TWO-PHASE FLOW COMBUSTION

CNRS/Inst. de Mecanique des Fluides de Toulouse Toulouse, Prance 

The previous chapters have discussed examples of instabilities in combustors where the fuel was gaseous. However, in most practical devices, fuel is liquid (gasoline or kerosene) and the problem becomes much more difficult. In this chapter, the specificities of two-phase flow combustion will be discussed and the construction of a numerical tool to perform LES of liquid fuel combustion will be discussed. This chapter will also present the equations solved for gaseous and liquid combustion in more details than the previous ones. 

The introduction of a dispersed liquid fuel raises two kinds of problems  

Attempts to extend RANS formulation to LES of two-phase combustion may be found in [318 354 317 255 292]. They are all based on a Euler-Lagrange (EL) description of the dispersed phase in which the flow is solved using an Eulerian method and the particles are tracked with a Lagrangian approach. An alternative is the Euler-Euler (EE) description, also called two-fluid approach, in which both the gas and the dispersed phases are 

In RANS codes, the weak numerical coupling of the phases makes the EL method well suited for gas turbine computations, but RANS with the EE approach may also be found for example in simulations of fluidized beds [277 335] or chemical reactors [284 272 289], two examples of two-phase flows with a high load of particles. The experience gained in the development of RANS has led to the conclusions that both approaches are useful and they are both found today in most commercial codes. Moreover, coupling strategies between EE and EL methods within the same application are considered for certain cases. In the framework of LES of gas turbines, it is interesting to compare again EL with EE formulations. 

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Aluminum-containing propellants deflver less than the calculated impulse because of two-phase flow losses in the nozzle caused by aluminum oxide particles. Combustion of the aluminum must occur in the residence time in the chamber to meet impulse expectations. As the residence time increases, the unbumed metal decreases, and the specific impulse increases. The soHd reaction products also show a velocity lag during nozzle expansion, and may fail to attain thermal equiUbrium with the gas exhaust. An overall efficiency loss of 5 to 8% from theoretical may result from these phenomena. However, these losses are more than offset by the increase in energy produced by metal oxidation (85—87). 

Detonation and Two-Phase Flow is discussed at ARS Propellants, Combustion and Liquid Rocket Conference in 1961. Published by Academic Press, NY (1962)... 

Intelligent design of circulating fluidized bed boilers depends on sufficient understanding of the physico-chemical hydrodynamics occurring in the combustors, such as chemical kinetics of coal combustion and pollutant formation, hydrodynamics of gas-solid two phase flow, mixing of gas and solids, distribution of heat released, and heat transfer between immersed... 

Among additional topics of interest in two-phase flows are questions of sound propagation in two-phase media [28], [51], [52] (see Section 9.1.4) and many other problems [53]-[55]. We shall return to two-phase flows in connection with spray combustion (Chapter 11) to give a more systematic development. 

Let us now consider combustion mechanisms that, strictly speaking, are not represented by the model illustrated in Figure 7.1. Specifically, at the interface in Figure 7.1, let us introduce the dispersed phase mentioned in Section 7.1. The consequent occurrence of two-phase flow adds substantial complication to the deflagration mechanism. 

Amplification expressions in general are not as simple as equation (51) for two-phase flows in rocket motors [128]. Equilibrium and frozen sound speeds with respect to droplet behavior may be identified (compare Sections 9.1.4.6 and 4.2.6), and a mass-source term may arise in equation (51) in the development of a conservation equation for the acoustic energy in the gas. From the viewpoint of equation (14), the quantity O must include amplification effects that arise from both energy sources and mass sources. Acoustic theories may be derived from the conservation equations of Chapter 11 for the purpose of analyzing acoustic amplification in spray combustion. 

The formulation that has been given here is not the only approach to the description of two-phase flows with nonequilibrium processes. Many different viewpoints have been pursued textbooks are available on the subject [43], [44], and a reasonably thorough review recently has been published [45]. Combustion seldom has been considered in this extensive literature. Most of the work that has addressed combustion problems has not allowed for a continuous droplet distribution function but instead has employed a finite number of different, discrete droplet sizes in seeking computer solution sets of conservation equations [5]. The present formulation admits discrete sizes as special cases (through the introduction of delta functions in fj) but also enables influences of continuous distributions to be investigated. A formulation of the present type recently has been extended to encompass thick sprays [25]. Some other formulations of problems of multiphase reacting flows have been mentioned in Sections 7.6 and 7.7. 

S. Z. Burstein, S. S. Hammer, and V. D. Agosta, Spray Combustion Model with Droplet Breakup Analytical and Experimental Results, in Detonation and Two-Phase Flow, vol. 6 of Progress in Astronautics and Rocketry, S. S. Penner and F. A. Williams, eds.. New York Academic Press, 1962, 243-267. 

Simonin O (1996) Combustion and turbulence in two-phase flows, von Karman... 

Saraiva PC, Azevedo JLT, Carvalho MG (1993) Mathematical Simulation of a Circulating Fluidized Bed Combustor. Combust Sci and Tech 93 223-243 Simonin O, Viollet PL (1989) Numerical study on phase dispersion mechanisms in turbulent bubbly flows. Proc Int Conf on Mechanics of Two-Phase Flows, 12-15 June, Taipei, Taiwan... 

Section 1 is aimed at providing new fundamental and practical data for the development of efficient combustion control strategies. It includes development of novel diagnostic techniques to provide in situ meeisurement capabilities, novel computational tools to acquire deeper insight into the fundamental mechanisms, and interactions in two-phase flows and flames relevant to realistic combustors as well as their operating conditions. Further, detailed experimental and numerical studies of the physical and chemical phenomena in turbulent flames, and the novel passive and active control methodologies to control combustion instabili-... 

Increasing interest in detailed experimental analysis of two-phase flows has led to a number of review papers on single point laser measurements. A more general overview on two-phase flow measurements was given for example by Taylor (1994) focusing on current activities in PDA development and PIV applications in two-phase flows. Applications of LDA and PDA for analyzing flows with combustion were reviewed by Heitor et al. (1993), and a more industrial orientated review on particle sizing methods can be found in Black et al. (1996). 

R. BOTghi Background on droplets and sprays. In Combustion and Turbulence in Two-Phase Flows, Lecture series 1996-02, Von Karman Institute for Fluid Dyanamics. 

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