Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) An Analysis of the Mixing and Diffuse Burning Processes in the Afterburning Chamber of a Scramjet Adrian COMAN Mircea BOŞCOIANU Aircraft Department Military Technical Academy 8-83 George Cosbuc 5 sector Bucharest ROMANIA adrico59@yahoo.fr Abstract: The study about burning process of a fuel gas who stroke like a supersonic major jet into an afterburning chamber together with a secondary airflow is make generally by determining the diffuse mixing condition of the two flows and the burning condition of fuel particles which is in contact whit an oxidant particle in a particular chosen moment. Pursuant to the literature a complete mixture of flows whit or not with combustion is obtaining the same length of cylindrical chamber. Otherwise the length of the burning flame which means the distance where the complete burning of the fuel product in air flux is realized is equal with the total length of inert product jet which stroke in the same airflow and is defined by the distance between the supersonic jet formatting section and the section where the distribution of speeds in uniformed. This finding is a confirmation of the hypothesis that the burning of a fuel particle (even if is a metal like Al Mg B etc.) is instantaneous (whit infinite speed) in the moment when this is in contact with the stoechiometric quantity of oxidant. In other words the time of oxidation of fuel molecules is infinite small comparative whit time necessarily for put in contact the fuel particle with the oxidant particle in the mixing chamber. Thus was give birth the concept of length of diffuse flame that estimate the necessary length of a mixing chamber and the burning of a jet who have in his composition fuel particle into an air flux concept which is meet very often in the literature. Some authors make reference about experimental values of this measurements of the composition and speed distribution in different sections at different positions from supersonic first jet section but others propose the possibility to determined the length of afterburning chamber of a scram-jet using a model of diffuse flame quasi-gases based on a semi-empiric theory of a turbulent mixture of a inert gas jet whit air flux. This idea is maintain by experimental studies which demonstrate that the length of diffuse flame is influence by factors determined by only the mixing process and no influence from the chemical burning reaction. In Section is proposed a mathematical model of mixing of the two flows and is demonstrate that growing the thin of limit layer of mixture is speedy therefore mixing is in the case when the speed of secondary airflow is bigger (at the same flow) realized on a shorter distance. While this is advantageous constructively for engine of scram-jet (the length necessarily to mixing chamber will be smaller) however energetically is desirable a slowing down more powerful of air jet that to obtain a more pronounced of this. In Section 3 is presented the mixture length and length of diffuse flame algorithm. In the case of a scramjet engine because is desire an efficient thermodynamic cycle of the engine air excess coefficient must strive to stoechiometric value (α ) therefore α<α Φ thus forever burning will continued downstream of section where the jet frontiers reach over the edge of afterburning chamber. In this situation the analytic framework presented in Section could not provide information about length of diffuse flame who determined necessarily length of afterburning chamber being necessarily supplementary an analysis of the variation of distribution of chemical species concentration in section downstream critical section x lim. In Section 4 are presented the contributions and concluding remarks. Key-Words: afterburning chamber scramjet secondary airflow
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) Introduction This study is referring to the mixing and diffuse burning process in the afterburner of a scramjet. The fuel gas stroke the supersonic principal flow into the afterburning chamber together with a secondary air flow. The analyze is make by determining first of all the diffuse mixing condition for the two flows and by choosing the burning condition of the fuel particle in the moment corresponding to the first contact with oxidant particles. A complete mixture of flows could be obtained in the same length of a cylindrical chamber. Otherwise the length of the burning flame which means the distance where is realized the complete burning of the fuel product in air flow is equal with the total length of inert product flow which stroke in the same air flow and is defined by considering the distance between the supersonic flow trigger section and the section where the distribution of speeds is uniform. This finding is a confirmation of the hypothesis that the burning of a fuel particle (even if is a metal like Al Mg B etc.) is instantaneous (with infinite speed) in the moment when this is in contact with a stoechiometric quantity of oxidant. In other words the duration of oxidation of the fuel molecules is infinite small comparative with the duration necessary for the contact of the fuel particle with the oxidant particle in the mixing chamber. In this way we introduce the concept of length of diffusing flame that estimates the necessary length of a mixing chamber and the trigger of a mixed flow. Some authors make reference about experimental values of the measurement of the composition and speed distribution in