A fast molten salt receiver model in MATLAB Cite as: AIP Conference Proceedings 2126, 030034 (2019); https://doi.org/10.1063/1.5117546 Published Online: 26 July 2019 Zhi Li, Zhifeng Wang, Qiangqiang Zhang, and Fengwu Bai
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AIP Conference Proceedings 2126, 030034 (2019); https://doi.org/10.1063/1.5117546 © 2019 Author(s).
2126, 030034
A Fast Molten Salt Receiver Model in MATLAB Zhi Li1, 2, 3, 4, Zhifeng Wang 1, 2, 3, 4, a), Qiangqiang Zhang1, 2, 3, 4, Fengwu Bai1, 2, 3, 4 1
Key Laboratory of Solar Thermal Energy and Photovoltaic System of Chinese Academy of Sciences, Beijing 100190, China 2 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China 3 University of Chinese Academy of Sciences, Beijing, 100049, China 4 Beijing Engineering Research Center of Solar Thermal Power, Beijing, China a)
Corresponding author:
[email protected] Abstract. The receiver model for fast calculation is needed to validate the real-time control on molten salt tower system. In this paper, a lumped parameter model is built to display the receiver working process. At first, the single tube model is built to demonstrate the physical heat transfer both in steady and unsteady state. Then the half-part receiver model is shown to simulate the real receiver operation by connecting single tubes together. By comparing the model results and the real data, the trend of average outlet temperature goes well with experimental data. Key words: receiver model, fast calculation, MATLAB Nomenclature
ε
emissivity
c e
specific heat at constant pressure(J/(kg K)) relative error(%)
σ Χ
Stefane-Boltzmann constant( 5.67 10 8 W/(m2 K4)) angle factor
h
convective heat transfer coefficient (W/(m2 K))
k
thermal conductivity (W/(m K))
Subscripts
M
mass(ton)
1
outside surface
M
mass flowrate(ton/h)
2
inside surface
Nu
Nusselt number
a
ambient
P
solar power(kW)
cond
conductive
Pr
Prandtl number
conv
convective
Q
thermal power(kW)
Exp.
experiment
Re
Reynolds number
m
metal tube
S
surface area(m2)
r2a
from receiver to ambient
T
temperature(oC)
rad
radiative
ΔQ
internal energy change(kW)
s
salt
sin
input salt
Greek symbols
sout
output salt
δ
Sim.
simulation
thickness(m)
SolarPACES 2018 AIP Conf. Proc. 2126, 030034-1–030034-8; https://doi.org/10.1063/1.5117546 Published by AIP Publishing. 978-0-7354-1866-0/$30.00
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INTRODUCTION With the successful commercial demonstration of molten salt tower power plants, such as Gemasolar and Crescent Dune, the technology is distinguished with other solar energy applications by its advantage on high operation temperature and non-intermittence electricity production. When the system is running, the receiver real-time control is needed to avoid risks, for example on receiver heat evacuation and antisolidification. So, a receiver model for fast calculation is needed to validate the real-time control on molten salt tower system. In this paper, a lumped parameter model is built to display the receiver working process. First, the physical heat transfer is shown by building the single tube model in steady state. Second, the single tube model is improved from steady state to unsteady state which can be used in real-time analysis & control system. Third, the half-part receiver model is shown to simulate the real receiver operation by connecting single tubes together. Finally, the model is considered reliable and suitable by comparing the model results and the real data to find the trend of average outlet temperature going well with experimental data.
MODEL For the model in this paper, the assumptions are: The axial heat transfer is NOT considered. The temperature is same in one tube. The tube surface is diffuse gray and has surface properties that are independent of temperature. The emissivity is an average value by considering the cavity receiver as a whole.
Single Tube Model in Steady State Zero-Dimensional Model The purpose of this paper is to give out a reliable molten salt receiver fast calculation model. Thus, the thermal model is chosen as zero-dimensional model. And the followings explain what have been taken into consideration. First, the model must be correct on physical mechanism. Second, every step calculation time must be short. For example, if one-second-step calculation time is 10 second or longer, this program can hardly be used into industrial. Third, the model should use as few calculating resource as possible. Because the total calculating resource is limited in industrial computer and the control subsystem is the core part, the receiver calculation model cannot use a lot of resource as only a part of whole molten salt model subsystem. Forth, highest temperature area on the receiver should be noted because this location is easily overheated. And zero-dimensional model in this paper can show the real-time weakest location and send alarm signals to control subsystem for response. From the above, zero-dimensional thermal model for single tube is chosen. Physical Model Using zero-dimensional model, what should be considered well is the heat transfer between air, metal and molten salt. As shown in Fig.1(a), solar energy is focused on the tube outside surface by heliostats. Then the tube receives the solar energy, changes it into heat energy and transfers to molten salt inside. And the molten salt, flowing inside the tube forced by pump, receives the heat energy to be heated and takes this energy out for the following heat storage or exchange.
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AIR
P
Qrad,1
Qconv,1
METAL
Qcond,1
ΔQm
Qcond,2
Qconv,2 SALT
ΔQs Qsin
(a) visual description
Qsout
(b) physical explanation
FIGURE 1. Physical Model of Single Tube in Steady State
The basic characteristics of tube is shown in Table 1. TABLE 1. The tube characteristics
Parameters Value Inlet diameter (mm) 14 Outlet diameter (mm) 16 Area of outlet surfaces (m2) 0.08 Material SS321 16 Conductivity (W/m•K) The visual description is shown in Fig.1(a) above while the physical explanation is shown in following Fig.1(b). From the outside solar to central salt, heat transfer process locates at four positions which are tube outside surface (T1), metal tube (Tm), tube inside surface (T2) and central molten salt (Ts). The arrow means the transfer direction and ambient temperature (Ta) is the remote reference temperature. The heat transfer original equations are:
P Qrad ,1 Qconv ,1 Qcond ,1 Q cond ,1 Qcond ,2 Qcond ,2 Qconv ,2 Qconv ,2 Qsin Qsout
(1)
Numerical Model Classical heat transfer laws[1] are taken into Eq.(1) while change of metal and molten salt internal energy is ignored in steady state. The heat transfer numerical equations are:
P S1 (T 4 T 4 ) h S (T T ) k1 S1 (T T ) 1 1 1 1 r 2a a a m 2 1 m 2 k2 S2 k1 S1 2 (T1 Tm ) 2 (Tm T2 ) m m k2 S2 2 (Tm T2 ) h2 S 2 (T2 Ts ) m M M h S T T c T c s s T 2 2 2 s sin sin out sout
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(2)
The tube outside surface convective heat transfer coefficient is given by[2]: h1 0.81 (T1 Ta )
0.426
(3)
The Nu coefficient in tube inside surface convective heat transfer uses Dittus-Boelter (D-B) equation.
0.023 Re 0.8 Pr 0.4 , if T2 Ts Nu 0.8 0.3 0.023 Re Pr , if T2 Ts
(4)
When calculating in receiver layer[3], the angle factor (Χr2a) in heat radiation is 0.926 according to the receiver geometric construction. But, the angle factor (Χr2a) here is 1 when calculating single tube. In addition, the ambient temperature is chosen as the reference temperature here.
Single Tube Model in Unsteady State Based on the steady state, the unsteady state model considers the change of metal and molten salt internal energy. The heat transfer original equations are:
P Qrad ,1 Qconv ,1 Qcond ,1 Q cond ,1 Qcond ,2 Qm Qcond ,2 Qconv ,2 Qconv ,2 Qsin Qs Qsout
(5)
And the heat transfer numerical equations are:
P S1 (T 4 T 4 ) h S (T T ) k1 S1 (T T ) 1 1 1 1 r 2a a a m 2 1 m 2 dTm k2 S2 k1 S1 2 (T1 Tm ) 2 (Tm T2 ) cm M m d m m k2 S 2 (T T ) h S (T T ) 2 2 2 s m 2 m 2 h S (T T ) c M T c M dTs c M T s s sin sin s s out sout 2 2 2 s d
(6)
Half-part Receiver Model Because the receiver arrangement is symmetric distribution[3], half-part receiver can well display the whole receiver physical mechanism. For easy comprehension, the half-part receiver model can be imagined that lots of single tubes are connected one after another. Just like shown in Fig.4, molten salt will be well heated by flowing through the connected tubes
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FIGURE 2. Physical Model of Half-Part Receiver
It should be noted that this model is calculating all the temperature at one time-step after another. The outlet temperature of one pipeline is used as the inlet temperature of the next pipeline at the next time-step. If one model calculates only one tube temperature at whole time-steps first and then another tube, it may get the same or better output temperature. However, it stands opposite against the physical mechanism and cannot be used into industrial.
