PhD Thesis - staffweb - University of Greenwich

APPENDIX 4 : SMARTFIRE TECHNICAL REFERENCE GUIDES radiosity= α ( E − R)(5c)1.1.5.2 Six-Flux Radiation ModelIn the six-flux radiation model heat fluxes R i , are calculated by solving additionalconservation equations in each component direction which have the form:dI= −dxdJ= +dxdK= −dydLdy= +dM= −dzdN= +dzs6s6s6( α + s) I + αE+ ( I + J + K + L + M + N)( α + s) J −αE− ( I + J + K + L + M + N )( α + s) K + αE+ ( I + J + K + L + M + N)s6( α + s) L −αE− ( I + J + K + L + M + N)s6s( α + s) M + αE+ ( I + J + K + L + M + N)⎪⎪⎪⎪⎪⎪⎪⎬( ) ( ) ⎪ ⎪⎪⎪⎪⎪⎪ α + s N −αE− I + J + K + L + M + N6⎭⎫(6a)where α is the absorption coefficient, s is the scattering coefficient E is the black bodyemissive power of the fluid and I, J, K, L, M and N the six coordinate direction radiativefluxes.Transfer of heat through radiation leads to a source in the enthalpy equation given by:S(( I − E) + ( K − E) + ( M − E) + ( J − E) + ( L − E) + ( N − E)six− flux= α (6b)1.1.5.3 Absorption CoefficientThe absorption coefficient is evaluated using the following piecewise linear approximation:T < 50 o C" = " ambientT > 50 o C and T < (T plume /2) " = " ambient + (c(T plume /2) - " ambient )/((T plume /2)-50)(T-50)T > (T plume /2) " = cT (6c)1.1.6 Species ConservationThe conservation of any scalar quantity, f, is represented by the equation given below:∂(ρf)+ div(ρu f ) = div∂t( Γfgrad( f) + SfAppendix 11.4 Page 144-9 9(7)