# Modeling and Characteristic Analysis of a Solar Parabolic Trough System: Thermal Oil as the Heat Transfer Fluid

Authors: Zhai Rongrong; Yang Yongping; Yan Qin; Zhu Yong
Journal: Journal of Renewable Energy
 (2013)

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## Abstract

The thermal oil is applied as the heat transfer fluid in a solar parabolic trough collector system. Firstly, the system dynamic model was established and validated by the real operating data in typical summer and spring days in references. Secondly, the alteration characteristics of different solar radiation, inlet water temperature and flow rate, and collectors’ area and length are analyzed and compared with the normal working condition. The model can be used for studying, system designing, and better understanding of the performance of parabolic trough systems.


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## Body

## 1. Introduction

Parabolic trough solar collector is a kind of line-focus concentrating solar utilizations for industry, with medium temperature, maximum working temperature 400–500°C. According to the heat transfer fluid types in the absorber, thermal oil and water/steam are the basic sorts. Both the two systems are wildly used in generating or heating in modern industry in recent years. The solar energy generating system with thermal oil as the heat transfer fluid, called SEGS, has been developed in several countries, especially in the USA. Therefore, the generated green electricity has increased the impetus of future research and development.Some of the published papers have studied the modeling and analysis of the heat transfer process of the thermal oil in parabolic trough collector systems. The one-dimension parabolic trough collector model had been developed by Odeh et al. [5], including synthetic oil and water/steam as the working fluid. The created model can be used to predict the performance of the collector. Rolim et al. [6] introduced an analytic model for a solar thermal electric generating system with parabolic trough collectors. The energy conversion of solar radiation into thermal power along the absorber tube of the parabolic collector is studied, taking into account the nonlinearity of heat losses and its dependence on the local temperature. The simulated results have been compared with experimental data. García-Valladares and Velázquez [7] developed detailed numerical simulations of thermal and fluid-dynamic behaviors of a single-pass and double-pass solar parabolic trough collector. The single-pass solar device numerical model has been carefully validated by experimental data. The parabolic trough collector and the main generating systems of the SEGS VI solar thermal oil power plant in California have been modeled by Stuetzle et al. [1, 2]; the control algorithms were established in MATLAB to control outlet temperature and flow rate. The one-dimension and two-dimension thermal oil solar parabolic collectors’ models were developed using EES software and validated by experimental data [8]. The detailed numerical simulation model of a single-pass and double-pass solar parabolic trough collector has been developed and validated by experimental data obtained from Sandia National Laboratories [7].However, the heat transfer has been analyzed in the above papers, but it has not been studied in detail in variable working conditions in these papers. The novelty of this paper lies in that it is focused on the details of heat transfer process with times along the flow direction, especially in the variable working conditions.In this paper, the Euler transformation method is introduced based on the forward modeling approach to simplify the dynamic model of parabolic trough with thermal oil as the heat transfer fluid. Meanwhile, the alteration characteristics in different input parameters are analyzed. The alterations include solar radiation, inlet oil temperature, and inlet oil mass flow rate and collector area. The model can be used for the analysis of parabolic trough system performances in variable working conditions.


## 2. Mathematic Modeling

As shown in Figure1, the linear parabolic concentrators are used to focus sunlight to heat the pumped heat transfer fluid in the absorber. The good light transmittance and heat-durability glass envelope are used to maintain the vacuum space between the absorber and the envelope in order to reduce heat loss and prevent corroding [9]. On the one hand, there should be vacuum between the receiver and glass envelope to reduce the heat loss. On the other hand, the luminousness should be increased by enhancing the optical performance of glass envelope. It means that the performance of luminousness and anticorrosion of glass envelope should be very good; otherwise there will be no vacuum when the glass is corroded. The heat and mass balance of absorber is listed in Figure 2.Figure 1
The schematic diagram of a parabolic trough solar collector system.Figure 2
Schematic diagram of the heat transfer analysis [1–3, 8].


