535 Proceedings of the Combustion Institute, Volume 29, 2002/pp. 535–542 A GENERAL SUPERSCALAR FOR THE COMBUSTION OF LIQUID FUELS WILLIAM A. SIRIGNANO University of California, Irvine Mechanical and Aerospace Engineering S 3202 Engineering Gateway Irvine, CA 92697-3975, USA A new integral solution is found to apply to liquid fuel combustion for a wide range of configurations: isolated droplet burning, droplet array burning, liquid film burning, or liquid stream burning; steady, quasi- steady, or (in some cases) unsteady gas fields; transient or steady liquid thermal conditions; and stagnant, forced-convective, or natural-convective gas fields. The major constraints are one-step chemical kinetics and unitary Lewis number. In particular, the superscalar S is contrived and shown after integration of the governing equations to be uniform (but possibly time varying) over the gas field. L L eff eff S  h  m Q  Y  Y O F   1  Y 1  Y Fs Fs where h, Y O , and Y F are the specific enthalpy, oxidizer mass fraction, and fuel vapor mass fraction, re- spectively, with the subscript s indicating a value at the liquid surface; Q, L eff , and m are the fuel heating value, energy flux per unit mass flux transferred to the liquid surface, and the fuel-to-air mass stoichiometric ratio, respectively. The value of S can be determined without a need to engage the continuity and mo- mentum equations. Similarly, the limiting flame temperature (for infinite kinetic rate) T f and the liquid surface temperature T s will depend only on ambient conditions, fuel properties, and L eff . That is, S, T f and T s are shown to depend on the hydrodynamics, transport phenomena, and geometrical configurations only through L eff and are readily calculable. Variations in the form of the superscalar are discussed for the cases of multicomponent liquid fuels and vaporization without burning. Comparisons of these results with a few previous results in certain classical configurations validate the new findings. Extensions to other configu- rations are discussed. The use of the superscalar to validate subgrid modeling for laminar and turbulent spray combustion is examined. Introduction Certain theoretical problems in fluid mechanics, transport science, and combustion science have been simplified by constructing new variables via lin- ear combinations of the primitive variables. Buse- mann and Crocco [1] each accomplished this task for compressible boundary layers by creating new variables from linear combinations of thermal and mechanical variables. These new dependent vari- ables were constant over the boundary layer under certain conditions. This immediately accomplished the integration of a partial differential equation and produced an algebraic relationship connecting the primitive variables. The Shvab-Zel’dovich variables [2] have accomplished the same purpose in many combustion problems. In constructing the new Crocco-Busemann or Shvab-Zel’dovich variables, some challenging terms are eliminated in the gov- erning partial differential equations: for example, viscous dissipation in the boundary layer equations and chemical kinetics in the combustion flow equa- tions. These contrived dependent variables have con- stant solutions typically in situations where the boundary conditions involve a uniform value of the variable or a zero value for the normal gradient of the variable over the boundaries. The premixed lam- inar flame is a problem where the Shvab-Zel’dovich variable can be constant under certain assumptions concerning transport and chemical kinetics. How- ever, in other combustion problems, the Shvab- Zel’dovich variables are not as powerful as a contri- vance. For example, in non-premixed flame problems and in problems related to the combustion of liquid fuels [3], non-uniform and/or non-zero gra- dient boundary conditions cause Shvab-Zel’dovich variables to vary over the domain. In this analysis for liquid-fuel combustion, we con- trive a new superscalar (or supervariable) S that is a linear combination of primitive dependent variables and becomes uniform for space over a wide range of configurations, including isolated fuel-droplet burn- ing, droplet-array combustion, group combustion, spray burning, pool burning, and liquid-fuel film combustion. Here, the Shvab-Zel’dovich variables