperature 0°C. Isopleth levels are s h o w n for 0.6-6000 d r o p s m - 2.
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2756
T.R. QUACKENBUSHet al.
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CONCLUSIONS
These initial results demonstrate several major points regarding the performance of the fuel jettisoning model. First, a workable coupling has been achieved between the evaporation and dispersion models that produces qualitatively and quantitatively reason-
able results for JP-4 and JP-8 type fuels. Second, the strong sensitivity of evaporation rate to temperature has been captured. Third, comparisons of deposition between JP-4 and JP-8 fuels at a given temperature and jettisoning conditions reflect the difference in volatility between these two fuels and again produce results that are at least qualitatively consistent with the results obtained by previous investigators. Several analytical and computational tasks must be undertaken to enhance the capabilities of the model. These include implementation of time-varying meteorology, verification of JP-8 component evaporation rate and Law's multicomponent model in this application, and determination of the most appropriate droplet distribution. Tests of droplet size distribution at
Fuel jettisoning effects full-scale mass flow rates would give an o p p o r t u n i t y to test the effect of different nozzles o n the a t o m i z a t i o n of the stream. Reducing the m e a n d r o p size t h r o u g h the use of new nozzle designs could be a way to c o u n t e r a c t the long droplet lifetime of low-volatility fuels such as JP-8, since small initial droplet size would e n h a n c e e v a p o r a t i o n of jettisoned fuel.
Acknowledgements This research was sponsored by SBIR Contract No. F08635-92-C-0067 from the Department of the Air Force, Air Force Engineering and Services Center, Environics Division, Tyndall Air Force Base, Florida 32403, Major Michael Moss and Capt. Floyd Wiseman, Technical Monitors.
REFERENCES
Bilanin A. J. and Teske M. E. (1984) Numerical studies of the deposition of material released from fixed and rotary wing aircraft. Contractor Report No. 3779. National Aeronautics and Space Administration. Langley. Bilanin A. J., Teske M. E, Barry J. W. and Ekblad R. B. (1989) AGDISP: the aircraft spray dispersion model, code development and experimental validation. Trans. Am. Soc. Agric. Engng 32, 327-334. Chin J. S. and Lefebvre A. H. (1983) Steady state evaporation characteristics of hydrocarbon fuel drops. AIAA J. 21, 1437-1443. Chin J. S., Durrett R. and Lefebvre A. H. (1984) The interdependence of spray characteristics and evaporation history of fuel sprays. Trans. ASME J. Engng Gas Turbines Power 106, 639-644. Clewell III H. J. (1980a) Fuel jettisoning by U.S. Air Force aircraft. Report No. ESL-TR-80-17. Air Force Engineering and Services Center. Tyndall Air Force Base. Clewell III H. J. (1980b) Evaporation and groundfall of JP-4 fuel jettisoned by USAF aircraft. Report No. ESL-TR-8056. Air Force Engineering and Services Center, Tyndall Air Force Base. Clewell III H. J. (1983) Ground contamination by fuel jettisoned from aircraft in flight. J. Aircraft 20, 382-384. Cross N. L. and Picknett R. G. (1973) Ground contamination by fuel jettisoned from aircraft. AGARD Conf. Proc. No. 125. Atmospheric Pollution by Aircraft Engines. 41st Meeting of the AGARD Propulsion and Energetics Board. London, pp. 12.1 12.9. Godsave G. A. E. (1953) Studies of the combustion of drops in a fuel spray the burning of single drops of fuel. Fourth Symp. (International) on Combustion, pp. 818-830. Williams and Wilkins, Baltimore. Good R. E. and Ctewell III H. J. (1980) Drop formation and evaporation of JP-4 fuel jettisoned from aircraft. J. Aircraft 17, 450-456. Good R. E., Forsberg C. A. and Bench P. M. (1978) Breakup characteristics of JP-4 vented from KC-135 aircraft. Report No. AFGL-TR-78-0190. Air Force Geophysics Laboratory. Hanscom Air Force Base. Law C. K. (1976) Multicomponent droplet combustion with rapid internal mixing. Combust. Flame 26, 219-233. Lefebvre A. H. (1989) Atomization and Sprays. Hemisphere, New York, 42t pp. Lowell H. H. (1959a) Free fall and evaporation of JP-4jet fuel droplets in a quiet atmosphere. Technical Note No. D-33. National Aeronautics and Space Administration. Langley. Lowell H. H. (1959b) Dispersion of jettisoned JP-4 jet fuel by atmospheric turbulence, evaporation, and varying rates of fall of fuel droplets. Technical Note No. D-84. National Aeronautics and Space Administration. Langley.
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Martel C. R. (1987) Cost savings possible with Air Force conversion to JP-8 as its primary fuel. Report No. AFWAL 7 TR-87-2037. Air Force Wright Aeronautical Laboratories. Wright-Patterson Air Force Base. Megaridis C. M. and Sirignano W. A. (1990) Numerical modeling of a vaporizing multicomponent droplet. 23rd Syrup. (International) on Combustion, pp. 1413-1421. Williams and Wilkins, Baltimore. Quackenbush T. R., Teske M. E., Polymeropoulos C. E. and Curbishley T. B. (1993) Microcomputer model for assessment of fuel jettisoning impact. Continuum Dynamics, Inc. Report No. 93-01. Sirignano W. A. (1983) Fuel droplet vaporization and spray combustion theory. Prog. Energy Combust. Sci. 9, 291-322. Spalding D. B. (1953) The combustion of liquid fuels. 4th Syrup. (International) on Combustion, pp. 847-864. Williams and Wilkins, Baltimore. Tennaukore K., Picot J. J. C., Chitiangad B. and Kristmanson D. D. (1980) Aircraft vortex studies in forest aerial spraying. Trans. Am. Soc. Agric. Engng 23, 1076-1083. Teske M. E.,. Bowers J. F., Rafferty J. E. and Barry J. W. (1993) FSCBG: an aerial spray dispersion model for predicting the fate of released material behind aircraft. Envir. Toxic. Chem. 12, 453-464. Trayford R. S. and Welch L. W. (1977) Aerial spraying: a simulation of factors influencing the distribution and recovery of liquid droplets. J. Ayric. Engng Res. 22, 183-196.
