Thermal and hydraulic characteristics of a large-scaled parabolic trough solar field (PTSF) under cloud passages

Abstract

To better understand the characteristics of a large-scaled parabolic trough solar field (PTSF) under cloud passages, a novel method which combines a closed-loop thermal hydraulic model (CLTHM) and cloud vector (CV) is developed. Besides, the CLTHM is established and validated based on a pilot plant. Moreover, some key parameters which are used to characterize a typical PTSF and CV are presented for further simulation. Furthermore, two sets of results simulated by the CLTHM are compared and discussed. One set deals with cloud passages by the CV, while the other by the traditionally distributed weather stations (DWSs). Because of considering the solar irradiance distribution in a more detailed and realistically way, compared with the distributed weather station (DWS) simulation, all essential parameters, such as the total flowrate, flow distribution, outlet temperature, thermal and exergetic efficiency, and exergetic destruction tend to be more precise and smoother in the CV simulation. For example, for the runner outlet temperature, which is the most crucial parameter for a running PTSF, the maximum relative error reaches −15% in the comparison. In addition, the mechanism of thermal and hydraulic unbalance caused by cloud passages are explained based on the simulation.

Keywords

parabolic trough solar field (PTSF) / thermal hydraulic model / cloud passages / transients

Introduction

Concentrating solar power (CSP) is considered as a potential technology to solve the energy crisis and reduce greenhouse gas emissions. Of all CSP technologies, the parabolic trough collector (PTC), which concentrates solar irradiance onto a focal line to transform it to useful thermal energy by heating the heat transfer fluid (HTF), is the ripest technology due to its excellent versatility and modularity [¹].

For a parabolic trough solar thermal power plant (PTSTPP), the biggest technical challenge is a thorough understanding of the characteristics of the parabolic trough solar field (PTSF) in unsteady solar irradiance. Numerous theoretical and experimental studies were performed concerning this issue. One of the first PTSTPP simulations was conducted by Lippke [²], and a steady-state model was developed for simulating the thermal and electric output of a 30 MW PTSTPP at full or partial load. Stuetzle et al. [³] developed a detailed thermal dynamic model of a PTC and studied the automatic control of plant based on the model. Patnode [⁴] developed a detailed steady-state model of a PTSTPP and validated the model by the measured data from the SEGS VI plant. García et al. [⁵] developed a PTSF model with a thermal storage system (TES) and compared the modeled results with the measured data from Andasol II 50 MW Power Plant. The comparisons showed a qualitative agreement in clear and cloudy periods. Silva et al. [⁶] developed a tri-dimensional nonlinear dynamic thermal hydraulic model of a PTC and coupled the model to an industrial process heat plant. Maliki et al. [⁷] improved the study in Ref. [⁵] by developing a full scaled dynamic model of a PTSTPP and validated the model by the measured data from Andasol II Power Plant during strongly cloudy days. The discrepancy of the comparisons is thought to be caused by the operation strategy. Salazar et al. [⁸] developed an analytic model of a PTSTPP from the perspective of energy flow, which permits a brief evaluation of the influence of the key parameters such as the PTC optical performance and thermal properties on plant behavior. Li et al. [⁹–¹²] prompted a series of studies of the direct steam generation technology, such as a steady fully-coupled multi-level analytical methodology for studying the system thermodynamic performance, the receiver stress, and thermal load [⁹–¹¹], or a completely-coupled thermo-hydraulic model for investigating the transient characteristics of a PTC loop [¹²].

Besides promoting the understanding of the PTSTPP behavior, these studies shared a simplified assumption, i.e., regarding the PTSF as a hydraulically and thermally uniform module. Under this assumption, all of the PTC loops have the same flowrate and solar irradiance, hence, the characteristics of the PTSF can be represented by any single PTC loop. However, errors caused by this assumption will increase with the PTSF scale. From a hydraulic perspective, a large-scaled PTSF is a complicated pipe network, a balanced flow distribution depends on the pump head and distribution of the flow resistance. From a thermal perspective, both the unbalanced flow distribution and ununiform solar irradiance can lead to a significant difference between the loop outlet temperatures. Some studies were conducted for seeking breakthroughs in the above issues. Abutayeh et al. [¹³] pointed out the existence of unbalanced flow distribution and proposed a method to balance the flow distribution by adjusting the opening of loop control valves (LCVs). Moreover, they proposed two control strategies in uniform and ununiform solar irradiance distribution. Giostri [¹⁴] developed a model, which contained a thermal part and a hydraulic part, to study the PTSF behavior in different transients. He simulated a cloud passages case in this study based on the cloud parameters from Ref. [¹⁵], while the lack of pump module made the simulation dependant on the total flowrate. Santos et al. [¹⁶] studied the effect of scattering PTC performance parameters and found that large discrepancy of outlet temperature existed among the loops even in a uniform flow distribution. Noureldin et al. [¹⁷] developed a virtual solar field (VSF) based on a model similar to that in Ref. [¹⁴], and demonstrated that the distributed weather station (DWS) would cause simulation errors under cloud passages. Therefore, the model is imprecise under cloud cover. Ma et al. [¹⁸] developed and validated a thermal hydraulic dynamic model (THDM) based on a pilot plant in Beijing [¹⁹], in which the method of balancing flow distribution proposed in Ref. [¹³] was also verified.

