The basic process

The basic parabolic trough STEGE process has a large area of parabolic reflectors that concentrate insolation to absorber pipes through which

a heat transfer fluid (typically) flows to receive the energy. The pipes have a selective surface and are surrounded by a clear glass concentric tube to minimize heat transfer to the surroundings, similar to the cover used in a flat plate solar energy collector.

The heat transfer fluid can be a synthetic oil, like Therminol VP-1, whose properties are given in Appendix B, that can withstand the high temperatures required to establish an efficient process. Yet, the devel­opment of new heat transfer fluids is an active area of research and in some cases molten salts are being considered. The preferred properties of these materials mean that they have a vastly reduced vapor pressure as a result of a high boiling temperature that does not limit the process. If water were used, high pressure steam would be directly generated in the absorber pipes placing some engineering constraints on the system.

A schematic of the process is shown in Fig. 9.6, demonstrating the two separate parts: the solar field which recirculates the heat transfer fluid and the Rankine cycle which has water as the working fluid to generate electricity. The solar field has Ns parabolic reflector units in series, called a loop as will be evident below, and there are Np of these series systems in parallel for a total of Nu = Ns x Np units.

The units placed in series will be used to heat the fluid up to its maximum temperature (i. e. from Tcold to Thot) while the units in parallel are required to increase the overall heat content that can be supplied to the Rankine cycle. The total rate of heat transfer is Qhe, which occurs within the heat exchanger, and is required to heat the water in the Rankine cycle. Of course, Qhe = Qb for the Rankine cycle, discussed above. The schematic has the two streams operating counter-currently in the heat exchanger, meaning that they travel in opposite directions. This mode of operation is fairly efficient in promoting heat transfer since the overall thermal driving force, the temperature difference between the two fluids, remains larger than for co-current operation. Co-current operation is used in cases where it is desired to reduce the average hot fluid temperature. This is useful if this fluid is temperature sensitive, however, a larger heat transfer area is required that will increase the cost. Suffice to say that the heat exchanger will be taken as a known quantity here and that it operates at 100% efficiency, allowing all the energy garnered within the solar field to be transferred to the water in the Rankine cycle.

The design of this plant begins with knowledge on the amount of electricity that one wants to generate Wnet which will be 30 MW for the example given in this section, a value for some operational units and enough power for a small town or village. Then other details of the cycle are assumed, as discussed below in Example 9.2, to ultimately produce

Qhe = Qb.

Modeling of the solar field is similar to that for the flat plate solar energy collector. The operating line comes from the FLOT while the design line is determined through detailed heat transfer calculations for the fluid flowing in the pipes. Of course, the operating point is at the intersection of the two lines. There is a difference between the design

discussed here to generate electricity and the flat plate water heater. In the previous chapter we typically had two or three units that were used to heat water, so, the area was previously assumed and all that was to be determined was the water temperature rise and ultimately how long it would take to heat up the hot water reservoir. Here the rate of heat generation is predetermined (Qhe = Qь), placing emphasis on making sure there is enough energy supplied to the Rankine cycle. This changes the design procedure somewhat as will become clear below. First consider the operating line and we write the FLOT for one parabolic collector unit as

mо [Hout – Hin] = [Cr |ат\PD (0) – qrrut] A operating line (9.7)

where m0 is the mass flow rate of heat transfer fluid through the pipe in the parabolic collector unit, Hin and Hout, the enthalpy in and out of the unit, respectively, Cr, the concentration ratio of insolation, |ат|, the calculated absorbance-transmittance product, PD(0), the insolation falling on the aperture whose plane is assumed to be normal to the direct beam, qout, heat loss out of the unit and A, the area of the absorber pipe. The area A is equal to nDL, where D is the absorber pipe outside diameter and L its length (see Figures 9.5 and 9.7). The definition of the parabolic unit should be made clear. Within the STEGE literature there are two terms/acronyms typically used: Solar Collector Assembly (SCA) and Heat Collection Element (HCE). The SCA is the parabolic mirror mounted on a frame, together with con­trollers to rotate the parabolic trough through the day. The HCE is the absorber pipe mounted at the focal line of the parabolic reflector. The SCA can be up to 100 m long, have apertures (W) of almost 6 m and are huge structures. On the other hand, the HCE is of order 4 m long with an absorber pipe, which has a selective surface, with a diameter of 70 mm. Although long, their diameter is small, compared to the SCA’s aperture, indicative of the amount of insolation that will be concentrated on them. The HCEs are joined together and mounted at the focal line in the massive SCA structures. Here the unit will be considered the SCA and HCE together and they are both assumed to be 4 m long, subse­quently joined in series. The schematic for the Solar Electric Generating System Number 6 or SEGS VI located in the Mojave Desert is shown in Fig. 9.8, which has 9600 of these (equivalent) units. The definition of the concentration ratio Cr should be made clear and is given by

glass envelope Fig. 9.7 Dimensions of the ab­sorber tube and the surrounding glass envelope.

