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1 Journal of Civil & Environmental Engineering ISSN: X Research Article Journal of Civil & Environmental Engineering AbRabbo et al., 016, 6:3 htt://x.oi.org/10.417/ x Oen Access Stuy the Proerties of Water Mist Drolet by Using FDS Mohame Fayek AbRabbo, Ayoub Mostafa Ayoub, Mohame Aly Ibrahim, an Abelsalam M. Sharaf elin* Benha University, El-Shahee Fari Naa, Banha, Al Qalyubia Governorate 1351, Egyt Abstract Fire suression systems are an extremely imortant art of every builing that ensures the safety of the occuants an limits amage ue to fire. Full scale moel is set u for the urose of reicting the geometry of fire srea an water mist articles istribution an movement. The results are base on full scale moel simulation for several roerties of water mist rolet. The water mist rolet see, mist flux, rolet size an rolet istribution are iscusse. It can be conclue that The water mist rolet movement, article size an rolet istribution lay a vital role to suress fire.the resent stuy is carrie out using Fire ynamic simulator (FDS) to erform the moel of room fire scenario require to investigate an comute article istribution, rolet velocity, mist flux an rolet size. Keywors: Drolet; FDS; Particle; Water mist Introuction The effects of water mist characteristics on fire suression for room fires are very imortant esecially water mist rolet. The water mist rolet characteristics of the atomizer, such as isersion, rolet movement or rolet ynamic, rolet istribution an mean article iameter will iscuss in this chater. A numerical simulation for a moel room with a single water mist nozzle will conuct in orer to stuy the rolet characteristics. The water mist systems, often the immeiate interest is in the size of the water rolets being rouce as this factor greatly effects how the sray will interact with the fire srea an which of the extinguishment mechanisms will lay significant roles. Many researchers have stuie the fire suression by using water mist in comartment. Simo Hostikka et al. [1] resente enhancements by using FDS to escribe an valiate the ynamic of water sray, air entrainment an raiation attenuation. Three tyes of nozzles are resente in this system (LN-) with three ressures A, B an C from Marioff Comany. Flow rate an article size istributions are etermine. Wighus et al. [] investigate in resonse to the nee for a fire suression system for iesel turbines on boar offshore rilling latforms. The exeriments tests carrie out by Wighus et al. confirme that water mist coul be use to successfully suress fires in turbines. Water mist rovies a goo fire suression solution for this tye of scenario as it can be continually injecte (unlike gas systems which have limite oerating time), an rovie less thermal shock to the turbine blaes than stanar srinklers. The mechanisms of water mist involve in suression inclue cooling an steam islacement an ilution of oxygen. Chuka et al. [3] stuie the effects of the article size an injection orientation by using water mist extinction of liqui ool fires. The base injection of articles evelos the extinction effectiveness by as much as two times comare with the to injection, an small rolets were more effective in every orientation. Simson et al. [4] stuie the effects an efficiency of water mist use within telecommunication an electrical cabinets through exerimental testes. In each test case the fire within a.44 m high, by 0.61 m wie an 0.46 m length electrical cabinet were all extinguishe within less than two secons using less than one liter of water of articular relevance in this set of exeriments is that while the low current tris on the circuit boars activate, the current was so low that electric shock was not consiere a erceivable anger. In aition to these extinguishment characteristics, after a short erio of rying out, all of the electrical systems coul be switche back on an continue to function. Petra Anerson et al. [5] stuie the effectiveness of water mist injection at low level into a 1/3 scale ISO room with an oen oor. It simulate ifferent fire ositions, nozzles ositions, water mist ensities an rolet sizes in. This research also reviewe how obstacles affecte the water mist articles. The results of these research inicate that a water mist ensities of between g/m 3 were neee for suression of a iffusion flame using fine water mist (fine articles). The rolet iameter ecrease with Lower values of water mist ensities. Calculations inicate that for the water articles to follow the airflow aroun an obstacle the articles neee to be in the region of 1-0 μm. Base on these finings they suggest the ieal water rolet size for a low level total flooing system is between 10 0 μm. They also note, however, that momentum neee to be given to the sray for it to reach all areas of the room, as other istribution moes were very slow. This research rovies the most information on water mist interaction in relation to the