APPENDIX A: LAGRANGIAN
MODEL
A Lagrangian approach is used to develop the equations of motion of discrete particles released from aircraft, with the resulting set of ordinary differential equations solved exactly from time step to step. Particle flight path as a function of time after release is computed as the locations (X, Y, Z) for all particles included in the simulation; velocity is denoted by (U, V, W). The X direction is taken as downstream of the aircraft flight path; the Y direction is off the right wing as viewed from the pilot; and the Z direction is vertical upward. The interaction of the material with the turbulence in the environment creates turbulent correlation functions for tile position and velocity, ( y v ) and (zw); for the velocity variance ( v v ) and (ww); and for the position variance, ( y y ) and (zz). The square root of these last two variables gives the horizontal and vertical standard deviations of the material motion about the mean described by Y and Z. The governing equations are derived (Bilanin and Teske, 1984) as d2Xi 1 [-7 d ~ =(Ui-V,)L~-pJ+gi (A1) dX~ --= dt
V~
(A2)
d dtt ( -'hxl ) = 2 (xl v~)
(A3)
d 1 ~ (x, vl ) = ( ( x l u ~ ) - ( x i v , ) ) I ~ l + (,vlv,)
(A4)
d kl ~t (vivi) =2((uivi) -(, vivi))
(A5)
where X~, V~, and U~ are the ensemble averaged ith components of material position, material velocity and local fluid velocity, respectively, while x~, v~, and u~ are the fluctuating ith components of material position, material velocity and local fluid velocity, respectively; and 9~ is (0, 0, -#). Inherent in the equations is a relaxation time zv, the e-folding time for the released particle to come up to speed with the local fluid
T.R. QUACKENBUSHet al.
2758
velocity (for Vi to approach and equal U~) defined by
4 zp 3
Dpt C D VrelPA
(A6)
where D is the droplet diameter, Pt is material density, Ca is the particle drag coefficient, V,ol is the relative velocity I U i - V d between the material velocity and the local background velocity, and PA is air density. Equations (A1)-(A5) cannot be solved without specifying relationships for the quantities (,xlui) and (u~vi), the correlations of the particle position and particle velocity fluctuations, respectively, with the local fluid velocity fluctuation. These expressions are developed by integrating their ensemble averaged frequency spectra using a spectral density function for transverse velocity fluctuations in isotropic turbulence 2
.¢
=q3 [ _rpK +~2 ]
(XiUi)
(A7)
standard deviation of the vertical spray distribution; (x, y, z) are the alongwind, crosswind and vertical coordinates of the point at which the deposition is calculated; f the m a s s fraction of the total source strength in the ith dropsize category (total number of dropsizes is NIl; ?i the reflection coefficient for the median drop by mass in the ith dropsize category; and Hm the depth of the surface mixing layer beneath a capping inversion. The lateral and vertical growth of the spray cloud due to turbulent mixing is assumed to be rectilinear, rrr = aA(X+ xV) and G = aE(X+ XV)= trA(X+ Xv)/k where aA is the standard deviation of the wind azimuth angle; aE the standard deviation of the wind elevation angle; k = trA/O'E; Xv the virtual distance=kao/aA--XR= O0/aE--XR; and a 0 is the standard deviation of the cloud distribution at the distance XR downwind from the volume source.
After substitutions for ay and G, and performing the indicated integration and differentiation, the deposition equation takes the form
q2
(A8)
3
with
2
1
y
3exp - - - -
2
-
• .NI
x,. '~ f~(1 -- ?i) [MM + NN ]
q2 = mean-squares turbulence level = (uu) + (vv) + (ww)
K
kQv
DEPv=
fl-3_(%:]l-,_r,]+
21.L
t,-c,) AL
1"/,/I-l_
r,J Vc,)
ilL
(B3)
i=l
where
_ F k2l'H - Vix/a'~2q MM=[H+ V ~ x v / u ] e x P L - - - ~ t ~ ) J
Vq) J
and z, is the travel time of the particle through a turbulent eddy of scale A, adjusted for the passive tracer limit
z, =A/(V~j +~q).
(B4)
NN= ~ 7~-' [2jHm--H--Vixv/a] ./=1
F kZf2jHm - H + Vix/a~2]
APPENDIX
B: G A U S S I A N
x expL-Tt,
MODEL
The dispersion model calculates deposition downwind from a nearly instantaneous elevated line source oriented at an arbitrary angle with respect to the mean wind direction. The axis of the spray cloud is assumed to be inclined from the horizontal plane by an angle proportional to Vdti, where Vii is the gravitational settling velocity for the ith drop size category and t/is the mean transport wind speed. The model uses a Cartesian coordinate system for a line source of length L at a release height H and a calculation point at R(e, 8, z). The amount of spray material released from an instantaneous volume source that is deposited on the ground through gravitational settling is obtained from the expression 1
y 2 NI 2t,,%} j , : x
Qv x/27ra,
/
d
dxL,,/7~az
) J
+ ~ ?i [2jHm+H+ ViXv/U] j=l
F k2f2jHm+n--vix/u'~2q
) J
x expL-T ,
The expression for deposition downwind from a line source oriented at an arbitrary angle 0 with the wind direction is derived through consideration of the appropriate line source geometry. A finite line source of length L may be directed along the 6 coordinate at height H with one end of the line source at the point 5=0, 6=0, and z=H. It may be shown that x = x' - 6' sin 0; y = 6' cos 0 + x' tan 0 - 8/cos 0; and x' = e cos 0 + 6 sin 0. When these expressions are substituted for x, y and x' in equation (B3), the deposition at any point R downwind from the line source becomes L
DEPL = tDEPv d6 x iA(x,z)dz ]
(B,)
-oo
~d
o or
where
F 1/2jHm--H+z+Vfx/Vt'~ 2]
o~ . +
y]+' e x p r .