4The heat capacity and all other heat transfer fluid properties will be deter­mined at the mean temperature, Tm = [Thot + Tcold]/2.

Fig. 9.8 An idealized version of the SEGS VI. There are Ns = 192 units in series, each unit is 4 m long, which makes up a loop. There are Np = 50 loops that op­erate in parallel making the to­tal number of units Ns x Np = 9600. The aperture W is 5.0 m and so the total aperture area is 192,000 m2 which is slightly greater than the area used in re­ality, 188,000 m2. The electri­cal power generated by this power plant is 30 MW. The total mass flow rate of the heat transfer fluid is mf and the mass flow rate in each loop is mо = mf /Np.

the operating line (eqn (9.7)) for the entire solar field can be written in two forms:

Q he = m f Cpf AT and

Q he = Np Ns [Cr aPn (0) – (lout ] A (9.9b)

which is the mass flow rate in each loop of Ns units.

The inherent assumption we will make in using eqn (9.9b) is that the absorber pipe temperature will be constant along its length. This sets qout (see eqn (9.12) below) and everything in the equation is known ex­cept Ns, after Np is determined. The proper, detailed way to determine the operating point of the system is to use eqn (9.7) as the operating line together with eqn (9.18), shown below, as the design line on each 4 m long unit and calculate the absorber pipe temperature as well as the heat transfer fluid temperature rise on that unit. The temperature rise is added to the entry temperature of the first unit and is taken as the entry temperature to the second unit and the operating point again
determined. This process is repeated until the heat transfer fluid reaches the required temperature and one can calculate Ns (once Np is known).

The procedure advocated here is conservative by assuming a value for the absorber pipe temperature (Tp) and will be justified later. The temperature Tp is set to be the maximum at which the heat transfer fluid can be used, its degradation temperature. This is typically of order 400 °C at least for contemporary organic oils. The temperature rise is set so that Tcold is not too low or the viscosity of the fluid will become too large and will increase the pressure drop in the loop. Operational STEGEs have AT equal to 100 °C thereby making Tcold = 300 °C since That ~ 400 °C. Having a smaller AT will reduce the pressure drop as well as subsequent pumping costs. If AT = 200 °C rather than 100 °C then pumping costs will increase by 10-20%, which is significant.

The conservative nature in assuming Tp = 400 °C is that the radiant heat loss will be larger than if the pipe temperature is allowed to grad­ually increase along the loop. This will occur as more solar energy is absorbed by the pipe and given to the heat transfer fluid. The error in the constant Tp assumption is only 10-15%, which is acceptable to the level of the design we wish to accomplish here (see Example 9.4).

A temperature rise in the solar field of 100 °C will be assumed and sets the heat transfer fluid mass flow rate

Q he

Cpf AT

after using eqn (9.9a). Remember Qhe is known since this must be the heat supply to run the Rankine cycle.

As mentioned above, the absorber pipe temperature Tp will be as large as possible, a temperature just at the organic oil’s degradation tempera­ture, and for Therminol VP-1 this is 400 °C. Other commercial products have similar degradation temperatures and Tp should be assumed ac­cordingly. Knowing this temperature allows the heat transfer rate from the absorber pipe to the atmosphere, qout, to be calculated from

qout = hpa [Tp – Ta] + ep&S [Tp – Tsky] (9.12)

since the convective and radiative heat transfer rates operate in parallel. Here hpa is the convective heat transfer coefficient for heat transfer from the absorber pipe to the air, Ta, the air temperature, ep, the (selective surface) absorber pipe emissivity and Tsky, the effective sky temperature for radiative heat transfer calculations (see note 2 in Section 8.1).

The convective heat transfer coefficient hpa can be estimated with a standard correlation for flow of air past a cylinder,

Nu = 0.35 + 0.56Re052 (9.13)

where Nu and Re are the Nusselt and Reynolds number, respectively, given by Nu = hpaD/kair and Re = pairvwD/pair. The parameters are: kair is the thermal conductivity of air, pair, the density of air, pair, the viscosity of air and vw, the wind velocity. As we have done before, the

physical constants for air will be determined at the mean temperature Tm = [Tp + Ta]/2. Since the mean temperature is so high for this system, a glass envelope is not used, the correlations given in Appendix B are not valid and the ones in Table 9.3 should be used.

