Shutdown Analysis

Description

The solver has “shutdown” logic to improve convergence during the very low power (and low pressure) conditions at the end of a transient mission for a gas turbine. Shutdown logic is applied after a user-supplied shutdown time. The shutdown logic converts most elements to fixed flow elements to maintain the percent core flow for each element. Chamber pressures are scaled with cycle or boundary pressures. A minimum heat transfer coefficient can also be set. The minimum HTC can be used for the entire transient, if needed.
Figure 1.


Figure 2.


Shutdown Analysis Inputs

Flow Simulator stores the variables needed for shutdown in the General Data section of the .flo file.
UIName (.flo label) Description
Start Shutdown (sec)

(SHUT_TIME)

 Time in the mission when the shutdown logic starts being used. All mission times after SHUT_TIME (for example, mission time > SHUT_TIME) uses the shutdown logic.
Minimum HTC Option

(HTC_MIN_OPT)

 Option for using the minimum HTC during the analysis. All calculated Heat Transfer Coefficients (HTC)are compared to HTC_MIN, according to one of the following options.

0: Not used - never use HTC_MIN (default).

1: Always used - always use HTC_MIN.

2: Use after Shutdown Time – only use HTC_MIN when mission time > SHUT_TIME.
Minimum HTC

(HTC_MIN)

 All calculated HTC’s are compared to HTC_MIN.

If the calculated HTC is less than HTC_MIN, HTC_MIN replaces the calculated HTC.
Pressure Scaling Option

(PRESS_OPT)

 Option to determine how chamber reference pressures are calculated when mission time > SHUT_TIME.

0: Use Cycle Parameters.

1: Use Boundary Chambers.
Low Pressure Cycle Parameter

(PRESS_LO)

 If PRESS_OPT = 0, low chamber reference pressure is extracted from this cycle parameter.
High Pressure Cycle Parameter

(PRESS_HI)

 If PRESS_OPT = 0, high chamber reference pressure is extracted from this cycle parameter.
Low Pressure Chamber

(PRESS_LO)

 If PRESS_OPT = 1, low chamber reference pressure is extracted from this chamber.
High Pressure Chamber

(PRESS_HI)

 If PRESS_OPT = 1, high chamber reference pressure is extracted from this chamber.
Flow/Thermal Coupling Limit Option

(CPL_PCT_OPT)

 Option to determine when the coupling limit percentage (CPL_PCT) is used to stop exchanging data between the flow and thermal solvers.

0: Not used - never use CPL_PCT (default).

1: Always used - always use CPL_PCT.

2: Use after Shutdown Time - only use CPL_PCT when mission time > SHUT_TIME.
Stop Coupling after % Max Iteration

(CPL_PCT)

 The percent of the maximum iterations to stop exchanging data between the flow and thermal solvers. This may improve convergence for some models. Do not make this value too small since it may lead to less accurate results. Recommended value is > 80%.
Minimum Mass Flow Rate

(FLOW_MIN)

 A minimum flow rate for elements when mission time > SHUT_TIME.

Shutdown Analysis Calculations

The different variables affected by the shutdown logic are described in this section.
Element Flow Rates
The flow rate for most elements is kept at a constant percentage core flow rate throughout the transient when mission time > SHUT_TIME. The core flow rate is usually the flow through the core of the gas turbine, but it can be any flow rate in the mission. The core flow rate is specified in the Reference Conditions window.
Figure 3.


