Domestic hot water storage tanks

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Only annual usage simulations can estimate the exact dimensions of a hot water storage tank. The size depends on the hot water demand, solar fraction (see Equation 3.59, p112), collector performance, collector orientation, pipes and last but not least on the annual solar irradiation. For central European climates, a rough estimate can be made. Here, the storage volume should be

1.5-2 times the daily demand. Besides the storage volume for the daily demand, a standby volume of 50 per cent and a preheating volume of 20 litres per square metre of collector surface should be considered. Commercial pressurized hot water tanks are available in sizes from less than 100 litres to more than 1000 litres. The recommended storage size for a one-family house with four to six persons is between 300 litres and 500 litres.

Most solar storage tanks have two heat exchangers (see also Figure 3.4). The heat exchanger of the solar cycle is in the lower part of the storage tank and the heat exchanger for the auxiliary heater is in the upper part. The tank has an opening near the middle of the heat exchangers for integrated temperature sensors for the control system. The cold water inlet is at the bottom and the hot water outlet at the top of the storage tank to achieve good heat stratification.

Figure 3.15 shows a horizontal, cylindrical hot water storage tank with spherical ends. Storage losses are calculated for this tank, as an example. Heat storage tanks always suffer heat losses due to heat transition through the insulation. Good insulation should have a thickness of at least 100 mm for a heat conductivity of A = 0.04 W/(m K). Some new materials have very low heat conductivities; for instance, a super-insulation glass fibre vacuum insulation can reach heat conductivities of A = 0.005 W/(m K) at pressures below 10-3 mbar.

The heat storage capacity of a hot water tank is:

This heat capacity depends on the temperature difference between the average storage temperature &S and the ambient temperature as well as on the heat capacity c and mass m of the storage medium. The heat capacity of water at a temperature of 50°C and with a density of pHlO = 0.9881 kg/litre is = 4.181 kJ/(kg K) = 1.161 Wh/(kg K). Hence, the heat storage capacity of a 300-litre hot water storage tank with a temperature difference of 70°C is 24 kWh.

The storage losses QS of a cylindrical and spherical hot water storage tank are the sum of the losses QS,cyl of the cylindrical part and the losses QS,sphere of both spherical caps:

The losses in the cylindrical part

can be calculated similarly to the losses of the pipes in the previous sections with the heat transition coefficient k', the length lcyl and the difference between the average storage temperature &S and the ambient temperature

The heat conductivity of the insulation A, the surface coefficient of heat transfer a between insulation and air as well as the outer diameter do and the h d\ dt

Ss u cvl

Figure 3.15 Cylindrical Hot Water Tank with Spherical Ends inner diameter d; of the heat insulation of the cylindrical part define the heat transition coefficient:

Linearly interpolated values between 10 W/(m2 K) for k' = 0.2 W/(m K) and 15.5 W/(m2 K) for k' = 0.5 W/(m K) are used to estimate the surface coefficient of heat transfer a.

With the temperature difference between the storage medium and ambient air, the coefficient of heat transfer k and the surface Asphere of the spherical caps, the heat losses of the spherical caps become:

With the surface coefficient of heat transfer a1 from the tank wall to the insulation and a2 from the insulation to the ambient air, the insulation thickness s, the heat conductivity A of the insulation, and assuming that the temperature of the tank wall is equal to the storage temperature &s, the coefficient of heat transfer becomes:

The surface coefficient of heat transfer from the tank wall to the insulation can be estimated as ax = 300 W/(m2 K). The surface coefficient of heat transfer a2 from the insulation to the ambient air depends on the orientation of the wall (VDI, 1982).