In fact, as a frequently encountered situation for a large-scaled PTSF, cloud passages will cause both the unbalanced flow distribution and the ununiform solar irradiance when they drift over a running PTSF. However, no published literature so far has studied the behavior of the PTSF under the unbalanced flow distribution and the ununiform solar irradiance. Therefore, the thermal and hydraulic characteristics of a large-scaled PTSF under cloud passages are studied in this paper according to the following steps:

First, a detailed closed-loop thermal hydraulic model (CLTHM) of a PTSF is established and validated, which contains a thermal part, hydraulic part, and can simulate the flow distribution, pump head, outlet temperature, thermal and exergetic efficiency, and the exergetic destruction.

Second, a large-scaled PTSF with typical layout and geometry size is introduced, and the opening of LCVs for a balanced flow distribution is demonstrated. Besides, the trace of a cloud vector (CV), which has the typical size, opacity, and velocity, is simulated based on the coordinates of the PTSF.

Finally, the complete simulated results are shown for understanding the thermal and hydraulic characteristics of the PTSF under cloud passages. In addition, the advantages of cloud over the DWS are demonstrated based on the simulated results.

This study may contribute to the PTC technology from two aspects: a more precise evaluation of PTSF output, and a piece of more accurate information about the flowrate and outlet temperature for coupling the PTSF to control strategy and the TES under cloudy days.

Model description

In this paper, the CLTHM is established based on the THDM in Ref. [¹⁸], and some improvement will be detailed below.

PTC and insulted pipe

For the PTC, as shown in Fig. 1, the energy conservation equations of a control volume with a length of ∆l (m) can be given as

(1){\rho }_{\mathrm{abs}}{A}_{\mathrm{abs}}{c}_{\mathrm{abs}}{\displaystyle \frac{\partial \overline{T}{}_{\mathrm{abs}}}{\partial t}}=P_{\mathrm{use}}-L_{\mathrm{abs}}-D_{\mathrm{abs}}\mathrm{\pi }h({\overline{T}}_{\mathrm{abs}}-{\overline{T}}_{\mathrm{f}}),

\left(\mathrm{\Delta }l\right)A_{\mathrm{f}}{\overline{\rho }}_{\mathrm{f}}{\overline{c}}_{\mathrm{f}}{\displaystyle \frac{\partial {\overline{T}}_{\mathrm{f}}}{\partial t}}+c_{\mathrm{f,\hspace{0.17em}out}}{Q}_{\mathrm{f,\hspace{0.17em}ou}t}{T}_{\mathrm{f,\hspace{0.17em}out}}-c_{\mathrm{f,\hspace{0.17em}in}}{Q}_{\mathrm{f,\hspace{0.17em}in}}{T}_{\mathrm{f,\hspace{0.17em}in}}

(2)=\left(\mathrm{\Delta }l\right)D_{\mathrm{abs}}\mathrm{\pi }h({\overline{T}}_{\mathrm{abs}}-{\overline{T}}_{\mathrm{f}}).