### 2.1. Energy and Mass Balance Equations

According to [1–3, 8], the following energy and mass balance equations are used to establish the model. Equations (1) and (2) are for thermal oil; (3)–(5) and (6)–(8) about absorber and glass envelop are the same as the heat balance in direct steam generating system.Consider(1)∂∂t(ΔQoil(z,t))=Qoil(z,t)-Qoil(z+Δz,t)+Q3(z,t)Δz,(2)ΔQoil(z,t)=coilρoilA1Toil(z,t)Δz,(3)∂∂t(ΔQabs(z,t))=(Q0(z,t)-Q1(z,t)-Q3(z,t))Δz,(4)ΔQabs(z,t)=cabsρabsAabsTabs(z,t)Δz.
Combining (2) and (3),
(5)cabsρabsAabs∂∂t(Tabs(z,t))=Q0(z,t)-Q1(z,t)-Q3(z,t),(6)∂∂t(ΔQg(z,t))=(Q1(z,t)-Q2(z,t))Δz,(7)ΔQg(z,t)=cgρgAgTg(z,t)Δz.
Combining (5) and (6),
(8)cgρgAg∂∂t(Tg(z,t))=Q1(z,t)-Q2(z,t).The above mentioned inlet or outlet heatQ1 and Q2 for absorber and glass envelope all consisted of two parts: radiation and convection. The solar radiation absorbed by per unit area absorber Q0′ [1, 3, 8] can be expressed as follows:
(9)Q0′=Wcos(θ)fθfsfeηfηefo.The heat absorbed by thermal oil isQ3; Q3=A1h1(Tabs-Toil).


### 2.2. Equations Solving

The explicit Euler method is introduced to solve the above mentioned partial differential equations to avoid the complex solving, if the partial differential solution is used to all the individual collectors.


#### 2.2.1. Introduction of the Explicit Euler Method

For normal ordinary differential equation (10),
(10)y′(x)=f(x,y),y(a)=y0,(a≤x≤b),
where [a,b] as the solution interval is partitioned equally, and h=(b-a)/m as the step length. Then, the solution is marked as xn=xn-1+h, n=1,2,…,m, separately. The solution of y(x) at x=x0 solved by forward difference method is as follows:
(11)y′(x0)=y(x1)-y(x0)h.
At the same time, y(x0)=f(x0,y(x0)); then,
(12)y(x1)-y(x0)h≈f(x0,y(x0)).
The approximation of y(x1) is expressed as (13) or (14),
(13)y1-y0h=f(x0,y0),or(14)y1=y0+h·f(x0,y0),(15)y′(xn)≈y(xn+1)-y(xn)h,(16)y′(xn)=f(xn,y(xn)).Combining (15) and (16), the approximate forward Euler solving solution of y(xn+1) is as follows:
(17)yn+1=yn+h·f(xn,yn).As shown in (17), the explicit Euler method is defined, and the value of yn+1 is calculated by yn directly.


#### 2.2.2. The Euler Transformation for Thermal Oil

The energy balance equation for thermal oil based on (1) and (2) can be transformed into the following:
(18)coilρoilA1∂Toil(z,t)∂t=coilρoilVoil(Toil(z,t)-Toil(z+Δz,t)Δz)+Q3(z,t).Each collector is defined as a whole, and the predigesting is as follows:(19)Toil(z,t)-Toil(z+Δz,t)Δz≈Toil(0,t)-Toil(L,t)L.Combining (19) and (18), then,
(20)coilρoilA1dToil(L,t)dt=coilρoilVoilToil(0,t)-Toil(L,t)L+Q3(z,t).Equation (20) is sorted as follows:
(21)dToil(L,t)dt=VoilToil(0,t)-Toil(L,t)L·A1+Q3(z,t)coilρoilA1.For a whole collector, the outlet temperature of thermal oil is transformed by explicit Euler method as follows:(22)Toil(L,t)=Toil(L,t)′+[VoilToil(0,t)-Toil(L,t)′L·A1+Q3(z,t)coilρoilA1]Δt.


#### 2.2.3. The Euler Transformation for Absorber

The heat transfer expression for a whole collector absorber is as follows:(23)cabsρabsAabsddt(Tabs(L,t))=Q0′·WL-Q1-Q3.The transformed equation is as follows:(24)Tabs(L,t)=Tabs′(L,t)+Q0′·S/L-Q1-Q3cabsρabsAabsdt.


#### 2.2.4. The Euler Transformation for the Glass Envelope

The heat transfer expression of glass envelope is as follows:(25)cgρgAgddt(Tg(L,t))=Q1-Q2.The transformed equation is as follows:(26)Tg(L,t)=Tg′(L,t)+Q1-Q2cgρgAgdt.The model and the program are established according to the aforesaid equations and solving approach. The schematic chart of the computer program is shown in Figures3 and 4.Figure 3
The schematic flow chart of the program to calculate the absorbed heat by absorber.Figure 4
The schematic flow chart of the program to simulate the thermal oil system.


## 2.1. Energy and Mass Balance Equations

According to [1–3, 8], the following energy and mass balance equations are used to establish the model. Equations (1) and (2) are for thermal oil; (3)–(5) and (6)–(8) about absorber and glass envelop are the same as the heat balance in direct steam generating system.Consider(1)∂∂t(ΔQoil(z,t))=Qoil(z,t)-Qoil(z+Δz,t)+Q3(z,t)Δz,(2)ΔQoil(z,t)=coilρoilA1Toil(z,t)Δz,(3)∂∂t(ΔQabs(z,t))=(Q0(z,t)-Q1(z,t)-Q3(z,t))Δz,(4)ΔQabs(z,t)=cabsρabsAabsTabs(z,t)Δz.
Combining (2) and (3),
(5)cabsρabsAabs∂∂t(Tabs(z,t))=Q0(z,t)-Q1(z,t)-Q3(z,t),(6)∂∂t(ΔQg(z,t))=(Q1(z,t)-Q2(z,t))Δz,(7)ΔQg(z,t)=cgρgAgTg(z,t)Δz.
Combining (5) and (6),
(8)cgρgAg∂∂t(Tg(z,t))=Q1(z,t)-Q2(z,t).The above mentioned inlet or outlet heatQ1 and Q2 for absorber and glass envelope all consisted of two parts: radiation and convection. The solar radiation absorbed by per unit area absorber Q0′ [1, 3, 8] can be expressed as follows:
(9)Q0′=Wcos(θ)fθfsfeηfηefo.The heat absorbed by thermal oil isQ3; Q3=A1h1(Tabs-Toil).


## 2.2. Equations Solving

The explicit Euler method is introduced to solve the above mentioned partial differential equations to avoid the complex solving, if the partial differential solution is used to all the individual collectors.


### 2.2.1. Introduction of the Explicit Euler Method

For normal ordinary differential equation (10),
(10)y′(x)=f(x,y),y(a)=y0,(a≤x≤b),
where [a,b] as the solution interval is partitioned equally, and h=(b-a)/m as the step length. Then, the solution is marked as xn=xn-1+h, n=1,2,…,m, separately. The solution of y(x) at x=x0 solved by forward difference method is as follows:
(11)y′(x0)=y(x1)-y(x0)h.
At the same time, y(x0)=f(x0,y(x0)); then,
(12)y(x1)-y(x0)h≈f(x0,y(x0)).
The approximation of y(x1) is expressed as (13) or (14),
(13)y1-y0h=f(x0,y0),or(14)y1=y0+h·f(x0,y0),(15)y′(xn)≈y(xn+1)-y(xn)h,(16)y′(xn)=f(xn,y(xn)).Combining (15) and (16), the approximate forward Euler solving solution of y(xn+1) is as follows:
(17)yn+1=yn+h·f(xn,yn).As shown in (17), the explicit Euler method is defined, and the value of yn+1 is calculated by yn directly.


