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Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No 2 (87 - 94) CALCULATION OF TURBULENT DIFFUSION JETS UNDER EFFECTS OF GRAVITY AND MOVING SURROUNDING AIR BUI VAN GA Technology School, Danang University NHAN HONG QUANG Centre for Labour Protection in Danang City JEAN MARC VIGNON Ecole Centrale de Lyon ABSTRACT. The basis theory for the turbulent diffusion of jet and flame has been presented previously [l, 2] . But that one applies only in quiet surrounding air with the effects of buoyancy neglected. In the present paper the theory is developed further by establishing an integral model for a jet in more general conditions with variable inclined angles, under effects of gravity and surrounding air velocity in any direction compared to the jet axis. The system of equations is closed by turbulence k-E model and is solved by 4th order RungeKutta method. In the first stage, the model is applied to predict the velocity field, the concentration field and width development of a 0.3 m diameter jet. 1. Introduction As compared to a premixed combustion process, the diffusion flame combustion of a nonpremixed mixture is process mainly controlled by the mass transfer of fuel and air comming from two separate sources. Considerations so far have provided little or no insight into the mechanism of the mass transfer but the most important point is how to determine the fuel distribution in diffusion jet. Then, basing on the distribution we can calculate both the combustion velocity and the formation of pollutants. Moreover, although turbulent diffusion flame are in common use, due to the lack of mathematical solution, many scientists have relied upon practical methods for determining the mechanism of mass transfer in order to improve· the diffusion process and limit pollution emission. Experimental measurement in the turbulent diffusion combustion process is considered to be very difficult and even impossible in some cases. So, mathematical modeling of the diffusion combustion process bears a great practical significance. This allows us to predict the phenomena occurring in turbulent diffusion flames then control them in the same yvay as we do with the premixed flames. For the purpose of modeling'the turbulent diffusion flan1e, a model of a turbulent jet has to be established. OD,e-dimensional Integral models were established 87 . and analysed for calculation of vertical turbulence diffusion jet in still air by many authors [l]. On the base of these researches, a modei of vertical turbulent diffusion flames in still air was established to calculate the pollutants exhausted from industrial chimneys as well as from the smoke of pool fires [2, 3]. Additionally, it was possible to calculate the turbulent process and formation of soot in Diesel engine [4] and N0 2 in a separate combustion chamber but neglecting swirl effects [5]. The assumption of stationary air surrounding turbulent jet plus the omission of gravitational for the purpose of simplifying the calculation sometimes causes trouble in the case of the swirl combustion chambers since the turbulent jet is strongly influenced by these fact.ors. So, establishing a mathematical model to calculate the structure of a general diffusion jet with different inclined angles in moving air will enhance practical application of the model. In this paper we will firstly consider the general diffusion jet in order to calculate the concentration field in a turbulent diffusion jet. We believe this better simulates the fire working condition in an engine thus making the combustion process more precise. I 2. Est~blishing Equations Equations describing the general laminar jet (Fig. 1) are din Wg/U + 27r Rpoof3IU - Uoo cos e1 dW - ds . = W9 +U 00 (2.1) u= cos eI u 2- ds din cose -d , (2.2) s de inU · - = 7rR 2 (p 00 din (p))gcose - Uoosine · -d , A - ~ s (2.3) where 00 W = 27r j pU 2 r · dr, (2.4) 0 00 in= 27r j pUr · dr, (2.5) 0 (J = W/in, (2.6) R=in/J7rpooW, (2 .7) {3 = 0.23JPst/ Poo , (2.8) W9 = 7rR (2.9) 2 · g · sinO(poo - (p)) 88 Fig. 1. Scheme of the general diffusion jet In case of diffusion flux, there is a presence of dynamic turbulent viscosity µ 7 in the mass conservation equation (2.1). By neglecting the influence of acceleration due to gravity and movement of the air, equation (2.1), as described by Tamanini [6], can be written as follows: din ds = Ck7r(µ + µT) (2.10) After being derived and re-arranged, equation (2.1) becomes: din W9 /(2U) + PcxiRU,B7rll - U=cosB/UI ds 1 - UCXl cos eI (2U) (2.11) On neglecting the influence of acceleration due to gravity (W9 = 0), in still air 7 rv pRU, we see that the two equations (2.10) and (2.11) are coincided. That allows us to re-write the general mass conservation equation (2.1) as follows: (U00 = 0) and vertical jet (cos e = 0), knowing that µ din W9 /(2U) + ck7r(µ + µt) ll - U=cosB/UI 1 - UCXl cos e/(2U) ds (2.12) Equation of momentum conservation (2.2) and equation governing the direction of jet (2.3) are unchanged . In equation (2 .1 2) dynamic turbulent viscosity µ 7 is allowed for by the use of mass weighted kinetic energy of turbulence k and its dissipation c: µT = k and E k2 Cµ. (p) . - c can be calculated by the following equations: d(kin) _ p _ D ds - d(cin) ds k (2.14) k, E = k(ce: 1 Pk 89 (2.13) Ce: 2 Dk), (2.15) where Pk . 