ABSTRACT: Concentrated solar power plants intend to be key in the pool of renewable energy production technologies in the next future because of their versatility and high efficiency. In this work a hybrid parabolic solar dish, coupled to a hybrid Brayton cycle, is simulated (Fig. 1 and Fig. 2). The system is composed of three subsystems (Fig. 3): Solar collector and receiver, combustion chamber and power block. It is considered hybrid since the turbine receives thermal energy from two sources: solar irradiation and combustion chamber. Depending on the metheorological conditions, the system will be working just with the solar collector (for good irradiance values), just with the combustion chamber (for example, during the night) or hybrid mode. A modelling scheme developed by our group that allows to obtain the expected thermodynamic and thermo-economic plant records is applied. Key indicators like subsystems efficiency, global efficiency, or net power output are calculated. This notebook considers only one point (just one value of irradiance and ambient temperature) to estimate these output indicators. CITATION (original article): J. García-Ferrero, R.P. Merchán, M.J. Santos, A. Medina, A. Calvo Hernández, Brayton technology for Concentrated Solar Power plants: Comparative analysis of central tower plants and parabolic dish farms, Energy Conversion and Management, 271, 2022, 116312,ISSN 0196-8904, https://doi.org/10.1016/j.enconman.2022.116312.
Definition of the nomenclature employed along the notebook
Definition of the nomenclature employed along the notebook
Input parameters
G (W/m2): Solar Irradiance (punto de diseño 860 W/m2)
Gmin: Minimum value for the solar part to be opetarive
Tl (K): Ambient temperature
T1lim (K): To calculate the adiabatic coefficient: 25°C + 273 = cp/cV
T3lim (K): A maximum value is set to avoid material degradation (900°C according to Semprini, 2016)
Turbine
mp (kg/s): Mass flow rate of the Mercury 50 turbine
rpexp: Pressure ratio of the Mercury 50 turbine
et: Expander efficiency
ec: Compressor efficiency
er: Recuperator efficiency (approximate real value)
e1: Heat exchanger efficiency for cooling the air. It is assumed ideal (no contact with the environment)
roh: Pressure drop in process 2–3
roc: Pressure drop in process 4–1
Heat Trasnfer fluid:
cp (J/ kg K): heat capacity at constant pressure for the HTF (air).
Calculated with the coefficient interpolated from RefProp of the curves at 0.5 Mpa ( 5 bar ). All the coeffs (a,b,c,d,e) are expressed as the final units of cpmol is J/mol K, so then is necessary to divide by the molecular mass (pma) to obtain cp in J/kg K
R (J / mol K ) = ideal gas constant
pma (kg / mol) = molecular mass of HTF in kg/ mol
γ = adiabatic index or heat capacity ratio of the HTF γ = cp/cV
k = relation of (γ-1)/γ
Combustion Chamber:
ehc: Combustion chamber heat exchanger efficiency (typical value 0.98)
nc: Combustion chamber efficiency. Standard value.
qlhv: Low Heating Value (natural gas, J/kg)
tempcam: Preset temperature for the combustion chamber
Solar subsystem:
α: Emissivity of the collector surface. Average emissivity.
n₀: Optical efficiency (depends on the solar plant; 0.7 < n₀ < 0.85).
ehs: Solar collector heat exchanger efficiency. Depends on the collector technology.
Aa (m²): Collector area.
Ar (m²): Receiver area.
C = Ac/Ar: Solar concentration factor.
Ul: Convection and conduction heat loss coefficient (standard value).
Gmin: Minimum value for the solar part to be opetarive
Tl (K): Ambient temperature
T1lim (K): To calculate the adiabatic coefficient: 25°C + 273 = cp/cV
T3lim (K): A maximum value is set to avoid material degradation (900°C according to Semprini, 2016)
Turbine
mp (kg/s): Mass flow rate of the Mercury 50 turbine
rpexp: Pressure ratio of the Mercury 50 turbine
et: Expander efficiency
ec: Compressor efficiency
er: Recuperator efficiency (approximate real value)
e1: Heat exchanger efficiency for cooling the air. It is assumed ideal (no contact with the environment)
roh: Pressure drop in process 2–3
roc: Pressure drop in process 4–1
Heat Trasnfer fluid:
cp (J/ kg K): heat capacity at constant pressure for the HTF (air).
