One-Dimensional Variable Area Ducts: The Afterburner and Nozzle

The afterburner and nozzle are modeled as a single component. The afterburner can be used in one of two modes, either including the combustor or by in a mode when no combustion takes place. Typically in supersonic flight, if an afterburner is used, it is only ignited at the time of takeoff and powered though the transonic flight regime. In a cruise condition, it usually operates in a non-combusting mode. Thus, if one is interested in simulating the flight in a cruise condition, a non­combusting mode of operation of the afterburner meets the requirements. The afterburner essentially acts as a large volume that is capable of attenuating dis­turbances. Furthermore, simulating the dynamics of the mass flow rate at the nozzle with a variable nozzle area must satisfy the exit boundary condition. The exit boundary condition is a typical choked flow. Even when the nozzle varies the exit area based on the corrected speed of the engine to match steady-state operating conditions, the choked flow must be maintained through the nozzle. All the additional variables used in the afterburner and nozzle subsystem are defined in the Table 5.5. The nozzle mass flow rate is given by,

KnzAnz_ref Pabt V

Pambient Cab 1 „ Pabt

cab 1

Pambient Cab

, Pabt

The variable nozzle area and flow coefficient are represented by Knz while Anz_ref is a reference nozzle throat area. This variable can be used as a tuning factor or as control variable to obtain the expected steady-state results.

The state equations for the combined nozzle and afterburner stage volume dynamics may be expressed as,

— (n i = (mab ~ mnz) /5 5 28

dt (pab-sV Vab ; (5.5.28)

dtimab = ^(Ptbt – Pabt)( 1 + Cab2-1Mb)’*", (5.5.29)

Tabt = — ^ (Ttbt^mab – Tabtmnz) . (5.5.30)

ot qab sv Vab

The afterburner nozzle outlet total pressure is related to the afterburner nozzle outlet total temperature by,

and the corresponding Mach number is,

Table 5.5 Definition of afterburner and nozzle subsystem variables Variable Description Aab Cross-sectional area of afterburner stage volume duct Aex Nozzle exhaust area Anz ref Reference nozzle throat area cp_ ab Specific heat at constant pressure in the afterburner Knz Nozzle coefficient lab Length of the afterburner stage volume duct m ab The afterburner inlet mass flow rate m nz Nozzle mass flow rate Mab Mach number in the afterburner stage volume P abt Afterburner outlet total pressure P ambient Ambient pressure Pexhaust Pressure in the nozzle exhaust Tabt Afterburner outlet total temperature Ue Velocity of exhaust gases U0 Velocity of jet engine Vab Volume of afterburner stage volume duct Cab Ratio of specific heats in afterburner stage volume Cnz Ratio of specific heats in the nozzle gnz Nozzle efficiency Pab_sv Afterburner stage volume density

The net thrust generated by the nozzle is the sum of the thrust generated due to the change in momentum and due to the pressure difference acting over the cross­sectional area of the exhaust and is,

T = (Ue — U0)hnz + (Pexhaust — Pambient)Aex (5.5.33)

where

cnz

Pexhaust = Pabt 1 — ‘. (5.5.34)

gnz(Cnz + 1)