William A. Sirignano

Droplet vaporization model for spray combustion calculations

Abstract The re-examination of the classical droplet vaporization model is made in order to develop the simple but sufficiently accurate calculation algorithm which can be used in spray combustion calculations. The new model includes the effects of variable thermophysical properties, non-unitary Lewis number in the gas film, the effect of the Stefan flow on heat and mass transfer between the droplet and the gas, and the effect of internal circulation and transient liquid heating. To evaluate the competing simplified models of the droplet heating, the more-refined, extended model of heat transfer within a moving circulating droplet is considered. A simplified, one-dimensional ‘effective conductivity’ model is formulated for the transient liquid heating with internal circulation. As an illustration, the dynamic and vaporization histories of the droplets injected into the steady and fluctuating hot air streams are analyzed.

Fluid Dynamics and Transport of Droplets and Sprays

1. Introduction 2. Isolated spherically symmetric droplet vaporization and heating 3. Convective droplet vaporization, heating, and acceleration 4. Multicomponent liquid droplets 5. Droplet behavior at near-critical, transcritical, and supercritical conditions 6. Droplet arrays and groups 7. Spray equations 8. Computational issues 9. Spray applications 10. Spray interactions with turbulence and vortical structures 11. Film vaporization 12. Stability of liquid streams.

Fuel droplet vaporization and spray combustion theory

Abstract A critical review is presented of modern theoretical developments on problems of droplet vaporization in a high-temperature environment and of spray combustion. Emphasis is placed upon analytical and computational contributions to the theory with some mention of empirical evidence. Four areas of basic phenomena are discussed in some detail: (i) droplet slip and internal circulation, (ii) transient heating of the droplets, (iii) multicomponent fuel vaporization, and (iv) combustion and vaporization of droplet arrays, groups, and sprays. Various relationships amongst these phenomena are analyzed as well. Several other problem areas are given brief mention. Future directions are suggested.

Theory of convective droplet vaporization with unsteady heat transfer in the circulating liquid phase

Abstract The problem of liquid droplet vaporization in a hot convective gaseous environment is analyzed. A new gas-phase viscous, thermal and species concentration boundary layer analysis is developed using an integral approach. The gas-phase analysis is coupled with a modified form of a previous liquid-phase analysis for the internal motion and heat transfer [S. Prakash and W. A. Sirignano, Int. J. Heat Mass Transfer21, 885–895 (1978)]. The coupled problem is solved for three hydrocarbon fuels (n-hexane, n-decane, and n-hexadecane). The results show that the droplet vaporization is unsteady, and that the temperature distribution within the droplet is nonuniform for a significant part of the droplet lifetime. Some of the results are compared with the already existing correlations after correcting them for the heat flux into the liquid phase.

Unsteady droplet combustion with droplet heating—II: Conduction limit☆

Abstract The spherically-symmetric, thin-flame combustion of a pure component droplet is analyzed by assuming quasi-steady gas-phase processes and conduction being the only heat transfer mechanism within the droplet. Exact numerical, and an approximate analytical, solutions are presented. Results show that droplet heating is the dominant heat utilization mode for the initial 10–20% of the droplet lifetime, during which rapid changes in all combustion characteristics occur; that although unsteadiness within the droplet can prevail until burnout, the droplet surface regresses almost linearly after about 20% of its lifetime; and that accurate predictions on the droplet size, mass, and lifetime can be obtained regardless of how internal heat transfer is modelled.

Numerical analysis of convecting, vaporizing fuel droplet with variable properties

Abstract Detailed analysis of a cold fuel droplet suddenly injected into a hot gas stream is examined. The effects of variable thermophysical properties, transient heating and internal circulation of liquid, deceleration of the flow due to the drag of the droplet, boundary-layer blowing, and moving interface are included. Several parametric studies are performed by changing the following quantities: initial droplet temperature, ambient temperature, initial Reynolds number, fuel type, and droplet heating model. The results show that for higher transfer numbers, the vaporization rate is larger and the drag coefficient is significantly reduced mainly due to a large reduction in friction drag. For lower transfer numbers, the boundary-layer blowing effect is weaker and the drag coefficient is dominated by the Reynolds number only. The results also indicate that the constant-property calculation overestimates the drag coefficient.