### 2.2.2. The Euler Transformation for Thermal Oil

The energy balance equation for thermal oil based on (1) and (2) can be transformed into the following:
(18)coilρoilA1∂Toil(z,t)∂t=coilρoilVoil(Toil(z,t)-Toil(z+Δz,t)Δz)+Q3(z,t).Each collector is defined as a whole, and the predigesting is as follows:(19)Toil(z,t)-Toil(z+Δz,t)Δz≈Toil(0,t)-Toil(L,t)L.Combining (19) and (18), then,
(20)coilρoilA1dToil(L,t)dt=coilρoilVoilToil(0,t)-Toil(L,t)L+Q3(z,t).Equation (20) is sorted as follows:
(21)dToil(L,t)dt=VoilToil(0,t)-Toil(L,t)L·A1+Q3(z,t)coilρoilA1.For a whole collector, the outlet temperature of thermal oil is transformed by explicit Euler method as follows:(22)Toil(L,t)=Toil(L,t)′+[VoilToil(0,t)-Toil(L,t)′L·A1+Q3(z,t)coilρoilA1]Δt.


### 2.2.3. The Euler Transformation for Absorber

The heat transfer expression for a whole collector absorber is as follows:(23)cabsρabsAabsddt(Tabs(L,t))=Q0′·WL-Q1-Q3.The transformed equation is as follows:(24)Tabs(L,t)=Tabs′(L,t)+Q0′·S/L-Q1-Q3cabsρabsAabsdt.


### 2.2.4. The Euler Transformation for the Glass Envelope

The heat transfer expression of glass envelope is as follows:(25)cgρgAgddt(Tg(L,t))=Q1-Q2.The transformed equation is as follows:(26)Tg(L,t)=Tg′(L,t)+Q1-Q2cgρgAgdt.The model and the program are established according to the aforesaid equations and solving approach. The schematic chart of the computer program is shown in Figures3 and 4.Figure 3
The schematic flow chart of the program to calculate the absorbed heat by absorber.Figure 4
The schematic flow chart of the program to simulate the thermal oil system.


## 2.2.1. Introduction of the Explicit Euler Method

For normal ordinary differential equation (10),
(10)y′(x)=f(x,y),y(a)=y0,(a≤x≤b),
where [a,b] as the solution interval is partitioned equally, and h=(b-a)/m as the step length. Then, the solution is marked as xn=xn-1+h, n=1,2,…,m, separately. The solution of y(x) at x=x0 solved by forward difference method is as follows:
(11)y′(x0)=y(x1)-y(x0)h.
At the same time, y(x0)=f(x0,y(x0)); then,
(12)y(x1)-y(x0)h≈f(x0,y(x0)).
The approximation of y(x1) is expressed as (13) or (14),
(13)y1-y0h=f(x0,y0),or(14)y1=y0+h·f(x0,y0),(15)y′(xn)≈y(xn+1)-y(xn)h,(16)y′(xn)=f(xn,y(xn)).Combining (15) and (16), the approximate forward Euler solving solution of y(xn+1) is as follows:
(17)yn+1=yn+h·f(xn,yn).As shown in (17), the explicit Euler method is defined, and the value of yn+1 is calculated by yn directly.


## 2.2.2. The Euler Transformation for Thermal Oil

The energy balance equation for thermal oil based on (1) and (2) can be transformed into the following:
(18)coilρoilA1∂Toil(z,t)∂t=coilρoilVoil(Toil(z,t)-Toil(z+Δz,t)Δz)+Q3(z,t).Each collector is defined as a whole, and the predigesting is as follows:(19)Toil(z,t)-Toil(z+Δz,t)Δz≈Toil(0,t)-Toil(L,t)L.Combining (19) and (18), then,
(20)coilρoilA1dToil(L,t)dt=coilρoilVoilToil(0,t)-Toil(L,t)L+Q3(z,t).Equation (20) is sorted as follows:
(21)dToil(L,t)dt=VoilToil(0,t)-Toil(L,t)L·A1+Q3(z,t)coilρoilA1.For a whole collector, the outlet temperature of thermal oil is transformed by explicit Euler method as follows:(22)Toil(L,t)=Toil(L,t)′+[VoilToil(0,t)-Toil(L,t)′L·A1+Q3(z,t)coilρoilA1]Δt.


## 2.2.3. The Euler Transformation for Absorber

The heat transfer expression for a whole collector absorber is as follows:(23)cabsρabsAabsddt(Tabs(L,t))=Q0′·WL-Q1-Q3.The transformed equation is as follows:(24)Tabs(L,t)=Tabs′(L,t)+Q0′·S/L-Q1-Q3cabsρabsAabsdt.


## 2.2.4. The Euler Transformation for the Glass Envelope

The heat transfer expression of glass envelope is as follows:(25)cgρgAgddt(Tg(L,t))=Q1-Q2.The transformed equation is as follows:(26)Tg(L,t)=Tg′(L,t)+Q1-Q2cgρgAgdt.The model and the program are established according to the aforesaid equations and solving approach. The schematic chart of the computer program is shown in Figures3 and 4.Figure 3
The schematic flow chart of the program to calculate the absorbed heat by absorber.Figure 4
The schematic flow chart of the program to simulate the thermal oil system.


## 3. Model Validation

The operating data from real solar power plant in SEGS-VI [1–3] is used to validate the developed model. The solar collectors are LS-2, manufactured by LUZ Company. Other parameters of the power plant are listed in Table 1. The synthesized oil, THERMINOL VP-1, supplied by SOLUTIA Company, is selected as the heat transfer fluid. The operating temperatures of the thermal oil are from 12°C to 400°C in liquid and steam operating conditions. The main physical and chemical characteristics are shown in Table 2 [4].Table 1
The system main parameters of the SEGS VI power plant [1–3].
Name
Parameters
Value
Unit
Power block
Name
SEGS VI in Kramer Junction, USA
Net capacity
30
MWe
Designed oil temperature
349
°C
Solar collector area
188000
m2
Solar collectors
Length of single collector
47.1
m
Width of single collector
5
m
Area of single collector
235
m2
Focal length of the collector
1.84
m
Focal ratio of the collector
71
—
Absorber external diameter
70
mm
Envelope external diameter
115
mmTable 2
Main physical and chemical characteristics of THERMINOL VP-1 [4].
Composition
Diphenyl oxide/diphenyl
Appearance
Clear/sediment free liquid
Maximum temperature
400°C
Kinematic viscosity (40°C)
2.48 mmm2/s
Density (15°C)
1068 kg/m3
Fire point
127°C
Autoignition temperature
621°C
Pour point
12°C
Normal boiling point (1013 mbar)
257°C
Coefficient of thermal expansion (200°C)
0.00097/°C
Average molecular weight
166In SEGS VI power plant, 50 groups of paratactic single circle parabolic trough collectors are the main heat resource. Each single circle is composed of 16 collectors connected in series. The outlet heated thermal oil enters into power block to heat water and generate steam, and then the cooled oil is back to each single circle by oil pump.It is obvious that the thermal oil temperature will change along the collectors. The physical characters will change in different temperatures, according to the data from SOLUTIA company [4]. The fitted equations between parameters and temperature are gained. The relation of density ρvp-1(kg/m3) and temperature t is as follows:
(27)ρvp-1=-0.90797·t+0.00078116·t2-2.367·10-6·t3+1083.25.The relation of heat capacitycvp-1 (kJ/kg·°C) and temperature t is as follows:
(28)cvp-1=0.002414·t+5.9591·10-6·t2-2.9879·10-8·t3+4.4172·10-11·t4+1.498.
The relation of heat conductivity λvp-1 (W/m·°C) and temperature t is as follows:
(29)λvp-1=-8.19477·10-5·t-1.92257·10-7·t2+2.5034·10-11·t3-7.2974·10-15+0.137743.
The relation of Kinematic viscosity νvp-1 (mm2/s) and temperature t is as follows:
(30)νvp-1=e(544.149/(t+114.43)-2.59578).Two typical operating data in spring (May 20th) and summer (June 11) days are selected as the base working conditions to validate the model. The simulated results will be compared with measured values in integral hours from 8:00 am to 7:00 pm. All the input parameters are set the same as the real SEGS VI power plant. The comparisons are drawn in Figures5 and 6.Figure 5
Comparison of simulated and measured results in spring working condition.Figure 6
Comparison of simulated and measured results in summer working condition.Figures5 and 6 show the comparison in spring and summer days, respectively. The solar radiation rate, oil input temperature, and flow rate are all input parameters in the model; the oil output temperature is the only output parameter. It can be seen in the two figures that the precisions are acceptable for engineering, with maximum temperature differences about 5°C. But it is negligible in steady solar radiation days for both spring and summer working conditions. The main sources of differences are caused by measuring hysteresis. For the real system, the real output oil is heated along the collectors, but the measured input solar radiation is only one point. The differences will be more obvious in multivariate solar radiation working days.


