modeling, simulation and identification of heat loss ...mathmod 2015 - 8th vienna international...

Modeling, Simulation and Identification of Heat Loss Mechanisms for Parabolic Trough Receivers in Concentrating Solar Thermal Power Plants German Aerospace Center (DLR) Institute for Solar Research Simon Caron, Marc Röger MathMod 2015 Conference 19th February 2015, Vienna

Agenda

• Introduction

• Thermodynamic Model

• Steady-State Validation • Transient Simulation • Parameter Identification

• Results & Conclusion

Slide 2 MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling

Introduction

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Thermodynamic model

Equivalent thermal network: 3 4

Labor


Lactive

Heat Loss Balance

• Stationary (Receiver):

• Transient (Glass envelope):

qcond,abs = qrad,abs-gl + qconv,abs-gl (1)

qrad,abs-gl + qconv,abs-gl = qcond,gl (2)

qcond,gl = qrad,gl-amb + qconv,gl-amb (3)

qrad,abs-amb + qcond,gl = qloss (4)

(5)

qin = qrad,abs-gl + qconv,abs-gl (6)

qout= qrad,gl-amb + qconv,gl-amb (7)

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Heat Loss Mechanisms (I)

Mechanism 1: Thermal radiation exchange

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Heat Loss Mechanisms (II)

Mechanism 2: Gas thermal conduction

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��𝑞𝑔𝑔𝑔𝑔𝑔𝑔,𝑔𝑔𝑎𝑎𝑔𝑔−𝑔𝑔𝑔𝑔 = 2.π.𝑅𝑅𝑔𝑔𝑎𝑎𝑔𝑔,𝑜𝑜. 𝐿𝐿𝑔𝑔𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 .𝒉𝒉𝒂𝒂𝒂𝒂𝒂𝒂. 𝑇𝑇𝑔𝑔𝑎𝑎𝑔𝑔,𝑜𝑜 − 𝑇𝑇𝑔𝑔𝑔𝑔,𝑎𝑎

Semi-transparent vs. opaque glass envelope

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Receiver Library SignalLibrary ModelLibrary

Package SimulationStudio OOP: Modelica Simulation: Dymola

• No graphical user interface • Inclusion of test data via external .dsu files


Steady-State Validation (I)

• Experimental set-up • DLR QUARZ®, ThermoRec Test Bench • National Renewable Energy Laboratory (U.S.A) • Chinese Academy of Science, Institute of Electrical Engineering

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Steady-State Validation (II)

Good agreement for specific heat losses Stationary model validated

Residual mismatch For glass temperature: Model calibration vs. Experimental errors


Transient Infrared Thermography

• Laboratory experimental set-up:


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Transient measurements

Measured temperature profiles (IR sensors)


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• Working point: • Average absorber temperature Tabs, av [°C] • Average Glass temperature Tgl,av [°C] • Average ambient temperature Tair,av [°C]

• Transient measurands:

• Amplitude ratio A(ω) [-] • Phase shift φ(ω) [rad] • Angular frequency ω [rad/s], [Hz]

• Simulated temperature profiles


Transient simulation (I)

Transient simulation (II)

Modeling approach: • Linear Time Invariant (LTI) System • First order system reponse analysis


𝐹𝐹(𝑗𝑗𝑗𝑗) = 𝐺𝐺

1 + 𝑗𝑗𝑗𝑗𝑗𝑗 𝐴𝐴(𝑗𝑗) =

𝐺𝐺1 + 𝑗𝑗2𝑗𝑗2

𝜑𝜑 𝑗𝑗 = −𝑡𝑡𝑡𝑡𝑡𝑡−1(𝑗𝑗𝑗𝑗)

Identification problem

SYSTEM {RECEIVER+SHIELD} (Materials, Geometry)

INPUT SIGNAL

SIMULATION Tabs,o (t)

NOISE SIGNALS

vair [m/s]

Tair (t)

THERMAL PROPERTIES

εabs [%]

hann [W/m2.K]

Tgl,o (t)

Tgl,o (t) = ?

MEASUREMENT

?

? Heat Loss Mechanism 2:

Heat Loss Mechanism 1:


Parameter Identification Strategy

• Combination of Global Search with Particle Swarm Optimization (PSO) with subsequent Local Search with Nelder Mead Simplex (NMS):

• Definition of candidate parameter vectors X0 with PSO • Tuning of parameter vector with NMS from X0 seed

Coupling between MATLAB and DYMOLA:

• MATLAB: • Measurement Data Processing • Optimization Wrapper Function (PSO + NMS)

• DYMOLA: • Numerical Simulation (6 sec per simulation)


Parameter Identification (I): Transient Analysis

• Routine 1: Multi-criteria optimization

• Search Space segmentation; PSO: 10 iter.; NMS: max. 200 iter.


Results (I): Transient Analysis

• Routine 1: Multi-criteria Optimization


Parameter Identification (II): Direct Identification

• Routine 2: Least Square Optimization

• Search Space Duplication; PSO: 50 iter.; NMS: max. 100 iter.