For a horizontal wall with heat transfer upwards:

For a horizontal wall with heat transfer downwards:

For a vertical wall (spherical cap) with heat transfer to the side:

With r and h defined in Figure 3.15, the surface of the spherical cap becomes:

The following example calculates the heat losses of a 300-litre storage tank. The ambient temperature and storage temperature are ûA = 20°C and ûS = 90°C, the dimensions of the tank are lcyl = 1.825 m, do = 0.7 m, di = 0.5 m, r = 0.45 m, h = 0.11 m and s = 0.1 m. With the heat conductivity of the insulation X = 0.035 W/(m K) and the surface coefficient of heat transfer a = 15.5 W/(m2 K) in the cylindrical part, the heat transition coefficient is k} = 0.64 W/(m K). With the surface area of the spherical cap of Asphere = 0.311 m2 and the heat transition coefficient of the spherical cap k = 0.33 W/(m2 K), the storage losses become:

The temperature &S of a stationary storage tank decreases with the time t. Thus, the storage losses decrease as well. If no heat is fed into or taken from the storage tank, the storage temperature

can be calculated as described for the pipes above. The value cm

is the time constant of the storage. It describes the time taken for the temperature difference to decrease to 1/e = 36.8 per cent of the initial value. The time constant of the example above is t = 250 h = 10.4 days.

Figure 3.16 shows the storage temperature of a stationary storage tank. It is obvious that a high portion of the stored heat is emitted again to the

0 I—t-(—I—(—i—i——; ; ; ;—i—i—! ; ; ;—:—i—:—:—t-t-

Time in days

0 I—t-(—I—(—i—i——; ; ; ;—i—i—! ; ; ;—:—i—:—:—t-t-

Time in days

Figure 3.16 Storage Temperature for a 300-litre Storage Tank without

Loading or Unloading environment. After more than 1 week, the storage temperature is only half the initial value. Such a storage tank can therefore only maintain the temperature for a few days. The ratio of volume to surface area increases for larger storage tanks, so the relative heat losses decrease. Storage systems of 1000 m3 or more can achieve time constants of about 6 months. Such systems can be used for seasonal storage, i.e. heat storage from summer to winter. Good insulation is also very important for seasonal storage systems to keep the storage losses low.

However, realistic integrated solar thermal system hot water storage is usually not operated under stationary conditions. The solar collector feeds heat continuously into the storage tank and consumers take hot water from the tank. Then, only detailed computer programs can estimate the variation of the storage temperature (see CD-ROM).

The storage temperatures calculated above are all average temperatures; however, most storage tanks have desirable temperature stratifications. The temperature at the top of the storage tank, i.e. near the water outlet, is higher than at the bottom, near the water inlet. This stratification can be considered if the storage is subdivided into several layers. In this case, the heat flow between all layers must be calculated separately.

Large systems for higher demands, such as for family houses, often use two storage tanks. Here, the tanks are connected in series. For a system with solar preheating, the first storage tank contains the solar heat exchanger and the second storage tank contains the heat exchanger for the auxiliary heater. The solar fraction of these systems is relatively low and the profitability of this system compared to one with low conventional fuel prices is relatively high. Another concept with two storage tanks contains a solar heat exchanger in both tanks. The solar collector can heat up both tanks separately. This can



Geothermal Hot And Cold Tank

Figure 3.17 Collector Systems with Two Storage Tanks



Figure 3.17 Collector Systems with Two Storage Tanks increase the solar fraction significantly. If the first storage tank is fully loaded, the control switches to the second storage tank. An auxiliary heater can heat up the second storage tank in both systems. Figure 3.17 shows the two described concepts with two storage tanks.

Swimming pools

The pool itself is the heat storage medium of a swimming pool system. The usefulness of the system lies in the storage. The solar heating system must compensate only for the storage losses, i.e. the losses of the pool (Figure 3.18). The pool losses QPool loss consist of convection losses Qconv, radiation losses Qrad, vaporization losses Q and transmission losses Qjrans:

The transmission losses Qtrans from the swimming pool to the earth can be neglected for solar-heated outdoor pools during the summer season.

Vaporization losses

Radiation and convection losses

Vaporization losses

Radiation and convection losses

Auxiliary heating

Transmission losses to the earth

Figure 3.18 Energy Balance of a Swimming Pool

Auxiliary heating

Transmission losses to the earth

Figure 3.18 Energy Balance of a Swimming Pool

With the ambient air temperature &A, the water temperature &W, the water surface area AW and the heat transfer coefficient given by:

the convection losses become:

The wind speed ^wind at a height of 0.3 m above the water surface can be calculated from measurements at other heights using the equations in Chapter 5, section headed 'Influence of surroundings and height', p185.

