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Show ^[NO] = At[HCN][()2ftxp ~[N2] = A2[HCN)[NO]exP 67 000 RT 60 000 ~RT~ (30) rlmtnl II.K- grid GO./.Q 0 200 <O0 600 000 000 A.OImml 0 200 (00 600 BOO 000 The above simplified H C N conversion scheme is very popular among mathematical modelers. Recently, Lockwood and Romo- Millares (1992) used the model to calculate the H C N conversion in turbulent flames of pulverized coal. Only fucl-NO was calculated and the effect of turbulence was not taken into account. After comparing the fucl-NO predictions with the values measured, the authors concluded that "realistic N O predictions arc obtainable from a simplified reaction scheme". Hill ct al. (1984) used the same HCN converslion scheme. They estimated the effects of the turbulence on the predicted N O concentrations. Two of their predictions illustrated the effects. One used only mean-values of local temperature and species composition, and thus ignored the fluctuations. The other accounted for the fluctuations. The predicted N O concentrations different by a factor of 600. Schnell (1991) and Gorner (1991) advocate an averaging Eqs. (30) over the temperature fluctuations reaching the adiabatic flame temperature. The above discussion indicates that there is no consensus among combustion models as to Ihc modeling of fucl-NO. Furthermore, there is hardly any systematic comparison and assessment of capabilities of various fucl-NO models. Numerical Solution Discretization and numerical solution of the balance equations introduce numerical diffusion in a similar way, as physical diffusion occurs in the real flow. Moreover, the truncation errors of the numerical algorithm affect the accuracy of the final solution. The extent to which the numerical diffusion and the truncation errors appear in the final solution is strongly dependent on the size of the numerical grid. Therefore, choice of both the discretization method and the numerical grid are very important The effects of numerical diffusion, associated with the first-order numerical schemes caused great concern with respect to their applicability to multi-dimensional flows. Therefore, the computational results presented in this paper are obtained with the quadratic upstream differencing (QUICK) of Leonard (1987). It has been demonstrated (Weber et al., 1990) that the differences between the second-order QUICK predictions and the first-order hybrid predictions can be as large as the differences stemming from the use of different turbulence models. Generally, computing of swirling flows with a first-order numerical scheme requires three to seven times more grid lines (in each direction) than computing with a second-order scheme if the same level of numerical accuracy is to be secured. Figure 6 demonstrates the necessity of applying fine numerical grids even when using the QUICK scheme. The time-mean velocities and turbulence of an ambient air flow, of 0.7 inlet swirl, were measured using laser velocimclry (Hagiwara et al., 1986). In Figure 6, the measured and computed contours of zero-axial velocity arc shown. The 2-dimcnsional computations were carried out using the three turbulence models and two numerical grids; a course grid containing 43x43 nodes, and a finer 60x40 grid. 0 200 «0 600 800 KXX) AOImml 0 200 «» 600 800 WOO 0 200 «D 600 800 OCX A£lmm| 0 200 WD 600 800 FIGURE 6: PREDICTED C O N T O U R S O F U=0 F O R T W O GRID SIZES A N D T H R E E T U R B U L E N C E M O D E LS ( measured; computed) Figure 6 demonstrates, that the numerical related errors can be so large, that they eliminate the benefits expected from the second-order turbulence modeling. Only when the imperfections of the numerical tool are minimized, the turbulence models can be properly assessed. FLOW-FIELD PREDICTIONS IN THE NEAR-BURNER ZONE Tvpe-0 Flames And Corresponding Isothermal Flows Numerous computations of (cold) isothermal , non-swirling and weakly swirling jets have indicated that good quality predictions of both velocities and turbulence within the jet are obtainable using the k-e model, provided that the numerical related errors are minimized. It is generally accepted that a little improvement can be gained by application of a second-order turbulence models to such flows. This is also valid for predictions of non-swirling, pulverized coal flames. A number of researchers (Lockwood and Salooja (1983), Zinzer (1987). Grjrner (1991), have performed simulations of the long, non-swirling flames of pulverized coal which w r e measured by Michel and Payne (1980). These calculations have demonstrated that good flame predictions can be obtained when applying the k-e model. Tvoe-2 Flames A n d Corresponding Isothermal Flows Over the last two decades, substantial efforts were allocated to the development of second-order turbulence models for predicting complex, highly-swirling flows (sec Launder, 1988; Hogg and Leschziner, 1989). Both the R S M and A S M predictions were rigorously tested against the velocity and turbulence measurements of fourteen highly-swirling flows, see Weber et al. (1986, 1990) and Visscr (1991). It was concluded that reliable engineering predictions of the swirling flows can be made if fine numerical grids are used in conjunction with the numerical QUICK method 8 11-11 |