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The exhaust nozzle component can be used for simulation of convergent nozzles, convergent/divergent nozzles with either fixed or variable geometry. Exhaust component models usually end the gas path of a GSP gas turbine model and simulate the expansion process of the gas to ambient or other user specified conditions. In the GSP equation system (unless the Disable Massflow Error Equation option is active), an exhaust component adds an error equation to enforce matching of the exhaust mass flow (calculated from exhaust gas conditions, flow cross-area and outside/ambient pressure) with the mass flow entering from the upstream component.

The variable geometry option allows control of either throat area only or both throat and exit area (in case of a convergent/divergent nozzle), using the nozzle control component. The exhaust nozzle component can be used for both thrust generating (jet-engine) nozzles including turboprop engine exhausts and turboshaft exhaust systems in which case thrust is minimal and not relevant. Exhaust stack pressure loss can be modeled by inserting a duct component.

Specify a velocity coefficient to represent losses in terms of a correction of the exit flow velocity resulting from isentropic expansion from entry to ambient pressure.

 

Note that for the design point, effective throat cross-flow area is not user specified, but calculated from the exhaust entry conditions, i.e. the area required for expansion to ambient conditions of the entry mass flow. Only by adapting component design data upstream of the exhaust nozzle component, design point nozzle area can be indirectly adapted. Decreasing design efficiency of an upstream turbine component for example will increase the area due to the decrease in turbine exit pressure resulting in lower density, requiring a large exhaust cross-flow area.

For a variable nozzle, off-design throat area can be directly specified using the nozzle control component, which effectively controls relative nozzle area (i.e. nozzle area/design nozzle area). Design point geometric

 

Thrust calculation

Ideal gross thrust is calculated using the customary equation for impulse reaction force of the flow plus the the static pressure difference from throat to ambient pressure times the throat area (only when choked):

 

 FG_ideal =  W*C_exit_ideal + A_exit*(Ps_exit-Po),

 

with C_exit_ideal, A_exit, and Ps_exit the ideal velocity, area and static pressure at the exhaust nozzle exit (either the convergent nozzle or con-di nozzle exit) and Po the ambient pressure.

 

Nozzle efficiency and losses

Two different ways are available to represent losses (efficiency) of the expansion process in the nozzle:

•CV velocity coefficient

The CV factor represents the extent to which C_exit_ideal is reached after expansion. The difference between ideal and real exit velocity is due to viscous friction losses for example in the boundary layers.

For the convergent nozzle, a CV value smaller than 1 results in a lower than ideal exit (i.e. throat) velocity and total pressure and higher exit static enthalpy Hs and temperature Ts (since the 0.5*C^2 term becomes smaller and total enthalpy remains constant). As a result, during design point calculations also the effective nozzle area A (usually A8) becomes little larger (do not confuse this effect with the CD discharge coefficient which represents the ratio between effective and geometric area). During off-design calculations, a smaller CV will decrease the flow rate. CV does not affect choking, only resulting throat exit velocity and static temperature are affected, exit static pressure is not affected by CV.

For the con-di nozzle configuration, CV applies to the exit (usually station) of the divergent part (not the throat). In this case, area A9 is not affected, exit velocity gets lower and Hs, Ts higher with decreasing CV. Ps remains unchanged.

Although the effect of CV as implemented in GSP cannot be simply seen as a factor reducing C_exit, the following equation will approximate the CV effect fairly well in many cases:

 

 FG = CX*(W*CV*C_exit_ideal + A_exit*(Ps_exit-Po))

 

•CX thrust coefficient

CX is a much simpler method than CV to represent losses and is simply a factor multiplied with FG_ideal to yield actual thrust:

 

 FG = CX*FG_ideal

 

Although it is not recommended (usually either CV or CX is used), CV and CX can be applied in a combined fashion resulting in a relation approximated by:

 

 FG = CX*(W*CV*C_exit_ideal + A_exit*(Ps_exit-Po))

 

CV and CX can be specified for Design Point and Off-design calculations separately. Note that design relative nozzle throat area (Aeff/Aeffdes) is defined 1.0. Relative nozzle area can be adapted in OD by the Manual Variable Exhaust Nozzle Control or derivatives of this control component.

 

Exhaust nozzle options:

General

Model options

Either choose a Fixed area nozzle or a Variable area nozzle to respectively model a fixed nozzle or a controlled exhaust nozzle. In the latter case a link appears on the component icon to connect an exhaust nozzle controller.

 

Velocity coefficient CV
Off-design CV (see above).

 

Thrust coefficient CX
Off-design CX (see above).

 

Design

Convergent-Divergent nozzle
Option to choose whether a convergent nozzle or a convergent-divergent nozzle is used.

 

Ideal con-di nozzle complete expansion

For con-di nozzle only, with this option on, complete ideal expansion from throat to ambient pressure is assumed (no shocks, no con-di nozzle calculations).

 

Velocity coefficient CV
Design CV (see above).

 

Thrust coefficient CX
Design CX (see above).

 

Note that normally either CX or CV are used since they more or less represent the same losses. Although it is possible, it is advised to not specify values deviating from 1 for both fields simultaneously.

 

Specify area as

•Specify effective areas and CD's (and have design geometric area/area ratio calculated). Also with a variable nozzle area nozzle, the nozzle control component controls effective throat area and (if option active) the con-di ratio as applied on effective areas. Geometric areas are calculated by dividing effective areas by the CD values.

•or specify geometric areas (and have design CD's calculated). Also with a variable nozzle area nozzle, the nozzle control component controls geometric throat area and (if option active) the con-di ratio as applied on geometric areas. Effective areas are calculated by multiplying geometric areas with the CD values.

 

Throat

•CD
Discharge coefficient used to calculate the design geometric area of the throat

•Ageom
Geometric area used to calculate throat throat CD in the design point used for subsequent DP and OD calculations.

•Update to DP (button)
Update inactive input field values to last calculated Design Point.
 

Exit

•CD
Discharge coefficient of the exit plane

•Condi area ratio
Con-di area ratio of effective or geometric areas, depending on above described option.

 

Disable Massflow Error Equation
This option can be used to disable the mass flow error equation of the exhaust where Werror = f(Win, Wout). For advanced users only: when a state variable is removed from the system (e.g. map beta in case "no map" option is chosen in a compressor) somewhere an error equation has to be removed as well. The nozzle error equation is a sensible candidate for this.

 

Depending on the option settings, input fields are disabled where appropriate.

 

Output tab sheet

The Output tab sheet, for specification of the simulation output parameters, further contains 2 elements to specify the station numbers (default '8' for throat and '9' for exit). To have only output on the throat station (for a convergent nozzle), set the nozzle exit station number equal to throat (e.g.  both '8'). Set to separate numbers for a con-di nozzle (e.g. '8' and '9').

 

Using the exhaust nozzle component

Take the following steps to configure a Exhaust Nozzle component in a GSP jet engine model: