# Impacts of Ventilation Ratio and Vent Balance on Cooling Load and Air Flow of Naturally Ventilated Attics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Model

_{0}specified to the outside ambient air temperature to correctly calculate the buoyancy effects. In all the cases reported in this study, T

_{0}= 305.15 K is assumed, and the pressures at the soffit and ridge vents are specified to be zero gauge pressure. Therefore, the obtained air flow is purely driven by the thermally induced buoyancy forces, i.e., the stack effect. At the soffit vent, the inlet air is assumed to enter at an ambient temperature of 305.15 K and a turbulent intensity of 1%.

**Figure 1.**Schematic of the computational domain and boundary conditions [29].

_{cb}and T

_{ct}are the temperatures at the ceiling-bottom and ceiling-top, respectively; and the heat transfer coefficient h

_{c}is determined by the thermal conductivity of ceiling material λ

_{c}divided by ceiling thickness t

_{c}. In this study, the ceiling-bottom temperature is kept at T

_{cb}= 295.15 K, while h

_{c}= 0.284 W/m

^{2}K is adopted to approximate a ceiling insulation level of R-20. Similarly, a roof-top temperature of T

_{rt}= 345.15 K and a heat transfer coefficient of h

_{r}= 4.733 W/m

^{2}K (equivalent to an insulation level of R-1.2) are specified to the roof boundary to simulate a condition of a 3 cm plywood roof. The roof-top temperature of T

_{rt}= 345.15 K specified in this study is corresponding to a typical peak roof temperature in summer days at several geographical regions in the United States, as evident in field measurements [4,30,31] and modeling predictions [21]. More discussions on the bases for the parameters chosen in the simulation can be found in [22], while the impacts of roof pitch and ceiling insulation on attic cooling load were reported in [29].

_{i}), pressure (p), and temperature (T) distributions in the attic space shown in Figure 1 are governed by the following continuity, momentum, and energy equations:

_{T}, and eddy thermal diffusivity α

_{θ}are determined by the employed turbulence model. In Equations (3,4), the substantial derivative terms include unsteady terms (partial derivative with respective to time) that account for all unsteadiness that does not belong to the turbulence, i.e., the unsteadiness that is not represented by the turbulence model [25].

^{+}value for the first grid close to the walls is everywhere less than 1, in order to best capture the details of boundary layers, including the viscous sublayer which typically has a thickness of y

^{+}~ 10. The numerical model employed in this paper is validated through grid and time step dependence tests as well as detailed comparison to previous experimental and large eddy simulation results of a benchmark problem of mixed turbulent convection in a square cavity [32,33,34], as reported in [29], where the same numerical model is employed to investigate the effects of roof pitch and ceiling insulation on attic cooling load and air flow.

## 3. Results and Discussion

**Figure 2.**Numerical results for the sealed attic case: (

**a**) streamlines (in kg/m s); (

**b**) isotherms (in K); (

**c**) horizontal velocity profile along the vertical line x = 2 m; and (

**d**) temperature profile along the symmetric line x = 0.

**Figure 3.**Predicted (

**a**) streamlines (in kg/m s) and (

**b**) isotherms (in K) for attics with balanced ridge and soffit vents at various ventilation ratios.

**Figure 4.**Predicted profiles of (

**a**) horizontal velocity along the vertical line x = 2 m; and (

**b**) temperature along the symmetric line x = 0 for attics with balanced ridge and soffit vents at various ventilation ratios.

**Figure 5.**Comparsion of predicted (

**a**) streamlines (in kg/m s) and (

**b**) isotherms (in K) between balanced attic ventilation case and two cases of unbalanced attic ventilation at ventilation ratio 1/133.

**Figure 6.**Comparsion of predicted profiles of (

**a**) horizontal velocity along the vertical line x = 2 m; and (

**b**) temperature along the symmetric line x = 0 between balanced attic ventilation case and two cases of unbalanced attic ventilation at ventilation ratio 1/133.

**Figure 7.**Predicted ventilating mass flow rate as a function of ventilation ratio for balanced and unbalanced attic ventilation cases.

**Figure 8.**Predicted attic cooling load as a function of ventilation ratio for balanced and unbalanced attic ventilation cases.

**Figure 9.**Predicted heat gain from roof as a function of ventilation ratio for balanced and unbalanced attic ventilation cases.