Equations (1) and (2) are for the absorber tube (with subscript abs) and the HTF (with subscript f), respectively; the subscripts in and out mean the inlet and outlet of the control volume; r, c, A, and D represent the density (kg/m³), specific heat capacity (J/(kg·K), sectional area (m²), and diameter (m), respectively; Q, and T represent the mass flowrate (kg/s) and temperature (°C); L_abs is the heat loss of the absorber (W/m), which can be simplified into a function of temperature and ambient parameters [²⁰]; h is the heat transfer coefficient between the HTF and the inner wall of the absorber tube (W/(m²·K¹), whose detailed calculation formula can be found in Ref. [²¹]. Finally, P_use, which is the useful solar thermal power reflected on the absorber tube (W/m), can be given by

(3)\begin{array}{l}{P}_{\mathrm{use}}=W_{\mathrm{PTC}}{I}_{\mathrm{use}}{r}_{\mathrm{cl}}\gamma \tau \alpha f_{\mathrm{shd}}{f}_{\mathrm{end}},\hfill \\ I_{\mathrm{use}}=I\kappa \left(\theta \right),\hfill \end{array}

where W_PTC is the width of the PTC; r_cl, g, t, and a are the clean mirror reflectivity, intercept factor, transmittance, and the absorbance of the PTC; and f_shd and f_end are two factors caused by row shading and end loss, whose detailed calculation can be found in Ref. [¹⁸]. Because the direct normal irradiance (DNI) and the incidence angle (q) change with the time and location of the PTSF, for the convenience of simulating, I_use(W/m²), which is the product of the DNI and the incidence angle modifier (k) will be applied in this paper to make the model universal regardless of time and location.

Besides the energy analysis, the continuity equation of the PTC according to Fig. 1 can be given by Ref. [¹⁴]

(4)\left(\mathrm{\Delta }l\right)A{\displaystyle \frac{\mathrm{d}\overline{\rho }}{\mathrm{d}t}}=Q_{\mathrm{f,\hspace{0.17em}in}}-Q_{\mathrm{f,\hspace{0.17em}out}},

where the left term represents the expansion or contraction of the HTF due to the significant temperature change.

The thermal efficiency (h_th) of the PTC is equal to the ratio of the produced useful heat to the available solar energy, which can be defined as Ref. [²²] demonstrated

(5){\eta }_{\mathrm{th}}={\displaystyle \frac{c_{\mathrm{f,\hspace{0.17em}out}}{Q}_{\mathrm{f,\hspace{0.17em}out}}{T}_{\mathrm{f,\hspace{0.17em}out}}-c_{\mathrm{f,\hspace{0.17em}in}}{Q}_{\mathrm{f,\hspace{0.17em}in}}{T}_{\mathrm{f,\hspace{0.17em}in}}}{P_{\mathrm{use}}{l}_{\mathrm{PTC}}}}.

where l_PTC is the length of PTC (m).

For the insulated pipe (with subscript ins), the heat loss calculation is established under an assumption of ignoring the thermal resistance of the pipe walls and the exterior air film [²³]

(6)L_{\mathrm{ins}}=\mathrm{2}\mathrm{\pi }{\displaystyle \frac{\overline{k}{}_{\mathrm{ins,\hspace{0.17em}f}}}{\ln \left((D_{\mathrm{ins}}+\mathrm{2}{\delta }_{\mathrm{ins}})/D_{\mathrm{ins}}\right)}}({\overline{T}}_{\mathrm{f}}-T_{\mathrm{a}}),

where {\overline{k}}_{\mathrm{ins,\hspace{0.17em}f}} is the thermal conductivity of the pipe insulation evaluated at the average temperature of HTF and insulted pipe (W/(m·K), d_ins represents the insulation thickness (m), and T_a is the ambient temperature.

Matrix representation of the hydraulic model

The graph theory, which is a powerful tool in water distribution system analysis [²⁴], is used to establish the hydraulic model of the PTSF. Based on the graph theory, the pipe network of the PTSF can be decomposed into several nodes, pipe sections, and circuits. The continuity equation can be expressed as [²⁵]

(7)\mathit{M}\mathit{G}=\mathrm{0},

where M is an m× b order incidence matrix if the PTSF has m nodes and b pipe sections, and G is the mass flowrate vector.

Similarly, the energy conversion equation of the PTSF can be expressed by [¹⁸,²⁶]

(8){\mathit{M}}^{\mathrm{T}}\mathit{p}=\left(\mathit{E}\mathit{S}\right)\left|\mathit{Q}\right|\mathit{Q}+\mathit{X}{\displaystyle \frac{\mathrm{d}\mathit{Q}}{\mathrm{d}\mathit{t}}}+\mathit{Z}-\overline{\mathit{\rho }}\mathit{g}\mathit{H},

(9){\mathit{X}}^{\left(\mathit{ij}\right)}=\{\begin{array}{ll}\mathrm{0}\hfill & \mathit{i}\ne \mathit{j}\hfill \\ {\displaystyle \frac{{\mathit{l}}^{\left(\mathit{j}\right)}}{\mathit{g}{\mathit{A}}^{\left(\mathit{j}\right)}{\overline{\mathit{\rho }}}^{\left(\mathit{j}\right)}}}\hfill & \mathit{i}=\mathit{j}\hfill \end{array}\mathrm{,}

where the superscripts i and j mean the row-coordinate and column-coordinate of a matrix, p is the node pressure vector, Z is the potential difference vector of the pipe section; X represents the pressure increasing vector provided by the pump, which can be calculated through the pumping head vector (H); g is the gravitational acceleration; and ES is a diagonal matrix, of which the elements of the principal diagonal is the pipe flow resistance. Detailed calculation of H and ES are shown as follows.