Now one can determine Ns since everything is known in eqn (9.9b), except Ns and Np, and will be found from

Q he

Np [CraPD (0) – <iout A

Of course the value of Np is one parameter that is not easily assumed, however, its value is determined by the amount of energy required by the Rankine power cycle and economic and pressure drop considerations. If it is too small then the flow rate in each loop is large, as is the pressure drop, which increases pumping costs. The pressure drop ДP can be determined from the definition of the friction factor f given in eqn (8.14) to be

where Dp is the inner diameter of the absorber pipe. The flow will be found to be turbulent in the absorber pipe and so the friction factor is fairly insensitive to the Reynolds number, see eqn (8.15b), and of order 3 x 10-2 for typical conditions within a loop. So, one can determine the variables to which the pressure drop is most sensitive by using eqns (9.10), (9.11), (9.14) and (9.15) to arrive at

where ~ means ‘scales as,’ see note 3 in Section 7.1. The dependence of the pressure drop on Np is large, as it is with Qhe, while it is less sensitive to ДТ. If Np is halved from 50, the value used for SEGS VI, the pressure drop is expected to increase by a factor of 8, quite large. In fact, a detailed calculation shows it will increase by a factor of 6.7, demonstrating that the simple relation in eqn (9.16) is a reasonable one. Note, increasing the heat load on the solar field Qhe similarly increases the pressure drop and doubling it also increases it by a factor of 6.7, again substantial. Thus, one must perform a true optimization for the process; an increase in Np will reduce ДР and the associated operational costs versus an increase in Np that will increase the capital cost of the power plant. This type of design is beyond the scope of this monograph.

Here the value of Np will be determined heuristically rather than having to perform a complete power plant design that would also have to include economic considerations. The SEGS VI STEGE has 1.67 loops/MW while more recent STEGEs in the Mojave Desert have 1.78 loops/MW and 1.85 loops/MW for the SEGS VIII and SEGS IX, respec­tively. Given these values one can assume a value of 1.75 loops/MW or

Np * 1.75 lW„et(MW) (9.17) Note Ns will be the same for all-sized power plants since this will set the heat transfer fluid temperature rise, all other variables being equal. The reader may notice that no consideration of heat transfer from the absorber pipe wall to the flowing heat transfer fluid has been mentioned. This was quite central to the design of the flat plate solar energy collec­tor. Consider the design line for flow of the fluid through the pipe which was given in eqn (8.17) and is written in the present variables as

0.11

f [Re – 1000]Pr

KTm)

(8.13)

Nu

1.07 + 12.7^1/ [Pr2/3 – 1] L h(Tp)

since we will find that flow is turbulent in the absorber pipes. Here Tm = [That + Tcold]/2 and the fluid viscosity is determined at both Tm and Tp, the mean and pipe wall temperatures, respectively. All the physical constants will be determined at Tm.6 The key factor is the ratio of parameters within the exponential term in eqn (9.18). It is the ratio of heat transfer through convection hf NsApAT to the sensible heat rise of the heat transfer fluid m 0Cpf AT. If this ratio is a large number then heat transfer is not a limiting factor and will be denoted as the Absorber Number or Ab

6The value of Nu can be increased by the heat transfer fluid absorbing ra­diation emitted by the absorber pipe. Since the pipe will have a wall temper­ature of » 400 °C it will emit radia­tion centered around a wavelength of » 4000 nm by using the Wien displace­ment law, eqn (2.7). This is in the in­frared region and if the absorption co­efficient a of the heat transfer fluid is large for this wavelength then the ef­fective heat transfer coefficient can in­crease. Two dimensionless parameters are important: aDp and ka/4n2asTp, where k and n are the heat trans­fer fluid’s thermal conductivity and re­fractive index, respectively, and as is the Stefan-Boltzmann constant. The larger the first parameter (> 10) and the smaller the second (< 0.1) then Nu is increased above that for pure con­vective heat transfer. For the condi­tions used in SEGS VI then a > 1 cm-1 and Tp > 400 °C for this effect to be important. Therminol VP-1 is a com­monly used heat transfer fluid, how­ever, its absorption coefficient is not known for ascertaining whether this is a large effect.