Review of theory of distortion and disintegration of liquid streams

Abstract Linear and nonlinear analyses of the instabilities and distortion of liquid streams injected into a gaseous media are discussed. The various fundamental mechanisms and the predictive capabilities for the distortions are emphasized. Round jets, planar sheets, annular sheets, and conical sheets are discussed in detail. The balance between capillary and inertial forces is primarily examined. The method for simplifying the analyses in the case of thin liquid sheets is discussed. The capabilities for representing the droplet size distribution that follows the stream disintegration are outlined.

Fluid Dynamics of Sprays—1992 Freeman Scholar Lecture

Various theoretical and computational aspects of the fluid dynamics of sprays are reviewed. Emphasis is given to rapidly vaporizing sprays on account of the richness of the scientific phenomena and the several, often disparate, time scales. Attention is given to the behavior of individual droplets including the effects of forced convection due to relative droplet-gas motion, Stefan convection due to the vaporization or condensation of the liquid, internal circulation of the liquid, interactions with neighboring droplets, and interactions with vortical eddies. Flow field details in the gas boundary layer and wake and in the liquid droplet interior are examined. Also, the determinations of droplet lift and drag coefficients and Nusselt and Sherwood numbers and their relationships with Reynolds number, transfer number, Prandtl and Schmidt numbers, and spacing between neighboring droplets are extensively discussed. The spray equations are examined from several aspects; in particular, two-continua, multi-continua, discrete-particle, and probabilistic formulations are given. The choice of Eulerian or Lagrangian representation of the liquid-phase equations within these formulations is discussed including important computational issues and the relationship between the Lagrangian method and the method of characteristics. Topics for future research are suggested.

Nonsteady burning phenomena of solid propellants - Theory and experiments.

Abstract : Non-steady burning of solid propellants was investigated both theoretically and experimentally, with attention to combustion instability, transient burning during motor ignition, and extinction by depressurization. The theory is based on a one-dimensional model of the combustion zone consisting of a thin gaseous flame and a solid heat up zone. The non-steady gaseous flame behavior is deduced from experimental steady burning characteristics; the response of the solid phase is described by the time-dependent Fourier equation. Solutions were obtained for dynamic burning rate, flame temperature, and burnt gas entropy under different pressure variations; two methods were employed. First, the equations were linearized and solved by standard techniques. Then, to observe nonlinear effects, solutions were obtained by digital computer for prescribed pressure variations. One significant result is that a propellant with a large heat evolution at the surface is intrinsically unstable under dynamic conditions even though a steady-state solution exists. Another interesting result is that the gas entropy amplitude and phase depend critically on the frequency of pressure oscillation and that either near-isentropic or near-isothermal oscillations may be observable. Experiments with an oscillating combustion chamber and with a special combustor equipped for sudden pressurization tend to support the latter conclusion. (Author)

On the equation for spherical-particle motion : effect of Reynolds and acceleration numbers

The existing model equations governing the accelerated motion of a spherical particle are examined and their predictions compared with the results of the numerical solution of the full Navier–Stokes equations for unsteady, axisymmetric flow around a freely moving sphere injected into an initially stationary or oscillating fluid. The comparison for the particle Reynolds number in the range of 2 to 150 and the particle to fluid density ratio in the range of 5 to 200 indicates that the existing equations deviate considerably from the Navier–Stokes equations. As a result, we propose a new equation for the particle motion and demonstrate its superiority to the existing equations over a range of Reynolds numbers (from 2 to 150) and particle to fluid density ratios (from 5 to 200). The history terms in the new equation account for the effects of large relative acceleration or deceleration of the particle and the initial relative velocity between the fluid and the particle. We also examine the temporal structure of the near wake of the unsteady, axisymmetric flow around a freely moving sphere injected into an initially stagnant fluid. As the sphere decelerates, the recirculation eddy size grows monotonically even though the instantaneous Reynolds number of the sphere decreases.