It is hard to give a specific expression of H because of the various layout and scale of the PTSF, in this paper. Therefore a universal method demonstrated in Ref. [²⁷] is used to derive the expressions of H.

When the pump is operated at nominal speed, the pumping head can be expressed as a function of the total mass flowrate (Q_tot)

(10)H_{\mathrm{nom}}\left(Q_{\mathrm{\hspace{0.17em}}\mathrm{tot}}\right)=a_{\mathrm{0}}+a_{\mathrm{1}}{Q}_{\mathrm{tot}}^{\mathrm{3}},

(11)a_{\mathrm{0}}=H_{\mathrm{nom，}\mathrm{0}},

(12)a_{\mathrm{1}}=\left(\mathrm{\Delta }{p}_{\mathrm{sys,}\mathrm{\hspace{0.17em}}\mathrm{des}}/\left({\overline{\rho }}_{\mathrm{f,pump}}g\right)-H_{\mathrm{nom,}\mathrm{\hspace{0.17em}}\mathrm{0}}\right)/Q_{\mathrm{tot,}\mathrm{\hspace{0.17em}}\mathrm{des}}^{\mathrm{3}},

where H_nom,0 is the pumping head at zero flowrate and nominal speed (m), a₀ and a₁ are two coefficients, {\overline{\rho }}_{\mathrm{f,pump}} is the average density of the HTF in pump pipe, and ∆p_sys,des and Q_tot,des represent the system pressure drop (Pa) and total mass flowrate at design condition, respectively.

The second term on the right-hand side of Eqs. (8) and (9) represents the hydraulic inertia caused by the change of valve opening and pump frequency, l and A are the pipe length and sectional area vector, and \overline{\mathit{\rho }} is the density vector.

Elements of ES can be expressed as

(13)\mathit{E}\mathit{S}=\mathrm{diag}(S_{\mathrm{1}},S_{\mathrm{2}}\mathrm{...}{S}_b),

where the subscripts 1 to b represent the number of pipe sections.

In one pipe section, as shown in Eq. (13), the total flow resistance is caused by three factors: the inner pipe wall (S_p), the pipe fitting (S_fit), and the valve (S_va).

(14)S_i=S_{\mathrm{p},\mathrm{\hspace{0.17em}}i}+{\displaystyle \sum _{j=\mathrm{1}}^{N_{\mathrm{fit}}}{S}_{\mathrm{fit},\mathrm{\hspace{0.17em}}i,\mathrm{\hspace{0.17em}}j}+S_{\mathrm{va},\mathrm{\hspace{0.17em}}i}},

where S_p and S_fit can be given by the Darcy-Weisbach equation in Ref. [²⁸], S_va has different expressions according to the flow characteristics of the valves, in this paper; both the LCV and the header control valve (HCV) are selected to have the equal-percentage flow characteristics; and S_va can be given by Ref. [²⁹].

(15)S_{\mathrm{va}}={\left({\displaystyle \frac{\mathrm{3600}}{f\left(\lambda \right)F_{\max }}}\right)}^{\mathrm{2}}{\displaystyle \frac{\mathrm{100}}{{\rho }_{\mathrm{f}}}},

(16)f\left(\lambda \right)=R^{(\lambda -\mathrm{1})},

where l is the valve opening, R is the valve range ability, and F_max represents the maximum flow coefficient.

Compared with the THDM in Ref. [¹⁸], the CLTHM adds the expansion or contraction of the HTF in the thermal part (Eq. (4)), and adds the hydraulic inertia item (Eqs. (8) and (9)) and pump module (Eq. (10)) in the hydraulic part. These improvements associate the pump head and capacity to the flow resistance of the PTSF, and makes the simulation and validation get rid of dependence on the total flowrate. However, the methods of decoupling the thermal part and hydraulic part demonstrated in Ref. [¹⁸] will equally be applied to the CLTHM to calculate the flow distribution and outlet temperature.