(9.20)

In most cases Ab will be much greater than 10 for a loop, making the exponential term essentially zero, implying Tp = Thot. Remember the absorber pipe temperature Tp was designed, by using the correct number of units in series, Ns, to be below the degradation temperature of the heat transfer fluid. Thus, it is the length of the loop that determines the heat transfer fluid’s temperature and it is not limited by heat transfer. One should always check eqn (9.18), however, it appears that for most industrial power plants heat transfer is not a rate limiting step.

Example 9.3

Given the 30 MW Rankine cycle in Example 9.2, design the solar field required to generate the steam in the power plant. By design it is meant to find mf, Np and Ns. Use the standard conditions in Table 9.4 and the heuristic for Np given in eqn (9.17). This solar field will be close to the size of the SEGS VI STEGE in the Mojave Desert.

The first parameter to be determined is Np. The heuristic given in eqn

(9.17)

is used to find, to the nearest integer and rounding up, Np = 53. Now Ns can be found from eqn (9.14),

however, qout is not known a priori. This is found from

(lout = hpa [Tp – Ta] + epPS [Tp – Tpky] (9.12)

since Tp will be assumed to be equal to 400 °C. Everything is known in this equation except hpa, the heat transfer coefficient between the absorber pipe and the surrounding air. This can be determined from eqn (9.13),

Nu = 0.35 + 0.56Де0’52 (9.13)

The mean temperature of the pipe and air is 212.5 °C and care must be taken to use the correlations in Table 9.3 for the physical properties of air. Since the wind velocity is 3 m/s one finds Re = 5960 and Nu = 51.8, making hpa = 29.0 W/m2-K, which is quite large. Inserting numbers in eqn (9.12), the rate of heat transfer from the system is found to be q_out = 1.26 x 104 W/m2-K.

One can determine Ns from eqn (9.14). Before this is done the net rate of heat transfer to the fluid is calculated by CroPd (0) – q_out to be 8.99 x 103 W/m2. So, even though the amount of heat coming into the system is large, CroPd(0) = 2.16 x 104 W/m2, there is a large rate of heat transfer out of the system, resulting in a relatively small net rate of heat transfer to the heat transfer fluid. This is obviously due to the fact that an envelope is not used around the absorber pipe and is a similar circumstance to the flat plate solar hot water heater without a cover.

Putting in all the numbers results in Ns = 186, close to that used in SEGS VI, which has approximately 200 in series. The total number of units is Nu = Ns x Np = 9858 and since the aperture area of each unit is 20 m2 the total aperture of the solar field is 1.97 x 105 m2, while that for SEGS VI is 1.88 x 105 m2.

Table 9.4 Standard conditions used in designing a solar thermal energy generated electricity power plant in this chapter. See Figures 9.5, 9.6 and 9.7 for definitions of some variables. The insolation was assumed to be 1000 W/m2, similar to the AM1.5G spectrum, allowing ready com­parison to solar photovoltaic devices and unless otherwise stated this is direct beam insolation. The parabolic trough unit aperture is the aper­ture of the solar collector assembly or SCA which is the device that holds the parabolic reflector and tilts the reflector to have the aperture normal to the direct beam. Each SCA holds a number of heat collec­tion elements or HCEs which are the absorber tubes and are called the parabolic trough unit length in the table.

Insolation (Bter)

Heat (energy) required (Qb)

Air temperature (Ta)

Wind velocity (vw)

Rankine cycle

Pump inlet water pressure (Pa)

Water state at pump entrance Heat exchanger exit temperature (Tc)

Heat exchanger exit pressure (Pc)

Solar field

Heat transfer fluid temperature rise (ДТ) Absorber pipe temperature (Tp)

Temperature difference (ST = Tp – Thot) Concentration ratio (Cr)

Focal length (f)

Parabolic trough unit aperture (W)

Parabolic trough unit length (L)

Absorber pipe inner diameter (Dp)

Absorber pipe outer diameter (D)

Envelope inner diameter (Dj)

Envelope outer diameter (Do)

Absorber pipe short wavelength absorbance (ap) Absorber pipe long wavelength emissivity (ep) Envelope absorptivity (ae)

Envelope emissivity (ee)

Heat transfer fluid

One should determine if heat transfer is a limiting process in a loop. The mass flow rate of the heat transfer fluid, mf, from eqn (9.11) is found first, which is written as mf = Qhe/Cpf AT. The heat load on the heat exchanger (or Qb) is 78.0 MW from Example 9.2, while the temperature rise for the fluid AT will be и 100 °C. All that needs to be determined is the the heat capacity for Therminol VP-1, which is given in Appendix B as a function of temperature.

