Improved Local Scale Generic Cycle Model for Aerothermodynamic Simulations of Gas Turbine Engines for Propulsion
Abstract
1. Introduction
2. Model Description
2.1. Design Point Model
2.2. Aerothermodynamic Design Point
2.3. Off-Design Model
2.4. Model Comparison
3. Results Discussion
4. Conclusions and Final Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Nomenclature
A | flow area | Greek letters | |
c | speed of sound | α | step size |
B | mxn Broyden matrix | β | bypass ratio |
CD | flow coefficient | θ | dimensionless temperature |
Cp | specific heat at constant pressure | δ | dimensionless pressure |
Cv | specific heat at constant volume | η | efficiency |
CV | velocity coefficient | Δ | difference |
D | Diameter | Φ | equivalence ratio |
FAR | Fuel-to-Air Ratio | mass flow bleed fraction | |
Fg | gross thrust | λs | numerical tolerance |
FF | Flow Function | τ | error function improvement tolerance |
Fn | net thrust | γ | specific heat ratio |
Fram | ram drag | σ | standard deviation |
h | specific enthalpy | μ | convergence tolerance |
J | mxn Jacobian matrix | ε | m-vector of errors |
LHV | Lower Heating Value of the fuel | ρ | density |
maxIt | maximum number of iterations | ζ | thermodynamic state |
mass flow | Γ | scrubbing drag due to external engine wet surfaces | |
MFP | Mass Flow Parameter | Subscripts | |
MN | Mach Number | bleed | at bleed extraction port |
n | sample size | cool | cooling |
N | rotational speed | Comp | compressor |
Ncorr | corrected rotational speed for a compressor | Comb | combustor |
NLcorr | corrected rotational speed for the LP spool | corr | corrected |
NHcorr | corrected rotational speed for the HP spool | cust | customer (i.e., aircraft) |
NP | corrected rotational speed for a turbine | demand | demand of dependent parameter |
p | step direction m-vector | fuel | parameter associated with the fuel entering the combustor |
P | pressure | ideal | corresponding to ideal process |
Pf | pressure bleed fraction | in | at the inlet of an engine component |
PR | Pressure Ratio (i.e., PR = P0,out/P0,in) | mech | mechanical transmission |
shaft power extraction | par | parasitic | |
net heat transfer | pri | engine primary stream | |
R | gas constant | out | at the exit of an engine component |
R-line | auxiliary coordinate | real | corresponding to real process |
s | specific entropy | sec | engine secondary (or bypass) stream |
S | scaling factor | stoich | stoichiometric |
SFC | Specific Fuel Consumption | state | state of the dependent parameter |
t95 | inverse of student’s t distribution (95% confidence) | std | standard day condition |
T | Temperature | Th | inlet duct throat |
V | flow velocity | Turb | turbine |
w | specific work (i.e., work per unit mass) | 0 | representing a total (or stagnation) thermodynamic property (e.g., h0, T0, P0) |
wf | work bleed fraction | ||
WAR | Water-to-Air Ratio | ||
shaft power | |||
x | n-vector of independent parameters | ||
x* | solution n-vector | ||
X | generic map parameter | ||
y | m-vector of dependent parameters | ||
Z | generic thermodynamic property (e.g., T, P, h, etc.) |
Appendix A
Component | Inputs | Modeling |
Ambient free stream | Flight conditions: e.g., geometric altitude, MN, ΔTICAO-SA, engine flow ( or ), FAR (normally, FAR = 0.0 at ambient conditions) | ICAO standard atmosphere model: [PICAO-SA, TICAO-SA] = f(geometric altitude) Static properties P = PICAO-SA; T = TICAO-SA + ΔTICAO-SA Initialize FARin = 0.0 (i.e., dry air) [static] = ζ(FARin, P, T) Flight velocity V = f(MNin, γ, R) Total properties T0 = f(MNin, γ, T); P0 = f(T0/T, γ) [total] = ζ0(FARin, P0, T0) |
