# A new design of a solar water storage wall: a system-level model and simulation

## Abstract

Some configurations have been proposed as passive solar wall, but nearly all of them suffer from common shortcomings such as high heat loss flux and low thermal capacity. In this paper, a modified design for building passive solar wall is proposed and a detailed computerized model for its dynamic behavior was developed as a triplet (S, Q, M) from first principles and empirical equations, such that the designer is able to alter any of the variables. Hence, the wall-room properties can be adjusted to improve the wall performance. In this model, S is a solar water wall which is designed on the south wall of a building with a water storage tank as the sensible thermal storage placed inside to passively heats the space with controlled heat transfer and a sufficiently sized storage. Also, Q is a question relating to S which is the performance evaluation of the proposed system including annual and monthly performance along with the room and storage temperatures. Finally, M is a set of mathematical statements \(\hbox {M}=\left\{ {\Sigma \_\hbox {1},\Sigma \_\hbox {2},\Sigma \_\hbox {3},\ldots } \right\} \) which can be used to answer Q. The statements M are based on the lumped capacitance approach which utilizes solar optocalorics, solar thermal conversion and convective heat transfer to simulate passive space heating of a small building. A code was developed to solve the problem and to evaluate parametric sensitivity for design features. A new TrnSys model was introduced and the code results were compared with TrnSys outcome.

## Keywords

Thermal Storage Solar Simulation TRNSYS Building## List of symbols

- \(R_i \)
Thermal resistance (\(\mathrm{m}^{2}\,{^\circ \mathrm{C}}/\mathrm{W})\)

- \(C_m \)
Specific heat (\(\mathrm{J/m}^{2}\,{^\circ \mathrm{C}})\)

- \(Q_r \)
Radiant source term (\(\mathrm{J/m}^{2})\)

- \(m_i \)
Mass of i\(\mathrm{th}\) node (kg)

- \(C_{p,i} \)
Specific heat of the i\(\mathrm{th}\) node (\(\mathrm{J/m}^{2}\,{^\circ \mathrm{C}})\)

- \(T_i \)
Temperature of the i\(\mathrm{th}\) node (\({^\circ \mathrm{C}})\)

- \(k_{nm} \)
Thermal conductance between the nodes m and n (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(q_{nm} \)
Energy flow between two nodes (\(\mathrm{J/m}^{2})\)

- \(E_i \)
Rate of heat transfer with external source at the i\(\mathrm{th}\) node

- \(\Delta t\)
Simulation step time (s)

*l*Characteristics length (m)

- \(L_{tank} \)
Tank wall thickness (m)

- \(k_{tank} \)
Tank wall conductivity (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(A_{tank} \)
Tank wall area (\(\mathrm{m}^{2})\)

*Nu*Nusselt number

*Pr*Prandtel number

- \(Ra_l \)
Rayleigh number

*P*Perimeter (m)

- \(A_s \)
Surface area (\(\mathrm{m}^{2})\)

*ET*Equation of time

- \(T_g \)
Glass cover temperature (\({^\circ \mathrm{C}})\)

- \(T_a \)
Absorber temperature (\({^\circ \mathrm{C}})\)

- \(T_{amb} \)
Ambient temperature (\(\,{^\circ \mathrm{C}})\)

*N*Number of covers

- \(\beta \)
Collector tilt

- \(\varepsilon _g \)
Glass cover emissivity

- \(\varepsilon _a \)
Absorber emissivity

*h*Wind heat transfer coefficient (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(L_h \)
Cube root of the house volume (\(\mathrm{m}^{3})\)

*V*Wind speed (m/s)

- \(\varvec{G}_{\varvec{d,t}} \)
Diffuse irradiance on the tilted surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{iso}} \)
Sky component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{cir}} \)
Circumsolar diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{hor}} \)
Horizon diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{gro}} \)
Ground diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{t}} \)
Total radiation on the tilted surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{F}_{\varvec{1}} \)
Circumsolar coefficient

- \(\varvec{F}_{\varvec{2}} \)
Horizon brightness coefficient

- \(\phi \)
Latitude

- \(\varvec{\rho } _{\varvec{g}}\)
Ground reflectance

- \(\varvec{a,b}\)
Constants in Perez model

- \(\varvec{G}\)
Total radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{b}} \)
Beam radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{d}} \)
Diffuse radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(G_{sc} \)
Solar constant (\(\hbox {W/m}^{2})\)

