The full spectrum k-distribution method is used to obtain radiative heat flux and divergence of radiative heat flux for two test cases, containing mixture of CO 2 and H 2 O at different concentration and temperature keeping pressure constant. The k-distribution for mixture of gases is obtained from individual gas k-distribution using three different mixing models, viz., superposition, multiplication and hybrid model. Further, the radiative transfer equation (RTE) is solved by the finite volume discrete ordinate method (FVDOM) to obtain the radiative flux and the radiation source term. The results obtained were compared with the FSK from spectral addition and LBL method. The multiplication mixing model provides better accuracy compared to other mixing models considered in the present study.
Three test cases in the categories of homogeneous non-isothermal, non-homogeneous isothermal and non-homogeneous non-isothermal have been developed to validate the two-dimensional interpolation technique for calculation of non-gray radiative heat flux on the walls of the system. The participating gases H 2 O and CO 2 of different mole fractions and temperatures are considered in different zones of the test cases. HITEMP-2010 database has been used to calculate the absorption coefficients of H 2 O and CO 2 at different mole fractions and temperatures. Further, the random variation of absorption coefficients with spectrum has been reordered in smooth monotonically increasing smooth function using full spectrum k-distribution method (FSK). A look-up table is developed for different mole fractions and temperatures of gases H 2 O and CO 2. The calculation of absorption coefficients at thermodynamic states other than look up table has been performed using two dimensional interpolation techniques. The geometry of test cases have been divided into three zones whose conditions on the first and last zones are same as available in look-up table while interpolation is used for the middle zone. The radiative transfer equation is solved numerically by finite volume discrete ordinate method (FVDOM). The results have been compared with FSK method and have been found that interpolation techniques are giving satisfactory results with extremely less computational resource and time.
A numerical study is performed to estimate thermal load on the nozzle base plate, which is in the upstream direction to the flow, from three hot plumes of pure (CO 2 ), (H 2 O) and 50-50 (%) composition of (CO 2 ) and (H 2 O) expanding through a convergent-divergent (CD) nozzle in a quiescent medium at 1.1 bar pressure and 298K temperature. The base plate of the nozzle heats up due to thermal radiation, emitting from the hot gases in the form of plumes. The spectral radiative properties of major participating gases such as (CO 2 ), (H 2 O) are calculated from HITEMP-2010 database. A small CD nozzle which is designed for the perfect expansion of air by 1D calculation with nozzle throat diameter 1.98 mm and area ratio 1.5942, is considered as the design of nozzle for present study [1]. All three plumes are in the under-expanded state for this CD nozzle and hence expands rapidly at supersonic speed as the plumes exit from the nozzle and forms a series of expansion and compression waves. The hot plumes emanating from the nozzle develop very high temperature in a small vicinity around the base plate, due to diffusion and develop very high temperature on the base plate. Barring this region, the maximum amount of radiative flux on base plate for these three plumes, i.e., CO 2 plume, mixture plume and H 2 O plume are 4000 W/m 2 , 2300 W/m 2 and 1300 W/m 2 , respectively and the maximum temperature developed due to these corresponding fluxes are 323 K, 312 K and 308 K, respectively.
In the present work, the full spectrum k-distribution method (FSK) has been adopted to calculate the radiative heat transfer in the presence of participating gaseous medium within an enclosure. The spectral radiative properties of the gaseous medium is obtained from the HITEMP-2010 database. Further, radiative properties have been assembled into a monotonically increasing function using the full spectrum k-distribution method. Moreover, a look-up table has been developed for these properties for different thermodynamic states of gases and a multi-dimensional linear interpolation technique for unavailable thermodynamic states of gases. Furthermore, the FSK method is extended for mixture of gases using different mixing models such as superposition, multiplication and hybrid mixing model. The multiplication mixing model produces most accurate results among the mixture models used here. The results obtained from FSK has been validated against line by line method (LBL). The radiation transfer equation (RTE) is solved by finite volume method to calculate the wall heat fluxes and the divergence of radiative heat flux for various test cases in different category of homogeneous isothermal and isobaric and non-homogeneous non-isothermal non-isobaric media having different conditions of temperature pressure and mole-fraction. The FSK method has been successfully applied to non-homogeneous non-isothermal non-isobaric gaseous media for single gas or mixture of gases with almost LBL accuracy at extremely less computational cost and resource.
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