Radiation exchange between the swimming pool surface and the sky causes radiation losses. With the Stefan-Boltzmann constant o = 5.6705140"8 W/(m2 K4), the emittance £W of water (eW ~ 0.9), water surface area AW and absolute temperatures TW and TSky of the water and the sky, respectively, the radiation losses become:

The sky temperature


can be calculated using the absolute ambient air temperature TA in K and the dew-point temperature $dew (Smith et al, 1994). The dew-point temperature

can be estimated from the humidity y and the saturated vapour pressure p:

The saturated vapour pressure p depends on the ambient air temperature &A and is measured in Pascals (1 Pa = 1 N/m2 = 0.01 mbar). The mean relative humidity y in moderate climates (e.g. Germany) is about 70 per cent during the outdoor pool season.

Table 3.12 Saturated Vapour Pressure p of Water and the Dew-point Temperature &dew at 70 per cent Relative Air Humidity as a Function of the Ambient Air Temperature

12 14

p in kPa 1.23 1.40 1.60 1.82 2.07 2.34 2.65 2.99 3.37 3.79 4.25 $-dew in °C 4.8 6.7 8.6 10.5 12.5 14.4 16.3 18.2 20.1 22.0 23.9

Table 3.12 shows the saturated vapour pressures and the dew-point temperatures calculated using equations (3.51) and (3.52) for various temperatures.

With the vaporizing mass flow mV (eg kg of water/hour) and the heat of vaporization hV = 2.257 kJ/kg of water, the vaporization losses are found from:

However, empirical equations are often used. When calculating the vaporization losses using the wind speed vWimJ at height 0.3 m and using the saturated vapour pressure p, the water temperature &W, the ambient air temperature &A, the relative humidity p and the swimming pool surface area AW, we get (Hahne and Kubler, 1994):

= ¿v (0.085- +■ 0.0508 ■ vu,iul > ■ ( /;( ) ~ 0" p{$A »

Neglecting the transmission losses, the total losses from a swimming pool with a surface area of AW = 20 m2, a wind speed vWind = 1 m/s, ambient air temperature &A = 20°C, water temperature &W = 24°C and relative humidity p = 0.7 become:

A large amount of energy would thus be needed to compensate for the losses. However, solar radiation onto the pool surface produces gains that reduce the losses significantly.

With solar irradiance E, water surface area AW and absorptance aabs, the solar radiation gains Qsol are estimated as:

The absorptance aabs of pools with white tiles is about 0.8, with light blue tiles 0.9 and with dark blue tiles over 0.95. The absorptance also increases with the depth of the water. A solar irradiance of E = 319 W/m2 at an absorptance of 0.9 already compensates for the losses of the 20 m2 swimming pool from the example above.

Covering the swimming pool during the night can reduce the heat losses by about 40-50 per cent.

The heat demand

Qu = "Ete^L^i' Afi-^LC-Afjiv^ Jfe^iO-^wJdi (3.56)

of a swimming pool can then be estimated by considering the difference between the losses and the solar radiation gains over the operating period ttot.

In moderate climatic regions (e.g. central Europe), the heat demand of a swimming pool without a cover and at a base temperature of 23°C is about 300 kWh/m2 per season. This demand can be provided easily by a solar heating system. The solar absorber size should be 50-80 per cent of the pool surface; however, these values can vary significantly. Therefore, simulations with professional computer programs can provide more exact values.

Heat Demand and Solar Fraction

The heat demand QD of domestic water systems can be calculated from the amount of water taken. With the heat capacity of water [cH 0 = 1.163 Wh/(kg K)], the taken water mass m, the cold water temperature &CW and the warm water temperature &HW, the heat demand becomes:

Table 3.13 shows typical values for the hot water demand in residential buildings in Germany. If no value for the cold water temperature is given, a value of $cw = 10°C can be used. In countries with higher annual ambient temperatures, a higher cold water temperature should be chosen. If washing machines or dishwashers with hot water inlets are used, the hot water demand increases.

Table 3.14 shows typical values for the hot water demand of hotels, hostels and pensions. The hot water demand of restaurants can be estimated as 230-460 Wh/ per set menu and of saunas as 2500-5000 Wh/user.