Subsonic inlet duct | ΔP/P, Aout (optional), CD | ; FARin = FARout Energy Conservation (EC): h0,in = h0,out P0,out = (1—ΔP/P) * P0,in [total]out = ζ0(FARout, P0,out, h0,out) If exit area (i.e., Aout = fan face area) is provided, go to P1 P1-begin and ). Initial guesses for MNout = 0.55 and hout = h0,out Hint. Use Matlab built-in function ‘fsolve’ [static]out = ζ(FARout, hout, ) , CD = 1.0 (for preliminary studies) MFPout,calc, Rout) h0,out,calc = f(hout, Tout, MNout, , Rout) P1-end Normalized entropy (s) Balance (NsB) ; λs = −0.0001 (allowance for small negative numerical error) |
Splitter | β | ; ; ; FARin = FARout,sec = FARout,pri EC: h0,in = h0,out,sec = h0,out,pri Assume no momentum loss, P0,in = P0,out,sec = P0,out,pri Secondary (bypass) stream [total]out,sec = ζ0(FARout,sec, P0,out,sec, h0,out,sec) Primary (core) stream [total]out,pri = ζ0(FARout,pri, P0,out,pri, h0,out,pri) |
Combustor | ΔP/P, η, T0,out, LHVfuel, hfuel | Exit pressure, P0,out = (1—ΔP/P) * P0,in EC: , iterating on FARout Initial guess for FARout = 0.005 Hint. Use Matlab built-in function ‘fsolve’ [total]out = ζ0(FARout, P0,out, T0,out) If solution attained, then |
Compressor (e.g., fan, LPC, HPC) | PR, η, Pf,i, | ; FARin = FARout; FARbleed,i = FARin Exit pressure after compression, P0,out = PR * P0,in ) [total]out,ideal = ζ0,ideal(FARout, P0,out, ) EC: No Bleed Extraction (NBE) Real compression, [total]out,real = ζ0,real(FARout, P0,out, h0,out,real) Energy compensation due to bleed fraction not compressed to Pout ith bleed extraction [total]bleed,i = ζ0,bleed,i(FARbleed,i, P0,bleed,i, h0,bleed,i) |
Duct (e.g., bypass duct) | ΔP/P | ; FARin = FARout EC: h0,in = h0,out Exit pressure, P0,out = (1–ΔP/P) * P0,in [total]out = ζ0(FARout, P0,out, h0,out) |
Turbine (e.g., HPT, LPT) | η, , | ; FARin = FARout EC: ) [total]out,ideal = ζ0,ideal(FARout, , ) ) [total]out,real = ζ0,real(FARout, , ) |
Nozzle (e.g., primary, secondary) | CD, CV | ; FARin = FARout EC: h0,in = h0,out P0,in = P0,out [total]out = ζ0(FARout, P0,out, h0,out) Static properties when nozzle throat is choked (i.e., MNout = 1.0) , iterating on Tout ) to ambient pressure Hint. Use Matlab built-in function ‘fsolve’ [static]out,chk = ζout,chk(FARout, Tout, ) If solution attained, then Determine if the nozzle is choked , nozzle is choked Then, Pout = Pout,chk Else, Pout = Pamb [static]out = ζ(FARout, Pout, ) ; MFPout = f(MNout,γout, Rout) Compute throat area, Compute nozzle gross thrust |
Bleed reinstatement to flow stream (e.g., chargeable and non-chargeable cooling flow) | ; EC: Assume flow mixing process occurs at constant pressure P0,in = P0,out = P0,bleed [total]out = ζ0,out(FARout, , ) NsB: | |
High-level performance | Γ, , V0 | Net thrust (Fn) For Fg,sec and Fg,pri see Nozzle calculations Note. Assumed Γ = 0.0, i.e., no scrubbing drag Specific Fuel Consumption (SFC) |
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Parameter | Assumed Value |
---|---|
Altitude | 35,000 ft (10,668 m) |
MN | 0.80 |
ΔTICAO-SA | 0.0 °F (0.0 °C) |
Combustor exit temperature (T0,040) | 2723.1 R (1512.8 K) |
Fan PR | 1.6 |
LPC PR | 1.6 |
HPC PR | 17.5 |
OPR | 28.0 |
β | 5.0 |
) | 177.11 lbm/s (80.34 kg/s) |
LHVfuel | 18,500 Btu/lbm (43,031 kJ/kg) |
hfuel | 176.0 Btu/lbm (409.4 kJ/kg) |
Parameter | Performance Metric | Assumed Value |
---|---|---|
Adiabatic fan efficiency | ηfan | 0.887 |
Adiabatic LPC efficiency | ηLPC | 0.892 |
Adiabatic HPC efficiency | ηHPC | 0.861 |
Combustor efficiency | ηComb | 0.995 |
Adiabatic HPT efficiency | ηHPT | 0.924 |
Adiabatic LPT efficiency | ηLPT | 0.917 |
HP spool mechanical efficiency | ηHP,mech | 0.975 |
LP spool mechanical efficiency | ηLP,mech | 0.975 |
Inlet duct normalized pressure loss | ΔP/Pinlet-duct | 0.0 |
