CONTROL STRATEGY 189

amount of collected energy. Since the water temperature at inlets to HSC is assumed to be constant during a year-round operation, the developed FE model of HSC tends to slightly underestimates the amount of collected energy. Nevertheless, the assumed magnitude of water temperature at the inlet is in range of temperature typical for GHS systems. According to Chwieduk [39], the operational temperature range of 10–30^◦C is typical for ground heat storage systems used in combination with solar collectors and space heating systems in single detached houses as well as terraced housing. The general schema of assumed control strategy for water mass flux in HSC is presented in Fig. 5.50. When the application of HSC aims at supplying a space-heating system, the water flow through the pipes is turned on when the outlet water temperature, Tw,out, for both the pipes is equal or just exceeds the value of 25^◦C.

On the other hand, the water flow is turned off when the outlet water temperature is lower than 20^◦C. This study also aims at verifying the ability of HSC to support domestic hot water system, as an additional part of the active solar system applied, mainly, to meet space-heating loads. For a purpose of this analysis, it assumed that the water starts to flow through the pipes when the magnitude of the outlet water temperature for both the pipes is equal or just exceeds the magnitude of 55^◦C. The flow is stopped when the outlet water temperature of the fluid flowing with the lowest allowable velocity cannot reach the level of 55^◦C. Such an approach is reasonable to maintain the temperature of 50^◦C in a typical water storage tank. After releasing the excess of energy in the water storage tank, the water is then transferred to the seasonal HS system before being returned to the solar collector. Hence, a considered magnitude of the inlet water temperature equal to 20^◦C. For both the investigated applications, the upper limit of considered range for water mass flux is 19 kg/(m²·s) (corresponding magnitude of water velocity is 0.019 m/s) The control strategy is based on the product magnitude of water mass flux and difference of average water temperature at inlet and outlet from pipes, m^· (Tw,out− T_w,in). The magnitude of water mass flux is modified so that the product is higher for the every following time increment. Based on several preliminary transient simulations, a constant magnitude of water mass flux change, ∆m^· , was set to 0.95 kg/(m²·s). The water flow is stopped when the application of minimum magnitude of water mass flux (0.95 kg/(m²·s)) does not increase the outlet water temperature over the required temperature level.

T_w,in, Tw,out,down , T_w,out,up, T_w,k, T_w,k-1, m_o, m_max, m_k, m_k-1, ∆m

T_w,k ≥ T_w,out

mk (Tw,k – Tw,in) > 0 m_k+1 = m_k - ∆m

m_k+1 = m_o m_k (T_w,k – T_w,in) > 0 m_k+1 = m_o + ∆m

m_k (T_w,k – T_w,in) > m_k-1 (T_w,k-1 – T_w,in) m_k+1 = m_k - ∆m YES

NO

T_w,k =min(Tw,out,down ; T_w,out,up)

NO YES YES NO

YES NO

m_k+1 = m_k + ∆m m_k+1 = m_k

end of time step k go to time step k=k+1

NO YES

m_k+1 = m_k + ∆m ≤ m_max

Figure 5.50: Schema of assumed water mass flux control strategy

5.6 Summary

FEM was applied to solve the problem of three-dimensional heat transfer in HSC under both unsteady and steady-state conditions. The developed FE model is based on several geometrical and physical assumptions as well as takes advantage of re-sults obtained from additional series of CFD analyses in order to reliably simulate the thermal behavior of the 3D system. Besides the convective and radiative heat exchange between the external collector surface and outdoor environment, conduc-tive heat transfer in solid layers, radiaconduc-tive heat exchange between the pipes and surfaces composing the air-cavity, and convective/radiative heat exchange between the internal collector surface and building interior, the model is capable to simulate the forced convective heat transfer in the water flowing through the collector’s pipes and to include the influence of convective heat transfer in the air layer on heat ex-change rate within the air-cavity without the use of computational-time-expensive CFD method. This is a great advantage which makes the model to be useful for the purpose of HSC performance analysis during a year-round operation. A compromise between the accuracy of results and time of calculation was achieved through the mesh design optimization. The developed FE model was positively compared against

5.6. SUMMARY 191

the CFD model. However, the conducted analysis was mainly aimed at validation of the approach applied in order to simulate convective heat transfer mechanism in the FE model. A complete and reliable validation of the FE model requires to compare the results of the numerical simulation with measured data from the experimental investigation of HSC. Such an investigation is, however, impossible to be carried out at the present stage of the research and stays as a target for the future work.

The commercial software package ABAQUS v 6.10 [49] was employed to develop the FE model and conduct numerical simulations of heat transfer in HSC under steady-state and unsteady conditions. Several existing user subroutines were mod-ified and several new subroutines (Fig. 5.51) were implemented in the FORTRAN language in order to:

• managing the entire process of FE simulation,

• processing of temporary results at each step and time increment of the un-steady simulation,

• generating final results of the simulation at each step and time increment of the unsteady simulation,

• modifying boundary conditions for heat exchange on inner (Eq. 5.3.23) and outer (Eq. 5.3.19) pipes’ surfaces at each step and time increment of the un-steady simulation in order to reach realistic results,

• modifying thermal conductivity coefficients for the air layer at each step and time increment of the unsteady simulation in order to indirectly simulate con-vective heat transfer in the air-cavity,

• modifying the magnitude water velocity uw, according to assumed control strategy for water mass flux (Section 5.5), at each step and time increment of the unsteady simulation in order to maximize the performance of HSC,

• processing the climate data of the Typical Meteorological Year for the North-East region of Poland (Elbląg) [164] in order to compute the sol-air temper-ature, Tsol (Eq. 5.3.15), and convective heat transfer coefficient at external collector surface, he (Eq. 5.3.16), and modify a boundary condition for heat transfer on external collector surface (Eq. 5.3.14) at each step and time incre-ment of the unsteady simulation in order to reach realistic results,

• controlling the current time increment, ∆t, in order to decrease the calculation time.

ABAQUS UEXTERNALDB Main_Definitions

Read_Mass_Flow

URDFIL Controller

FILM

UMASL

Write_Header Write_Row Assign_Interactions SolarTemperatureSTEP2 SolarTemperatureSTEP1

Set_Time_Step Boundary conditioner

Max time increment

controller Results processor

Climate database miner FEA manager

Figure 5.51: FORTRAN program controlling simulation of unsteady heat transfer in FE model of HSC developed in ABAQUS [49]

Chapter 6