Calculated with the coefficient interpolated from RefProp of the curves at 0.5 Mpa ( 5 bar ). All the coeffs (a,b,c,d,e) are expressed as the final units of cpmol is J/mol K, so then is necessary to divide by the molecular mass (pma) to obtain cp in J/kg K
R (J / mol K ) = ideal gas constant
pma (kg / mol) = molecular mass of HTF in kg/ mol
γ = adiabatic index or heat capacity ratio of the HTF γ = cp/cV
k = relation of (γ-1)/γ
Combustion Chamber:
ehc: Combustion chamber heat exchanger efficiency (typical value 0.98)
nc: Combustion chamber efficiency. Standard value.
qlhv: Low Heating Value (natural gas, J/kg)
tempcam: Preset temperature for the combustion chamber
Solar subsystem:
α: Emissivity of the collector surface. Average emissivity.
n₀: Optical efficiency (depends on the solar plant; 0.7 < n₀ < 0.85).
ehs: Solar collector heat exchanger efficiency. Depends on the collector technology.
Aa (m²): Collector area.
Ar (m²): Receiver area.
C = Ac/Ar: Solar concentration factor.
Ul: Convection and conduction heat loss coefficient (standard value).
Results
temcol: Calculated temperature of the solar collector (Ths).
t3sim (K): Turbine inlet temperature.
fsim: Solar Share (f = 1 → all the energy supplied to the fluid is solar; f = 0 → all the energy supplied to the fluid comes from the combustion chamber).
nssim: Solar collector efficiency.
nhsim: Turbine efficiency.
nsim: Overall system efficiency.
nesim: Economic efficiency (efficiency relative to fuel consumption).
Pad: Dimensionless power generated by the turbine.
Psim (W): Net power output in watts.
mdf (kg/s): Fuel consumption (kg/s).
t1sim: (1) Initial temperature.
t2sim: (2) Temperature at compressor outlet (the fluid is compressed from state 1 at T₁ to state 2 at T₂).
t3sim: (5) Turbine inlet temperature. The system is in contact with the combustion chamber and moves from state x′ to state 3.
t4sim: (6) After reaching the maximum temperature (T₃), the system expands irreversibly in the turbine to point 4.
tysim: (7) From point 4, heat is released to the surroundings.
txsim: (3) Thanks to the regenerator, the system temperature increases from T₂ to Tₓ, taking advantage of the high temperature of the gases at the turbine outlet (if there is no regenerator, then Tₓ = T₂).
tpxsim: (4) Temperature at the solar collector outlet (not constant in the dynamic case). The system temperature rises from Tₓ to Tₓ′.
temcol: Calculated temperature of the solar collector (Ths).
t3sim (K): Turbine inlet temperature.
fsim: Solar Share (f = 1 → all the energy supplied to the fluid is solar; f = 0 → all the energy supplied to the fluid comes from the combustion chamber).
nssim: Solar collector efficiency.
nhsim: Turbine efficiency.
nsim: Overall system efficiency.
nesim: Economic efficiency (efficiency relative to fuel consumption).
Pad: Dimensionless power generated by the turbine.
Psim (W): Net power output in watts.
mdf (kg/s): Fuel consumption (kg/s).
t1sim: (1) Initial temperature.
t2sim: (2) Temperature at compressor outlet (the fluid is compressed from state 1 at T₁ to state 2 at T₂).
t3sim: (5) Turbine inlet temperature. The system is in contact with the combustion chamber and moves from state x′ to state 3.
t4sim: (6) After reaching the maximum temperature (T₃), the system expands irreversibly in the turbine to point 4.
tysim: (7) From point 4, heat is released to the surroundings.
txsim: (3) Thanks to the regenerator, the system temperature increases from T₂ to Tₓ, taking advantage of the high temperature of the gases at the turbine outlet (if there is no regenerator, then Tₓ = T₂).
tpxsim: (4) Temperature at the solar collector outlet (not constant in the dynamic case). The system temperature rises from Tₓ to Tₓ′.
