The ray effect is a serious problem in radiative heat transfer computations. Continuously varying radiation fields are approximated numerically by sampling a limited number of angular directions. The discrete transfer method (DTM) is a conceptually simple technique suitable for general-purpose calculations of thermal radiation in complex geometries. Over the years a large variety of quadratures based on fixed ray firing patterns has been suggested for use in conjunction with the DTM. Arguably, in absence of a comprehensive error analysis, the efficacy of all these quadratures has only been proved for limited collections of radiation problems. Recently, sharp error bounds for the heat flux integral in the DTM have been established for irradiation distributions of three different continuity classes: smooth fields, fields with discontinuous angular derivatives and piecewise constant fields. The resulting error formulas have paved the way for a new adaptive quadrature strategy. Results are presented of its application to an idealized jet flame and to radiative exchanges inside a cube-shaped enclosure, along with brief comments on the viability of this approach in general-purpose CFD/radiation computations. In this paper, the following capabilities of the new adaptive angular quadrature are demonstrated: Evaluation of DTM heat flux integrals to a pre-specified tolerance for any intensity distribution; Excellent accuracy with very low ray numbers for irradiation due to small view factor sources; and Good heat flux estimates for piecewise constant sources, provided that the starting mesh is selected carefully.

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This paper reviews the past research, experimental techniques and scaling relationships used in the studies of oscillatory buoyant diffusion flames and reports an experimental investigation conducted to determine the pulsating characteristics of such flames. The experimental data were obtained by using three techniques, namely, pressure fluctuation measurements, thermal imaging and high‐speed video photography. Present findings are compared with data sets reported in the literature and correlations for pulsation frequency suggested by previous studies are independently verified. Analysis of the experimental data on frequency of pulsations in different burners shows that for a fixed‐diameter flame the pulsation frequency is almost independent of fuel flow rate. The equation f=1.68D−0.5 gives the best approximation for the relationship between pulsating frequency and diameter over a wide range of data. An alternative way of expressing the relationship between the key variables is St=0.52*(1/Fr)0.505. This proves to be a better way of expressing the relationship since it can include the effect of the fuel flow rate. Slight modifications to this expression allows prediction of flame oscillations under elevated/reduced gravity and isothermal buoyant plumes. This relationship and the observations of the present study confirm the hydrodynamic nature of flame puffing: interplay of buoyancy and fluid motion. © 1996 by John Wiley & Sons, Ltd.

• This is the pre-peer reviewed version of the article which has been published in final form at: http://dx

This paper reviews the past research, experimental techniques and scaling relationships used in the studies of oscillatory buoyant diffusion flames and reports an experimental investigation conducted to determine the pulsating characteristics of such flames. The experimental data were obtained by using three techniques, namely, pressure fluctuation measurements, thermal imaging and high-speed video photography. Present findings are compared with data sets reported in the literature and correlations for pulsation frequency suggested by previous studies are independently verified. Analysis of the experimental data on frequency of pulsations in different burners shows that for a fixeddiameter flame the pulsation frequency is almost independent of fuel flow rate. The equation f= 1.68D-as gives the best approximation for the relationship between pulsating frequency and diameter over a wide range of data. An alternative way of expressing the relationship between the key variables is St=0.52*(1/Fr)0Jos. This proves to be a better way of expressing the relationship since it can include the effect of the fuel flow rate. Slight modifications to this expression allows prediction of flame oscillations under elevatedlreduced gravity and isothermal buoyant plumes.