Exergetic model

Similar to the thermal efficiency, the exergetic efficiency (h_ex) of the PTC can be defined as the ratio of the exergy output to the exergy input, which can be expressed as Ref. [²²]

(17){\eta }_{\mathrm{ex}}={\displaystyle \frac{E_{\mathrm{u}}}{E_{\mathrm{s}}}},

where E is the exergy (kJ), the subscript u means the useful exergetic output of the HTF, while the subscript s means exergy flow of the undiluted solar irradiance.

E_u can be expressed as Ref. [³⁰] demonstrated.

E_{\mathrm{u}}=c_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{out}}{Q}_{\mathrm{\hspace{0.17em}}\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{out}}{T}_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{out}}-c_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{in}}{Q}_{\mathrm{\hspace{0.17em}}\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{in}}{T}_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{in}}

(18)-{\overline{Q}}_{\mathrm{\hspace{0.17em}}\mathrm{f}}{\overline{c}}_{\mathrm{f}}{T}_{\mathrm{a}}\ln \left({\displaystyle \frac{K_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{out}}}{K_{\mathrm{f,}\mathrm{\hspace{0.17em}}\mathrm{in}}}}\right)-{\overline{Q}}_{\mathrm{\hspace{0.17em}}\mathrm{f}}{T}_{\mathrm{a}}{\displaystyle \frac{\mathrm{\Delta }{P}_{\mathrm{PTC}}}{{\overline{\rho }}_{\mathrm{f}}{\overline{T}}_{\mathrm{f}}}},

where K means the Kelvin temperature (K).

E_s can be represented by Ref. [³¹].

(19)E_{\mathrm{s}}=P_{\mathrm{use}}{l}_{\mathrm{PTC}}\left[\mathrm{1}-{\displaystyle \frac{\mathrm{4}}{\mathrm{3}}}\left({\displaystyle \frac{K_{\mathrm{a}}}{K_{\mathrm{s}}}}\right)+{\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}{\left({\displaystyle \frac{K_{\mathrm{a}}}{K_{\mathrm{s}}}}\right)}^{\mathrm{4}}\right],

where K_s is the temperature of outer sun layers, which is estimated to be 5770 K.

Besides the efficiency, an integrated exergetic model also includes the analysis of the exergetic optical loss, exergetic thermal loss, and exergetic destruction. A detailed information about the exergetic loss and exergetic destruction caused by heat transfer is demonstrated in Ref. [²²]. In the present paper, a special exergetic destruction, which is caused by the mixing flows with different outlet temperature and usually happens under the cloud passages, is introduced as follow.

Figure 2 shows a typical mixing flows which exists in a subfield of the PTSF. Based on the second law of thermodynamics, the entropy balance equation can be given by Ref. [³⁰]

(20)S_{\mathrm{pro}}^i=Q_{\mathrm{\hspace{0.17em}}\mathrm{hh}}^i{s}_{\mathrm{in,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^i-Q_{\mathrm{hh}}^{i-\mathrm{1}}{s}_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^{i-\mathrm{1}}-Q_{\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{a}}{s}_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{a}}-Q_{\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{b}}{s}_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{b}},

where S_pro is the entropy production (kJ/K), s is the specific entropy (kJ/(kg·K), the subscript hh represents the hot header, the superscript i means the ith loop, while a and b represent two sides of the hot header.

The exergetic destruction of the mixing flow can be expressed as

E_{\mathrm{d}}^i=T_{\mathrm{a}}{Q}_{\mathrm{\hspace{0.17em}}\mathrm{hh}}^i(c\ln \left({\displaystyle \frac{K_{\mathrm{in,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^i}{K_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^{i-\mathrm{1}}}}\right)+x^{\mathrm{a}}c\ln \left({\displaystyle \frac{K_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^{i-\mathrm{1}}}{K_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{a}}}}\right)

(21)+x^{\mathrm{b}}c\ln \left({\displaystyle \frac{K_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{hh}}^{i-\mathrm{1}}}{K_{\mathrm{out,}\mathrm{\hspace{0.17em}}\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{b}}}}\right)),

(22)x^{\mathrm{a}}={\displaystyle \frac{Q_{\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{a}}}{Q_{\mathrm{hh}}^i}},

(23)x^{\mathrm{b}}={\displaystyle \frac{Q_{\mathrm{loop}}^{i,\mathrm{\hspace{0.17em}}\mathrm{b}}}{Q_{\mathrm{hh}}^i}},

where x is the mass fraction.