exeriments covere in this stuy. Evans et al. [6] stuie the injection of water mist into a methane flame through nozzles that coul be locate in ifferent ositions. The exeriments showe an escribe that the most effective irection for the water mist to be injecte was vertically u, in line with the flame. The require mass rate water to mass rate of methane in this test was aroximately four for extinguishment. In comarison horizontal injection resulte in an extinguishment ratio of 9.5 an oose flow injection resulte in an extinguishment ratio of 0. This inicate that the flow atterns in relation to the reactants were very imortant to the success of extinguishing the fire. Hua et al. [7] use a numerical moel to investigate the influence of nozzle characteristics on fire suression. The mono iserse sray was treate using a Lagrangian s aroach. They conclue that a water sray with a soli cone attern an a finer water rolet is more efficient in suressing fires than a hollow cone attern an a coarser water size. This research exlores the ossibility of using the comutational flui ynamics rogram Fire Dynamics Simulator (FDS) as a *Corresoning author: Abelsalam M. Sharaf elin, Benha University, El- Shahee Fari Naa, Banha, Al Qalyubia Governorate 13511, Egyt, Tel: ; a.sharafelin84@gmail.com Receive Aril 06, 016; Accete Aril 0, 016; Publishe Aril, 016 Citation: AbRabbo MF, Ayoub AM, Ibrahim MA, Sharaf elin AM (016) Stuy the Proerties of Water Mist Drolet by Using FDS. 6: 4. oi:10.417/ x Coyright: 016 AbRabbo MF, et al. This is an oen-access article istribute uner the terms of the Creative Commons Attribution License, which ermits unrestricte use, istribution, an rerouction in any meium, rovie the original author an source are creite.

2 Page of 10 comutational esign. FDS has been use for various alications incluing moeling smoke flow in multi-floors builings, tunnel fires an ifferent ventilation conitions. FDS Moel The FDS moel room imension is.6 m x.6 m x.4 m (length x with x height) an a oor oening is locate at the front of the comartment. The fire is moele with a cubic heat source, the fire source has imension of 0. m x 0. m x 0.6 m (length x with x height) (Figure 1). A water mist nozzle is use where is locate at the.3 m from the base of the center of room. The fuel is use in the simulation is methane. The secifications of nozzle will use in chater four are {k-factor = 0.433, sray angle = 1 egree, rolet iameter = 79 μm} [1]. The fire takes laces at the en of comartment which ignite fire in couch.the oor in all cases are taken to be fully oene, as given in Figure 1. Gri Resolution A 0.05 m gri is secifie for the moeling normal room, with a total of cells. This simulation took aroun 48 hours each to run. The selection of mesh size get from FDS user guie [8], it states to use a D*/x ratio between 4 an 16 to calculate the aroriate mesh size. In that ratio, x is the nominal size of a mesh cell, an D* is a iameter of fire efine in the equation (1): /5. * Q D = (1) ρ * C * T * g. Where Q is heat release rate ( HRR), ρ is the air ensity ( 1.04 kg/m 3 ), C is the air secific heat (1.005 kj/kg.k), T is the ambient temerature(93 K), an g is the acceleration ue to gravity(9.81 m/s ). The finest mesh size we woul have to use is with a D*/x ratio of 16. Governing Equations of Moel This art iscusses the basic of conservation equations for energy, mass, an momentum for a Newtonian flui.the escrition of the equations, the notation, an the ifferent aroximations emloye by Anerson et al. [9]. A six ifferential equations for six unknowns, all functions of three satial imensions an time: the ensity (ρ), the three velocity comonents U = [u; v; w], the temerature (T), an the ressure (). The continuity equation can be simlifie as the following relation: u u u u u u u ρ + u + υ + w = + µ ρ gz (6) t x y z z x y z Note that gravity has been accounte for as a boy force, an g x,g y,g z values will be een on the orientation of gravity with resect to chosen set of coorinates. The energy equation in a multi-comonent reacting system, there are several mechanisms that contribute to the total heat flux, the most common known as conuction, convection an raiation. Mainly two aitional effects are encountere in the literature; these are the effect of mechanical work one on the system ue to buoyancy an the socalle Dufor effect. The latter escribes the heat flux in a system ue to concentration graients an in general, this term can be neglecte ue to the low velocities involve in a fire the mechanical work term can be ignore as well. The energy equation can be written in ifferent ways eening on which quantity is use as the eenent variable. Using the total enthaly, h total = c T+ Y α H where H is the comonent r r heat of reaction, as eenent variable, the conservation of energy equation becomes: λ h ( ρh ) + ( ρvjh ) = + q r j (7) T Xj T Xj C Xj The rogram goes eely in calculating all secies quantities using comlicate