71'µ.,.(Uo - U00 cos0) 2, Dk = (p)c7r R2 , (2.16) (2.17) Uc is the maximum axial velocity of flux 2W Uc=-.-· (2.18) m In summary, the system of equations, which control the general diffusion jet with different inclined angles in moving air includes 5 equations: (2.2), (2.3), (2.12), (2.14), (2.15). The system of equations is performed by using the 4th order RungeKutta method. For all presented results, the nozzle diameters is 0.3 m taken as representative of industrial chimneys. 3. Numerical Results Figure 2 illustrates the influence of effective exit velocity in case of constant air velocity and gas density is p = 2 kg/m 3 . With a small exit velocity, substances in turbulent jet (their density being more than that of air) will fall down more closely to the source than in the case of strong exit velocity. When changing air velocity we have the same result (Fig. 3). That allows us predict the area that is under influence of pollutants exhausted from industrial chimneys for the purpose of designing chimneys and planning residential areas. 15 V~=3m/s 20 40 x(m) (j) U0 =5m/s Fig. 2. Influence of exit velocity to jet = 5m/s; p = 2kg/m D = 0.3m; () = 90°) profile (U00 3 Fig. 3. Influence of air velocity to jet profile ; (Uc = lOm/s; p = I.5kg/m3 ; D = 0.3m; () = 90°) The specific density of substance strongly effects the jet profile. In the similar condition, the higher specific density of gas, the polluted area is closer to the nozzle source air due to gravitational acceleration. \\Then the specific density of polluted is smaller than that of air, pollutants will diffuse in the ambient because of gravity 90 acceleration. Fig. 4 illustrates jet profiles for the case of pollutants with different specific densities based on the assumption that the initial concentration of pollutant is unity (c = 1) . In the practice of industrial chimneys, the initial concentration of pollutants is very small and reduces rapidly because of the air entrainment. Fig. 4. Influence of specific density of pollutants to jet profile (Uc = 10 m/s; p = 1.5kg/ m 3 ; D = 0.3m; = 90°) e Fig. 5 illustrates the velocity profiles of pollutants inside a diffusion jet for different surround air velocities. The influence of initial exit velocity tends toward reducing along the jet axes farther from jet source where there is only the influence of the surrounding air wind. U0 = l Om/s; U~=Sm/s; p= l ,Skg/m'; 8=90° . -80 -40 -60 -20 U.,= l Om/s; U~=3 m/s; p= l ,Skg/m'; 8=90° I0 -5 0 20 40 x(m) 60 80 Fig. 5. Influence of set of different factors to jet profile The pollutant distribution inside a diffusion jet (when its initial concentration c = 1) is illustrated in Fig. 6 and Fig. 7. The initial concentration of pollutants rapidly reduces in the direction away from the jet source because of air entrainment. 80% 10--5 -5 -I 0 -15 -20 Fig. 7. Concentration distribution in jet (U00 = 3m/s; Uc =lOm/s; p =2kg/ m 3 ; D =0.3m; e =90° ) Fig . 6. Concentration distribution in jet (U00 = lm/s; Uc = 5m/ s; p = l.5kg/ m 3 ; D ~ o.3m; e =90°) 91 4. Comparison with experimental data The performance of the model has been evaluated by making comparison with experimental data that were obtained from the smoke-jets with different source diameters, different inclined angles and different air velocities. Comparisons between experimental data on radial velocity and predictions of the model in case of changing inclined angle of jet are shown in Fig. 8. The experimental radial velocities have been measured with 8 nodes over the half-width of the jet and a maximum radial step size corresponding to 53 of the current radius of the flow. Fig. 9, Fig. 10 and Fig. 11 illustrate the comparisons that are performed by changing source diameter, exit Y(m) 0.8 -0.8 Y(m) -0.4 0.4 0.8 -I -0.5 0.5 Fig. 8. Comparison of radial profiles of Fig. 9. Comparison of radial profiles of axial velocity measured experimentally and calculated. Exit velocity: 40m/s; .ltiF: velocity: 2.2m/s; Jet diameter: O.Olm axial velocity measured experimentally and calculated. Exit velocity: 40m/s; Air velocity: 2.2m/s; Inclined angle:() = 7r /3 0.6 Y(m) 0.6 Y(m) V,=2.2m/s X(m) -1 -0.5 -I 0.5 . - -·- · ~ -· -0.5 0.5 r Fig. 10. Comparison of radial profiles of Fig. 11 . Comparison of radial profiles of axial velocity measured experimentally and calculated. Jet parameters: Jet diameter: 0.0lm; Air velocity: 2.2m/s; Inclined angle: B = n/3 axial velocity measured experimentally and calculated. Jet parameter: Exit velocity: 40m/s; Jet diameter: O.Olm Inclined angle; B 7r /3 = 92 velocity and velocity of air. . The numerical results obtained with the model and experiment?