F
)
+ ~ ),/-1 e x p / _ = / . s=l L z\
-az
m
,
y. (o2) exp ~--ff-P
DEPL=sinO/=~lfi(1 - ~i) t
2F
x[expLd'___ Vl L L \a 2F} J
lf2jH,,+H--z-V:IC&2G
+ ~ ~,~e x p / - - - / j:, L 2\
•
2S
J l(2;n.+n+z-ExlC~ -
/ /
,1 ] az
(BS)
1 (B2)
where Qv is the strength of the volume source; o-r the standard deviation of the crosswind spray distribution; az the
Gx/~
1
G
(B6)
Fuel jettisoning effects
(j2 )
®
Cexp ~ - - P
I
j
f
F
/'1
J'~q
2
x {erflx/~(~-- J ) ] - - erf I x / l ( ! - - J ) ]
}}
2759
equations for the multicomponent evaporation model. The overall form of the expressions that result are similar to th6se given in the classical studies of single-droplet evaporation of Spalding (1953). First, given knowledge of the mole fraction for a given species as well as its molecular weight, the mass fraction of the component can be computed. Here /~,. is the ratio of the molecular weight of species i to that of an inert reference species that does not participate in the evaporation process (typically air)
x~,~(t) wi
y,,s(t)
__ (C1) E xi,~(t)] + Z xi, s(t) Wi where x~,s(t) is the mole fraction of component i in the vapor phase. Using [1 -
+ j=, ET[
exp - E
2E
a--2"E
- - e x p [ - - E ( ~ - - ~ E ) 2]
y,,s(t)[1 --y,,s(t)] (C2) 3,Yl,s(t) the aggregate latent heat of vaporization can be defined as ei(t)=yi, s(t)
Kx/~ 2x/E (
L
1 K \b 2EJJ
3,eiLi (C3) Lr where L~ is the latent heat of vaporization and Lr is a reference latent heat value. Defining the terms L(t) =
-erf [~/E(!-~E)]}}
}
(B7)
where
a=~/-2~rA(X' + XV) b=,~/2aA(x'-FXv-I sin O) B = H + Vixv/~ C = 2j H m - H - Vixv /~ D = 2 j H , , + H + EXv/~ E=k2D2+N 2 F=k2B2+N 2
G = ~/2/o"A [ 11/Bk 2/t~+ N cot 01 I=kECZ + N 2
J = --N~/aA [ V i C k 2 / a + N cot 01 K=~/2/o A [ViDk2fij + N c o t 01 N = ( x ' + x v ) c o t O+x' tan 0 - f / c o s 0 P = 1/2a~ [(k Vi/fi)2 +(cot 0)21 S=Qvk/2z
~6+~ cot 0; 6+ecotO<~L /=effective line length = (L; 6 +e cot 0> L.
H(t)
F 1 -- 3"y,,s (t) ] [ T ~ - Ts(t) 1 -- L(t) E y i,s (t)
3,yi,~(t)
B(t)
The following development defines the major relationships used in Law's analysis to derive the governing
(C5)
where Too is the ambient temperature and Ts is the droplet surface temperature. The aggregate normalized evaporation rate may be defined using re(t) = In I-1+ B(t)] (C6) while the evaporation of any individual component can be computed using mi(t) = el(t) m(t). (C7) With these equations in hand, the computational procedure used in the multicomponent evaporation model can be outlined as follows. Given initial values for the fractional radius R, as well as for the surface temperature T~ and the mole fraction of each species xi, s we can define first order differential equations for the rate of change of radius, temperature, and component mass dR dt dT~ dt
A P P E N D I X C: E V A P O R A T I O N M O D E l ,
T~ -- T~(t)
L(t) + H(t)
(C4)
1 re(t) 3 R(t)p(t)
(c8)
H(t)m(t) R2(t)p(t)
(C9)
dM, --=--ei(t)mi(t)
(C10)
dt
where p(t) is density and Mi is mass. The equations are advanced in time as the drop descends to the surface.
Pergamon
Atmospheric Environment Vol. 28, No. 16, pp. 2751 2759, 1994 Copyright © 1994 Elsevier Sclence Ltd Printed in Great Britain. All rights reserved 1352-2310/94 $7.00+0.00
1352-2310 (94) E0076-V
A MODEL FOR ASSESSING FUEL JETTISONING EFFECTS TODD R. QUACKENBUSH a n d MILTON E. TESKE Continuum Dynamics, Inc., P.O. Box 3073, Princeton, NJ 08543, U.S.A. and CONSTANTINE E. POLYMEROPOULOS Rutgers University, Department of Mechanical and Aerospace Engineering, P.O. Box 909, Piscataway, NJ 08855, U.S.A. (First received t0 August 1993 and in final form 5 January 1994)
Ahstrac~The present effort addresses the technical issues associated with hydrocarbon fuel jettisoning from aircraft, including the adaptation of an existing aerial application model for pesticide deposition. The analysis produces qualitatively and quantitatively reasonable results both in multicomponent evaporation calculations for isolated droplets, as well as in fully coupled calculations of airborne fuel jettisoning. Both classes of computations confirm earlier conclusions that the likely groundfall of JP-8 jet fuel is substantially higher than the more volatile JP-4 jet fuel, and reiterate the need for a careful assessment of the environmental impact of fuel jettisoning events involving JP-8. The preliminary model appears to be a suitable starting point for full-scale development of a flexible, practical fuel jettisoning simulation code. Key word index: Modeling, spray behavior, multicomponent evaporation, fuel jettisoning.
INTRODUCTION Fuel jettisoning has always been an option for the U.S. Air Force and the commercial airline industry, in response to an in-flight emergency, unforeseen operational requirement, or in preparation for a carrier landing. It is typically performed to reduce the weight of the aircraft and increase the likelihood of a safe landing. In most cases this operation occurs above the mixing layer height but below the top of the troposphere (1-12 km altitude). Previous work in this area has dealt mostly with the jettisoning of JP-4 jet fuel and its impact on the environment, including simplified preliminary analyses (Lowell, 1959a, b), in situ studies in the atmosphere (Good et al., 1978; Good and Clewell, 1980; Clewell~ 1980a, b), and measured ground contamination (Clewell, 1983; Cross and Picknett, 1973). These references conclude that if JP-4 jet fuel were jettisoned above a certain altitude, the ultimate groundfall would be insignificant and the corresponding environmental impact minimal. Recently, however, JP-8 jet fuel has been replacing JP-4 jet fuel, with still wider use projected for the years ahead. JP-8 (like commercial Jet A) exhibits significantly lower volatility than JP-4, and it is therefore anticipated that a significant portion of JP-8 jettisoned from any position in the troposphere will reach the surface. Pioneering work on the analysis of fuel jettisoning was conducted in the United States by Lowell and
Clewell, and in the United Kingdom by Cross and Picknett. The first flight experiments involved lowlevel (15 m altitude) passes with fuel jettisoned perpendicular to the oncoming airstream. Collection of the jettisoned droplets on sample paper provided early estimates of the droplet size distribution during jettisoning events. Efforts with JP-4 fuel involved several interrelated tasks: a data gathering effort, summarizing over three years of operational experience with fuel jettisoning scenarios in worldwide USAF operations; experimental studies, including in-flight measurements of drop size and laboratory tests of evaporation; and development of a preliminary computational model. The gathered data provided a valuable profile of jettisoning events and indicated that both tactical aircraft (e.g. F-4, F-111) and strategic aircraft (e.g. KC135, RC-135, FB-111) generated a significant number of events. It was found that among strategic aircraft, roughly 60% of jettisoning events were caused by emergency situations, with the remainder being due to operational requirements or aborted missions. Tactical aircraft accounted for the largest number of events, with the weight of fuel jettisoned averaging 2-4 metric tons (roughly 17.8-35.6 kN). Jettisoning events by strategic aircraft (predominantly tankers) averaged 15-20 metric tons (roughly 133.5-177.9 kN) and accounted for the majority of the total fuel jettisoned despite the smaller number of events. Sites were also surveyed and it was found, not surprisingly, that the
2751
2752
T.R. QUACKENBUSHet al.
