Abstract
A generalized one-dimensional compressible flow analysis with heat addition and/or friction is given for a prescribed pressure-area relation (similar method may be applied to temperature-area relation). The critical condition of thermal and/or frictional choking associated with conventional Mach number of unity for constant area duct is shown here to be associated with a generalized Mach number of unity for the non-constant area duct. The generalized Mach number reduces automatically to the conventional Mach number when duct area becomes a constant. Special cases of particular interest from the present generalized analysis include: (1) a ‘generalized Rayleigh line’ or ‘heat addition without friction in a non-constant area duct’ (which reduces automatically to the conventional ‘Rayleigh line’ when duct area becomes a constant). (2) a ‘generalized Fanno line’ or ‘flow with friction but without heat addition in a non-constant area duct’ (which reduces automatically to the conventional ‘Fanno line’ when duct area becomes a constant), (3) ‘constant ( T ω / T) heat addition with friction in a non-constant area duct’ and (4) ‘constant Mach number heat addition with friction in a non-constant area duct.’ The analysis given here may be applied to subsonic and supersonic combustion ram-jets, rocket-ramjet hybrid engines, and other non-constant area heat addition and friction flow problems.
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