# Numerical Investigation of Pipelines Modeling in Small-Scale Concentrated Solar Combined Heat and Power Plants

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## Abstract

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## 1. Introduction

_{2}emissions in Europe. For this reason several EU Directives, such as the Directive 2018/2001 and the Directive 2018/2002 [2], have set the specifications for high-energy performance buildings and for the adoption of energy efficiency measures that will be transposed by 30 June 2021 by the Member States. Among the different technologies to efficiently convert and supply energy into buildings, combined heat and power (CHP) plants in combination with district heating (DH) networks have already proved their appreciable benefits as confirmed by various EU research projects since 2000 [3]. Moreover, according to Persson and Werner [4], who analyzed the average excess heat from thermal power generation and industrial processes and the related recovery rate in the EU27 Member States, a higher exploitation of district heating distribution systems could give a key contribution to the fulfillment of European Union energy and climate goals.

^{2}parabolic-trough-collectors solar field obtaining a gross electrical efficiency of the ORC unit up to 8%. Manfrida et al. [13], instead, numerically assessed the performance of parabolic-trough-collectors solar field coupled with an ORC unit and a phase-change-material thermal energy storage (TES) system, finding a weekly average overall efficiency of 3.9% (solar-to-electricity). In previous works [14,15] some of the authors of the present paper have investigated the performance of a microsolar organic Rankine cycle plant based on linear Fresnel reflectors (LFR) solar field and designed for residential applications. Among the obtained results, they found a significant amount of thermal loss in the pipelines connecting the different subsystems. More precisely, the thermal inertia of the pipelines, the multiple-supply temperature levels of the transfer medium and the variability of the local renewable energy source entailed significant fluctuations of the plant operation also, according to [16]. Indeed, any shutdown and restart of the system as well as variations in the oil flow rate affect the ability of the solar field to generate thermal power or that of the TES to rise in temperature because of the thermal gradient along the pipe itself.

## 2. Methods and Models

#### 2.1. Two-Dimensional Tube Model

#### 2.2. One-Dimensional Longitudinal Model

#### 2.3. One-Dimensional Radial Model

#### 2.4. Lumped Model

_{in}is given at time t = 0:

## 3. Results

^{2}linear Fresnel reflectors (LFR) solar field, (ii) a 3.8 ton latent heat thermal energy storage system equipped with reversible heat pipes, and (iii) an organic Rankine cycle unit designed for a power production of 2 kWe/18 kWth, as extensively discussed in [19]. For the purpose of this analysis, the characteristics of the tubes (length, internal diameter and insulating material) are the same as in the Innova Microsolar, thus making possible in the future the comparison of the numerical simulations with the experimental data once the plant is in full operation.

^{7}kJ compared to 1.93 × 10

^{7}kJ of the Simulink 1N). This is mostly due to the lower running time of the plant (9.42% lower). On the other hand, the ORC unit works most of the time at operating conditions having higher electrical efficiencies and as a result the mean electric efficiency is 3% higher (6.65% compared to 6.44% of the Simulink 1N). The CPU time in Table 3 is measured on a workstation equipped with 32 GB of RAM and the Intel Xeon E5530 @ 2.4 Ghz processor whilst the code is able to use a single thread only.

## 4. Discussion

^{2}∙K, while in the Simulink models it depends also on the wind velocity (Equations (9) and (13)); second, the thermal conduction of the insulating material is fixed in the middle of the operating conditions, equal to 0.07 W/m∙K (see Table 2), whilst in the 1D longitudinal model it depends on the mean temperature between the HTF and the external ambient for each thermal node, thus reflecting the real operating conditions of the tubes.

## 5. Conclusions

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- the 1D radial model entails significant deviations on the predicted output temperature for HTF velocities in the range 0.1–1 m/s when rr > 3;
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- the 1D longitudinal model is in good agreement with the results of the 2D model at any rr for HTF velocities higher than 0.1 m/s;
- ■
- the lumped model agrees with the results of the 2D model at HTF velocities >1 m/s.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | internal cross section area of the tube (m^{2}) |

c | specific heat at constant pressure (J/kg·K) |

CHP | combined heat and power |

D | diameter (m) |

DH | district heating |

DNI | direct normal irradiance (W/m^{2}) |

EE | electrical energy |

fr_{D} | Darcy friction coefficient |

g | gravity (m^{2}/s) |

h | convective coefficient (W/m^{2}·K) |

k | thermal conductivity (W/m·K) |

L | length of the tube (m) |

LFR | linear Fresnel reflectors |

ORC | organic Rankine cycle |

p | pressure (Pa) |

Pr | Prandtl number |

R | thermal resistance (K·m/W) |

r | radius (m) |

rr | angular coefficient of the temperature increase/decrease (K/s) |

Ra | Rayleigh number |

Re | Reynolds number |

S | internal “wetted” area of the tube (m^{2}) |

T | temperature (K) |

TE | thermal energy |

TES | thermal energy storage |

t | time (s) |

u | velocity of the heat transfer fluid (m/s) |

x | longitudinal axis |

$\dot{\mathrm{Q}}$ | heat transfer rate (W/m) |

Subscripts and superscripts | |

1 | internal part of the tube |

2 | external part of the tube |

2-amb | mean properties between the external part of the tube and the external ambient |