Table 3.13 Hot Water Demand of Residential Buildings in Germany

Hot water demand in litres/(day and person)

&HW = 60°C &HW = 45°C

Specific heat content in Wh/(day and person)

Low demand




Average demand




High demand




Source: VDI, 1982

Table 3.14 Hot Water Demand

of Hotels, Hostels and Pensions in Germany

Hot water demand in

Specific heat content in

litres/(day and person)

Wh/(day and person)

V = 60°C

Ûhw = 45°C

Room with bath




Room with shower




Other rooms




Hostels and pensions




Source: VDI, 1982

Source: VDI, 1982

Because the tables give only a rough estimate, it is recommended that a more exact analysis be made when planning a solar thermal system. Table 3.15 gives some further information.

Besides the annual hot water requirements, the demand on shorter timescales must also be considered. If there are significant differences between various days or considerable seasonal differences between summer and winter, the sizing of the solar energy system changes. In this case, computer simulations are prerequisites for an exact system sizing and output prediction.

The heat demand QD, the heat losses (piping heat-up losses Qpheatup, circulation losses Qcirc in the collector cycle and storage losses QS) and the solar collector power output Qout define the amount of auxiliary heat required:


Besides piping losses in the collector cycle, there are also piping losses from the storage to the taps. These losses can be calculated similarly to the losses in the collector cycle. Simulations usually calculate the heat flows and add them to give annual heat values.

An important parameter for solar energy systems is the solar fraction SF. This parameter describes the share of the heat demand provided by the solar thermal system. It is defined as the ratio of the heat that the solar cycle feeds into the storage to the total heat demand that consists of the heat demand QD and the storage losses QS:

Table 3.15 Hot Water Usage for Various Activities



Heat content

Dishwashing per person Hand wash (one time) Bath (one time) Shower (one time) Hair wash (one time)

550-700 Wh/day 95-160 Wh 5200 Wh 940-1400 Wh 310-470 Wh

o co

400 1 tank __

—'200 11


Collector surface in m=

Collector surface in m=

Note: Location: Berlin, Collector Inclination: 30°, Heat Demand: 10 kWh/day

Figure 3.19 Solar Fraction as a Function of the Collector Surface: Simulation by the Software Getsolar.

Solar energy systems for domestic water heating in moderate climates are usually designed for solar fractions of about 50-60 per cent. This is a compromise between desired high solar fractions and economic considerations. However, the solar fraction in regions with high annual irradiations can be much higher. If there are only small differences between summer and winter, the solar fraction can approach 100 per cent.

Figure 3.19 shows the solar fraction as a function of the collector surface for two different volumes of storage tank calculated for Berlin. The heat demand was constant for all calculations. The curve shows that the solar fraction increases very quickly with the collector surface area for relatively small collectors. However, in the given example, the collector surface must be doubled to increase the solar fraction from 60 to 70 per cent. Large storage volumes are counter-productive for small collector surfaces because the storage losses are disproportionately high in such a case. If the solar collector surface increases significantly, the storage volume should be increased as well.

Another important parameter for analysis is the solar collector cycle efficiency nCC. It describes the total efficiency of the solar thermal system. It is defined as the ratio of the annual heat that the solar cycle feeds into the storage system to the annual solar radiant energy on the collector surface. With annual irradiation HSokr on the collector surface and collector area AC, the collector cycle efficiency becomes:

Ulft a


Solar collector cycle efficiencies are usually between 20 and 50 per cent in temperate climates. Next to the build quality of the system, the solar fraction is the dominant factor on the cycle efficiency. The solar collector cycle efficiency decreases significantly with increasing solar fraction.

To calculate the saved primary energy Epe, the electrical energy demand

EE f^i a nnmn <-i f^ r\ a i^AnffAl nnit int" +■

electricity utilities must be considered. Hence, the amount of saved primary energy is:

E of the pump and the control unit for the solar cycle, the primary energy efficiency naux of the auxiliary heater and the efficiency nE of the public

Cyrill t?imiup ^

if the energy demand for the production of the solar thermal system is neglected. The primary energy demand of the solar collector pump is between 2 and 15 per cent of the collector output. To keep the pumping energy demand low, the diameters of the pipes and the design of the pump must be estimated carefully. The simulation programs on the CD-ROM accompanying this book can provide further advice for this task.

Chapter 4

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