Case study for this example
#1: 30 kWe power output
#1: 30 kWe power output
Definition of the numerical values for the parameters
Definition of the numerical values for the parameters
SetDirectory[NotebookDirectory[]];
Input parameters
Gmin=15;(*W/m^2*)Tllim=278.35;(*K*)T3lim=1173.15;(*K*)mp=0.3379;(*massflowratekg/s*)rpexp=3.84;(*pressureratio*)R=8.314472;(*idealgasconstantJ/(molK)*)pma=28.9644*10^-3;(*airmolecularweightkg/mol*)
Coefficients to obtain cp
Data RefProp, 1.9 bar Lemmon, E . W .; Huber, M . L . McLinden, M . O . NIST Standard Reference Database 23 : Reference Fluid Thermodynamic and Transport Properties - REFPROP, Version 9.1 2013
a1=29.36631/pma;(*toconvert"J/mol·K"intoJ/kg·K,divideby"pma"*)b1=-0.0056878/pma;c1=(1.90528*^-5)/pma;d1=(-1.21744*^-8)/pma;e1=(2.46249*^-12)/pma;
Power block parameters
et=0.76;(*IsoentropicEfficienciesofexpander*)ec=0.77;(*IsoentropicEfficienciesofcompresor*)er=0.85;(*RecuperatorEffectiveness*)el=1;(*Ambientheatexchangerefectiveness*)roh=0.875;(*hotlinepressuredrop*)roc=1;(*coldlinepressuredrop*)
Combustion chamber parameters
ηc=0.97;(*Combustorefficiency*)ehc=0.97;(*Combustionchamberheatexchangerefficiency*)qlhv=47.141*10^6;(*LHVNaturalgas,J/kg*)tempcam=1173.15;(*Temperaturelimit*)
Solar subsystem parameters
η
0
-8
10
Calculating mean “cp
Calculating mean “cp
In order to properly calculate mean “cp” value, a first estimation of the different cycle temperatures is performed
From the previous temperatures, now mean “cp” is calculated, as well as the rest of the efficiencies, solar share and power output
HeadingsTableRes=;TableForm[AllRes,TableHeadings->{HeadingsTableRes}]
Out[]//TableForm=
INPUT DATA | - |
[G] DNI (W/m^2) | 900 |
[Tl] Ambient temperature (K) | 300 |
[Tllim] Limit ambient temperature (K) | 278.35 |
[T3lim] Limit turbine temperature (K) | 1173.15 |
[mp] Air mass flow (kg/s) | 0.3379 |
[rpexp] Compressor pressure ratio (-) | 3.84 |
[ehc] Combustion chamber HEX efectiveness (-) | 0.97 |
[ehs] Solar collector HEX efectiveness (-) | 0.7951 |
[el] Ambient heat exchanger efficiency (-) | 1 |
[roh] Heat absorption pressure drop (-) | 0.875 |
[roc] Heat release pressure drop (-) | 1 |
[et] Expander effieciency (-) | 0.76 |
[ec] Compressor efficiency (-) | 0.77 |
[er] Recuperator efficiency (-) | 0.85 |
[ηc] Combustion chamber efficiency (-) | 0.97 |
[η₀] Solar collector optical efficiency (-) | 0.9083 |
[α] Emissivity (-) | 0.1 |
[Aa] Solar collector aperture area (m^2) | 211.8 |
[Ul] Global conduction and convection heat tranfer coefficient (W/K) | 5 |
RESULTS | - |
[tempcam] Combustion chamber temperature (K) | 1173.15 |
[tempcol] Solar collector temperature (K) | 1250.7 |
[fsim] Simulated solar share (-) | 0.999382 |
[ηssim] Solar efficiency (-) | 0.896781 |
[ηhsim] Turbine efficiency (-) | 0.261916 |
[ηsim] System global efficiency (-) | 0.186782 |
[ηesim] Thermo-economic efficiency (-( | 399.043 |
[t1sim] Temperature before the compressor (K) | 300. |
[t2sim] Temperature after the compressor (K) | 480.618 |
[txsim] Temperature after recuperator heat input (K) | 871.326 |
[txpsim] Temperature after solar collector heat input (K) | 1172.96 |
[t3sim] Temperature after combustion chamber heat input& Turbine inlet temperature (K) | 1173.14 |
[t4sim] Temperature after expander (K) | 940.274 |
[tysim] Temperature after recuperator heat release (K) | 549.567 |
[potsim] Simulated power output (W) | 30547.8 |
[mdf] Fuel mass flow rate (kg/s) | 1.62391× -6 10 |
[Qhssim] Input power from solar collector (W) | 116560. |
[Qhcsim] Input power from combustion chamber (W) | 72.0283 |
[Qhsim] Total turbine input power (W) | 116632. |
[Qlsim] Power released to the ambient (W) | 86084.4 |
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Brayton technology for concentrated solar power: analysis of central tower and parabolic dish plants
by Judit García Ferrero, R.P. Merchán, María Jesús Santos Sánchez, Alejandro Medina, Antonio Calvo-Hernández
Wolfram Community, STAFF PICKS, November 7, 2025
https://community.wolfram.com/groups/-/m/t/3572063
by Judit García Ferrero, R.P. Merchán, María Jesús Santos Sánchez, Alejandro Medina, Antonio Calvo-Hernández
Wolfram Community, STAFF PICKS, November 7, 2025
https://community.wolfram.com/groups/-/m/t/3572063