Besides the subfield, the mixing flows also exist in the hot runner, and the exergetic production can be calculated by using the method similar to Eqs. (20) and (21).

Model validation

The reliability and accuracy of the CLTHM should be validated before further analysis. Experimental data, which is obtained from a 1 MW pilot plant located in Beijing, is used for the validation. The flow diagram of the PTSF in the 1 MW pilot plant is depicted in Fig. 3. More detailed information of the PTSF can be found in Ref. [¹⁸]. Besides, the information of the main measurements is listed in Table 1.

The total flowrate, flowrate distribution, and outlet temperature are the three main simulated parameters for the CLTHM. The validation is performed by comparing the simulated results of these parameters with the experimental data.

The experiment was conducted from 11:00 to 14:30 on September 11, 2017. As demonstrated in Fig. 4(a), both the DNI and ambient temperature are high enough for heating the HTF to a high temperature in the experiment. Figure 4(b) shows that the positions of LCV in Loops 1 and 3 are fully or partially open, while the LCV in Loop 2 is closed in the experiment. Besides, the solar collector assemblies (SCAs) in Loops 1 and 3 are totally concentrated, which have caused the increase in header inlet temperature. Finally, the pump is operated at full load in the experiment.

Figure 5(a) shows a good agreement between the comparison of measured and simulated header inlet flowrate with a small root mean square errors (RMSEs). The periodic change of header flowrate is caused by the change in the position of the LCVs. The simulation errors are caused by the uncertainty of valve actuator and misestimate of the flow resistance, such as the pipe size and the number of pipe fittings.

The comparison between the measured and simulated flow distribution is shown in the lower part of Figs. 5(b) and 5(c). The good agreement owes to the effectiveness of the hydraulic part of the CLTHM, and the simulation errors are caused by the same reasons as the comparison of header inlet flowrate. The comparisons between the measured and simulated loops outlet temperature are shown in the upper part of Figs. 5(b) and 5(c).The good agreement owes to two reasons: the accuracy of the hydraulic part of the CLTHM for calculating the flowrate in each loop and the efficiency of the thermal part for calculating the outlet temperature based on the calculating flowrate. The simulation errors of loops outlet temperature are mainly caused by the accumulative errors from the simulated flow distribution.

The CLTHM is established and validated in this section. It is worth mentioning that the validation is performed based on the PTSF of a 1 MW pilot plant, which is smaller than a commercial plant, but the essential elements such as flow distribution, energy conversation are presented in the pilot plant. Therefore, the availability can be extended to the large-scaled PTSF in the upcoming section.

Description of large-scaled PTSF and CV

PTSF

In a commercial PTSTPP, an “H” layout of the PTSF will be applied when the area of the collector is greater than 40000 m² [³²]. A typical “H” layout of the PTSF is displayed in Fig. 6. The cold HTF flows into the four subfields after twice dividing by the primary and secondary cold runner. In each subfield, the cold HTF is distributed to 2 × n symmetric PTC loops (the west subsection and the east subsection) by the cold header and heated to a high temperature. Then the hot HTF is collected by the hot header and flows into the steam generator in the power block after twice convergence with the primary and second hot runner. The cooled HTF which flows out from the power block is pumped to the PTSF and a cycle of the HTF flowing is finished.

The most common commercial PTC equipment is applied in this study. An individual loop consists of 4 EUROTROUGH-150 SCAs, of which the key parameters can be found in Ref. [³³]. The SCHOTT PTR70 is selected to be the absorber tube, of which the key parameters and the fitting polynomial of heat loss are listed in Ref. [²⁰]. Therminol VP-1, which is a frequently-used synthetic oil is selected to be the HTF, whose physical properties are thoroughly tested and fitted to be the polynomials in temperature [¹⁴].

After the PTC and HTF are determined, a significant parameter, i.e., the design mass flowrate in a single PTC loop must be calculated through the steady form of Eqs. (1) and (2). Besides the design mass flowrate, the number of loops in a subfield must be determined before verifying the pipe size of the whole PTSF. In this paper, this value is assumed to be 38 (n = 19 in Fig. 6), and the nominal net power of the PTSTPP is 80 MW when a subfield has 38 loops [³²].

According to the above parameters, the diameters of the runners and headers can be identified when 3 m/s is chosen to be the best velocity [³²].