equation which will be very easy to be solve now a ays by PC s other than manual ol metho. The rogram relations an equations can be foun on site in a PDF file [8] for more etails. Water Mist Drolet Moels The technicality of energy transfer between the water mist rolets an fire are the surface tension is necessary to break-u the articles or rolets, the momentum to accelerate the articles because of the ambient gases velocity, an energy to increase the temerature of the articles because of the ambient temerature an the energy of latent heat. Meanwhile, it is assume in our work that the collisions between water mist rolets are negligible because the water mist sray seems to be relatively sarse [10]. Vaorization Moel The energy transfer an the mass between the liquis an gases rolets can be consiere as follows [11]: ρ ( ρu) ( ρv) ( ρw) = 0 () t x y z When the flow is at steay -state, ρ oes not change with resect time. The equation is reuce to: ( ρu) ( ρv) ( ρw) + + = 0 (3) x y z The momentum equations with the comonents of velocity are tyically name u, v, w. while the three equations are : u u u u u u u ρ + u + υ + w = + µ ρ g t x y z x x y z u u u u u u u ρ + u + υ + w = + µ ρ g t x y z y x y z y x (4) (5) Figure 1: Schematic of normal room moel (Smoke view).

3 Page 3 of 10 ml = Ahmρ( Yl Yg) t Tl ml m = ( ) + lcl Ah Tg Tl qr + hv t t where,( m l ) is the mass of article or rolet, (A) is liqui rolet area, (h m ) is the coefficient of mass transfer to be iscusse below, (ρ) is the ensity of gas, (c l ) is the secific heat of liqui, (h) is the coefficient of heat transfer between the gases an the liquis, ( q r ) is the raiative rate heating of the article or rolet, an( h v ) is the vaorization latent heat of the liqui. In the equation of mass transfer (7), (Y g ) is the mass of vaor fraction of the gas which obtaine from the mass conservation equations of gas hase an (Y l ) is the equilibrium vaor of liqui mass fraction obtaine from the Clausius-Claeyron equation [1,13]. Heat an mass transfer between gases an liquis are escribe with analogous emirical correlations. The coefficient of mass transfer, (h m ) an (h) the coefficients of heat transfer are escribe by the emirical relationshis [11].. h = Nu k (10) L. h = Nu k (11) L Here, D lg is the mass iffusion coefficient of water vaor in gas mixture;( L) is a scale length equal to the iameter of rolet or article. (k) is the gas thermal conuctivity. The Sherwoo number Sh is evaluate from the Ranz an Marshall correlation [13] as follows: 1 0.6Re Sh = + D Sc (1) (Re D ) is the rolet Reynols number (accoring to the iameter, D, an the relative air velocity -rolet velocity). The Nusselt number Nu is evaluate with an analogous relationshi as Sherwoo number Sh, Nu = + 0.6ReD Pr (13) Break-U Moel Break u moel occurs when the rolet imacts the surface at incoming the Weber number equal or greater than the critical Weber number. The isintegrate number of rolets or articles will increases with the increases in Weber number. This is because of the imact energy an the eformation of the rolet increase with the Weber number [14,15]. The rag force F acts as a eforming force. The surface tension on the other han acts as a restoring force. The contracting force aroun the erimeter of a rolet, F σ is given by the surface tension σ multilie by the length of the circumference: F = πσ (14) σ The criterion of break-u can be exresse in terms of the relative velocity of rolet an the gas flow, Weber number which is the ratio between the inertia an surface tension forces( can be use to inicate the rolet shae an eventually break u) given by ρ v = σ We (15) Where σ is the water surface tension. (8) (9) The break-u of water mist rolets is moele by Reitz an Diawaker moel [16]. In their moel, a two rolets or articles breaku regimes are consiere. These are bag break-u when ρv We = > 6 (16) σ An striing break u when We Re > 0.5 Drag Moel Simulation (17) In FDS, the equation of motion for a single sherical rolet is etermine by m 1 v = mg ρgcdπr vrel vrel t (18) Re = ρ v / µ rel g Where (m ) is the rolet or article mass, v is the rolet velocity, ρ g is the ensity rolet of the surrouning gas. v rel = v - v g (19) Where v the rolet or article velocity relative to the rel surrouning gas is v is the gas velocity g. (Re ) is the Reynols number of rolet or article. (C D ) The coefficient of rag is given by 4 / Re Re < C D = 4( Re ) / Re 1 < Re < 1000 (0) 0.44 Re > 1000 Accoring the value of Re,the C D will be calculate (C D as a function of Re number). A curve reresenting the aroximate exression for rag force coefficient for Renols Number between [0.5,1] (Figure ). The arrangement of two rolets is irectly in line, the hyroynamic reuction forces to the secon (trailing) shere because of the wake effect were iscusse [17]. They stuie in the next analytical formula for the force of hyroynamic to the secon shere. C C (1) D D Figure : Drag coefficient C D an Re number.