- \(G_{on} \)
Extraterrestrial radiation incident on the plane normal to the radiation (\(\hbox {W/m}^{2})\)

- \(R_b \)
Beam radiation tilt factor

- \(\varvec{\epsilon }\)
Clearness

- \(\Delta \)
Brightness

- \(L_{st} \)
Local standard time

*L*Longitude

*ET*Equation of time

- \(\left( {\tau \alpha } \right) \)
Transmittance-absorptance product

- \(\gamma \)
Surface azimuth angle

- \(\omega \)
Hour angle

*n*Number of day

- \(\delta \)
Declination

- \(f_{ij}\)
Constants in calculation of brightness coefficients \(F_1 \) and \(F_2 \)

- \(q_{abs}\)
Absorbed energy in the system (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(\theta _b\)
Angle of incidence

- \(\theta _z\)
Zenith angle

- \(\theta _d\)
Effective incidence angle of isotropic diffuse radiation

- \(\theta _g\)
Effective incidence angle of ground-reflected radiation

- \(\theta _r\)
Angle of refraction

- \(n_a\)
Index of refraction for aerogel

- \(n_g\)
Index of refraction for glass

- \(\tau _r\)
Transmittance based on the refraction losses only

- \(\tau _a\)
Transmittance in regard with absorption losses only

- \(\tau \)
Transmittance

- \(r_\parallel \)
Parallel component of the unpolarized radiation

- \(r_{\bot }\)
Perpendicular component of the unpolarized radiation

- \(\alpha _n\)
Absorptivity at normal incidence

- \({\upalpha }\)
Absorptivity

- \(Q_{aux,\,j}\)
Monthly auxiliary heating (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(Q_{dem,\,j}\)
Monthly heating demand (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(\mathcal{F}\)
Annual solar fraction

- \(T_{min}\)
Set point temperature (lower comfort limit) (\({^\circ \mathrm{C}})\)

- \(W_{tank}\)
Tank width (m)