highest concentratiori of jettisoning events occurred close to U.S. Air Force bases, with some sites recording over 200 events per year; however, scattered events were recorded across much of the continental United States and Europe. Jettisoning events took place in a wide variety of seasonal and climatic conditions, circumstances that can strongly affect total groundfall. Clewell's work included reports on flight tests using chase aircraft equipped with impact droplet measurement devices. These tests produced estimates of the droplet size distribution roughly 90 s after the passage of a KC-135. This information was used as input into a computational model that produced estimates of the groundfall for JP-4 released from various altitudes. The capsule recommendations that emerged from this study were that a critical altitude of 1500m was identified for tactical aircraft, above which dumps of JP-4 could be made with minimal chance for significant groundfall; the corresponding critical altitude for fuel jettisoning by strategic aircraft, given the larger average volume dumped by these aircraft, was estimated to be 6000 m. Recent events have made it desirable to revisit this issue. As noted by Martel (1987), introduction of JP-8 by the U.S. Air Force will save money due to reduced evaporation losses in stored fuel; however, this reduced volatility will inevitably increase groundfall of jettisoned fuel. The issue of JP-8 evaporation was not addressed in detail by Clewell, but it was suggested that groundfall of JP-8 would increase substantially. The predictive model used by ClewelI neglected aircraft wake effects on the jettisoned fuel; the experience of previous investigations into aerial spray events indicates that wake effects are in general quite important (Tennaukore et al., 1980). Moreover, in recent years mo.e advanced experimental techniques have arisen and have made it both possible and desirable to re-examine the issue of droplet size in the jettisoned fuel stream, especially since droplet size distribution is a particularly critical feature of any evaporation model. Also, community awareness of environmental impact of military activities is if anything higher than at the time of the original work on this topic, a circumstance that makes continuous updating of procedures used to study it very important.
AERIAL SPRAY M O D E L I N G
Over the last 20 years the USDA Forest Service and the U.S. Army have been developing computer models to predict the deposition distribution of aerially released material. The USDA Forest Service selectively uses aerial spray applications to control forest pests, while the U.S. Army is interested in assessing the effectiveness of chemical and biological materials released to the atmosphere in military applications. Both agencies have been interested in achieving a more complete understanding of the behavior of spray
material from the time the spray is released from an aircraft until it has deposited or, in the case of spray drift, diffused to levels below some threshold toxicity. Because mathematical spray dispersion models are useful in determining the interactions of the many factors affecting spray operations, these agencies have supported the continued development and application of these models. The two operational models are A G D I S P (for AGricultural DISPersal) and FSCBG (for Forest Service, Cramer, Barry and Grim, its developers). A G D I S P (Bilanin and Teske, 1984; Bilanin et al., 1989) is based on a Lagrangian approach to the solution of the equations of motion, and includes simplified models for aircraft wake and ambient turbulence effects (including wing-tip vortices, jet engines and propellers, crosswind, vortex decay and material evaporation). FSCBG is a Gaussian line-source model that takes the near-wake results of A G D I S P and predicts downwind dispersion. FSCBG operates on personal computers, with a menu-driven user interface and extensive graphics capability. An overview of its operation, and details on the equations in the model, may be found in Teske et al. (1993). The fuel jettisoning model discussed here retains a substantial portion of the near-wake A G D I S P and downwind dispersion FSCBG working code. The principal modification here is the replacement of the original water-based droplet evaporation model with a multicomponent evaporation model able to predict the evaporation of hydrocarbon fuels. Appendices A and B summarize the Lagrangian and Gaussian formulations in the fuel jettisoning model.
MULTICOMPONENT EVAPORATION The literature on multicomponent evaporation of hydrocarbon droplets is drawn in large part from combustion research, the motivation for this work typically being the combustion of droplet sprays in hot atmospheres. For a given droplet size distribution and composition of the droplet, several critical features of the evaporation process must be modeled if the evolution of the drop size and the ultimate composition of the groundfall are adequately captured. First, because the various components of the droplet will not in general evaporate at a uniform rate, the composition of the droplet will change over time as evaporation proceeds; hence, the time history of the individual evaporating components must be tracked. Second, the energy exchange due to the change of phase of the various components from liquid to vapor must be addressed, and the subsequent transport of the vapor into the ambient atmosphere must be modeled using suitable assumptions about mass and energy flows within the droplet and near its surface. Several different approximations have been used to address this problem. First, a particularly simple
Fuel jettisoning effects formulation can be developed by assuming what is typically called the d2-1aw of evaporation
2
2
ds, o - d~ = 2t
where ds,o is the initial drop diameter, t is time, and 2 is the evaporation constant (Lefebvre, 1989). The model assumes uniformly mixed spherical drops and negligible radiation heat transfer (Godsave, 1953; Spalding, 1953). Initial efforts to apply this model were centered on experimentally determining an appropriate evaporation constant. The simplicity of this approach found its way into other simple evaporation approaches (Trayford and Welch, 1977) where 2 is replaced by the inverse of an evaporation relaxation time t e that includes the wet-bulb temperature depression and a series dependence on the Reynolds number based on relative air speed. Simple numerical models using this approach (Chin and Lefebvre, 1983; Chin e t a l . , 1984) have been developed to examine the evaporation characteristics of JP-4 and JP-5 jet fuel sprays prior to combustion. Another possible approach to multicomponent evaporation is a detailed solution of the partial differential equations governing heat and mass transfer within and surrounding the drop. Typical detailed numerical models (Megaridis and Sirignano, 1990) include equations for the gas and liquid phases (species, energy, state, vorticity, and stream function) and gas-liquid interface conditions at the surface of the drop. Approaches of this type were judged to be too complex for the quick solution desired here. However, using the same governing differential equations and invoking reasonable simplifications regarding the internal structure of the droplet can provide a basis for developing an appropriate model. Combustion researchers in general focus on a hot ambient environment, while the troposphere does not generally fit this description. Sirignano (1983) suggests that low ambient temperatures permit the researcher to discard many of the driving assumptions in the more complicated models, since droplet lifetime is so long that mass concentration of particular components in the droplet may be assumed uniform but time vaiying. In his discussion of such simplified evaporation models, Law (1976) expands on this point by identifying two useful limiting cases that illustrate the major assumptions involved in analyzing droplet evaporation: the first is the case of a very viscous fluid in which diffusion is the dominant transport mechanism; the second is that of a less viscous fluid in which internal convection dominates. In the latter case, internal mixing in the droplet can be assumed to be so fast that at any instant in time the mass fraction of each component within the droplet is approximately spatially uniform (an assumption similar to that later suggested by Sirignano). This is an especially helpful assumption near the surface, since the mixture properties at the surface dominate the evaporation rate for the various components.