Results (II): Direct Identification

• Routine 2: Least Square Optimization


Conclusion & Outlook

• Object Oriented Thermodynamic Model simulates PTRs for: • Stationary measurements (Off-sun, Laboratory) • Transient measurements (Off-sun, Laboratory + Field)

• Direct Identification tends to work better than Transient Analysis:

• Least Mean Square Optimization Criterium is easier to interprete • Analysis method is more robust for noisy data (field measurements)

• Optimization potential:

• PSO/NMS Fine Tuning for a faster convergence • Parallel Computing for multi-session simulation


Thank you for your attention!

• Do you have any question ? • [email protected]


mailto:[email protected]

References (I)

Plataforma Solar de Almeria, Largest European research centre devoted Concentrating Solar Energy (2013): http://www.psa.es/webesp/instalaciones/ Folleto%20PSA%202013_EN_131202.pdf

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4 Forristall, R., Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver Implemented in Engineering Equation Solver, U.S. National Renewable Energy Laboratory, NREL/TP-550-34169, 2003


Burkholder, F., Kutscher, C., Heat Loss Testing of Schott‘s 2008 PTR70 Parabolic Trough Receiver, U.S. National Renewable Energy Laboratory, NREL/TP-550-45633, 2009

Lei,D., Li, Q., Wang, Z., Li,J., Li,J., An experimental study of thermal characterization of parabolic trough receivers, Journal Energy Conversion and Management, Vol. 69 (2013) pp. 107-115

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6 Planck Law of Radiation: http://de.wikipedia.org/wiki/Plancksches_Strahlungsgesetz# mediaviewer/File:BlackbodySpectrum_lin_150dpi_de.png

Tesfamichael, T., Characterization of Selective Solar Absorbers : Experimental and Theoretical Modeling, PhD Dissertation, Uppsala University, 2000

http://www.psa.es/webesp/instalaciones/Folleto%20PSA%202013_EN_131202.pdf

http://www.psa.es/webesp/instalaciones/Folleto%20PSA%202013_EN_131202.pdf

http://de.wikipedia.org/wiki/Plancksches_Strahlungsgesetzmediaviewer/File:BlackbodySpectrum_lin_150dpi_de.png




References (II)

Schott Premium Receivers with noble gas capsules: http://www.schott.com/csp/english/ schottsolar-ptr-70-premium-receivers.html?so=iberica&lang=spanish


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Pfänder, M., Pyrometrische Temperaturmessung an solarthermischen Hochtemperatur-Receivern, PhD Dissertation, Deutsches Zentrum für Luft- und Raumfahrt, 2006

Röger, M., Potzel, P., Pernpeintner, J., Caron, S., A Transient Thermography Method to Separate Heat Loss Mechanisms in Parabolic Trough Receivers, Journal of Solar Energy Engineering, Vol. 136, 011006-1:9, 2014

Caron, S., Röger, M., Pernpeintner, J., Transient Infrared Thermography Heat Loss Measurements on Parabolic Trough Receivers under Laboratory Conditions, Conference Proceedings,SolarPaces Beijing 2014

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http://www.schott.com/csp/english/schottsolar-ptr-70-premium-receivers.html?so=iberica&lang=spanish

http://www.schott.com/csp/english/schottsolar-ptr-70-premium-receivers.html?so=iberica&lang=spanish

Routine 1; Ergebnisse (1) PTR Category Cat. A Working point WP-A1 WP-A2 WP-A3 Tabs [°C] 359.4 411.7 457.7

TRANSIENT

εabs [%] 12.42% 14.60% 16.18% hann [W/m2.K] 0.040 0.010 0.004 Optimization criterium δ 3.0 e-3 4.9 e-3 1.9e-2 Q'th,loss [W/m]

TRANSIENT (A)

Standard conditions (25°C, 0 m/s)

226.7 365.4 526.1

STEADY-STATE Q'th,loss [W/m]

THERMOREC (B) 208.4 306.7 413.0

Absolute deviation; (A-B) [W/m] 18.3 58.7 113.1 Relative deviation; (A-B)/B [%] 8.8% 19.1% 27.4%

MATERIAL DATA,

SIMULATIONS

εabs [%] (material data)

(FTIR Spectrophotometer) 8.89% 10.27% 11.75%

hann [W/m2.K] (specifications)

(annulus pressure , Table 1) 0.013 0.013 0.012

Q'th,loss [W/m]

SIMULATION (C)


163.2 260.9 387.4


Routine 2; Ergebnisse (1) PTR Category Cat. A Working point WP-A1 WP-A2 WP-A3 Tabs [°C] 355.9 407.7 450.5

TRANSIENT

εabs [%] 11.87% 11.98% 12.59% hann [W/m2.K] 0.064 0.013 0.032 Optimization criterium δ 0.19 0.47 0.55 Q'th,loss [W/m]

TRANSIENT (A)


213.2 295.3 399.1


THERMOREC (B) 208.2 307.4 407.0

Absolute deviation; (A-B) [W/m] +5.0 -12.1 -7.9 Relative deviation; (A-B)/B [%] +2.4% -3.9% -2.0%