The above main parameters of the PTSF are listed in Table 2. The range ability and maximum flow coefficient of the valves are determined by the data from the valve manufacturer based on the design pipe size and flowrate. The other parameters, such as the pipe length, number and pressure drop coefficient of the pipe fittings (such as the elbow and ball joint) can be found in Ref. [³²].

Balanced flow distribution

Under desired uniform solar irradiance, all loops in the PTSF receive the same solar thermal power. This requires a balanced distribution of the total flowrate which can make every loop has the same flowrate and outlet temperature. A method of balancing the flow distribution by changing the opening of LCVs is demonstrated in Ref. [¹³] and validated in Ref. [¹⁸], hence, the opening of the LCVs must be determined first.

Based on the mentioned method, the opening of LCVs for a balanced flow can be solved. Figure 7 shows the opening of LCVs in half subsection of the subfield (the PTSF can be divided into 8 half subsections for the 4 subfields as shown in Fig. 6). The LCVs which is closer to the power block are set to have less opening to compensate the header pressure loss. Because of the symmetry of the PTSF, the opening of LCVs in the other 7 half subsections must be set to equal values as shown in Fig. 7 for the balanced flow distribution.

CV

A cloud can be characterized by the velocity, movement direction, opacity, frequency, and the shape [¹⁵] which will influence the response of the PTSTPP when the cloud drifts over the PTSF. The comprehensive data of the cloud is hard to be obtained and implemented to the CLTHM. Therefore, as shown in Fig. 8, the statistical analysis from Ref. [¹⁵] is applied for defining the size and velocity of cloud at the maximum probability (2 km and 4 m/s). Reference [³⁴] divides the cloud into several levels according to different opacities. In this paper, an extreme case, i.e., the opacity equals to 1 is considered to characterize the cloud. The DNI will mutate to zero at this opacity when the cloud drifts over.

As shown in Fig. 9, the cartesian coordinate system is used to model the movement locus of the CV, because of the arbitrariness of the cloud movement. The initial and end coordinates of the center of cloud and the movement direction of the cloud are defined as (−2829, −2829), (1829, 1829), and 45°N-E, respectively. This locus guarantees that the PTSF can be uncovered, partially covered, and totally covered with cloud passages. Besides the CV, the distributed weather stations (DWSs), which are the most popular devices for obtaining information about the solar irradiance distribution in the PTSF, are exhibited in Fig. 9. Once the cloud drifts over one DWS, the DNI to all loops in the subfield where the DWS located is considered to be zero [¹⁷]. Obviously, compared with the DWS, the CV can reveal the solar irradiance in a more detailed and realistically way.

Results and discussion

Based on the CLTHM, the PTSF and CV whose parameters are known, the detailed thermal and hydraulic characteristics of the PTSF under cloud passages can be simulated. In this section, the results are divided into three sections for presenting: the loop parameters, the header and runner parameters, and the efficiency. Moreover, to show the novelty of this paper more directly, the results are compared with the data which is simulated when the DNI distribution is obtained from the DWSs. Because the loop and header parameters have almost the same trend in the DWS simulation, the comparisons are conducted from the second section.

Loop parameters

Figure 10 shows the outlet temperature of all loops in the four subfields. In each figure, the top part represents the west subsection while the bottom part represents the east one. Because of the different location of the subfields, the outlet temperature of loops has the discrepant trend. For the subfield SW and NE, the irregular cooling and heating trends of the outlet temperature mean that the cloud drifts in and out these two subfields in partial covering. For the subfield NW, the cooling trend of the outlet temperature means that the cloud drifts over the subfield one loop by one loop from south to north, and the heating trend indicates that the width of the cloud edge sweeps all of the loops from west to east when the cloud leaves the subfield. For the subfield SE, the cooling and heating trends, which are contrary to subfield NW, indicate that the cloud drifts oppositely over the subfield.

Header and runner parameters

Based on the results in Section 4.1, the trends of loops outlet temperature have considerable differences among the four subfields, which will cause the change in the flowrate in runners, flowrate distribution in headers, and pump head due to the varying of physical properties of the HTF.

The physical properties of Therminol VP-1 determine a kind of rule when the PTSF applies this liquid as the HTF: at the same inlet temperature, the pipe where the cold HTF flows through has less pressure loss than the pipe where the HTF is heated up to a high temperature. The reason for this is that even the viscosity of the HTF decreases with increasing temperature, and the decreasing density leads to a higher velocity under the governance of continuity equation (Eq. (4)). According to Eqs. (8) and (9), compared with the flow resistance which is mainly determined by the viscosity, the pressure loss is more susceptible to the flowrate because the pressure loss is the quadratic function of flowrate.

