Solar thermal collectors and applications

F-Chart method and program

The method was developed by Beckman et al. [122]. The method provides a means for estimating the fraction of a total heating and cooling that will be supplied by solar energy for a given solar heating system. The primary design variable is the collector area whereas secondary variables are collector type, storage capacity, fluid flow rates, and load and collector heat exchanger sizes. The method is a correlation of the results of many hundreds of thermal performance simulations of solar heating systems performed with TRNSYS. The conditions of simulations were varied over appropriate ranges of parameters of practical system designs. The resulting correlations give f, the fraction of the monthly load supplied by solar energy as a function of two dimensionless parameters. One is related to the ratio of collector losses to heating loads, and the other is related to the ratio of absorbed solar radiation to heating loads. The f-charts have been developed for three standard system configurations, liquid and air systems for space (and hot water) heating and systems for service hot water only. Detailed simulations of these systems have been used to develop correlations between dimensionless variables and f, the monthly fraction of loads carried by solar energy. The two dimensionless groups are:

AcFRUl(Tef - Ta)At




For the purpose of calculating the values of the dimensionless parameters X and Y, Eqs. (84) and (85) are usually rearranged to read:

FR - . Ac

X = Fr Ul - R (Tref - Ta) A - c (86)



The reason for the rearrangement is that the factors FrUl and FR(ra)n are readily available form standard collector tests (Section 4.1). The dimensionless parameters X and Y have some physical significance. The parameter X represents the ratio of the reference collector total energy loss to total heating load or demand (D) during the period At, whereas the parameter Y represents the ratio of the total absorbed solar energy to the total heating load or demand (D) during the same period.

The method can be used to simulate standard water and air systems configurations. The fraction f of the monthly total load supplied by the solar space system and air or water heating system is given as a function of the two parameters, X and Y, which can be obtained from charts [122] or from the following equations:

For air heating systems: f = 1.040Y - 0.065X - 0.159Y2 + 0.00187X2

- 0.0095Y3 (88)

For liquid-based systems: f = 1.029Y - 0.065X - 0.245Y2 + 0.0018X2

+ 0.0215Y3 (89)

The F-Chart was developed for a storage capacity of 0.25 m3 of pebbles per square metre of collector area for air systems and 75 l of stored water per square meter of collector area for water systems. Other storage capacities can be used by modifying X by a storage size correction factor Xc/X as given by Duffie and Beckman [97].

For air heating systems for 0.50 # (actual/standard storage capacity) # 4.0:

Xc/X = (Actual/Standard storage capacity)-030 (90)

For liquid-based systems for 0.50 # (actual/standard storage capacity) # 4.0:

Xc/X = (Actual/Standard storage capacity)-025 (91)

Also air heating systems must be corrected for the flow rate. The standard collector flow rate is 10 l/s of air per square meter of collector area. The performance of systems having other collector flow rates can be estimated by using appropriate values of FR and Y and then modifying the value of X by a collector air flow rate correction factor Xc=X to account for the degree of stratification in the pebble bed.

For 0.50 # (actual/standard air flow rate) # 2.0:

Xc/X = (Actual/Standard air flow rate)0 28 (92)

Although the F-Chart method is simple in concept, the required calculations are tedious, particularly the manipu­lation of radiation data. The use of computers greatly reduces the effort required. Program F-Chart [123] was developed by the originators of TRNSYS is very easy to use and gives predictions very quickly. The model is accurate only for solar heating systems of a type comparable to that which was assumed in the development of the F-Chart. However, the model does not provide the flexibility of detail simulations and performance investigations as TRNSYS does.

F-Chart method was used by Datta et al. [124] for the optimisation of the collector inclination angle. It was also used by the author for a feasibility study on the use of PTC for hot water production [125].

Подпись: P =

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