The exit temperature from a given loop is Thot which is ST below the absorber pipe temperature Tp. This takes into account any heat losses, such as to the SCA structure itself, that are not accounted for, as well as reduction in the heat transfer due to fouling the inside of the absorber pipe. Thus, the mean temperature is Tm = [Thot + Tcold]/2 = 345 °C and Cpf is 2465 J/kg-K. Combining the above results in mf = 316.5 kg/s, quite large!

This allows mo to be determined from eqn (9.10), which is 5.971 kg/s. The Reynolds number can be found for the heat transfer fluid (Re = [4/n] x [m0/pDp]) after calculating the viscosity p at Tm for Therminol VP-1 to be 6.13 x 105 Pa-s. The friction factor is calculated with eqn (8.15b) to be 2.82 x 10-3. Now the Nusselt number Nu can be determined with eqn (8.13) and is equal to 2.25x 103, quite large too!

The heat transfer coefficient hf is now calculated to be 2.97 x 103 W/m2-K after the thermal conductivity for the fluid is determined at Tm (0.0873 W/m-K). This makes the absorber number Ab equal to 31.2 for the 186 units in series. Clearly, based on eqn (9.18) heat transfer is not a limiting factor.

Although the absorber pipe temperature is assumed constant to be at 400 °C this is not a poor assumption and greatly simplifies the design. The next example is given to gauge the goodness of this assumption and a more detailed calculation is given.

Example 9.4

Determine how accurate the assumption of a constant absorber pipe tem­perature is in Example 9.3.

Demonstrating this is not conceptually difficult, one must apply eqn (9.9b) on each unit, starting with the first where the cold heat transfer fluid enters. This equation is re-written as

Qo = Щг = [Cro-Pd(0) – qout] A operating line (9.21)

Np

for a single 4 m long unit. The definition of the rate of heat transfer required for each loop Q0 is evident from the equation. The rate of heat transfer out of the unit is given by eqn (9.12) and is

qout = hpa [Tp – Ta] + ep&S [Tp – Tsky]

The design line for a unit is given in eqn (9.18) and is re-written as

where Tin and Tout are the inlet and outlet temperatures to/from the unit. The initial unit’s inlet temperature will be Tcold and the final unit’s outlet temperature will be Thot. The heat transfer fluid’s physical properties will be determined at the mean temperature for the given unit, Tm = [Tin + Tout]/2. The heat transfer coefficient will be found from the Nusselt number correlation given by eqn (8.13).

Everything is known in the above equations except Tp and Tout for each unit. One starts with the first unit and then continues to the next and so-forth. The result of this calculation is given in Fig. 9.9 assuming each unit to be 4 m long. The cold heat transfer fluid enters the first unit at 295.0 0C and the absorber pipe achieves a temperature of 300.2 0C while there is a 0.81 0C fluid temperature rise to make Tout = 295.8 0C. The second unit now has an inlet temperature of 295.8 0C and so on. The upper graph in Fig. 9.9 shows this calculation, which requires about 166 units to have Tout = 400 0C.

The lower graph in the figure shows the effect of unit length on the total loop length to achieve a final outlet temperature of 400 0C. Various unit lengths L were assumed to discretize the system more and more coarsely until only one unit of length 744 m was assumed, which is the loop length in the previous example. Of course for this unit length the absorber pipe temperature was also 400 0C for its entire length.

Remarkably, assuming unit lengths of 4-80 m made little difference and a total loop length of 664 ± 3 m was required. As mentioned above, having only one unit in the loop makes the overall heat loss from the system greater, requiring a longer loop length. The heat transfer rate out of the system qout was 1.26 x 104 W/m2 using a single unit with a length of 744 m in the loop, compared to 1.02 x 104 W/m2 if 166 x 4 m long units were placed in series and the absorber pipe temperature was allowed to gradually increase. Interestingly, the result of this calculation is that it is only 12% longer than that from the more detailed calculation making this a reasonable approximation.

These examples demonstrate an approximate way to design a solar thermal energy generated electricity system. However, to keep the anal­ysis as simple as possible, the effect of an envelope around the absorber pipe was not considered. This complicates the analysis in the same manner that a cover did for the flat plate solar hot water heater, an additional criterion for equilibrium must be established. Most power plants have envelopes and the effect of this additional element in the STEGE is discussed in the next section.