2753
The evaporation model implemented in the present effort is drawn from the work of Law. This model treats the computation of evaporation from an isolated droplet composed of an arbitrary number of hydrocarbon compounds. Implementation of this model, and comparisons with two-component mixtures of hexane and octane, are in agreement with those predicted by Law, and are not reproduced here, but may be found in Quackenbush et al. (1993). Appendix C summarizes the model formulation.
FUELEVAPORATIONDIFFERENCES JP-4 and JP-8 may be represented by 33 and 27 major components, respectively (Clewell, 1980a, 1983). Before addressing the airborne evaporation of jettisoned fuels, it is instructive to compare the evaporation histories of representative droplets of JP-4 and JP-8 to scale the relative evaporation time of the two substances, and point out the volatility problem. For each fuel, evaporation calculations were undertaken for stationary droplets in a constant temperature atmosphere at 253, 273 and 293 K ( - 2 0 , 0, and 20°C), and one atmosphere pressure. The normalization of the calculation is such that the evaporation time history for a given initial droplet diameter can be easily generalized to those from any other initial diameter by rescaling the solution time step. For definiteness, we assume that the droplet has an initial diameter of 300/~m, near the center of the previously determined experimental distribution for JP-4 droplet sizes. The results of these calculations are shown in Figs 1 and 2. The JP-4 computation in Fig. 1 indicates that at 20°C, evaporation (here defined as the time to lose 99.7% of the initial droplet mass) proceeds very rapidly. The normalization of the time step is such that each nondimensional time unit is equivalent to 0.75 s;
~'Btl e.E
\\ ....
/ - 20 ° C
'\, , a ~ 0° C ~ . . . . .
~ONDiMEHSIOHAL TIME E+03
Fig. 1. Temporal variation of total mass of a JP-4 droplet undergoing evaporation at one atmosphere and three different ambient temperatures.
2754
T.R. QUACKENBUSHet al. change the conclusions regarding the long droplet life of jettisoned JP-8 compared to JP-4, since similar corrections would apply in both cases.
6.8\\ '\
._J
~z O.G ~---
6,4
~
- . %,~-
A TYPICAL FUEL JETTISONING
20 ° C
~'
~-'--~-.-
<7-0°c HOHOIMENSIONAL
TIME E+04
Fig. 2. Temporal variation of total mass of a JP-8 droplet undergoing evaporation at one atmosphere and three different ambient temperatures. thus, the 5000 time units in Fig. 1 correspond to 60 min of physical time. Reducing the temperature to 0°C slows the evaporation substantially, stretching the time to go to completion to beyond 60 rain; even in this case, however, the particle loses all but 10% of its mass in roughly 10min. Reducing the temperature still further to - 2 0 °C leaves a residual mass of nearly 20% of the original particle even after a full hour has elapsed. To put this time into context, a rough estimate for the time for a 300/~m droplet to fall from 1500 m altitude is approximately 20 min. Although detailed calculations of groundfall (taking into account drift, dispersion, a range of particle sizes, and extreme temperature conditions) would have to be taken into account, Clewell's estimate of 1500 m as a safe release altitude for small scale fuel jettisoning events is seen to be reasonable. Since temperatures in the first 1500 m of the troposphere will, under most conditions, be in the range 0-20 °C, it may indeed be concluded that in most cases only a small fraction of the initial mass of JP-4 will appear as groundfall. The situation changes dramatically when JP-8 is introduced in place of JP-4, as shown in Fig. 2. A similar qualitative progression of results is evident here as the temperature is decreased, although the time scale of the evaporation process increases dramatically. Even at 20°C, the droplet evaporation requires roughly 45 min; at the low end of the temperature range, nearly 40% of the droplet mass still remains after 10 h have elapsed. These results clearly confirm the observation by Clewell that use of JP-8 will lead to substantially increased groundfall of jettisoned fuel. Other effects not included in these calculations, such as free stream convection, can also affect the evaporation rate. For the flow rates and droplet sizes of interest here, this effect will produce an increase in evaporation rate that is by no means negligible, and can be as high as 60-70%. However, this effect will not
SCENARIO
The following calculations use published information on the planform and engine characteristics of the F-15 to define the wing wake and engine exhaust interaction with the jettisoned fuel. Discussions with U.S. Air Force personnel indicated that the fuel jettisoning port on the F-15 is a rectangular orifice 1.0 in (2.54 cm) by 3.5 in (8.8 cm) located 5.0 in (12.7 cm) inboard of the right wingtip. A typical fuel jettisoning rate is 140 gpm (530 f min- 1). One of the most disadvantageous jettisoning scenarios from the point of view of fuel groundfall is a system failure immediately after takeoff. In such conditions the aircraft will in general be unable to climb to altitude to jettison fuel. Assuming the failure to be serious but not catastrophic, the aircraft would enter its landing pattern and jettison its fuel at a relatively low speed of roughly 200 kts (100 m s - l ) . For the present, a jettisoning altitude of 300 m is assumed. For consistency a uniform wind of 1.0 m s - 1 will be assumed at all altitudes, although the model can accommodate wind profiles of an essentially arbitrary character. However, these inputs are adequate for illustrating the capability of the present analysis. Fuel jettisoning is assumed to take place over a finite length flight path of 1400 m. The flight path length could be easily extended, but the assumed length was judged convenient for presenting the results that follow. The ambient temperature was assumed to be 0°C. Finally, for these cases the fuel stream was assumed to consist entirely of 300 pm droplets; other droplet distributions can be easily specified, but are not done so here. A direct comparison of the deposition of JP-4 and JP-8 may be seen in Figs 3 and 4. Deposition is predicted over a 17 x 25 grid of receptors, forming a 1.1 km x 2.0 km measurement grid. Isopleths of deposition (in drops m -2) enable a quick comparison between the two cases. Replacing JP-4 by JP-8 greatly increases the groundfall at this temperature. The more rapid evaporation of JP-4 droplets is the clear cause of the reduced deposition area shown in Fig. 3. The fuel that survives to reach the ground has undergone a substantial shift in its composition, with the less volatile components surviving to become part of the groundfall. Figures 5 and 6 show the initial and final mass fractions for the deposition of JP-4 and JP-8, respectively, from 300 m altitude and at 0°C. These graphs number the components in order of increasing molecular weight, and show the mass fraction (expressed as the mass taken up by a particular component of a droplet as a fraction of the initial droplet mass) at the start of the calculation and at the time of groundfall. Clearly, the mass of the heavier, less
Fuel jettisoning effects
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DISTANCE
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qO0 ]
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Fig. 3. Isopleths of deposition of 300/~m droplets from an F- 15 aircraft at 300 m altitude jettisoning JP-4 fuel; ambient temperature 0°C. Isopleth levels are s h o w n for 0.6-6000 d r o p s m - 2.
