Dynamics and Heat and Mass Transfer of Liquid-Droplet Cloud in the Emergency Discharge of Aviation Fuel into the Atmosphere

Transcription

1 Dynamics and Heat and Mass Transer o Liquid-Drolet Cloud in the Emergency Discharge o Aviation Fuel into the Atmoshere Evgeny Maslov 1,,*, Amgalan Badmaev, and Irina Zharova 1 1 National Research Tomsk State University, Tomsk, Russia National Research Tomsk Polytechnic University, Tomsk, Russia Abstract. A mathematical model or the roagation o liquid-drolet cloud in the atmoshere during the emergency discharge o aviation uel is resented. The results o a numerical analysis o the dynamics and heat and mass transer o a liquid-drolet cloud in the emergency discharge o aviation uel into the atmoshere, deending on the season-climatic and meteorological conditions o seciic regions o Russia are given. 1 Introduction To reduce the ossible risks in the event o emergency situations during light it is the ractice o duming uel into the atmoshere rom illing tanks beore an urgent landing (Fig. 1) [1]. Fig. 1. Emergency discharge o uel rom the aircrat Northwest Airlines Boeing 747. Since the mass o jet uel to be discharged is tens o tons, it is necessary to rovide emergency discharge conditions in which the uel drolets deosition on the earth's surace will be minimized. Currently, the conditions or the duming o aviation uel in emergency situations are regulated by the rules o the International Civil Aviation Organization (ICAO). The minimum height o uel discharge is 1850 m or lights over Western Euroe territory in accordance with ICAO rules. These conditions ensure that the bulk o the uel evaorates in the atmoshere, and only ~ 8 % o the mass o the uel reaches the ground surace. It should be noted that when lying over the territories o other regions whose climatic conditions are signiicantly dierent rom those in Western Euroe, these regimes * Corresonding author: maslov_eugene@mail.ru The Authors, ublished by EDP Sciences. This is an oen access article distributed under the terms o the Creative Commons Attribution License 4.0 (htt://creativecommons.org/licenses/by/4.0/).

2 o discharging do not always guarantee that there is no signiicant amount o uel on the earth's surace. The aim o the resented aer is to analyze the dynamics and heat and mass transer o a liquid-drolet cloud in the emergency discharge o aviation uel into the atmoshere, deending on the season-climatic and meteorological conditions o seciic regions o Russia. Mathematical modeling o dynamics and heat and mass transer o liquid-drolet cloud in the emergency discharge o aviation uel into the atmoshere Numerical analysis was carried out under the ollowing assumtions. At the initial time, the volume o uel injected into the atmoshere was considered as a dro o sherical shae (a liquid-drolet cloud) with a diameter equal to the characteristic width o the imact jet (Fig. 1). The initial velocity o the liquid-drolet sherical cloud was equal to the seed o the aircrat. It was believed that the liquid-drolet cloud roagates in the atmoshere under the inluence o gravity, the orce o aerodynamic drag and wind orce. The rocesses o reeated crushing o dros, evaoration and heat exchange with the ambient air were taken into account. Within the ramework o the assumtions made, the mathematically considered rocess is described by a system o equations [ 4]. The motion o a dro in a Cartesian coordinate system was described by the equations o motion in the velocity ield o the steady gas low with allowance or the orces o viscous drag and gravity: dvx 3 C U V U V dt 4 d ( t) dx Vx, dt dvy 3 CD U V U y Vyg, dt 4 d ( t) dy dt V y, D x x, (1) where t is time; d is the drolet diameter; ρ, ρ are the density o air and drolet substances, resectively; U x, U y, V x, V y are rojections o the velocity o air movement and the velocity o the drolet movement on the axis o the Cartesian coordinate system; X, Y are the current coordinate o the dro movement along the x and y axes, resectively; C D is coeicient o aerodynamic drag, g = 9.81 m/s is acceleration o gravity. The thermal state o a dro was described by the thermal conductivity equation in a sherical coordinate system [3 5]:,, T r t 1 T r t ( T( r, t)) с( T( r, t)) ( T (, )) r t r, () t r r r where r is the sherical coordinate; r is the radius o a dro; T is dro temerature; c and λ are the seciic isobaric heat caacity and the coeicient o thermal conductivity o the drolet substance, resectively. Taking into account the rocesses o evaoration and convective heat exchange with air, equation () was sulemented by the ollowing initial and boundary conditions [3, 6]:

3 0 t 0, 0 r r: Т r =Т, (3) t T t >0, r 0 : 0, (4) r t T t >0, rr : T t T T t qvawva t, (5) r where Т 0 is the initial dro temerature; T is ambient temerature (air); q va is the heat o evaoration o dro substance; w va (t) is the rate o dro evaoration; α is the coeicient o heat exchange with air. The coeicient o heat transer α in (5) is determined by the ormula or low ast a sherical article: t Nu, (6) d where λ is the thermal conductivity coeiciente o the air; Nu is the Nusselt number. The Nusselt number in (6) is determined by the Rantz-Marshall relationshi [5] under the conditions considered: t 1/ 1/3 Nu ( 0.6Re Pr ), (7) where Re is Reynolds number; Pr is Prandtl number. The Reynolds and Prandtl numbers or the low around a sherical dro by air are determined by the relations Re U V d, Pr c, (8) where μ, c, and λ are the dynamic viscosity coeicient, the seciic isobaric heat caacity and air thermal conductivity coeicient. The change o a dro diameter due to evaoration was determined by the ormula []: d t G( t), (9) dt () t S () t where d (t) is a dro diameter; G (t) = w va (t) dt is the mass o the evaorated substance in a time dt; S (t) is the surace area o a sherical dro. The crushing o dros under the action o inertia orces (Rayleigh-Taylor instability) was taken into account by calculating the value o the Bond s number d t Bo, (10) where Δρ = ρ - ρ ; Δρ is the surace tension coeicient o a dro; ω is the modulus o acceleration vector o a dro. The crushing o dros under the action o aerodynamic drag (Kelvin-Helmholtz instability) was taken into account by calculating the value o the Weber s number 3

4 U V d t We (11) It was assumed that when the critical value o the Bond number is Bo. 5 or the, the dro is slit into two sherical dros o equal mass critical Weber number We 17 with an initial velocity equal to the velocity o dro initial []. When the mathematical model (1) (5) was arametrized, it was taken into account that in the conditions o emergency uel discharge rom the illing tanks, the liquid-drolet cloud initially alls into the trace into dragged by co-current aircrat wing low. Thus, at the initial moment o time, the liquid-drolet cloud has a velocity equal to the airlow velocity in the trace. The air velocity roile in the trace is described by the equation [7] in case o an axisymmetric co-current: u U 3 / 1, (1) 0 where u is the airlow velocity in the trace ; U 0 is the seed o the aircrat; η = y s /δ, y s is the distance rom the trace axis, δ is the hal-width o the trace. The hal-width o the trace δ was estimated according to [7]: F U x 0 1/3, (13) where F x is the lit orce o the wing, U 0 is the aircrat seed at the moment o uel discharge. The mathematical model (1) (5) is imlemented as a sotware ackage. 3 Analysis o the results o numerical modelling A numerical study was made o the eect o the most signiicant actors limiting the crushing o drolets during the roagation o a liquid-dro cloud in the atmoshere on the basis o the mathematical model (1) (6). Based on the results o the analysis o the reliminary calculations, the size o the dros ormed during crushing during gravity deosition was estimated, deending on the initial size o the liquid-dro cloud. The initial size o the liquid-dro cloud was varied in the range d =( ) m. The seed o the aircrat varied in the range U 0 =( ) km/h at the time o emergency uel discharge. It is ound that dros orm o diameter d ~ 10-3 m during the time o ~ 1 s in the whole range o seed o the aircrat, regardless o the initial size o the liquid-dro cloud. At U 0 = 600 km/h, the minimum dro size was d m, at U 0 = 900 km/h d m. The aerodynamic crushing is comleted when the dro is vertically moved to a distance o < 10 m, deending on the initial size o the liquid-drolet cloud. The dro size decrease is determined by the evaoration rocess in the rocess o urther roagation in the atmoshere. The minimum height h min o the emergency uel discharge, which ensures comlete evaoration o uel drolets in the atmoshere were determined, deending on the season-climatic conditions. Analysis is erormed or the regions o Russia located in dierent climatic zones: Kaliningrad and Novosibirsk Regions, Yakutia (Sakha Reublic). The atmosheric arameters averaged over time are taken rom [8]. The results o the minimum height calculating h min are showed in Fig. 4. 4