-1 data also shown in the figures exhibit good agreement over the whole of the jets with almost predictions giving reasonable representations of the experimental data. especially, the model closely predicts the centerline velocities of the jets. 4. Comparison with experimental data The performance of the model has been evaluated by making comparison with . experimental data that were obtained from tl}e smoke-jets with different source diameters, different_inclined angles and different air veloci~ies [9]. 5. Conclusion The general diffusion jet model allows us to calculate p'rofile, velocity distribution, and concentration distribution inside the diffusion jet. On the basis of these research, it is also possible to develop for calculation the turbulent diffusion flame in Diesel engine, including swirl effects and calculate the concentrations distribution of gas inside engine combustion cham~er. Nomenclature s : axial coordinate [mJ r : radial coordinate [mJ x : horizontal coordinate [mJ y : vertical coordinate [mJ R : radius of section [mJ (; : average axial velocity [m/s] U00 : average horizontal velocity of surrounding air [m/s] Uc : axial velocity at centre of section [m/s] W : momentum [NJ in : mass flow [kg/ sJ g : gravity acceleration [m/s 2 ] k : turbulence kinetic [m2 / s 2 J ck, cµ : constant Cc:i , cc 2 : constant (3 : constant (p) : average specific mass [kg/m3 ] p00 : specific mass of surrounding air · [kg/m3 J e : direction angle [0 J µ : dynamic viscosity [kg.s/mJ µr : turbulence dynamic viscosity [kg.s/mJ c : rate of dissipation of turbulence kinetic [m2 /s~] This research is financed by the Fundamental Research Program "Modeling of Pollutants Formation in Combustion" of the Council for Natural Science of Vietnam. REFERENCES 1. Bui Van Ga. Calculation of pollutants emission in the atmosphere, Science and Technology 19-20, 1999, pp. 109-115 (in Vietnamese) . 93 2. Bui Van Ga. Calculation of formation and Diffusion of Soot in Smoke of Pool Fires, Conference on Fluid Mechanics and disaster .prevention, Dalat, 7/1999 (in Vietnamese). . 3. Bui Van Ga, Pham Xuan Mai, Brun M, Vignon J. M. Modele integral de flammes turbulentes de diffusion pour le calcul de la combustion diesel, Entropie No 216, 1Q99, pp. 52-59 (in French). · 4. Bui Van Ga, Tran Thanh Hai Tung, Tran Van Te. Calculation of NOx concentration in separate combustion chamber of diesel engines, Science and Technology 21, 1999, pp. 1-4 (in Vietnamese). 5. Vigon J. M., Bui Van Ga. An integral model for computation of buoyant turbulent diffusion jet flames, The International Conference on Automotive Technology, ICAT 96, pp. 70-77, Hanoi, 11-13 December, 1996. 6. Tamanini F. An integral model of turbulent fire plumes, 18th Symposium oh Combustion, The Combustion Institute, 1991, pp. 1081-1090. 7. Bui Van Ga, Nhan Hong Quang. Modeling of laminar jet in moving air: Review of Labour Protection, 8-2000, pp. 15-18 (in Vietnamese) . 8. Bui Van Ga, Nhan Hong Quang, Nguyen Huu Huong. Investigation of pollutants distribution in turbulent diffusion jets: . Review of Labour Protection, 11-2000, pp. 8-10 (in Vietnamese). 9. Nhan Hong Quang. Theoretical an:d experimental study of turbulence jet with different inclined angles in moving surround air: Master Degree Thesis, University of Danang, December 2000 (in Vietnamese) Received January 4, 2001 TfNH TOAN TIA PHUN KHUYECH TAN ROI Ket qua nghien CUu tia phun va ng<;m lua khuyech tan roi trong moi . tnremg k1;16ng khi yen tinh, bo qua Ive tr9ng tnremg da duqc gi&i thi~u trong cac cong trlnh tru&c day (1; 2]. Bai bao nay phat trien nhfmg ket qua ~t duqc bang vi~ thiet l~p m<)t mo hlnh tfch phan ung v&i tia phun tong quat hem c6 g6c nghieng bat ky, du6i tac di,mg cua Ive tr9ng truang trong moi truemg khong khf chuyen d<)ng theo ht.rang bat ky so v6i trvc tia . .H~ phucmg trlnh duqc khep kfn b&i mo lilnh roi k-£ va duqc giro bang phuang phap Runge-Kutta b~c 4. Bu&c dau mo hlnh duqc ap dvng de xac d.!nh truang toc d<),· truemg nong d<) va bien d<:tng cua tia phun c6 duang kf~ 0,3m. 94