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~
~...,.~..~
± ~,,~
+~""~'"'~'"~'"T"'~"'~''~''~''~''~4 +
+
+
+
+
+
+
+
+
+_.,+.....P~
I t+ ++ ++ + + + + + + ~ + 1 ++ ++~ +~- - ~
+ + + ~ + + +
+ + + + +
+ + + + + +__+..-~+ ~ + - ~ - ' - ~ ' ~ + + ~ + ~ + + + + + + + ~ + ~ + + + + + ~ + ~ + / + + + + +....+..~ + ~ + ~ + + +j+...~+ + ..+.--+~ + +
~+ + + + +
I.--r" I,--" ,ZI -2000 0 O")
-2500 -I000
I
I
-800
I
+ + +
~
~ + + + ~ + + ÷ + + + ÷ + ~ + + + ÷ ~ ÷ ÷ + ÷ ÷ ÷ ÷ + ÷
+
÷
I
I
,
I
,
-400 NEST
TO
I -200
EAST
,
I 0
DISTANCE
+ + +
+ + +
, 200 (M
~
~
+ + +
-600
+ + + ~ + ~+ + +~+ +~ + +~+ +~ + +
~
~
~
a
I 400 )
,
I
,
60D
800
0.6000 6.00 60.00 GO0. O0 6000.00
Fig. 4. Isopleths of deposition of 300 p m droplets from an F-15 aircraft at 300 m altitude jettisoning J P-8 fuel; ambient temperature 0°C. Isopleth levels are s h o w n for 0.6-24000 d r o p s m - 2 .
2756
T.R. QUACKENBUSHet al.
0.15
I
0.1
I
t
1
I
I
I
o
Initial
[]
Final
I
C
Fraction
0.05
0
' ~ c ~ . v ~ ~
0
5
10
15 20 Species
25
30
35
Fig. 5. Initial and final mass fraction distributions for JP-4 fuel jettisoned from 300 m altitude; ambient temperature 0°C. Species plotted in order of increasing molecular weight.
!
0.15
i
i
i
i
i
I o
0.1 Mass
Fraction
0.05
0
5
10
15 Species
t
ir~
20
25
30
Fig. 6. Initial and final mass fraction distributions for JP-8 fuel jettisoned from 300 m altitude; ambient temperature 0°C. Species plotted in order of increasing molecular weight. volatile species in JP-4 are essentially unchanged, while the loss of mass in the droplet has come primarily from the more volatile, lighter components. This trend is even more severe for JP-8 in Fig. 6, where it is seen that only the more volatile components disappear from the drop.
CONCLUSIONS
These initial results demonstrate several major points regarding the performance of the fuel jettisoning model. First, a workable coupling has been achieved between the evaporation and dispersion models that produces qualitatively and quantitatively reason-
able results for JP-4 and JP-8 type fuels. Second, the strong sensitivity of evaporation rate to temperature has been captured. Third, comparisons of deposition between JP-4 and JP-8 fuels at a given temperature and jettisoning conditions reflect the difference in volatility between these two fuels and again produce results that are at least qualitatively consistent with the results obtained by previous investigators. Several analytical and computational tasks must be undertaken to enhance the capabilities of the model. These include implementation of time-varying meteorology, verification of JP-8 component evaporation rate and Law's multicomponent model in this application, and determination of the most appropriate droplet distribution. Tests of droplet size distribution at
Fuel jettisoning effects full-scale mass flow rates would give an o p p o r t u n i t y to test the effect of different nozzles o n the a t o m i z a t i o n of the stream. Reducing the m e a n d r o p size t h r o u g h the use of new nozzle designs could be a way to c o u n t e r a c t the long droplet lifetime of low-volatility fuels such as JP-8, since small initial droplet size would e n h a n c e e v a p o r a t i o n of jettisoned fuel.
Acknowledgements This research was sponsored by SBIR Contract No. F08635-92-C-0067 from the Department of the Air Force, Air Force Engineering and Services Center, Environics Division, Tyndall Air Force Base, Florida 32403, Major Michael Moss and Capt. Floyd Wiseman, Technical Monitors.
