e - Propulsion and Combustion Laboratory

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Axisymmetric Radiation – Formulations (Continued.)‣ M-FVM (Modified Finite Volume Method) (Murthy and Mathur, 1998)• axisymmetric mappingmn mn mn mn mn mne( w) ce( w) Pce( w)E W ce wwhere⎛0, n = 1 ⎞ ⎛0,n≠Nφ⎞χn= ⎜ , χs1, n 1⎟ =⎜ ⎟⎝ ≠ ⎠ ⎝1,n=Nφ⎠• Final discretization equations∑( ) ( ) ( ( ) )I D = I max D ,0 −I max −D,0I D = χ I D , I D = χ I Dmn mn mn mn mn mn mn+1 mnn cn n P cn s cs s P cs( ) ( )a = max ∆ AD ,0 + κ + σ ∆V∆Ω + χ ∆A Dmn mn mn mnP i ci a s n n cni=e, w, t,bmn mn mn mn mn mn mn+I= max −∆i ci,0 ,P=R∆ ∆Ω + χPs∆s cs P( ) ( )1a AD b S V AD I‣ Geometric Relationsn e= ⎡⎣∆ ze x+ d−c e z⎤⎦ ∆ z + d− c , n w= ⎡⎣−∆ ze x+ b−a e z⎤⎦∆ z + b−an n=−sin ( 0.5∆ φ0) e x+ cos( 0.5 ∆ φ0) e z, n s= sin( −0.5∆φ0) e x−cos( −0.5∆φ0)ez n = − n = e( ) ( ) ( ) ( ) ( ) ( )2 2 2 2t b x( ) ( ) ( ) φ ( ) ( ) ( )2 2 2 20 w0∆ A = 0.5 ∆ φ c+ d ∆ z + d−c , ∆ A = 0.5∆ a+ b ∆ z + b−ae2 2 2 2( ) ( ) ⎤⎦φ0( ) φ0( )( ) ( )∆ An =∆ As = 0.5 ⎡⎣d− a + c−b ∆z, ∆ At = 0.5 ∆ c −b , ∆ Ab= 0.5∆ d −a2 2 2 2∆ V =∆φ0∆ z⎡ c cd d a ab b ⎤⎣+ + − + +⎦626 Propulsion and Combustion Lab.
Axisymmetric Radiation – Example 1‣ Side Wall Diffuse Incidence• Effect of anisotropic scattering• Effect of optical thickness• Scattering phase function10B21B1isotropicΦΨ ( )F30.1F20.010 45 90 135 180Scattering Angle, Ψ°()27 Propulsion and Combustion Lab.
Page 1 and 2: 2004 Fluent User’s Group MeetingA
Page 3 and 4: Introduction - Combustor Analysis
Page 5 and 6: Introduction - Heat Transfer Modes
Page 7 and 8: Radiation - Electromagnetic Spectru
Page 9 and 10: Radiation - Radiative Property‣ M
Page 11 and 12: Radiation - Solution Models‣ Solu
Page 13 and 14: 3D Finite-Volume Radiation (Continu
Page 15 and 16: 3D FVM - Example 2‣ Axisymmetric
Page 17 and 18: 3D FVM - Example 4‣ A 3D Rectangu
Page 19 and 20: Radiation Grid Systems - Example 1
Page 25: Axisymmetric Radiation - Formulatio
Page 29 and 30: Axisymmetric Radiation - Example 3
Page 31 and 32: Combined Conduction and Radiation -
Page 33 and 34: Combined Heat Transfer - Formulatio
Page 35 and 36: Combustion with Radiation - Formula
Page 37 and 38: Combustion with Radiation - Results
Page 39 and 40: References1. 김태국, 1995, “FU

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