The above rule can clearly explain the trends of parameters shown in Fig. 11. At the beginning of cloud passages, only the subfield SW is covered. Therefore, the header flowrate in this subfield increases first. In the middle of cloud passages, the four subfields are covered. Therefore, the header flowrate in these subfields vary to be almost the same value. At the end of cloud passages, only the subfield NE is covered. Therefore, the header flowrate in this subfield is always bigger than the other three subfields until the cloud drifts out. The above phenomenon demonstrates the relative change of header flowrate among the four subfields. The absolute change of flowrate can be explained as follows. The viscosity and density have the opposite effects on the flow resistance, as shown in Fig. 12(a). When the effect of density exceeds the viscosity (before 900 s), the total flowrate continues increasing with the decreasing pump head. Hence, when the effect of viscosity exceeds the density (after 900 s), the total flowrate and pump head have the opposite trends. Another remarkable phenomenon, which is shown in Figs. 11(b) and 12(a), is the drastic fluctuation of flowrate and pump head in the DWS simulation. The reason for this is that when the cloud covers one DWS, all loops in the subfield where the DWS locates are cooled down simultaneously, which have a significant impact on the flow resistance and pump head.

Figure 12(b) is a comparison of the most critical parameter, i.e., the runner outlet temperature. Because of the lack of detailed information about the DNI distribution in the PTSF, compared with the CV simulation, the DWS simulation is unable to calculate the runner outlet temperature accurately with a maximum relative error of −15%.

Efficiency

In Section 4.1, the difference of runner outlet temperature and flowrate between the CV and DWS simulations are presented. The discrepancy of these two parameters will be further reflected in the comparisons of the simulated efficiency. As shown in Figs. 13(a) and 13(b), the thermal and exergetic efficiency are similar to the runner outlet temperature, and the fluctuation of flowrate causes the small fluctuations in DWS simulation. Figure 13(c) shows the simulated total exergetic destruction in the cloud passages. In the DWS simulation, the exergetic destruction caused by mixing flows shows a sudden increase at about 650 s, which is synthetically caused by two reasons. On the one hand, once the DWS in subfield SW is covered, the HTF in all loops in this subfield surrender a sudden cooling, which causes a drastic decrease in flow resistance and an uprush in flowrate. On the other hand, the cooling loops cause a huge temperature difference among subfield SW and the other three subfields, which causes a huge entropy production in the mixing of flows. The similar reason causes the fluctuation of the exergetic destruction at about 1500 s in the DWS simulation. In addition, there exists a small fluctuation in the CV simulation. The reason for this is that the more subtle difference of outlet temperature among the loops can be calculated in the CV simulation. The exergetic destruction happens not only in the mixing of headers flow but also in the mixing of loops flow. Figure 10 shows that the outlet temperature of loops in each subfield is complicated under cloud passages, which causes the persistent fluctuation of the exergetic destruction in the CV simulation. Besides the fluctuation, compared with the DWS simulation, the more elaborate calculation of loops outlet temperature in the CV simulation leads to a greater entropy production, which, then, leads to a higher exergetic destruction.

Conclusions

This paper mainly outlines the method and results of simulating the thermal and hydraulic characteristics of a large-scaled PTSF under cloud passages. The CLTHM is established and validated, which, compared with the previous models, fully considers all the major components and physical properties of the HTF and can simulate the total flowrate, flow distribution, outlet temperature, exergetic efficiency, and exergetic destruction in detail. Besides, a typical large-scaled PTSF and its key parameters are presented, including design values, layout, pipe size, and opening of the LCVs for a balanced flow distribution. Moreover, the CV, which is characterized by the size, velocity, opacity, movement direction locus, is presented for further simulation. Two main conclusions can be reached based on the simulation.

When cloud passages deal with the CV rather than the traditionally DWSs, the CLTHM can simulate the loop outlet temperature in a more detailed way and the runner outlet temperature more accurately. Besides, the flow distribution, total flowrate, pump head, thermal and exergetic efficiency, and the exergetic destruction are more realistic in the CV simulation.

Thermal and hydraulic characteristics will be changed greatly when the PTSF is covered by cloud passages, and the ununiformly distributed solar irradiance causes a huge thermal and hydraulic unbalance.

In the future, the model and results in this paper will be further coupled with the control strategy and TES for improving the study on the PTC technology.

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