3 Receiver model applications
3.2 Central receiver system model
3.2.6 Results
The system is simulated at the equinox (θaz= °0 ,θel=66.2°) under 1,000 W.m -2
of DNI. First the concentrated flux incident on the receiver was determined using SolarPILOT and a simple aim-point strategy in which each heliostat points at the centre of the closest bank of tubes. The results, in Figure 3-30 (a) show a peak flux of 2,975 kW.m-2 and an average flux of 1,170 kW.m-2. Solar salt decomposition temperature, material corrosion and themo-
mechanical cycling limits require fluxes on solar salt receivers lower than 1.2 MW.m-2 [129]. In
order to obtain a lower receiver incident flux, a new aiming strategy, “image size priority” option in SolarPILOT, is used to produce a lower and more homogeneous flux distribution on the receiver. More information on these aiming strategies can be found in the SolarPILOT manual online [106]. Because of the high average flux obtained originally, the receiver size had to be changed to allow for more space to distribute the concentrated flux and the receiver height was changed from 6.33 m to 10 m to increase the receiver surface area. The result of this new configuration is shown in Figure 3-30 (b) and show an average flux of 764 kW.m-2 and
a peak flux of 1,180 kW.m-2. This last configuration is chosen for the rest of the case study.
Figure 3-30: Flux distributions on the receiver surface for (a) a “simple aim points” strategy and a receiver height of 6.33 m; and (b) “image size priority” aiming strategy and a receiver height of 10 m.
Chapter 3: Receiver model applications 108 Table 3-7: ASTRI heliostat field efficiencies for both the simple aim points and image size priority aiming strategies
at equinox noon. cos η 80.3% atm η 95.7% shad η 100% ref η 90% bloc η 99.2%
con atm bloc ref
η =η η η 85.4% con,tot atm bloc ref cos shad
η =η η η η η 68.6%
The receiver operation details are presented for the single flow path configuration first and the dual flow-path after that.
3.2.6.1 Single pass counter-clockwise flow-path.
The net heat flux and absorber temperature distributions in Figure 3-31 show the progressive heating of the outer wall of the tubes as the heat gets transferred to the HC flowing in the tubes. The net heat flux to the HC is higher where the flux is higher.
Figure 3-31: (a) Net heat flux and (b) temperature distribution on the reference receiver using a single counter- clockwise flow-path.
In Figure 3-32, the incident flux and net heat flux are compared along the flow path. The uneven flux distribution on each bank of tubes is clearly revealed by the wave pattern along the flow-path: the flux is much lower at the inlet and outlet of each bank. The effect of the flow-path strategy on the flux distributions is also highlighted here: the flux, more intense on
109 3.2 Central receiver system model
the South facing side of the receiver, is on average higher at the start and at the end of the flow path and lowest in the middle of the flow-path where the tubes face North. The aiming strategy used is not able to produce perfectly even flux along the tube banks and some oscillations can be seen on each of the tube bank.
Figure 3-32: Incident and net heat flux along the single flow-path of the reference receiver.
The difference between the incident flux and the net heat flux is higher at the end of the flow-path than at the start because of the higher losses presented in more detail in Figure 3-33. Reflective losses dominate at the start of the flow-path and show an evolution directly proportional to the incident flux on the receiver. Convective loss slowly increases, proportionally with the increase of the temperature of the outer wall of the receiver. Radiative loss is a function of this same temperature to the power four and is the highest heat loss mechanism at the end of the flow path.
Figure 3-33: Heat losses flux along the along the single flow-path of the reference receiver.
The integrated absolute heat loss breakdown is given in Table 3-8 and highlights the larger contribution of the reflective loss followed by the radiative emission loss and the convective loss.
Table 3-8: Integrated heat losses over the central receiver.
ref Qɺ [MW
th] Qɺconv,ext[MWth] Qɺrad[MWth]
Chapter 3: Receiver model applications 110 The evolution of the temperatures along the flow path, presented in Figure 3-34 show the progressive heating of the HC and the large temperature differences between the bulk HC, the inner wall of the tubes and the outer wall. The conduction resistance through the tube imposes a large difference of temperature across the tube wall, as a function of the net heat transfer through it. The temperature difference between the inner wall of the tube and the HC is lower at the end of the flow-path than at the start. This is mostly due to the improved convective heat transfer, as shown in Figure 3-35, due to the larger velocities and favourable change in heat transfer properties of the solar salt at higher temperatures. The heat transfer coefficient at the end of the flow-path is close to double the initial one, from 9,109 W.m-2.K-1
to 17,773 W.m-2.K-1.
Figure 3-34: Temperature distributions along the single flow-path of the reference receiver.
The flow velocity is shown in parallel with the pressure drop along the flow path in Figure 3-35. The flow accelerates due to thermal expansion and the acceleration is higher when the HC circulates in the highly irradiated region and the net heat flux gain is higher.
Figure 3-35: HC velocity and pressure drops along the single flow-path of the reference receiver.