RESULT Simulation of Single Tube in Steady State Input and output parameters are shown in Table 2 and the characteristic temperature value result is shown in Fig.3. Type INPUT OUTPUT
TABLE 2. Input and output parameters Name Temperature (oC) Mass Flow Rate (ton/h) Input Solar Energy for whole receive(MWt) Temperature(oC) Mass Flow Rate (ton/h)
FIGURE 3. Calculating Speed
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Value 290 5.7 1 300.7158 5.7
As shown in Fig.3, the program can get result only after 8 calculating step. In addition, this result error is less than 1106 oC and elapsed time is 2.15 102 seconds in MATLAB on a low configuration computer. And this model is
very suitable for industrial operation.
Simulation of Single Tube in Unsteady State The input temperature and mass flow rate are still 290oC and 5.7 ton/h while the input solar energy becomes changing value. The output temperature is shown in Fig.3.
FIGURE 4. Output Temperature V.S. Input Solar Energy
As shown in Fig.4, the output temperature changes just following input solar energy. And this is very reasonable for single tube model in unsteady state. In addition, this result error is less than 1103 ºC and elapsed time for 60 steps calculation is just 0.353 seconds in MATLAB on a low configuration computer. And this model is very suitable for industrial operation.
Comparison of Simulation and Experiment Output Temperature for Half Receiver In the simulation, the input solar energy(DNI), volume flow rate and input temperature are all real data during one hour. All the input parameters are relative smooth for a long time. And all the inputs and outputs are shown in Fig.5.
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300
6 DNI Volume Flowrate
200 100 0
2
0
10
20
30
40
50
60
Time (min)
290
Temperature (oC)
4
0
10
280
5 Exp. output temperature
270
Sim. output temperature
0 260 Exp./Sim. input temperature
250 240
0
10
20
30
Time (min)
Volume Flowrate (m3/h)
8
Error Line
40
50
-5
60
Error Line (%)
DNI (W/m2)
400
-10
FIGURE 5. Comparison between the Experiment and Simulation Output Temperature
Easy to known, the value between the model and real output temperature is close to each other. And the error between experiment and simulation is from -3.45% to 1.35% which is calculated using e
TExp.sout TSim.sout TExp.sout
. Thus,
the model can be accepted for its T-out absolute value. It’s easily noticed that the real input DNI is the most changing parameter and the model output temperature follows this changing closely. Because the zero-dimensional model has least parameter limit, the half-part receiver model changes faster and more dramatically than the real one. For the requirement of accurate simulation, this model may be not suitable. However, this model is just very satisfied for part of industrial real-time control subsystem because it can give significant temperature trend forecast. And this model is very suitable for industrial operation.
CONCLUSION In this paper, a lumped parameter model is built to display the receiver working process. First, the physical heat transfer is shown by building the single tube model in steady state. Second, the single tube model is improved from steady state to unsteady state. The brief analysis of result shows that this model needs just a few computing resource and takes short time for every step calculation. Third, the half-part receiver model is shown to simulate the real receiver operation by connecting single tubes together. By comparing the model results and the real data, the trend of average outlet temperature can be found going well with experimental data. Above all, the model is proved a fast calculation MATLAB model and can be considered a preliminar evaluation for the real-time control on molten salt tower system. However, it is not suitable for accurate simulations.
ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China (No. 51606184) and the Beijing Natural Science Foundation (No. 3164052).
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REFERENCES 1. 2. 3.
S. Yang, W. Tao, Heat Transfer (4th edition) (Higher Education Press, Beijing, 2006), pp. 5-15. X. Li, W. Kong, Z. Wang, C. Chang, F. Bai, Thermal model and thermodynamic performance of molten salt cavity receiver, Renewable Energy, Volume 35, Issue 5, 981-988 (2010). Z. Li, X. Li, Q. Zhang, Z. Wang, Z. Liao, C. Chang, Badaling 1MWt molten salt tower power plant, in SOLARPACES 2016, AIP Conference Proceedings 1850, (2017), pp. 030033.
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