## 4. Conclusions

- (1)
- Air flows in the attics are steady and exhibit a general streamline pattern that is qualitatively insensitive to the investigated variations of ventilation ratio and vent configuration. Except for the soffit regions, the attic spaces are dominated by thermal stratification.
- (2)
- Along with the increase in ventilation ratio, the ventilating air flow rate increases and the cooling load decreases. In case of the balanced ventilation configuration, for example, increasing ventilation ratio from 1/200 to 1/100 results in an increase of 70% in ventilating mass flow and a decrease of 23% in attic cooling load. However, the benefit of increasing ventilating air flow rate and reducing cooling load by increasing ventilation ratio drops gradually with the increasing ventilation ratio, and only marginal reduce in cooling load is observed as the ventilation ratio increases from 1/50 to 1/25 (Figure 8).
- (3)
- Compared with unbalanced vent configurations, balanced attic ventilation is shown to be the optimal solution in both maximizing ventilating flow rate and minimizing cooling load for attics with ventilation ratio lower than 1/100.
- (4)
- For attics with ventilation ratio higher than 1/67, the configuration consisting of big ridge vent and small soffit vent favors ventilating air flow enhancement, while the configuration consisting of small ridge vent and big soffit vent is associated with the lowest cooling load.

## Acknowledgments

## Nomenclature

c_{p} | specific heat |

d | vent width |

g | gravitational acceleration |

h | heat transfer coefficient |

H | attic height |

k | fluctuation kinetic energy |

ṁ | mass flow rate |

p | pressure |

p_{atm} | atmospheric pressure |

Q | heat transfer rate |

t_{c} | ceiling thickness |

T | temperature |

T_{0} | reference temperature |

T_{in} | inlet air temperature |

u | velocity component |

W | half width of attic |

x,y | coordinates |

## Greek symbols

α | thermal diffusivity |

α_{θ} | eddy thermal diffusivity |

β | thermal expansion coefficient |

λ | thermal conductivity |

λ _{c} | ceiling thermal conductivity |

ν | kinetic viscosity |

ν_{T} | eddy viscosity |

ρ | density |

## Subscripts

c | ceiling |

cb | ceiling-bottom |

ct | ceiling-top |

r | roof |

rt | roof-top |

## References

- Federal Housing Administration. Property Standards and Minimum Construction Requirements for Dwellings; Federal Housing Administration: Washington, DC, USA, 1942. [Google Scholar]
- Rose, W.B.; TenWolde, A. Venting of attics and cathedral ceilings. ASHRAE J.
**2002**, 44, 26–33. [Google Scholar] - Hutchings, J.I. National Codes Handbook; McGraw Hill: New York, NY, USA, 1998. [Google Scholar]
- Rudd, A.F.; Lstiburek, J.W. Vented and sealed attics in hot climates. ASHRAE Trans.
**1998**, 104, 1199–1210. [Google Scholar] - Kamiyo, O.M.; Angeli, D.; Barozzi, G.S.; Collins, M.W.; Olunloyo, V.O.S.; Talabi, S.O. A comprehensive review of natural convection in triangular enclosures. ASME Appl. Mech. Rev.
**2010**, 63, 1–13. [Google Scholar] [CrossRef] - Saha, S.C.; Khan, M.M.K. A review of natural convection and heat transfer in attic-shaped space. Energy Build.
**2011**, 43, 2564–2571. [Google Scholar] [CrossRef][Green Version] - Flack, R.D.; Witt, C.L. Velocity measurements in two natural convection air flows using a laser velocimeter. ASME J. Heat Transf.
**1979**, 101, 256–260. [Google Scholar] [CrossRef] - Flack, R.D. The experimental measurement of natural convection heat transfer in triangular enclosures heated or cooled from below. ASME J. Heat Transf.
**1980**, 102, 770–772. [Google Scholar] [CrossRef] - Poulikakos, D.; Bejan, A. Natural convection experiments in a triangular enclosure. ASME J. Heat Transf.
**1983**, 105, 652–655. [Google Scholar] [CrossRef] - Holtzman, G.A.; Hill, R.W.; Ball, K.S. Laminar natural convection in isosceles triangular enclosures heated from below and symmetrically cooled from above. ASME J. Heat Transf.
**2000**, 122, 485–491. [Google Scholar] [CrossRef] - Asan, H.; Namli, L. Laminar natural convection in a pitched roof of triangular cross-section: Summer day boundary conditions. Energy Build.
**2000**, 33, 69–73. [Google Scholar] [CrossRef] - Ridouane, E.H.; Campo, A.; McGarry, M. Numerical computation of buoyant airflows confined to attic spaces under opposing hot and cold wall conditions. Int. J. Therm. Sci.