## References

- 1.Sameti, M.: Electrical energy efficient building through distributed generation. Int. J. Renew. Energy Res.
**4**(3), 777–783 (2014)Google Scholar - 2.Sameti, M., Jokar, M.A.: Numerical modeling and optimization of the finite-length overhang. Intell. Build. Int.
**8**(2016). doi: 10.1080/17508975.2015.1134426 - 3.Sameti, M., Haghighat, F.: Optimization approaches in district heating and cooling thermal network. Energy Build.
**140**(1), 121–130 (2017)CrossRefGoogle Scholar - 4.Sameti, M., Jokar, M.A., Astaraei, F.R.: Prediction of solar Stirling power generation in smart grid by GA-ANN model. Int. J. Comput. Appl. Technol.
**55**(2), 147–157 (2017)CrossRefGoogle Scholar - 5.Sameti, M., Kasaeian, A.: Numerical simulation of combined solar passive heating and radiative cooling for a building. Build. Simul.
**8**(3), 239–253 (2015)CrossRefGoogle Scholar - 6.Pirkandi, J., Jokar, M., Sameti, M., Kasaeian, A., Kasaeian, F.: Simulation and multi-objective optimization of a combined heat and power (CHP) system integrated with low-energy building. J. Build. Eng.
**5**, 13–23 (2016)CrossRefGoogle Scholar - 7.Razi Astaraei, F., Sameti, M., Jokar, M.A., Pourfayaz, F.: Numerical simulation of solar-driven Kalina cycle performance for centralized residential buildings in Iran. Intell. Build. Int. (2016). doi: 10.1080/17508975.2016.1197092
- 8.Sameti, M., Ghasemipour, S.S.: Thermodynamic study and performance simulation of a renewable-based Kalina cycle in distributed generation. Int. J. Model. Simul.
**37**(1), 54–66 (2017)CrossRefGoogle Scholar - 9.Schnieders, J., Feist, W., Rongen, L.: Passive houses for different climate zones. Energy Build.
**105**, 71–87 (2015)CrossRefGoogle Scholar - 10.Zamora, B., Kaiser, A.: Thermal and dynamic optimization of the convective flow in Trombe wall shaped channels by numerical investigation. Heat Mass. Transf.
**45**, 1393–1407 (2009)CrossRefGoogle Scholar - 11.Koyunbaba, B.K., Yilmaz, Z., Ulgen, K.: An approach for energy modeling of a building integrated photovoltaic (BIPV) Trombe wall system. Energy Build.
**67**, 680–688 (2013)CrossRefGoogle Scholar - 12.Stazi, F., Mastrucci, A., di Perna, C.: The behaviour of solar walls in residential buildings with different insulation levels: an experimental and numerical study. Energy Build.
**47**, 217–229 (2012)CrossRefGoogle Scholar - 13.Abbassi, F., Dimassi, N., Dehmani, L.: Energetic study of a Trombe wall system under different Tunisian building configurations. Energy Build.
**80**, 302–308 (2014)CrossRefGoogle Scholar - 14.Chan, H.Y., Riffat, S.B., Zhu, J.: Review of passive solar heating and cooling technologies. Renew. Sustain. Energy Rev.
**14**(2), 781–789 (2010)CrossRefGoogle Scholar - 15.Onbasioglu, H., Egrican, A.N.: Experimental approach to the thermal response of passive systems. Energy Convers. Manag.
**43**(15), 2053–2065 (2002)CrossRefGoogle Scholar - 16.Shen, J., Lassue, S., Zalewski, L., Huang, D.: Numerical study on thermal behavior of classical or composite Trombe solar walls. Energy Build.
**39**(8), 962–974 (2007)CrossRefGoogle Scholar - 17.Saadatian, O., Sopian, K., Lim, C.H., Asim, N., Sulaiman, M.Y.: Trome walls: a review of opportunities and challenges in research and development. Renew. Sustain. Energy Rev.
**16**(8), 6340–6351 (2012)CrossRefGoogle Scholar - 18.Shen, J., Lassue, S., Zalewski, L., Huang, D.: Numerical study of classical and composite solar walls by TRNSYS. J. Therm. Sci.
**16**(1), 46–55 (2007)CrossRefGoogle Scholar - 19.Rabani, M., Kalantar, V., Dehghan, A.A., Faghih, A.K.: Experimental study of the heating performance of a Trombe wall with a new design. Sol. Energy
**118**, 359–374 (2015)CrossRefGoogle Scholar - 20.Hu, Z., Luo, B., He, W.: An experimental investigation of a novel Trombe wall with venetian blind structure. Energy Proc.
**70**, 691–698 (2015)CrossRefGoogle Scholar - 21.Brownson, J.R.S.: Solar Energy Conversion Systems. Elsevier, Amsterdam (2014)Google Scholar
- 22.“Weather Data Sources,” U.S. Department of Energy, [Online]. Available: http://apps1.eere.energy.gov/buildings/energyplus/weatherdata_sources.cfm. Accessed 15 Sept 2015
- 23.Rawlings, R.: Capturing Solar Energy. CIBSE Publications, London (2009)Google Scholar
- 24.Eicker, U.: Solar Technologies for Buildings. Wiley, New York (2006)Google Scholar
- 25.Albanese, M.V., Robinson, B.S., Brehob, E.G., Sharp, M.K.: Simulated and experimental performance of a heat pipe assisted solar wall. Sol. Energy
**86**(5), 1552–1562 (2012)CrossRefGoogle Scholar - 26.Çengel, Y.A., Ghajar, A.J.: Heat and Mass Transfer: Fundamentals and Applications. McGraw-Hill, New York (2014)Google Scholar
- 27.Bergman, T.L., Incropera, F.P., Lavine, A.S.: Fundamentals of Heat and Mass Transfer. Wiley, New York (2011)Google Scholar
- 28.Kalogirou, S.A.: Solar Energy Engineering: Processes and Systems. Elsevier, Amsterdam (2013)Google Scholar
- 29.Tarazi, N.K.: A model of a Trombe wall. Renew. Energy
**1**(3), 533–541 (1991)CrossRefGoogle Scholar - 30.Duffie, J.A., Beckman, W.A.: Solar Engineering of Thermal Processes. Wiley, New York (2013)CrossRefGoogle Scholar
- 31.Robinson, B.S., Sharp, M.K.: Heating season performance improvements for a solar heat pipe system. Sol. Energy
**110**, 39–49 (2014)CrossRefGoogle Scholar - 32.TRNSYS 16: A Transient System Simulation Program, University of Wisconsin (2007). http://www.trnsys.com/