Bypass-duct normalized pressure loss | ΔP/Pbypass-duct | 0.0 |
Combustor pressure normalized pressure loss | ΔP/PComb | 0.06 |
Primary nozzle velocity coefficient | CV,pri | 0.945 |
Secondary nozzle velocity coefficient | CV,sec | 0.945 |
Primary nozzle flow coefficient | CD,pri | 1.0 |
Secondary nozzle flow coefficient | CD,sec | 1.0 |
Parameter | Performance Metric | Assumed Value |
---|---|---|
HP parasitic shaft power extraction, hp (kW) | 155 (115.6) | |
HP customer shaft power extraction, hp (kW) | 0.0 | |
ECS mass fraction (none) | 0.0 | |
HPT non-chargeable cooling mass fraction (none) | 0.25 | |
HPT non-chargeable cooling pressure fraction (none) | Pf,cool | 0.9364 |
HPT non-chargeable cooling work fraction (none) | wf,cool | 0.9686 |
i, j | xi | ystate,j | ydemand,j |
---|---|---|---|
1 | |||
2 | β | ||
3 | Fan map R-line | ||
4 | LPC map R-line | ||
5 | HPC map R-line | ||
6 | HPC map Ncorr | ||
7 | |||
8 | HPT map PR | ||
9 | LPT map PR |
FAR | Φ | Δh Btu/lbm (kJ/kg) | Δs Btu/lbm/R (kJ/kg/K) | Δγ (None) | ΔR Btu/lbm/R (kJ/kg/K) |
---|---|---|---|---|---|
0.000000 | 0.00 | −130.2 (−302.85) | 0.053 (0.222) | 0.000 | 0.000 |
0.016907 | 0.25 | −455.0 (−1058.3) | 0.066 (0.276) | 0.000 | 0.000 |
0.033814 | 0.50 | −769.1 (−1788.9) | 0.072 (0.301) | 0.000 | 0.000 |
0.050721 | 0.75 | −1073.2 (−2496.3) | 0.073 (0.305) | 0.000 | 0.000 |
0.067628 | 1.00 | −1364.7 (−3174.3) | 0.065 (0.272) | 0.000 | 0.000 |
Parameter | Ground | Flight 1 | Flight 2 |
---|---|---|---|
Altitude, ft (m) | SL | 20,000 (6096) | 35,000 (10,668) |
MN, none | 0.00 | 0.60 | 0.80 |
ΔTICAO-SA, °F (°C) | 0.0 and +27 (+15) | 0.0 and +18 (+10) | 0.0 and +18 (+10) |
NLcorr, % | 50.0–100.0 | 57.5–100.0 | 67.5–100.0 |
ΔT0,041 (R) | ΔT0,041 (K) | |
---|---|---|
ΔHPC PR = +31.4% | 55.8 | 31.0 |
Δβ = +26.0% | 322.3 | 179.1 |
Total | 378.1 | 210.1 |
Parameter | Fan | LPC | HPC | HPT | LPT |
---|---|---|---|---|---|
Ncorr (compressors) NP (turbines) | 1.0000 | 1.0000 | 1.0000 | 3.4719 | 1.5518 |
(compressors) FF (turbines) | 0.2642 | 0.4060 | 0.4152 | 0.6711 | 0.4871 |
PR | 0.8863 | 0.8446 | 0.7132 | 0.8125 | 0.5996 |
η | 1.0192 | 0.9945 | 1.0480 | 1.0022 | 1.0000 |
Parameter | ΔFn (%) | ΔSFC (%) |
---|---|---|
0.67 | –3.59 | |
hp (–115.6 kW) | 0.10 | –1.53 |
Δhfuel = –176 Btu/lbm (–409.4 kJ/kg) | 0.02 | 0.97 |
Parameter | AGCM | Ref. [22] | Δ (%) |
---|---|---|---|
Dfan, in (m) | 46.2 (1.173) | 45.90 (1.165) | 0.65 |
, lbm/s (kg/s) | 421.08 (191.0) | 405.44 (183.9) | 3.86 |
β, none | 5.18 | 4.33 | 19.63 |
OPR, none | 23.83 | 20.23 | 17.80 |
Fn,CR, lbf (N) | 2790.44 (12,412.4) | 2734 (12,161.4) | 2.06 |
SFCCR, lbm/h/lbf (kg/h/N) | 0.6889 (0.07025) | 0.6919 (0.07056) | −0.43 |
SFCTKOF, lbm/h/lbf (kg/h/N) | 0.3592 (0.03663) | 0.4112 (0.04193) | −12.65 |
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Gurrola Arrieta, M.d.J.; Botez, R.M. Improved Local Scale Generic Cycle Model for Aerothermodynamic Simulations of Gas Turbine Engines for Propulsion. Designs 2022, 6, 91. https://doi.org/10.3390/designs6050091
Gurrola Arrieta MdJ, Botez RM. Improved Local Scale Generic Cycle Model for Aerothermodynamic Simulations of Gas Turbine Engines for Propulsion. Designs. 2022; 6(5):91. https://doi.org/10.3390/designs6050091
Chicago/Turabian StyleGurrola Arrieta, Manuel de Jesús, and Ruxandra Mihaela Botez. 2022. "Improved Local Scale Generic Cycle Model for Aerothermodynamic Simulations of Gas Turbine Engines for Propulsion" Designs 6, no. 5: 91. https://doi.org/10.3390/designs6050091
APA StyleGurrola Arrieta, M. d. J., & Botez, R. M. (2022). Improved Local Scale Generic Cycle Model for Aerothermodynamic Simulations of Gas Turbine Engines for Propulsion. Designs, 6(5), 91. https://doi.org/10.3390/designs6050091