At the first time step after SHUT_TIME:
P C F s h u t t i m e _ e l e m e n t = m ˙ e l e m e n t m ˙ c o r e * 100 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbGaam4qaiaadAeapaWaaSbaaSqaa8qacaWGZbGaamiAaiaa dwhacaWG0bGaamiDaiaadMgacaWGTbGaamyzaiaac+facaWGLbGaam iBaiaadwgacaWGTbGaamyzaiaad6gacaWG0baapaqabaGcpeGaeyyp a0ZaaSaaa8aabaWdbiqad2gapaGbaiaadaWgaaWcbaWdbiaadwgaca WGSbGaamyzaiaad2gacaWGLbGaamOBaiaadshaa8aabeaaaOqaa8qa ceWGTbWdayaacaWaaSbaaSqaa8qacaWGJbGaam4BaiaadkhacaWGLb aapaqabaaaaOWdbiaacQcacaaIXaGaaGimaiaaicdaaaa@5935@
P C F s h u t t i m e _ e l e m e n t = P e r c e n t   c o r e f l o w   a t   m i s s i o n   t i m e   = ˜   S H U T _ T I M E MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbGaam4qaiaadAeapaWaaSbaaSqaa8qacaWGZbGaamiAaiaa dwhacaWG0bGaamiDaiaadMgacaWGTbGaamyzaiaac+facaWGLbGaam iBaiaadwgacaWGTbGaamyzaiaad6gacaWG0baapaqabaGcpeGaeyyp a0JaamiuaiaadwgacaWGYbGaam4yaiaadwgacaWGUbGaamiDaiaacc kacaWGJbGaam4BaiaadkhacaWGLbGaamOzaiaadYgacaWGVbGaam4D aiaacckacaWGHbGaamiDaiaacckacaWGTbGaamyAaiaadohacaWGZb GaamyAaiaad+gacaWGUbGaaiiOaiaadshacaWGPbGaamyBaiaadwga caGGGcGafyypa0ZdayaaiaWdbiaacckacaWGtbGaamisaiaadwfaca WGubGaai4xaiaadsfacaWGjbGaamytaiaadweaaaa@72CF@
For mission time > SHUT_TIME:
m ˙ e l e m e n t =   P C F s h u t t i m e _ e l e m e n t * m ˙ c o r e 100 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWGTbWdayaacaWaaSbaaSqaa8qacaWGLbGaamiBaiaadwgacaWG TbGaamyzaiaad6gacaWG0baapaqabaGcpeGaeyypa0JaaiiOamaala aapaqaa8qacaWGqbGaam4qaiaadAeapaWaaSbaaSqaa8qacaWGZbGa amiAaiaadwhacaWG0bGaamiDaiaadMgacaWGTbGaamyzaiaac+faca WGLbGaamiBaiaadwgacaWGTbGaamyzaiaad6gacaWG0baapaqabaGc peGaaiOkaiqad2gapaGbaiaadaWgaaWcbaWdbiaadogacaWGVbGaam OCaiaadwgaa8aabeaaaOqaa8qacaaIXaGaaGimaiaaicdaaaaaaa@5A59@
The solver converts most elements to fixed flow elements after SHUT_TIME. The three types of tube elements (standard compressible, advanced tube, and incompressible tube) are converted so that they can still calculate the heat transfer with the tube wall. Vortex elements are not converted since they do not calculate a flow rate based on pressures. m ˙ e l e m e n t   MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWGTbWdayaacaWaaSbaaSqaa8qacaWGLbGaamiBaiaadwgacaWG TbGaamyzaiaad6gacaWG0baapaqabaGcpeGaaiiOaaaa@3F34@ is compared to FLOW_MIN.
Chamber Pressures
After SHUT_TIME, the flow rates are no longer calculated in the usual way, so the internal (non-boundary) chamber pressures are also no longer calculate in the usual way. After SHUT_TIME, the chamber pressure is based on a linear interpolation between a high and low pressure.
At the first time step after SHUT_TIME:
η s h u t t i m e _ c h a m b e r = P c h a m b e r − P l o w P h i g h − P l o w MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaH3oaApaWaaSbaaSqaa8qacaWGZbGaamiAaiaadwhacaWG0bGa amiDaiaadMgacaWGTbGaamyzaiaac+facaWGJbGaamiAaiaadggaca WGTbGaamOyaiaadwgacaWGYbaapaqabaGcpeGaeyypa0ZaaSaaa8aa baWdbiaadcfapaWaaSbaaSqaa8qacaWGJbGaamiAaiaadggacaWGTb GaamOyaiaadwgacaWGYbaapaqabaGcpeGaeyOeI0Iaamiua8aadaWg aaWcbaWdbiaadYgacaWGVbGaam4DaaWdaeqaaaGcbaWdbiaadcfapa WaaSbaaSqaa8qacaWGObGaamyAaiaadEgacaWGObaapaqabaGcpeGa eyOeI0Iaamiua8aadaWgaaWcbaWdbiaadYgacaWGVbGaam4DaaWdae qaaaaaaaa@5F2B@
P h i g h = r e f e r e n c e   h i g h   p r e s s u r e   a t   m i s s i o n   t i m e   = ˜   S H U T _ T I M E MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaBaaaleaapeGaamiAaiaadMgacaWGNbGaamiAaaWd aeqaaOWdbiabg2da9iaadkhacaWGLbGaamOzaiaadwgacaWGYbGaam yzaiaad6gacaWGJbGaamyzaiaacckacaWGObGaamyAaiaadEgacaWG ObGaaiiOaiaadchacaWGYbGaamyzaiaadohacaWGZbGaamyDaiaadk hacaWGLbGaaiiOaiaadggacaWG0bGaaiiOaiaad2gacaWGPbGaam4C aiaadohacaWGPbGaam4Baiaad6gacaGGGcGaamiDaiaadMgacaWGTb GaamyzaiaacckacuGH9aqppaGbaGaapeGaaiiOaiaadofacaWGibGa amyvaiaadsfacaGGFbGaamivaiaadMeacaWGnbGaamyraaaa@6CBD@
