Swimming Pool
The swimming pool module is created as a component with two connections. The fresh water supply is taken into consideration, which can be inserted as a parameter. The physical models also include evaporation values, heat losses to the environment, convection, thermal emission and irradiation. The parameters used for the swimming pool are geometric measures (length, width, depth) also as the U-value between pool and soil.
The operating periods are indicated by the date (day of the month) and by the hour of opening (hour of the day). Also with “cover” and “gap losses cover” the user can indicate if and how the pool is covered at times of non-use.
Double-clicking on a swimming-pool out of the catalog you will be able to select either an indoor swimming-pool or an open-air pool. For open-air pools room temperature, relative humidity of air and the recovery of heat evaporation are not taken into account. On the other hand wind portion and swimming-pool absorption have no influence on the indoor swimming-pool. The level of absorption of global radiation by the swimming-pool ranges based on colour, depth and covering between 60% and 90% (Duffie and Beckman 60%). The reflection of light on the water surface amounts to 8% and is already taken into account.
Definitions of Fundamental Parameters
\(A_{surf} = area\ of\ the\ pool\ surface\ \lbrack m^{2}\rbrack\)
\(T_{pool} = water\ temperature\ inside\ the\ pool\ \ \lbrack{^\circ}C\rbrack\)
\(T_{amb} = ambient\ temperature\ in\ the\ air\ outside\ the\ pool\ \lbrack{^\circ}C\rbrack\ \)
\(v_{wind} = wind\ speed\ \lbrack\frac{m}{s}\rbrack\)
Heat Transfer to Soil Surrounding the Pool
\(Q_{H} = u\ \cdot A_{walls} \cdot T_{pool} – \ T_{soil}\)
\(A_{walls} = total\ wall\ and\ floor\ area\ \lbrack m^{2}\rbrack\)
\(u = U – value\ \lbrack\frac{W}{m^{2}K}\rbrack\)
\(T_{soil}(t) = \frac{\Delta t}{\tau} \cdot T_{soil}(t – \Delta t) + \left( 1 – \frac{\Delta t}{\tau} \right) \cdot T_{amb}(t)\)
with a temporal constant of = 7 days.
This corresponds to the formula \(x(t) = 1 – e^{- t/\tau}\).
Heat Losses due to Evaporation from the Water Surface
Formula according to Transsolar (TRNSYS TYPE 144):
\({\dot{Q}}_{Evap} = A_{surf} \cdot c_{0} \cdot (c_{1} + c_{2}\sqrt{v_{wind}}) \cdot ({\widehat{P}}_{pool} – \rho \cdot {\widehat{P}}_{amb})\)
\({\widehat{P}}_{pool,amb} = k_{0} + \left( k_{1}{\cdot T}_{pool,amb} \right) + \left( k_{2} \cdot T_{pool,amb}^{2} \right) + (k_{3} \cdot T_{pool,amb}^{3})\)
\(\rho = relativ\ humidity\ \lbrack\frac{kg}{kg}\rbrack\)
with the fit parameters [Auer96]
\(c_{0} = 1.01325 \cdot 10^{5}\ Pal\ atm\)
\(c_{1} = 42.39\ m/s\)
\(c_{2} = 56.52\ \sqrt{m/s}\)
\(k_{0} = 4.82 \cdot 10^{- 6}\ atm\)
\(k_{1} = 7.11 \cdot 10^{- 7}\ atm/K\)
\(k_{2} = – 3.52 \cdot 10^{- 9}atm/K^{2}\ \)
\(k_{3} = 7.22 \cdot 10^{- 10}\ atm/K^{3}\)
The following illustration shows the influence of the wind and relative air humidity on the area related evaporation heat \({\dot{Q}}_{Evap}/A_{surf}\).
Heat Losses due to Thermal Emission
\({\dot{Q}}_{S} = A_{surf} \cdot \varepsilon \cdot \sigma \cdot \left( \left( 273.15 + T_{Pool} \right)^{4} – \left( 273.15 + T_{Sky} \right)^{4} \right)\)
\(\varepsilon = 0.9\)
\(\sigma = Stefan\ Boltzman\ constant = 5.67 \cdot 10^{- 8}\)
Heat Gains by Means of Direct Solar Irradiation
\({\dot{Q}}_{\mathbf{S}} = L_{up} – L_{i} + \alpha \cdot G_{h} \cdot (1 – \rho)\)
Heat Losses due to Convection
\({\dot{Q}}_{conv} = A_{surf} \cdot (b_{1} + b_{2} \cdot v_{wind}) \cdot (T_{pool} – T_{amb}) \cdot (1 – \eta_{cover} + \eta_{cover} \cdot \frac{u_{cover}}{b_{1}})\)
\(b_{1} = 3.1\frac{W}{m^{2}K} = heat\ transfer,\ no\ wind\)
\(b_{2} = 4.1\frac{W\ s}{m\ K} = correction\ term\ for\ finite\ wind\ speed\)
\(u_{cover} = u – Value\ of\ the\ cover\ \lbrack\frac{W}{m^{2}\ K}\rbrack\)
\(\eta_{cover} = percentage\ of\ covered\ pool\ surface\ \)
Heat Losses due to Exchange of Pool Water (Fresh Water Supply)
\({\dot{Q}}_{F} = \dot{V} \cdot d \cdot c \cdot (T_{Pool} – T_{Fresh})\)
\(c = fresh\ water\ supply\ \ \lbrack\frac{l}{h}\rbrack\).
Normally: 2% of pool volume per day or 50 l a day per swimmer.
\(c = Water\ density = 1\ kg/l\)
\(c = specific\ heat\ capacity\ of\ water = 1.16\frac{W\ h\ }{kg\ K}\)