Chapter III Model of the pre-existing solar thermal energy system at UKZN
3.2 Model of the pre-existing solar thermal energy system at UKZN
3.2.2 Summary of physical working principles of the thermal energy system
temperature (about 100/150ºC), otherwise the pump may be damaged.
This has the negative implication that the TES cannot be fully charged to temperatures above that mentioned above.
(c)Also the discharging outlet temperature from the utilization system should not be allowed to exceed the discharging pump’s maximum operating temperature.
(d)The receiver’s steel pipes: To insure that the melting temperature of steel (about 1370 °C) will not be attained, a stagnation (and higher) temperature should not be allowed to develop in the receiver. Such levels of temperatures can develop at the receiver if it is focused to the sun and the fluid flow is left null (pumping speed is zero).
(e)The receiver’s surface should not be allowed to exceed the maximum operating temperature of the absorbing material (about 3000C);
(f) The conducting pipes: There are flexible conducting pipes at the inlet and outlet of the receiver, made of ptfe (Teflon), with a maximum safe operating temperature of about 260ºC. So, it is important to insure that the fluid temperature is maintained below 260ºC.
Other oil conducting pipes are made of either steel or copper (about 1085°C melting point). So, if the previous and most of the other constraints are met, these steel and copper pipes are safe.
All these safety operating conditions, and others not mentioned, must be taken into consideration for a safe operation.
It is essential that the monitoring and control system be given that knowledge base and made capable of performing the required preventive actions or taking corrective actions whenever a critical condition is detected.
3.2.2 Summary of physical working principles of the thermal energy system
disturbances (like poor cleanness), etc. is the effective surface area of the collector aperture, taking into account the following subtractive factors: the gaps between the trapezoidal mirrors and collector’s aperture shading by the supporting and the receiver assemblies.
On the other hand, as mentioned earlier, equals the energy flux effectively absorbed by the receiver plus the receiver’s heat losses to the environment, as expressed by:
? ) (3.2)
, the effective energy output from the receiver, which is also the energy flux passed to the oil, can be inferred from the following law:
? }"#i (3.3)
Where is the oil’s charging circuit mass flow rate (see also eq. 3.10 below), cf(T) is the oil’s temperature dependant specific heat capacity, TRin and TRout are the oil’s inlet and outlet temperatures of the receiver, respectively. There are many factors that determine the magnitude of, namely, the characteristics of the absorbing material, the geometry and construction of the absorber (which includes insulation), atmospheric and environmental conditions (which includes outside temperature and wind), as well as radiactive losses (which increase with temperature).
The effective energy gained by the oil is further depleted by losses between the receiver’s outlet and the storage inlet:
? $ (3.4)
where is the TES inlet energy flux and are the mentioned losses between the receiver’s outlet and the storage inlet.
In turn, the heat storage has its own energy losses (), so the effective energy stored in a specific period of time, may be expressed as:
? · (3.5)
where is the TES efficiency, which can be expressed as:
?S
(3.6)
In turn, the maximum energy that can be stored in a pebble bed TES is a function of its physical and geometrical properties (height, cross section, pebbles size, pebbles heat capacity, pebbles porosity, etc).
The theoretical maximum energy QTESmax that can be absorbed by the TES by raising its temperature from an initial temperature of TTESo to a final temperature
that equals the inlet temperature TTESin, can be expressed as:
? . . "$ # (3.7)
Or:
? . . %"1 $ !#"$ # (3.8)
Where is the specific heat capacity of rock bed material, its total effective mass, its density, VTES the total TES volume and ! is the pebbles void fraction which accounts for the porosity between the pebbles.
The above energy is gained as a result of heat exchange with the oil that traverses the TES, whose energy flux is:
? "#. %."#. "$ # (3.9)
If can be neglected, that is, the efficiency approaches 100%, then, the integral of over the charging period (the time that took the TES temperature to be raised from TTESo to TTESin) equals and .
For a more detailed study of the heat storage dynamics, taking into account the above mentioned TES constructive characteristics and the heat losses, other variables and models should be considered. The Schumann as well as Mumma and Marvin models, addressed by (Duffie, et al., 2006), may be a good starting point. Worth considering for the same purpose is the recent oil-pebble TES system simulation by (Mawire, et al., 2008).
The charging pump, with a pumping constant of approximately ? 6.12ml per revolution, forces heat transfer oil to travel from the TES to the receiver and from this, back to the TES, with a mass flow rate, which can be expressed as:
? "#. %? "#. . & (3.10)
Where "# is the density of Calflo oil as function of temperature, % is the oil’s charging circuit volumetric flow rate, and &is the rotating speed of the charging pump in revolution per unit time. From the previous equation, the pump speed can be derived:
&? I
"#. (3.11)
This law can be used as set point for controlling the pump speed (for example to keep the mass flow rate constant, independently of the temperature).
In turn, the laws that govern the discharging process as compared to that of the charging are identical, although the source of heat is now the TES. Thus, for the discharging process, a relation can also be derived to control the discharging pump rotational speed as a means of controlling the mass or volumetric flow rates to fit the required values within time, according to the desired temperature profile
to be followed. This profile is defined by the specific user application (boiling water for tea, bake a bread, etc.). It is worth noting that the amount of heat stored in the TES will affect the controller’s ability to follow the required temperature profile. The higher the temperature difference (TES – user load) and the higher the stored heat, then, the higher the performance of the utilization system. That is why the system performance will be affected by fluid’s max temperature of 316ºC, as well as other constraints.
Further discussion of the system working will be done in the next sections, where the specific design of the controller system is addressed.