MATERIAL DATA,

SIMULATIONS





Q'th,loss [W/m]

SIMULATION (C)


158.4 252.0 365.0


Routine 1; Ergebnisse (2) PTR Category Cat. B Working point WP-B1 WP-B2 WP-B3 Tabs [°C] 191.4 231.4 271.5

TRANSIENT

εabs [%] 78.45% 73.88% 69.69% hann [W/m2.K] 2.63 3.14 3.88 Optimization criterium δ 7.9e-7 8.2 e-6 7.0e-7 Q'th,loss [W/m]

TRANSIENT (A)


327.8 461.6 625.0


THERMOREC (B) 337.9 493.8 686.4

Absolute deviation; (A-B) [W/m] -10.1 -32.2 -61.4 Relative deviation; (A-B)/B [%] -3.0% -6.5% -9.0%

MATERIAL DATA,

SIMULATIONS





Q'th,loss [W/m]

SIMULATION (C)


305.1 445.4 620.7


Routine 2; Ergebnisse (2) PTR Category Cat. B Working point WP-B1 WP-B2 WP-B3 Tabs [°C] 189.6 225.4 262.0

TRANSIENT

εabs [%] 90.50% 92.59% 92.21% hann [W/m2.K] 1.57 0.50 0.21

Optimization criterium δ 0.22 0.21 0.18 Q'th,loss [W/m]

TRANSIENT (A)


332.8 446.2 606.3


THERMOREC (B) 331.1 465.7 639.4

Absolute deviation; (A-B) [W/m] +1.8 -19.5 -33.1 Relative deviation; (A-B)/B [%] +0.5% -4.2% -5.2%

MATERIAL DATA,

SIMULATIONS





Q'th,loss [W/m]

SIMULATION (C)


299.6 422.4 576.0


Routine 1; Ergebnisse (3) PTR Category Cat. C Working point WP-C1 WP-C2 WP-C3 Tabs [°C] 193.2 232.8 273.0

TRANSIENT

εabs [%] 84.10% 70.43% 62.71% hann [W/m2.K] 3.67 6.20 8.46 Optimization criterium δ 4.3e-7 7.4e-6 5.9e-7 Q'th,loss [W/m]

TRANSIENT (A)


362.8 510.8 692.3


THERMOREC (B) 358.1 513.8 703.9

Absolute deviation; (A-B) [W/m] 4.7 -3.0 -11.6 Relative deviation; (A-B)/B [%] 1.3 % -0.6% -1.7%

MATERIAL DATA,

SIMULATIONS





Q'th,loss [W/m]

SIMULATION (C)


381.6 535.8 725.4


Routine 2; Ergebnisse (3) PTR Category Cat. C Working point WP-C1 WP-C2 WP-C3 Tabs [°C] 186.0 225.5 264.5

TRANSIENT

εabs [%] 90.23% 88.72% 91.68% hann [W/m2.K] 4.56 4.40 4.58

Optimization criterium δ 0.20 0.29 0.30 Q'th,loss [W/m]

TRANSIENT (A)


363.6 507.7 676.4


THERMOREC (B) 334.3 483.7 665.5

Absolute deviation; (A-B) [W/m] +29.3 +24.1 +11.0 Relative deviation; (A-B)/B [%] +8.8% +5.0% +1.7%

MATERIAL DATA,

SIMULATIONS





Q'th,loss [W/m]

SIMULATION (C)


357.1 505.1 682.5


Heat Loss Balance Heat flow Heat Transfer from … to… Mechanism

qcond,abs (W) Absorber (inner to outer surface) Temperatures: Tabs,i (K); Tabs,o (K)

Conduction (3D)

qrad,abs-gl (W) Absorber

(outer surface) Tabs,o (K)

Envelope (inner surface)

Tgl,i (K)

Radiation (1D)

qrad,abs-amb (W) Absorber


Ambient (Sky temp.)

Tsky (K)

Radiation (1D)

qconv,abs-gl (W) Absorber


Envelope (inner surface)

Tgl,i (K)

Convection (1D)

qcond,gl (W) Envelope (inner to outer surface) Temperatures: Tgl,i (K); Tgl,o (K)

Conduction (3D)

qrad,gl-amb (W) Envelope

(outer surface) Tgl,o (K)

Ambient (Sky temp.)

Tsky (K)

Radiation (1D)

qconv,gl-amb (W) Envelope

(outer surface) Tgl,o (K)

Ambient (air temp.)

Tair (K)

Convection (1D)


• Particle Swarm: • Basic Version • Parameters:

• 10 Particles • Weight W=0.5 • Social Constant: 2 • Cognitive Constant: 2

• Hit on boundary constraints:

• Coordinate re-sampled

• Nelder Mead Simplex • Version: FminsearchBnd • Operations:

• Initial Simplex • Reflect • Expand • Contract Outside • Contract Inside • Shrink

• Parameters (default): • Rho = 1 • Chi = 2 • Psi = 0.5 • Sigma = 0.5

Optimization Algorithms


MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling

modeling, simulation and identification of heat loss ...mathmod 2015 - 8th vienna international...

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