P l o w = r e f e r e n c e   l o w   p r e s s u r e   a t   m i s s i o n   t i m e   = ˜   S H U T _ T I M E MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaBaaaleaapeGaamiBaiaad+gacaWG3baapaqabaGc peGaeyypa0JaamOCaiaadwgacaWGMbGaamyzaiaadkhacaWGLbGaam OBaiaadogacaWGLbGaaiiOaiaadYgacaWGVbGaam4DaiaacckacaWG WbGaamOCaiaadwgacaWGZbGaam4CaiaadwhacaWGYbGaamyzaiaacc kacaWGHbGaamiDaiaacckacaWGTbGaamyAaiaadohacaWGZbGaamyA aiaad+gacaWGUbGaaiiOaiaadshacaWGPbGaamyBaiaadwgacaGGGc Gafyypa0ZdayaaiaWdbiaacckacaWGtbGaamisaiaadwfacaWGubGa ai4xaiaadsfacaWGjbGaamytaiaadweaaaa@6B17@
For mission time > SHUT_TIME:
P c h a m b e r =   P l o w + η s h u t t i m e _ c h a m b e r * P h i g h − P l o w MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaBaaaleaapeGaam4yaiaadIgacaWGHbGaamyBaiaa dkgacaWGLbGaamOCaaWdaeqaaOWdbiabg2da9iaacckacaWGqbWdam aaBaaaleaapeGaamiBaiaad+gacaWG3baapaqabaGcpeGaey4kaSIa eq4TdG2damaaBaaaleaapeGaam4CaiaadIgacaWG1bGaamiDaiaads hacaWGPbGaamyBaiaadwgacaGGFbGaam4yaiaadIgacaWGHbGaamyB aiaadkgacaWGLbGaamOCaaWdaeqaaOWdbiaacQcadaqadaWdaeaape Gaamiua8aadaWgaaWcbaWdbiaadIgacaWGPbGaam4zaiaadIgaa8aa beaak8qacqGHsislcaWGqbWdamaaBaaaleaapeGaamiBaiaad+gaca WG3baapaqabaaak8qacaGLOaGaayzkaaaaaa@6285@
P h i g h = r e f e r e n c e   h i g h   p r e s s u r e   a t   c u r r e n t   m i s s i o n   t i m e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaBaaaleaapeGaamiAaiaadMgacaWGNbGaamiAaaWd aeqaaOWdbiabg2da9iaadkhacaWGLbGaamOzaiaadwgacaWGYbGaam yzaiaad6gacaWGJbGaamyzaiaacckacaWGObGaamyAaiaadEgacaWG ObGaaiiOaiaadchacaWGYbGaamyzaiaadohacaWGZbGaamyDaiaadk hacaWGLbGaaiiOaiaadggacaWG0bGaaiiOaiaadogacaWG1bGaamOC aiaadkhacaWGLbGaamOBaiaadshacaGGGcGaamyBaiaadMgacaWGZb Gaam4CaiaadMgacaWGVbGaamOBaiaacckacaWG0bGaamyAaiaad2ga caWGLbaaaa@698D@
P l o w = r e f e r e n c e   l o w   p r e s s u r e   a t   c u r r e n t   m i s s i o n   t i m e MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaBaaaleaapeGaamiBaiaad+gacaWG3baapaqabaGc peGaeyypa0JaamOCaiaadwgacaWGMbGaamyzaiaadkhacaWGLbGaam OBaiaadogacaWGLbGaaiiOaiaadYgacaWGVbGaam4DaiaacckacaWG WbGaamOCaiaadwgacaWGZbGaam4CaiaadwhacaWGYbGaamyzaiaacc kacaWGHbGaamiDaiaacckacaWGJbGaamyDaiaadkhacaWGYbGaamyz aiaad6gacaWG0bGaaiiOaiaad2gacaWGPbGaam4CaiaadohacaWGPb Gaam4Baiaad6gacaGGGcGaamiDaiaadMgacaWGTbGaamyzaaaa@67E7@
The high and low pressure can be from the mission file or from the boundary chambers. Select the high and low pressures that are representative of the circuit source and sink pressures.
Heat Transfer Coefficients
After SHUT_TIME, the HTCs are calculated the same as before SHUT_TIME, but the HTCs can get very low if flow rates get very low. A minimum HTC can be assigned to increase the HTC to a reasonable value that may account for free convection, machine vibration, and so on. The minimum HTC can also be used for all times of a steady state or transient solution by setting HTC_MIN_OPT=”Always Used”.
Flow/Thermal Coupling Limit
Only use the coupling limit if the model is having convergence problems and a “Relaxation Factor on Thermal-Fluid Coupling” < 1.0 is not helping. For most analysis types, the thermal solver is not called after a (CPL_PCT) percentage of the flow solver iterations is completed. For the Quasi Steady Flow + Transient Thermal, the flow solver is not called after a (CPL_PCT) percentage of the thermal solver iterations is completed. This limit can be used for all times of a steady state or transient solution by setting CPL_PCT_OPT=”Always Used”.