4 Page 4 of 10 Where (C D0 ) is the rag coefficient of single rolet an (F/F 0 ) is the ratio of hyroynamic force of trailing rolet or article to single rolet: F Re1 1 Re1 1 = W 1 + ex () F L/ L/ Where (Re 1 ) is the Reynols number of single rolet, (L) is the istance between the rolets an (W) is the non-imensional velocity in the center of the trailing rolet or article. C 0 Re1 1 D W = 1 1 ex (3) 16 1 L/ The FDS moel assumes that the sheres are travelling irectly inline with each other. Particle Size Distribution The istribution of rolet sizes in a sray in terms of an iealize rolet size istribution. This coul facilitate comarison between various srays, algebraic maniulation, theoretical analyses an interolation/extraolation of ata. A variety of moel rolet size istributions are in common use, an are either emirical (e.g. Rosin-Rammler, log-normal, root-normal, etc.) or analytical (e.g. Maximum Entroy, an Discrete Probability Function). Analytical aroaches are base on conservation of mass, momentum, surface energy, kinetic energy. Detaile escritions of these istributions are available in [18,19]. A comlete lot of the rolet sizes is a better exression than the single values escribe above. It is ossible for two srays having, for examle, the same volume mean iameter, to have wiely iffering ranges of rolet sizes. The cumulative volume fraction of rolet or article iameters in FDS follows a istribution that is a combination of lognormal an Rosin-Rammler istributions: 1 1 e F ( ) = π 0 σ 1 e By efault σ = 1.15 / γ ' ln( / ) m ' σ ' γ m m m < (4) Drolets or articles with iameters smaller than min are assume to vaorize instantly. The oerating ressure effect on the meian rolet size. The etermining of exerimental rolet size istribution at certain ressure this variation in rolet 1 size is taken into account by scaling the meian rolet size as α 3 P The arameters of rolet size istribution were foun by least squares fit of the mathematical form of the FDS rolet size sectrum to the exerimentally calculate cumulative volume istribution at low ressures Figure 3 [1]. Fitting the FDS cumulative number istribution to the exerimentally measure cumulative number istribution was also teste an it was iscovere that these two methos resulte in significantly ifferent istribution arameters. m Secifie Outut The following quantities are secifie to be recore in outut files from the stanar outut generate by FDS: a) Drolet size an see evices measurement (PDPA) are ositione vertically at 70 cm an 100 cm below the nozzle. b) The ressure an rolet flux evices measurement (PDPA) are ositione vertically at 70 cm an 100 cm below the nozzle. c) The rag force of rolet. Results an Discussion In resent stuy, the rag coefficient is calculate numerically for a single rolet moves vertically own.the rolet velocity was investigate from FDS simulation. In Figure 4 a curve reresenting the aroximate exression for rag force coefficient for Reynol s Number, was use for comuting rag force. The rolets will slow own Due to the frictional force; also the maximum velocity it can reach is when the net force is equal zero in equation (18) (Figure 5). The falling rate of rolet as it asses through the lume. As a rolet becomes smaller the rag force create across its surface Figure 3: FDS an exerimental rolet size istribution 0 bar [1]. Figure 4: Drag coefficient (C D ) an Re for move rolets.

5 Page 5 of 10 Figure 5: FDS article size istribution for nozzle at 70 bar. Figure 6: Drolet see with coefficient of rag force an rolet iameter. becomes larger in relation to its mass an hence the gravitational force on it. Hence large rolets will fall quickly to the floor while small rolets will fall at a much slower rate. If the velocity within the lume is higher than falling rate then the rolet will be lifte within the lume an circulate within the comartment (Figure 6). The article or rolet size istribution arameters are resente by least squares fit of the mathematical form of the FDS rolet size sectrum etermine cumulative volume istribution for resent stuy case can be seen in Figure 6. In this section the secifications an characteristics for nozzle B were use with resent moel. The fire extinction erformance of water mist is eenent on the characteristic arameters of velocity istribution, rolets or article size istribution an flux. Such arameters can be measure using the Phase Doler Particle Analyzer (PDPA) system. Initial velocity istribution of water mist will affect the erformance of the suression system. The see of the rolet reuces ue to rag an ossibly energy lost in rolet collisions (Figure 7). In Figure 8, the slice at center of room or nozzle shows the velocity of rolets ecrease. The momentum regime occurs when water mist exits from the nozzle an breaks u into small rolets or articles. The gravitation regime occurs after the rolets begin to reach their resective settling velocities. The smaller rolets are entraine into the sray center, which is forme by the air currents rouce by the nozzle. The majority of sray water flux is containe in the sray core. The remainer of the larger rolets has sufficient momentum to reach the outer eges of the sray. Figure 8 also shows the location of the measurement oints 70 an 100 cm below the nozzle in the transition regime. Although measurements were taken at all oints, ata was analyze only u to a raial istance of 15 cm, as the images from the outer measurement oints containe very little rolets. A rolet size istribution can be resente in terms of surface area, volume, or number (i.e. count) as mentione above. When fitting a ataset to a istribution, it is therefore imortant to choose a form aroriate to the source of the ata, an the intene alication of the moel istribution. In the next Figures resents the rofiles for average rolets iameter, average mean velocity, an average mist flux. The average values at each istance are calculate over the four measuring oints at that istance (excet for the oint at the sray axis).

6 Page 6 of 10 Figure 7: Variations of rolet velocity with istance from nozzle. Figure 8: Slice of velocity of rolet in the room. Figure 9: Drolet see with raial istance at 70 an 100 cm below nozzle.

7 Page 7 of 10 In Figure 9, the maximum velocity in the center of the sray the velocity rofile becomes broaer further away from the nozzle. Maximum velocity reuces from away the center of sray. The water concentration in the sray at the center reaches a maximum.the water concentration levels out an water becomes relatively evenly istribute over the area.as can be shown in slice Figure 10. Drolets size further vary within the sray fiel as the samle Figure 10: Water concentration below the nozzle (slice at the center of the room). Figure 11: Mean iameter of rolet an raial istance at 70 an 100 cm below nozzle. Figure 1: Mist flux of roletslet an raial istance at 70 an 100 cm below nozzle.

8 Page 8 of 10 oint moves from the central axis of the nozzle out to the erimeter of the sray attern, as well as with istance from nozzle orifice. The reicte iameter rofile can be seen in Figure 11. A flat mean iameter rofile is reicte for nozzle. In short besie or near of the nozzle, the entraine air will ten to ull rolets or articles towars the centre of the sray. Smaller rolets or articles have shorter times resonse an thus are entraine more easily. These rocesses shoul result in a iameter rofile that shows more small rolets or articles in the centre of the sray an larger rolets from away the centre or (on the sray bounaries). In Figure 1, the water mist flux is high in the center of sray an reuces whenever away from the center. The velocity in the canter of the jet is higher than further out, leaing to larger rolets velocities an higher mist flux. The increase in rolets iameter is cause by entrainment. In Figure 13, it shows that a arent (initial) rolet or article is breaking u into many chil water mist rolets. Also the chil rolets iameter ecreases as a function of the number of fragments forme can be seen in Figure 14. Figures show the relation between numbers of rolets with raial istance for two ositions of measurement evice at 70, 100 cm below the nozzle. It can be seen the number of rolets is maximum in the center of sray an otherwise. Conclusion A FDS rogram is use to simulate the fire comartment an show outut results of the rolet velocity an iameter of rolet for several moels. After running many comuter simulations, the following conclusions are estimate: The rolet iameter, rolet see, water mist flux, number of rolet an rolets istribution were simulate in case of normal room. The flux of water mist is high at the center of sray an reuces whenever away from the center. The rolet see is highest in the center of the sray.the velocity rofile becomes broaer further away from the nozzle. Maximum velocity reuces from away the center of sray. Figure 13: Drolets break u simulation. Figure 14: Chil rolets iameter with number of fragments forme.