## 4. Characteristic Analysis

The working condition at 12:00 am in a summer day is selected as the base condition to analyze the relations with different alterations. The alterations include solar radiation, oil inlet temperature, oil inlet flow rate, and collector length (area). The details of the base conditions are listed in Table3.Table 3
Parameters of the base condition.
Parameters
Unit
Value
Time
H:m
12:00
Solar radiation
W/m2
925
Inlet oil temperature
°C
285
Output oil temperature
°C
360
Output oil mass flow rate
kg/s
500
Collectors total area
m2
188000 (235 × 16 × 50)
Collectors total length
m
37600 (47 × 16 × 50)


### 4.1. Solar Radiation Alteration

Solar radiation alteration simulates the possible working conditions of radiation sharp changes in cloudy days or when the parabolic trough solar collectors are barred by surrounding buildings. Then based on the base working condition in Table3, the output oil temperature will change following the changed solar radiation but maintaining other inlet parameters. Figure 7 shows the relation between output oil temperature and solar radiation alterations from the range of 805 W/m2 to 1045 W/m2. In Figure 7, every changed solar radiation 20 W/m2 will increase or reduce the output oil temperature about 2°C. Therefore, the figure can be used to analyze or forecast the operating performances in the range of solar radiation changing working conditions.Figure 7
The relation between output oil temperature and solar radiation alterations.


### 4.2. Inlet Oil Temperature Alteration

In the thermal oil heat transfer system, the heated oil will be cooled in the oil/water heat exchanger to heat water and generate steam. Then, the cooled oil will return to the entry of solar collector as a new beginning point for a circle. Therefore, the performance of cooling system will affect the output parameters of heat transfer oil directly. Figure8 shows the changes of output oil temperature with the inlet temperature from 258°C to 294°C at the interval of 3°C. Therefore, the steady heat transfer is an important operation evaluation point.Figure 8
The relation between output oil temperature and oil inlet temperature alterations.


### 4.3. Inlet Oil Flow Rate Alteration

Flow rate influences the heat transfer effect directly, and the output oil temperature will be reduced when increasing flow rate in the same solar radiation working condition. Therefore, adjusting the inlet flow rate is the main way to control and set the output parameters in operation. Figure9 shows the changed output oil temperatures when changing the inlet mass flow rate in the range of 625 kg/s–375 kg/s. It is clear that the rate speed from 350 kg/s to 500 kg/s is much faster than that in the range of 525 kg/s–625 kg/s. The maximum temperature difference between 350 kg/s and 625 kg/s is about 80°C.Figure 9
The relation between output oil temperature and inlet oil mass flow rate alterations.


