A key question is how the value of m affects the prediction of plant power. As a reference condition use the case where V = Vmax/(n+1)1/n and pt/pp = n/(n+1), and denote it with an asterisk (*). When pt/pp = n/(n+1) in the power law model, then from Eqs. (1), (2) and (3):

к

= (n + 1)V. n-m (19)

-L

Substitute Eq. (19) into Eq. (6) to get the volume flow at MFP condition:

Vmfp = (m + 1)V. n-m )

= (m + 1)1/(n-m)V. (20)

By substituting Eqs. (20) and (21) into (4), the fluid power at the MFP condition follows:

Pmfp = [1-m)(1 + m)(1+m)/(n-m)P* (22)

In the table below, volume flow, pressure potential and power, all at MFP condition, are listed as a fraction of the respective reference value over a range of collector transfer efficiencies at n = 2. At a collector transfer efficiency of 70 % (m = -0.70) we can see that the MFP volume flow may be as low as 64 %, the MFP turbine pressure drop may be as high as 185 % and the power production may be 118 % compared to the reference value. Even at moderate collector floor-to-exit efficiencies of around 50 % the optimal turbine pressure drop may be seriously underestimated by using the 2/3 rule.

Schlaich (1995) gives typical values of ncoll around 0.55 and a around 0.80, leading to ncfe = 0.69. Applying the above model we get m = -0.69 and from Eq. 8 and assuming n = 2 the optimal ratio is pt/pp = (n-m)/(n+1) = 2.69/3 = 0.90. This value is much higher than the value of 2/3, and also higher than the value of 0.82 derived from values in a table of data given by Schlaich (1995). On the other hand, a value of pt/pp = 0.82 corresponds to ncfe = 0.46, and if a = 0.8, to ncoll = 0.8×0.46 = 0.37, which is very low. The value of 0.9 agrees with the value recommended by Bernardes (2003). In his analysis he found optimum values of as high as 0.97, resulting in m = -0.91. This would, in combination with his value of collector floor absorption coefficient, a = 0.9, imply a collector transfer efficiency of 0.91/0.9, which exceeds 100 %. If the value of 0.8 for a given by Schlaich is replaced by 0.9 in his data set, then ncfe = 0.61, with optimal ratio of pt/pp = 0.87.

As the tabulated data in Schlaich (1995) were not obtained with a pt/pp ratio of 2/3, we cannot apply Eqs. (20-22) directly to come up with the values for volume flow, turbine pressure drop and power at MFP condition. We first have to find the equivalent * condition, by using Eqs. (1) and (2) to get values for Kp and KL. Assuming these coefficients as well as the exponents m and n to remain constant over a restricted range of flow rate and using the * condition together with Eqs. (1) and (2) from Eq. (19) V* is:

1

m-n

(23)

The value of m follows from ^cfe, and n is taken as 2. We can then find V* and evaluate pp*, pt*, pL*, and P*, and find values for the same variables at the MFP condition with Eqs. (20-22).

Since n is numerically about three times as large as m, V* is rather insensitive to the exact value of m. Taking m = -0.66 and working with the 100 MW plant data we find that PMFP is 3.7 % higher than PSchlaich (for the 30 MW plant it is 3.5 % and for the 5 MW it is 3.0 %). Changing m by 20 % to -0.79 leads to a PMFP that is 8.4 % higher than PSchlaich, a change of only 4.5 %.