9 Page 9 of 10 Figure 15: Number of rolets an raial osition at 70 cm below the nozzle. Figure 16: Number of rolets an raial osition at 100 cm below the nozzle. References 1. Hostikka S, Vaari J, Sikanen T, Paajanen A (011) Proceeings: Fire an Evacuation Moeling Technical Conference, Baltimore, Marylan, August 15-16, 011. Wigus R, Aune P, Drangshot G, Stensaas JP, (1993) Fine Water Sray System Extinguishing Tests in Meium an Full Scale Turbine Hoo. P Int Water Mist Conference, Sweish Testing Institute, Boras, Sween, Nov Nubizu CC, Ananth R, Tatem PA (000) The effects of rolet size an injection orientation on water mist suression of low an high boiling oint liqui ool fires. Combust Sci Technol 157: Simson T, Smith DP (1993) A Fully integrate water mist fire suression system or Telecommunications an other electronics cabinets. Fire an Safety International, Colnbrook, UK. 5. Aerson P, Arvison M, Holinstet G (1996) Small scale exeriments an theoretical asects of flame extinguishment with water mist. Luns tekniska hogskola, Lun University. 6. Evans D, Pfenning D (1985) Water srays suress gas-well blowout fires. Oil an Gas J. 7. Hua H, Kumar K, Khoo BCJ (00) A numerical stuy of the interaction of water sray with a fire lume. Fire Safety J 37: htt://fssmv.googlecoe.com/svn/trunk/fs/trunk/manuals/all_pdf_files/ FDS_5_technical_reference_guie.PDF}.

10 Page 10 of Anerson DA, Tannehill JC, Pletcher RH (1984) Comutational flui mechanics an heat transfer. hemishere ublishing cororation, Philaelhia, Pennsylvania,11, Haman S, Klaus-Jürgen K, Reinhar G (009) Interaction of water mist with fire lume by using FDS. Jahresbericht 006/007/008, IF Sachsen-Anhalt, Heyrothsberge. 11. Incroera FP, De Witt DP (1996) Funamentals of heat an mass transfer. John Wiley an Sons, (4then). New York, 1. McGrattan KB, Hostikka S, Floy JE, Baum HR, Rehm RG (007) Fire ynamics simulator (Version 5), technical reference guie. NIST Secial Publication 10185, National Institute of Stanars an Technology, Gaithersburg, Marylan. 13. Ranz WE, Marshall WR (195) Evaoration from rolet: art II. Chemical Engineering Progress, 48: Hatta N (1997) Exerimental stuy of eformation mechanism of a water rolet iminging on hot metallic surfaces above Leien frost Temerature. Transactions of the ASME Hatta N (1995) Collision ynamic of water rolet iminging on a rigi surface above Leien frost Temerature. ISIJ int Diwakar R, Reitz RD (1986) Effect of rolets breaku on fuel srays. SAE Reort Ramírez-MJ, Soria A, Salinas-RE (007) Hyroynamic force on interactive sherical articles ue to the wake effect. Int J Multihase Flow 33: Crowe C, Sommerfel M, Tsuji Y (1988) Multihase flows with rolets an articles. CRC Press. 19. Babinsky E, Sojka, PE (00) Moelling rolets size istributions. Progress in Energy an Combustion Science. OMICS International: Publication Benefits & Features Unique features: Increase global visibility of articles through worlwie istribution an inexing Showcasing recent research outut in a timely an uate manner Secial issues on the current trens of scientific research Secial features: Citation: AbRabbo MF, Ayoub AM, Ibrahim MA, Sharaf elin AM (016) Stuy the Proerties of Water Mist Drolet by Using FDS. 6: 4. oi:10.417/ x Oen Access Journals 50,000+ eitorial team Rai review rocess Quality an quick eitorial, review an ublication rocessing Inexing at major inexing services Sharing Otion: Social Networking Enable Authors, Reviewers an Eitors reware with online Scientific Creits Better iscount for your subsequent articles Submit your manuscrit at: htt://