3.2.6.2 Dual hemi-cylindrical flow-path.
The net heat flux and temperature distributions for the dual hemi-cylindrical flow-path in Figure 3-36 are symmetrical and the hottest region is at the back of the receiver where the flux is the lowest. The absorber temperature range is similar to the previous case.
111 3.2 Central receiver system model
Figure 3-36: (a) Net heat flux and (b) temperature distribution on the reference receiver using a dual hemi- cylindrical flow-path.
The evolution of the incident and net heat flux on each flow path in Figure 3-37 shows the decreasing trend in average flux as the flow path progresses towards the north side of the receiver.
Figure 3-37: Incident and neat heat flux along the flow-paths of the reference receiver using a dual hemi-cylindrical flow-path.
In Figure 3-38, the heat losses follow the same trend as presented earlier but the radiative and convective heat loss are higher than in Case A as shown in Figure 3-38.
Chapter 3: Receiver model applications 112
Figure 3-38: Heat losses flux along the flow-paths of the reference receiver using a dual hemi-cylindrical flow-path. Table 3-9: Integrated heat losses over the central receiver using a dual hemi-cylindrical flow-path.
ref Qɺ [MW
th] Qɺconv,ext[MWth] Qɺrad[MWth]
4.659 3.013 4.807
The cause of the higher radiative and convective losses is the higher wall temperatures which are mostly caused by higher resistance to the heat transfer between the HC and the inner tube wall as can be seen when comparing Figure 3-39 and Figure 3-34.
Figure 3-39: Temperature distributions along the flow-paths of the reference receiver using a dual hemi-cylindrical flow-path.
Having divided the HC flow in two distinct flow-paths, the velocity in the tubes (Figure 3-40) is accordingly reduced and causes a reduction in the internal convective heat transfer coefficient which is now 4,745 W.m-2.K-1 at the start of the flow-paths and 9,130 W.m-2.K-1 at
113 3.2 Central receiver system model
the end. The benefit of the reduction of the velocity in the pipes is a significant reduction of the pressure drop in the pipes as shown in Figure 3-40.
Figure 3-40: HC velocity and pressure drops along the flow-path of the reference receiver using a dual hemi- cylindrical flow-path.
With these results a general comparison of the two cases is carried out in the next section.
3.2.6.3 Central receiver reference model summary
A summary of the receiver efficiency is presented in Table 3-9.
Table 3-10: Summary of the efficiency metrics for the four receiver configurations evaluated. Flow-path
Single counter-clockwise Dual hemi-cylindrical
int η 93.9% abs η 96.8% hx η 95.2% 94.4% th abs hx η =η η 92.1% 91.3%
rec intercept abs hx
η =η η η 86.5% 85.7%
The change in flow path affects the thermal efficiency of the receiver. For the dual flow path, the HC circulates more slowly in the tubes, lowering the heat transfer coefficient and causing an increase in the inner and outer tube wall temperature, ultimately leading to increased thermal losses to the environment. The area averaged absorber wall temperature changes from 789 K for the single flow-path to 833 K for the dual flow-paths. The efficiency values cannot be exactly validated with literature data because the heliostat field and receiver
Chapter 3: Receiver model applications 114 dimensions being unique; however, they are in the right order of magnitude compared with systems of similar size or technology [18, 125].
These results do not consider the cost of the pressure drops in the system performance. To do so a simple approximation can be made by evaluating the work produced by the system and subtract the work necessary to compensate for the pressure drops from this value. The work available from the receiver HC outlet can be evaluated using the Carnot efficiency:
amb rec abs,net HC,out 1 T W Q T = − ɺ ɺ (3-35)
Assuming a pump efficiency of ηpump =0.8, the power consumption cause by the pressure drops is approximated by:
(
HC)
p
pump HC,out HC,in
2m p W η ρ ρ ∆ ∆ = + ɺ ɺ (3-36)
Table 3-11: Receiver efficiency comparison including the pressure drop loss. Flow-path
Single counter-clockwise Dual hemi-cylindrical rec Wɺ [MW] 79.10 78.34 p Wɺ∆ [MW] -0.253 -0.033 tot rec p Wɺ =Wɺ +Wɺ∆ [MW] 78.85 78.3 tot con Wɺ Qɺ 0.548 0.546
The single flow-path case loses most of the advantage shown against the dual flow paths case. Considering the pipe headers or degraded pumping efficiencies could quickly make the dual flow-path the best option from this very basic design perspective. In relative terms however, the work involved in compensating the pressure drops represents ~0.3% of the total work extracted by the receiver which does not look like an excessive value. Optimising the diameter of the pipes in each case could lower the pressure drops or improve the receiver efficiency; however, this goes beyond the scope of the work developed in this section which is to apply the model to reference cases and highlight design parameters impact and trade-offs.
Detailed design of an external receiver of the type simulated here would involve consideration of the thermo-mechanical limits of the materials and the HC, control and flexibility of operations, costing, etc. These criteria are not solely energy related and are