REFERENCES
Bilanin A. J. and Teske M. E. (1984) Numerical studies of the deposition of material released from fixed and rotary wing aircraft. Contractor Report No. 3779. National Aeronautics and Space Administration. Langley. Bilanin A. J., Teske M. E, Barry J. W. and Ekblad R. B. (1989) AGDISP: the aircraft spray dispersion model, code development and experimental validation. Trans. Am. Soc. Agric. Engng 32, 327-334. Chin J. S. and Lefebvre A. H. (1983) Steady state evaporation characteristics of hydrocarbon fuel drops. AIAA J. 21, 1437-1443. Chin J. S., Durrett R. and Lefebvre A. H. (1984) The interdependence of spray characteristics and evaporation history of fuel sprays. Trans. ASME J. Engng Gas Turbines Power 106, 639-644. Clewell III H. J. (1980a) Fuel jettisoning by U.S. Air Force aircraft. Report No. ESL-TR-80-17. Air Force Engineering and Services Center. Tyndall Air Force Base. Clewell III H. J. (1980b) Evaporation and groundfall of JP-4 fuel jettisoned by USAF aircraft. Report No. ESL-TR-8056. Air Force Engineering and Services Center, Tyndall Air Force Base. Clewell III H. J. (1983) Ground contamination by fuel jettisoned from aircraft in flight. J. Aircraft 20, 382-384. Cross N. L. and Picknett R. G. (1973) Ground contamination by fuel jettisoned from aircraft. AGARD Conf. Proc. No. 125. Atmospheric Pollution by Aircraft Engines. 41st Meeting of the AGARD Propulsion and Energetics Board. London, pp. 12.1 12.9. Godsave G. A. E. (1953) Studies of the combustion of drops in a fuel spray the burning of single drops of fuel. Fourth Symp. (International) on Combustion, pp. 818-830. Williams and Wilkins, Baltimore. Good R. E. and Ctewell III H. J. (1980) Drop formation and evaporation of JP-4 fuel jettisoned from aircraft. J. Aircraft 17, 450-456. Good R. E., Forsberg C. A. and Bench P. M. (1978) Breakup characteristics of JP-4 vented from KC-135 aircraft. Report No. AFGL-TR-78-0190. Air Force Geophysics Laboratory. Hanscom Air Force Base. Law C. K. (1976) Multicomponent droplet combustion with rapid internal mixing. Combust. Flame 26, 219-233. Lefebvre A. H. (1989) Atomization and Sprays. Hemisphere, New York, 42t pp. Lowell H. H. (1959a) Free fall and evaporation of JP-4jet fuel droplets in a quiet atmosphere. Technical Note No. D-33. National Aeronautics and Space Administration. Langley. Lowell H. H. (1959b) Dispersion of jettisoned JP-4 jet fuel by atmospheric turbulence, evaporation, and varying rates of fall of fuel droplets. Technical Note No. D-84. National Aeronautics and Space Administration. Langley.
2757
Martel C. R. (1987) Cost savings possible with Air Force conversion to JP-8 as its primary fuel. Report No. AFWAL 7 TR-87-2037. Air Force Wright Aeronautical Laboratories. Wright-Patterson Air Force Base. Megaridis C. M. and Sirignano W. A. (1990) Numerical modeling of a vaporizing multicomponent droplet. 23rd Syrup. (International) on Combustion, pp. 1413-1421. Williams and Wilkins, Baltimore. Quackenbush T. R., Teske M. E., Polymeropoulos C. E. and Curbishley T. B. (1993) Microcomputer model for assessment of fuel jettisoning impact. Continuum Dynamics, Inc. Report No. 93-01. Sirignano W. A. (1983) Fuel droplet vaporization and spray combustion theory. Prog. Energy Combust. Sci. 9, 291-322. Spalding D. B. (1953) The combustion of liquid fuels. 4th Syrup. (International) on Combustion, pp. 847-864. Williams and Wilkins, Baltimore. Tennaukore K., Picot J. J. C., Chitiangad B. and Kristmanson D. D. (1980) Aircraft vortex studies in forest aerial spraying. Trans. Am. Soc. Agric. Engng 23, 1076-1083. Teske M. E.,. Bowers J. F., Rafferty J. E. and Barry J. W. (1993) FSCBG: an aerial spray dispersion model for predicting the fate of released material behind aircraft. Envir. Toxic. Chem. 12, 453-464. Trayford R. S. and Welch L. W. (1977) Aerial spraying: a simulation of factors influencing the distribution and recovery of liquid droplets. J. Ayric. Engng Res. 22, 183-196.
APPENDIX A: LAGRANGIAN
MODEL
A Lagrangian approach is used to develop the equations of motion of discrete particles released from aircraft, with the resulting set of ordinary differential equations solved exactly from time step to step. Particle flight path as a function of time after release is computed as the locations (X, Y, Z) for all particles included in the simulation; velocity is denoted by (U, V, W). The X direction is taken as downstream of the aircraft flight path; the Y direction is off the right wing as viewed from the pilot; and the Z direction is vertical upward. The interaction of the material with the turbulence in the environment creates turbulent correlation functions for tile position and velocity, ( y v ) and (zw); for the velocity variance ( v v ) and (ww); and for the position variance, ( y y ) and (zz). The square root of these last two variables gives the horizontal and vertical standard deviations of the material motion about the mean described by Y and Z. The governing equations are derived (Bilanin and Teske, 1984) as d2Xi 1 [-7 d ~ =(Ui-V,)L~-pJ+gi (A1) dX~ --= dt
V~
(A2)
d dtt ( -'hxl ) = 2 (xl v~)
(A3)
d 1 ~ (x, vl ) = ( ( x l u ~ ) - ( x i v , ) ) I ~ l + (,vlv,)
(A4)
d kl ~t (vivi) =2((uivi) -(, vivi))
(A5)
where X~, V~, and U~ are the ensemble averaged ith components of material position, material velocity and local fluid velocity, respectively, while x~, v~, and u~ are the fluctuating ith components of material position, material velocity and local fluid velocity, respectively; and 9~ is (0, 0, -#). Inherent in the equations is a relaxation time zv, the e-folding time for the released particle to come up to speed with the local fluid
T.R. QUACKENBUSHet al.
2758
velocity (for Vi to approach and equal U~) defined by
4 zp 3
Dpt C D VrelPA
(A6)
where D is the droplet diameter, Pt is material density, Ca is the particle drag coefficient, V,ol is the relative velocity I U i - V d between the material velocity and the local background velocity, and PA is air density. Equations (A1)-(A5) cannot be solved without specifying relationships for the quantities (,xlui) and (u~vi), the correlations of the particle position and particle velocity fluctuations, respectively, with the local fluid velocity fluctuation. These expressions are developed by integrating their ensemble averaged frequency spectra using a spectral density function for transverse velocity fluctuations in isotropic turbulence 2
.¢
=q3 [ _rpK +~2 ]
(XiUi)
(A7)
standard deviation of the vertical spray distribution; (x, y, z) are the alongwind, crosswind and vertical coordinates of the point at which the deposition is calculated; f the m a s s fraction of the total source strength in the ith dropsize category (total number of dropsizes is NIl; ?i the reflection coefficient for the median drop by mass in the ith dropsize category; and Hm the depth of the surface mixing layer beneath a capping inversion. The lateral and vertical growth of the spray cloud due to turbulent mixing is assumed to be rectilinear, rrr = aA(X+ xV) and G = aE(X+ XV)= trA(X+ Xv)/k where aA is the standard deviation of the wind azimuth angle; aE the standard deviation of the wind elevation angle; k = trA/O'E; Xv the virtual distance=kao/aA--XR= O0/aE--XR; and a 0 is the standard deviation of the cloud distribution at the distance XR downwind from the volume source.