different sections and from first supersonic section. Other researchers proposed a methodology to determine the length of the afterburner of a scram-jet by using a model of diffuse flame quasi-gases based on a semiempirical theory of turbulent mixture of an inert gas jet with air flow. This idea is justified by experimental studies which demonstrate that the length of diffuse flame is influenced by factors determined only by the mixing process with no influence from the chemical burning reaction. Fig. Sensibility analysis for the length of diffuse flame for the afterburner of a scramjet In fig. the character of influence of different factors on the length of diffuse flame into afterburner of a scram-jet is presented. We use the following notations: L Φ - the length of diffuse flame [m]; α- the coefficient of air excess αn/l ng a /G I ; L - stoichiometric ratio of fuel define by the necessary quantity of air for complete burn of the mass unity of fuel; j I - specific impulse of primary combustor [Ns/kg]; f cri F cri /F K the relative critical area of primary combustor; F cri - the area of critical section of primary combustor nozzle [m ]; F K - the area of transversal section of secondary combustor [m ]; f crii F crii /F K the relative critical area of secondary combustor; F crii - the area of critical section of secondary combustor nozzle [m ]; T * a- stagnation temperature of secondary air flow [K]; L Φc - the length of diffuse flame at nominal regime (for calculation) [m]; The physical model of mixing and burning of a supersonic jet of fuel product into a coaxial subsonic jet and a cylindrical chamber is presented in fig. fig. 3 and fig 4. Along the afterburner there are considered the following sections with different flowing regime and distinct mixture: section I where a nucleus of fuel product which not interferences with air exists together with an air flow in outside; between them a zone of a mixture air-fuel product it exists; section II where fuel product in initial form is not present but untrained air in mixing zone it exists; section III where there are not more either untrained air in mixing zone; along this section the air and fuel combustion mixture became uniform in transversal section of chamber; Section IV where post combustion products are accelerating by detente in the nozzle. In any transversal section in the turbulent mixing zone the mixture of air and fuel product is not uniform and the concentration of fuel product come down from the chamber axis to the frontier of the mixing zone; that s why the burning zone begin actually from the section where the two flows are in contact and is developed until the section where in the chamber axis arrive the stoechiometric quantity of air necessary to complete burning of gas fuel from there. Otherwise the thickness of the burning zone into a transversal section along the afterburner chamber is equal with the radius corresponding to the limits of the fuel particle in different stage of burning and depends on the quantity of oxidant which is in contact with given fuel particle till that moment. Depending on the initial parameters of the two flows and especially on the flow ratios the burning
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) zone (diffuse flame) will end before in or after the section where the frontier of primary flow (the limit of mixing zone) is in contact with the edge of afterburner therefore at different intensities of diffusing of the two flows. For the calculus of the air excess coefficient (αα ) some authors proposed an empirical relation experimentally determined in which for a fuel with stoechiometric coefficient L it determine a complete burn in the axis of the supersonic jet in the section where its frontier reach the edge of the afterburner (fig 3): 5 α Φ 5+ () L For α<α the frontier of the jet reach the edge of afterburner before the end of burning in jet axis (fig ) and for α>α the burning in jet axis will end before the external limits of jet to reach over the edge of afterburner (fig 4). This explication will be done after the presentation of the theoretical model. Some studies propose a model for determination of the necessarily length of the afterburner for a scramjet only from the condition that the secondary air flow is complete assimilate by the primary jet of fuel particle and uniformed of flowing parameters in transversal section of resulting jet neglecting combustion phenomenon in the mixing period. This assumption is not far from reality because the ignition of particle which arrives in contact in a proper moment does not influence the qualitative aspect of the distribution of flow parameters into a transversal section of chamber. In this case is possible to analyze the distribution of the flow parameters for the two competitor jets in transversal sections along the longitudinal axis of the afterburner. Fig. 3 Physical model of mixing and burning into afterburner of scram-jet when αα Fig. The physical model of mixing and burning into the afterburner of a scram-jet when α<α Fig. 4 The physical model of mixing and burning into afterburner of scramjet when