5 Fig.. Minimum heights o emergency uel discharge or dierent regions o Russia, U 0 =600 km/h. Fig. 3. Minimum heights o emergency uel discharge or dierent regions o Russia, U 0 =900 km/h. Fig. 4. The minimum heights o uel discharge above the territory o the Kaliningrad region deending on the seed o the aircrat. From the data ones shown in Fig. it ollows that when seed o aircrat is 600 km/h, the minimum uel discharge heights, ensuring no reciitation o aviation uel to the earth's surace, do not meet the requirements o the ICAO in the cold months o the year. This eriod is rom January to Aril and rom October to December or the territory o the Novosibirsk region, rom January to May and rom Setember to December or Yakutia, rom January to March and December or the Kaliningrad region. There is a risk o reciitation o unevaorated uel to the surace o the earth in these eriods. Emergency discharge o aviation uel with an increase in aircrat seed to 900 km/h allows to reduce ecologically dangerous eriods o the year (Figure 3) or the regions o Yakutia and the Novosibirsk region. The minimum heights o the emergency discharge above the territory o the Kaliningrad region ensure the evaoration o uel drolets in the atmoshere throughout the year at this seed. The obtained results are in satisactory agreement with ICAO rules develoed or lights over the territory o Western Euroe (Fig. 4). This is exlained by the comliance o the seasonal and climatic conditions o the Kaliningrad region with the conditions o the Euroean regions. Seasonal and climatic 5

6 conditions o Yakutia and the Novosibirsk region are signiicantly dierent rom Euroean by continuance o cold eriods and by air temerature ranges during these eriods. Based on the mathematical model (1) (5), the values o the mass raction o aviation uel, alling on the earth's surace in ecologically dangerous eriods deending on the seed o the aircrat at the time o discharge were determined. In articular, it was obtained that ~ 0.5 mass o uel is deosited on the earth's surace during emergency discharge rom an airlane over the territory o Yakutia in the coldest eriod o the year (rom December to February). 4 Conclusion Analysis o the results o mathematical modeling o dynamics and heat and mass transer o a liquid-drolet cloud in the emergency discharge o aviation uel, deending on the season-climatic and meteorological conditions o seciic regions o Russia, showed that the seed o the aircrat, at which an emergency uel discharge occurs, is one o the most signiicant actors aecting the rocesses o crushing and evaoration o dros in the atmoshere. It seems advisable to develo regional rules, similar to ICAO rules, regulating the organization o uel duming in accidents, taking into account the seasonal and climatic conditions o seciic regions. The develoment o regional rules can be carried out on the basis o mathematical modeling using the roosed model. This study was unded by grant rom the Russian Science Foundation (Project No ). Reerences 1. Electronic resource: the website o news agency Newsru, htt:// V.A. Arkhiov, E.A. Kozlov, I.K. Zharova, A.S. Tkachtnko, Atmosheric and Oceanic Otics, 6 (013) 3. Ye.A. Maslov, I.K. Zharova, N.S. Fedotova, Selected Reorts o All-Russian Scientiic and Technical Conerence London, 5 (014) 4. V.A. Arkhiov, E.A. Kozlov, S.S. Titov, A.S. Tkachenko, A.S. Usanina, I.K. Zharova, Arabian Journal o Geosciences, 9,114 (016) 5. M.A. Pakhomov, V.I. Terekhov. Flow, Turbulence and Combustion, 98 (017). 6. A. Semenov, G. Kuznetsov, D. Zaitsev. Evaoration o an intensively heated sessile drolet into the oen atmoshere, MATEC Web Con., 84 (016) 7. R.I. Nigmatulin. Dynamics o Multihase Media (Hemishere Publishing Cororation, New York, 1991) 8. New Aeroclimatic Reerence Book o the Free Atmoshere over the USSR (Gidrometeoizdat, Moscow, 1990) [In Russian] 6