After substitutions for ay and G, and performing the indicated integration and differentiation, the deposition equation takes the form
q2
(A8)
3
with
2
1
y
3exp - - - -
2
-
• .NI
x,. '~ f~(1 -- ?i) [MM + NN ]
q2 = mean-squares turbulence level = (uu) + (vv) + (ww)
K
kQv
DEPv=
fl-3_(%:]l-,_r,]+
21.L
t,-c,) AL
1"/,/I-l_
r,J Vc,)
ilL
(B3)
i=l
where
_ F k2l'H - Vix/a'~2q MM=[H+ V ~ x v / u ] e x P L - - - ~ t ~ ) J
Vq) J
and z, is the travel time of the particle through a turbulent eddy of scale A, adjusted for the passive tracer limit
z, =A/(V~j +~q).
(B4)
NN= ~ 7~-' [2jHm--H--Vixv/a] ./=1
F kZf2jHm - H + Vix/a~2]
APPENDIX
B: G A U S S I A N
x expL-Tt,
MODEL
The dispersion model calculates deposition downwind from a nearly instantaneous elevated line source oriented at an arbitrary angle with respect to the mean wind direction. The axis of the spray cloud is assumed to be inclined from the horizontal plane by an angle proportional to Vdti, where Vii is the gravitational settling velocity for the ith drop size category and t/is the mean transport wind speed. The model uses a Cartesian coordinate system for a line source of length L at a release height H and a calculation point at R(e, 8, z). The amount of spray material released from an instantaneous volume source that is deposited on the ground through gravitational settling is obtained from the expression 1
y 2 NI 2t,,%} j , : x
Qv x/27ra,
/
d
dxL,,/7~az
) J
+ ~ ?i [2jHm+H+ ViXv/U] j=l
F k2f2jHm+n--vix/u'~2q
) J
x expL-T ,
The expression for deposition downwind from a line source oriented at an arbitrary angle 0 with the wind direction is derived through consideration of the appropriate line source geometry. A finite line source of length L may be directed along the 6 coordinate at height H with one end of the line source at the point 5=0, 6=0, and z=H. It may be shown that x = x' - 6' sin 0; y = 6' cos 0 + x' tan 0 - 8/cos 0; and x' = e cos 0 + 6 sin 0. When these expressions are substituted for x, y and x' in equation (B3), the deposition at any point R downwind from the line source becomes L
DEPL = tDEPv d6 x iA(x,z)dz ]
(B,)
-oo
~d
o or
where
F 1/2jHm--H+z+Vfx/Vt'~ 2]
o~ . +
y]+' e x p r .
F
)
+ ~ ),/-1 e x p / _ = / . s=l L z\
-az
m
,
y. (o2) exp ~--ff-P
DEPL=sinO/=~lfi(1 - ~i) t
2F
x[expLd'___ Vl L L \a 2F} J
lf2jH,,+H--z-V:IC&2G
+ ~ ~,~e x p / - - - / j:, L 2\
•
2S
J l(2;n.+n+z-ExlC~ -
/ /
,1 ] az
(BS)
1 (B2)
where Qv is the strength of the volume source; o-r the standard deviation of the crosswind spray distribution; az the
Gx/~
1
G
(B6)
Fuel jettisoning effects
(j2 )
®
Cexp ~ - - P
I
j
f
F
/'1
J'~q
2
x {erflx/~(~-- J ) ] - - erf I x / l ( ! - - J ) ]
}}
2759
equations for the multicomponent evaporation model. The overall form of the expressions that result are similar to th6se given in the classical studies of single-droplet evaporation of Spalding (1953). First, given knowledge of the mole fraction for a given species as well as its molecular weight, the mass fraction of the component can be computed. Here /~,. is the ratio of the molecular weight of species i to that of an inert reference species that does not participate in the evaporation process (typically air)
x~,~(t) wi
y,,s(t)
__ (C1) E xi,~(t)] + Z xi, s(t) Wi where x~,s(t) is the mole fraction of component i in the vapor phase. Using [1 -
+ j=, ET[
exp - E
2E
a--2"E
- - e x p [ - - E ( ~ - - ~ E ) 2]
y,,s(t)[1 --y,,s(t)] (C2) 3,Yl,s(t) the aggregate latent heat of vaporization can be defined as ei(t)=yi, s(t)
Kx/~ 2x/E (
L
1 K \b 2EJJ
3,eiLi (C3) Lr where L~ is the latent heat of vaporization and Lr is a reference latent heat value. Defining the terms L(t) =
-erf [~/E(!-~E)]}}
}
(B7)
where
a=~/-2~rA(X' + XV) b=,~/2aA(x'-FXv-I sin O) B = H + Vixv/~ C = 2j H m - H - Vixv /~ D = 2 j H , , + H + EXv/~ E=k2D2+N 2 F=k2B2+N 2
G = ~/2/o"A [ 11/Bk 2/t~+ N cot 01 I=kECZ + N 2
J = --N~/aA [ V i C k 2 / a + N cot 01 K=~/2/o A [ViDk2fij + N c o t 01 N = ( x ' + x v ) c o t O+x' tan 0 - f / c o s 0 P = 1/2a~ [(k Vi/fi)2 +(cot 0)21 S=Qvk/2z
~6+~ cot 0; 6+ecotO<~L /=effective line length = (L; 6 +e cot 0> L.
H(t)
F 1 -- 3"y,,s (t) ] [ T ~ - Ts(t) 1 -- L(t) E y i,s (t)
3,yi,~(t)
B(t)
The following development defines the major relationships used in Law's analysis to derive the governing
(C5)
where Too is the ambient temperature and Ts is the droplet surface temperature. The aggregate normalized evaporation rate may be defined using re(t) = In I-1+ B(t)] (C6) while the evaporation of any individual component can be computed using mi(t) = el(t) m(t). (C7) With these equations in hand, the computational procedure used in the multicomponent evaporation model can be outlined as follows. Given initial values for the fractional radius R, as well as for the surface temperature T~ and the mole fraction of each species xi, s we can define first order differential equations for the rate of change of radius, temperature, and component mass dR dt dT~ dt
A P P E N D I X C: E V A P O R A T I O N M O D E l ,
T~ -- T~(t)
L(t) + H(t)
(C4)
1 re(t) 3 R(t)p(t)
(c8)
H(t)m(t) R2(t)p(t)
(C9)
dM, --=--ei(t)mi(t)
(C10)
dt
where p(t) is density and Mi is mass. The equations are advanced in time as the drop descends to the surface.