OCR Text |
Show a scheme takes into account dissociation into multiple species and the effects of such dissociation on specific heat capacities of the mixture, a phenomenon that is difficult to simulate when using the Magnussen model. Also, unlike the Magnussen model , it does not require adjusting of model constants. The disadvantages primarily rest in the fact that when finite rate chemistry effects are very important (i.e., when the reaction and mixing time scales are of the same order), the scheme does not predict the correct behavior. In the pdf model, the instantaneous thermochemical state of the fluid is related to a single conserved scalar quantity, namely, the mixture fraction f, defined by (5) where Zk is the element mass fraction for some element, k. Subscript 0 refers to the value at the oxidizer stream inlets and subscript F refers to the value at the fuel stream inlets. Then, for any <Pi, where <Pi can represent instantaneously, temperature or concentration of any desired species, and <Pi = [P(f)<Pi(f)d/ where p(f) represents the probability density function for the scalar f. (6) (7) For this relationship to hold, the requirements necessary are: (i) the flame must be of the diffusion type, with separate fuel and oxidizer inlets (ii) the system should be adiabatic and incompressible and (iii) the Lewis number must be unity. vVhen the flame is non-adiabatic, the influences of heat loss on turbulent enthalpy fluctuations are ignored, and averaging is done by assuming that <Pi = <Pi(!, Ii), where Ii is the time mean enthalpy. A {3 pdf shape is assumed for the probability distribution function, and equilibrium chemistry is used with a partial equilibrium mL'\."t.ure fraction limit of 0.064, the assumption being that equilibrium exists upto this near-stoichiometric value of the mixture fraction. Chemical equilibrium is computed by means of an algorithm for Gibbs' free energy minimization. Thirteen (13) species and radicals were assumed to exist in the equilibrium mixture, namely, CH4 , C2H6 1 C3Hg , C4HlO , CO2 , N2 , O2 , CO, H20, H2 , OH, Hand O. The so-called "look-up" table is computed once, and this allows the solver to interpolate for the desired species concentrations from the table as a function of the mixture fraction, mixture fraction variance, and enthalpy. The adiabatic flame temperature at atmospheric pressure and inlet fuel and air temperatures of 312 K was predicted to be 2200 K at stoichiometry. Numerical Procedure FLUENT/UNS uses a general collocated finite volume scheme, where the cells can be arbitrary unstructured convex polyhedra. Quadrilateral, hexahedral, triangular, tetrahedral or prismatic cells may be used. The transport variables are stored at cell centers, thereby ensuring conservation for arbitrary control volumes. The discretization scheme used is second order accurate, the pressure-velocity coupling is handled using the SIMPLE algorithm and the solution procedure uses a variant of the multigrid procedure detailed in Hutchinson and Raithby[4]. Specifications set out in the benchmark experiments for the inlet air velocity profiles and wall temperatures were followed when setting boundary conditions. The computational grid is a non-orthogonal quadrilateral grid containing 100 by 183 nodes in the radial and axial directions respectively (9784 quadrilateral cells). Appropriate clustering of nodes is observed in the quarl region as well as near the centerline (Figure 3). For the structured solution, a total of 18300 cells were used, thus FL -ENT/UNS allowed the same solution with half the memory usage. A unique feature available in FLUENT/UNS is the capability of solution adaption, whereby one may adapt/refine the grid to gradients of any desired variable. This is extremely useful when resolving high gradients locally, instead of carrying unnecessary baggage in the form of grid points at. places where they may not be necessary as would be the case in a structured solver. (Figure 4) 4 |