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) Moreover if the supersonic jet have a given airflow resulting from () the section where mixing is uniformed is in fact the section in which the frontiers of jet reach the edge of chamber; therefore the critical length for realizing the afterburning process x lim (fig. 5). Obvious the acceptance of the same mixing and burning ratio make possible a shorter afterburner with impact on the overall engine dimensions and energetic efficiency. I m ρv ρ A πρ I a maa ρavaa ρa Aaa πρa ( ) a From (3) it results: / R r r R a gr ( ) d( ) + ( ) ( ).(4) The limit layer parameter (R gr /R ) depends only on the distance x. Fig. 5 The model for determining the mixing parameters of the two coaxial flows in a cylindrical chamber In a scram-jet with central air-plug and cylindrical afterburner there are two coaxial cylindrical flows (complete characterized from thermodynamic point of view by the following parameters: p - static pressure [N/m ]; T - temperature [K]; ρ - mass density [kg/m 3 ]; - speed [m/s]): the supersonic principal flow; the subsonic secondary The analysis of the flow and mixing parameters will be analyzed by using the model from Fig.5. The model of mixing the two flows Let consider the equation for the primary jet impulse: m I dm ρ da ct. () A Where: I - jet impulse (move quantity) [kg m/s];dm - gas mass which cross in time unit an elementary surface of primary jet section [kg];ρ- density of gas jet (ρρ a ρ ) [kg/m 3 ]; - gas speed in considerate point of jet [m/s]; da - area of elementary surface of primary jet section [m ]. For a cylindrical shape it results: I π r r I + I a (3) ρ d Where: I - primary jet impulse in trigger section [kg m/s]; I a - impulse of air mass totally captured in primary jet [kg m/s] with: Now let ηr/r gr and (4) becomes: r η. (5) Also the speed of the current point can be expressed: xr (6) xr Where xr is the speed in central axis. If r /R R gr /R (4) could be writhed: R xr gr R + a gr dη.(7) If we considered: ηdη 464 xr From (7) it results: R xr gr R + a gr *464 (8) Then it results the expression for the radius of a jet border (the limit layer of the mixture): a R gr. (9) R 98 xr a From (9) for a it results: 33 xr For the initial zone (x<x ) xr from (9) it results:
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) a ct. K () a 98 For a it results for the transition zone R gr 33R the transition zone. At a constant global mass flow n a fat speedy limit layer of mixture the mixing process is realized on a shorter distance. While the mixing chamber of the scramjet will be smaller the energetic efficiency is affected and it is necessary an optimal solution. The problem is simplified at high speeds when dynamic compression is powerful and it is easy to maintain a high speed of air at the inlet of the afterburner. The volumetric mass flow parameter dv / [m 3 /s] between a certain section from base zone of jet (x>x ) could be expressed: dv R xr gr πxr ηdη πr ηdη xr xr Whereπ /. Solving: () ηdη 985 xr And using the expression of (R gr /R ) given by (9) it results: : dv a xr 985 98 xr dv dv a x x x x a () The mass flow for the initial zone is: a. 97 98 a (3) The average speed of the mixture is: dv dv med. (4) A πr gr In initial section of jet the average speed of fuel gas mixture is:. A πr med Then dv / / And by using relations () and (): a xr.98 a med 97 xr a 98 a xr (5) In any cross section it results an average speed which is 5 time smaller that the speed corresponding at the central axis of the section. These characteristics are typical for the basic section and depend only on the speed of the mixture fuel and the speed of the air from principal section. There are some empirical relations xr f(x) recommended for the supersonic jet for <x /R <36: xr 86 (6) 37 x And results: 37 x R 86. (7) xr The frontier of jet will reach the edge of chamber when the whole quantity of secondary flow air will be captured by the principal flow corresponding for: dvx xlim dva + ( n+ ) ( αl + ). (8) Combining (8) with () it results: a xlimr α L + 985 xlimr 98 a (9)
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics Elounda Greece August -3 6 (pp9-4) 3 The analysis of the mixture length x lim and length of diffuse flame L Φ It was demonstrate that the length of diffuse flame L Φ is different from the length of mixing x lim. If α<α Φ L Φ > x lim because near the jet axes there still exist a quantity of mixture fuel- gas which will burn after the time necessarily for an air particle to be captured at the edge of the chamber towards its longitudinal axes. If α>α Φ the concentration of oxidant particle in the central zone of the afterburning chamber reach over the stoechiometric value before capturing the entire air quantity from the secondary flow. 4 Conclusions The length of mixing and the length of a scramjet afterburner could be determined with (7) expressed for the section defined by x lim Φ (Fig.6 b) L x 37 lim Φ R (86 ) () x r lim Φ Where xlim Φr is given by equation () when αα Φ : a xlimφr 985 αl +. xlim 98 Φr a () Fig.6 Scheme to calculate the length of mixture and afterburner. a) real case: α<α Φ ; b) equivalent case: αα Φ References: [] Annuskin Iu. K teorii optimalinovo raketnopriamotocinovo dvigatelia s dojiganiem topliva v vozdusnoi kamere Ed. Masinostroienie Moskva 98; [] Orlov B.V. Osnovi proiectirovaniia raketno-primotocinih dvigatelei Ed. Masinostroienie Moskva 967; [3] Masuya G. A study of air breathing rockets-subsonic mode combustion Acta Astronautica 98; [4] Coman A. Procese termogazodinamice specifice sistemelor de propulsie combinate de tip statoracheta Ed. Military Technical Academy Bucharest. The two cases are similar because the length of diffuse flame is determined by the capacity for absorption of the principal flow which remain the same; by growing the chamber radios R corresponding to growing the mass flow it is possible to modify only x lim (fig 6).