### 4.4. Collectors Area (Length) Alteration

As mentioned earlier, the collectors in SEGS VI power plant consisted of 50 groups of single circles. And each single circle is composed of 16 LS-2 collectors connected in series. The alteration sources of collectors’ area and length are one or more collectors fault. Figure10 shows the relation between output oil temperature and the area of collectors. The range of area and length in Figure 10 means the removed one to nine series-wound collectors (each 47 m length and 235 m2) in a single circle. The average changed temperature with every removed collector is about 8°C. In addition, the changing speed rate from 1645 m2 to 2350 m2 is sharper than the other range. For example, the output temperature difference between 1645 m2 and 1880 m2 is 5°C, but it is 9.4°C between 3525 m2 and 3760 m2.Figure 10
The relation between output oil temperature and collector area (length) alterations.


## 4.1. Solar Radiation Alteration

Solar radiation alteration simulates the possible working conditions of radiation sharp changes in cloudy days or when the parabolic trough solar collectors are barred by surrounding buildings. Then based on the base working condition in Table3, the output oil temperature will change following the changed solar radiation but maintaining other inlet parameters. Figure 7 shows the relation between output oil temperature and solar radiation alterations from the range of 805 W/m2 to 1045 W/m2. In Figure 7, every changed solar radiation 20 W/m2 will increase or reduce the output oil temperature about 2°C. Therefore, the figure can be used to analyze or forecast the operating performances in the range of solar radiation changing working conditions.Figure 7
The relation between output oil temperature and solar radiation alterations.


## 4.2. Inlet Oil Temperature Alteration

In the thermal oil heat transfer system, the heated oil will be cooled in the oil/water heat exchanger to heat water and generate steam. Then, the cooled oil will return to the entry of solar collector as a new beginning point for a circle. Therefore, the performance of cooling system will affect the output parameters of heat transfer oil directly. Figure8 shows the changes of output oil temperature with the inlet temperature from 258°C to 294°C at the interval of 3°C. Therefore, the steady heat transfer is an important operation evaluation point.Figure 8
The relation between output oil temperature and oil inlet temperature alterations.


## 4.3. Inlet Oil Flow Rate Alteration

Flow rate influences the heat transfer effect directly, and the output oil temperature will be reduced when increasing flow rate in the same solar radiation working condition. Therefore, adjusting the inlet flow rate is the main way to control and set the output parameters in operation. Figure9 shows the changed output oil temperatures when changing the inlet mass flow rate in the range of 625 kg/s–375 kg/s. It is clear that the rate speed from 350 kg/s to 500 kg/s is much faster than that in the range of 525 kg/s–625 kg/s. The maximum temperature difference between 350 kg/s and 625 kg/s is about 80°C.Figure 9
The relation between output oil temperature and inlet oil mass flow rate alterations.


## 4.4. Collectors Area (Length) Alteration

As mentioned earlier, the collectors in SEGS VI power plant consisted of 50 groups of single circles. And each single circle is composed of 16 LS-2 collectors connected in series. The alteration sources of collectors’ area and length are one or more collectors fault. Figure10 shows the relation between output oil temperature and the area of collectors. The range of area and length in Figure 10 means the removed one to nine series-wound collectors (each 47 m length and 235 m2) in a single circle. The average changed temperature with every removed collector is about 8°C. In addition, the changing speed rate from 1645 m2 to 2350 m2 is sharper than the other range. For example, the output temperature difference between 1645 m2 and 1880 m2 is 5°C, but it is 9.4°C between 3525 m2 and 3760 m2.Figure 10
The relation between output oil temperature and collector area (length) alterations.


## 5. Conclusions

In the paper, the thermal oil heat transfer process of the solar parabolic trough collector from input solar radiation to heated oil output is analyzed. The process is sorted into the three following separate sections: glass envelop heat transfer with solar radiation, absorber heat transfer with solar radiation, and absorber heat transfer with thermal oil. Then the partial differential equations are simplified by, Euler method to develop the dynamic model. The model has been validated by real operating data in typical spring and summer days. In the end, the alteration characteristics of different solar radiation, inlet water temperature and flow rate, and collectors’ area and length are analyzed and compared with the selected normal working condition. The results can be used to research and forecast the performance of solar collectors in special working conditions.



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