Pool Heat Loss Calculation
Accurate calculation of swimming pool heat losses and the pool energy consumption is essential for the efficient design and simulation of thermal energy systems. Polysun provides a comprehensive modeling environment to simulate the thermal behavior of swimming pools by incorporating key heat loss mechanisms such as evaporation, convection, radiation, conduction to surrounding soil, and fresh water exchange. With Polysun’s swimming pool module, planners can input geometric details, operating schedules, and environmental conditions to accurately estimate energy demands and optimize heating system performance. This article explains the underlying physical models and calculation methods used in Polysun to determine pool heat losses and highlights factors influencing energy efficiency in pool heating. More about pool heat pump calculation and solar heating panels for pools, and dynamic system simulation can be found here.
Pool Heat Loss Calculation Model
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 \(x(t) = 1 – e^{- t/\tau}\).
Pool Heat Loss Calculation 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 \({\dot{Q}}_{Evap}/A_{surf}\).
Poll Heat Loss Calculation 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
\({\dot{Q}}_{\mathbf{S}} = L_{up} – L_{i} + \alpha \cdot G_{h} \cdot (1 – \rho)\)
\(T_{sky} = \left( T_{amb} – 237.15 \right)\left( s_{1} + s_{2} \cdot T_{dp} + s_{3} \cdot T_{dp}^{2} + q \cdot \cos(15 \cdot t) \right)^{\frac{1}{4}} + 237.15\)
\(s_{1} = 0.711,\ s_{2} = 0.0056\ 1/K\)
\(q = 0.013\)
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)
\({\dot{Q}}_{F} = \dot{V} \cdot d \cdot c \cdot (T_{Pool} – T_{Fresh})\)
\(\dot{V} = fresh\ water\ supply\ \ \lbrack\frac{l}{h}\rbrack\).
Normally: 2% of pool volume per day or 50 l a day per swimmer.
\(d = Water\ density = 1\ kg/l\)
\(c = specific\ heat\ capacity\ of\ water = 1.16\frac{W\ h\ }{kg\ K}\)
How can the heat loss of a pool be accurately calculated?
Calculating pool heat loss requires considering various factors such as evaporation, radiation, convection, and solar gains. Polysun provides a detailed simulation of these parameters to realistically reflect the actual heat loss. Unlike simplified Excel formulas, dynamic operating conditions are taken into account, resulting in more precise calculations.
Which factors should be considered when calculating the energy consumption of a pool?
Determining pool energy consumption involves accounting for heat losses as well as factors such as usage frequency, humidity, water temperature, and building insulation. Polysun integrates all these variables into a dynamic simulation to assess energy consumption under real operating conditions.
How can the efficiency of pool heating systems be optimized?
The efficiency of heating systems such as heat pumps or solar collectors can be improved by accurately analyzing pool heat loss and pool energy consumption. Polysun allows different heating systems to be simulated and their performance compared under varying conditions to identify the optimal solution for pools, indoor swimming pools, or wellness facilities.
Why is a dynamic simulation more effective than a static Excel calculation?
Static Excel calculations generally consider only simplified assumptions and constant conditions. A dynamic simulation accounts for temporal fluctuations, different operating states, and changing environmental conditions, providing more realistic and reliable results. This enables precise planning and improved energy efficiency.
Can Polysun determine the optimal pool size and heating configuration based on heat loss?
Polysun supports the selection of the appropriate pool size and heating system configuration by analyzing pool heat loss and expected pool energy consumption, ensuring efficient operation, lower costs, and optimal comfort.