amb | external ambient |

conv,int | internal convective |

conv,ext | external convective |

cond | conductive |

del | delay |

ext | external |

HTF | heat transfer fluid |

i | i-th cross section along x direction |

in | inlet |

int | internal |

ins | insulating material |

j | j-th along the radial direction |

k | k-th time step |

loss | losses |

Nu | Nusselt number |

oil | diathermic oil |

out | outlet |

R | radius |

sc | Simscape |

Steel | stainless steel metal |

th | thermal |

w | wall |

Greek symbols | |

∆x | finite space difference along the longitudinal direction x (m) |

∆r | finite space difference along the radial direction (m) |

∆t | finite time difference (s) |

α | thermal diffusivity (m^{2}/s) |

β | thermal expansion coefficient (1/K) |

ν | kinematic viscosity (m^{2}/s) |

η | efficiency |

ρ | density (kg/m^{3}) |

## References

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**Figure 1.**Fluid regime at organic Rankine cycle (ORC) outlet (

**a**) and at linear Fresnel reflectors (LFR) outlet (

**b**), in percent of total time for an annual simulation. HTF is heat transfer fluid.

**Figure 3.**(

**a**) Relative error in the one-dimensional (1D) longitudinal model; (

**b**) Relative error in the 1D radial model; (

**c**) Relative error in the zero-dimensional (0D) model.

**Figure 5.**(

**a**) Simscape/Simulink 1N monthly averaged energy variations; (

**b**) Simulink 1N/20N monthly averaged energy variations.

**Figure 8.**Temperature and flow rate at the outlet of the LFR and ORC. DNI is direct normal irradiance.

Re_{2} | C | m |
---|---|---|

1–40 | 0.75 | 0.4 |

40–10^{3} | 0.51 | 0.5 |

10^{3}–2 × 10^{5} | 0.26 | 0.6 |

2 × 10^{5}–10^{6} | 0.076 | 0.7 |

Temperature (°C) | Thermal Conductivity (W/m∙K) |
---|---|

50 | 0.042 |

100 | 0.049 |

150 | 0.059 |

200 | 0.071 |

250 | 0.086 |

300 | 0.105 |

Parameter | Simscape | Simulink 1N | Simulink 20N |
---|---|---|---|

TE,out LFR (kJ) | 3.86 × 10^{8} | 3.87 × 10^{8} | 3.87 × 10^{8} |

TE,loss LFR (kJ) | 7.96 × 10^{7} | 7.71 × 10^{7} | 7.73 × 10^{7} |

TE,in TES (kJ) | 9.61 × 10^{7} | 1.00 × 10^{8} | 1.01 × 10^{8} |

TE,in ORC (kJ) | 2.99 × 10^{8} | 2.99 × 10^{8} | 2.98 × 10^{8} |

TE tube loss (kJ) | 6.58 × 10^{7} | 6.06 × 10^{7} | 6.11 × 10^{7} |

EE,out ORC (kJ) | 1.78 × 10^{7} | 1.90 × 10^{7} | 1.93 × 10^{7} |

Eff ORC (%) | 6.65 | 6.44 | 6.58 |

Time on (s) | 1.09 × 10^{7} | 1.19 × 10^{7} | 1.19 × 10^{7} |

CPU time (s) | 2.30 × 10^{4} | 3.01 × 10^{4} | 7.95 × 10^{4} |

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**MDPI and ACS Style**

Tascioni, R.; Cioccolanti, L.; Del Zotto, L.; Habib, E.
Numerical Investigation of Pipelines Modeling in Small-Scale Concentrated Solar Combined Heat and Power Plants. *Energies* **2020**, *13*, 429.
https://doi.org/10.3390/en13020429

**AMA Style**

Tascioni R, Cioccolanti L, Del Zotto L, Habib E.
Numerical Investigation of Pipelines Modeling in Small-Scale Concentrated Solar Combined Heat and Power Plants. *Energies*. 2020; 13(2):429.
https://doi.org/10.3390/en13020429

**Chicago/Turabian Style**

Tascioni, Roberto, Luca Cioccolanti, Luca Del Zotto, and Emanuele Habib.
2020. "Numerical Investigation of Pipelines Modeling in Small-Scale Concentrated Solar Combined Heat and Power Plants" *Energies* 13, no. 2: 429.
https://doi.org/10.3390/en13020429