**2005**, 44, 944–952. [Google Scholar] [CrossRef] - Lei, C.; Armfield, S.W.; Patterson, J.C. Unsteady natural convection in a water-filled isosceles triangular enclosure heated from below. Int. J. Heat Mass Transf.
**2008**, 51, 2637–2650. [Google Scholar] [CrossRef] - Kent, E.F. Numerical analysis of laminar natural convection in isosceles triangular enclosures. J. Mech. Eng. Sci.
**2009**, 223, 1157–1169. [Google Scholar] [CrossRef] - Saha, S.C.; Patterson, J.C.; Lei, C. Natural convection and heat transfer in attics subject to periodic thermal forcing. Int. J. Therm. Sci.
**2010**, 49, 1899–1910. [Google Scholar] [CrossRef][Green Version] - Saha, S.C. Unsteady natural convection in a triangular enclosure under isothermal heating. Energy Build.
**2011**, 43, 695–703. [Google Scholar] [CrossRef][Green Version] - Ridouane, E.H.; Campo, A.; Hasnaoui, H. Turbulent natural convection in an air-filled isosceles triangular enclosure. Int. J. Heat Fluid Flow
**2006**, 27, 476–489. [Google Scholar] [CrossRef] - Talabi, S.O.; Olunloyo, V.O.S.; Kamiyo, O.M.; Collins, M.W.; Karayiannis, T.G. Flow field and Reynolds stress distribution in low turbulence natural convection in a triangular cavity. In Proceedings of Fifth International Symposium on Turbulence, Heat and Mass Transfer, Dubrovnik, Croatia, 26–29 September 2006; pp. 511–514.
- Medina, M.A.; O’Neal, D.L.; Turner, W.D. A transient heat and mass transfer model of residential attics used to simulate radiant barrier retrofits, Part I: Development. ASME J. Sol. Energy Eng.
**1998**, 120, 32–38. [Google Scholar] [CrossRef] - Medina, M.A.; O’Neal, D.L.; Turner, W.D. A transient heat and mass transfer model of residential attics used to simulate radiant barrier retrofits, Part II: Validation and simulations. ASME J. Sol. Energy Eng.
**1998**, 120, 39–44. [Google Scholar] [CrossRef] - Moujaes, S.F.; Alsaiegh, N.T. Numerical heat transfer attic model using a radiant barrier system. J. Energy Eng.
**2000**, 126, 32–51. [Google Scholar] [CrossRef] - Wang, S.; Shen, Z.; Gu, L. Numerical simulation of buoyancy-driven turbulent ventilation in attic space under winter conditions. Energy Build.
**2012**, 47, 360–368. [Google Scholar] [CrossRef] - Walters, D.K.; Cokljat, D. A three-equation eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow. J. Fluid Eng.
**2008**, 130, 1–14. [Google Scholar] [CrossRef] - Ozoe, H.; Mouri, A.; Ohmuro, M.; Churchill, S.W.; Lior, N. Numerical calculations of laminar and turbulent natural convection in water in rectangular channels heated and cooled isothermally on the opposing vertical walls. Int. J. Heat Mass Transf.
**1985**, 28, 125–138. [Google Scholar] [CrossRef] - Henkes, R.A.W.M.; van der Vlugt, F.F.; Hoogendoorn, C.J. Natural-convection flow in a square cavity calculated with low-Reynolds-number turbulence models. Int. J. Heat Mass Transf.
**1991**, 34, 377–388. [Google Scholar] [CrossRef] - Henkes, R.A.W.M.; Hoogendoorn, C.J. Scaling of the turbulent natural convection flow in a heated square cavity. ASME J. Heat Transf.
**1994**, 116, 400–408. [Google Scholar] [CrossRef] - Hsieh, K.J.; Lien, F.S. Numerical modeling of buoyancy-driven turbulent flows in enclosures. Int. J. Heat Fluid Flow
**2004**, 25, 659–670. [Google Scholar] [CrossRef] - ANSYS FLUENT, version 13.0; ANSYS, Inc.: Canonsburg, PA, USA, 2011.
- Wang, S.; Shen, Z.; Gu, L. The impact of roof pitch and ceiling insulation on cooling load of naturally-ventilated attics. Energies
**2012**, 5, 2178–2196. [Google Scholar] [CrossRef] - Winandy, J.E.; Barnes, H.M.; Hatfield, C.A. Roof Temperature Histories in Matched Attics in Mississippi and Wisconsin; Research Paper FPL-RP-589; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2000.
- TenWolde, A. FPL Roof Temperature and Moisture Model; Description and Verification; Research Paper FPL-RP-561; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2000.
- Blay, D.; Mergui, S.; Niculae, C. Confined turbulence mixed convection in the presence of a horizontal buoyant wall jet. ASME Heat Transf. Div.
**1992**, 213, 65–72. [Google Scholar] - Zhang, W.; Chen, Q. Large eddy simulation of natural and mixed convection airflow indoors with two simple filtered dynamic subgrid scale models. Numer. Heat Transf. A
**2000**, 37, 447–463. [Google Scholar] [CrossRef] - Zhang, Z.; Zhang, W.; Zhai, Z.; Chen, Q. Evaluation of various turbulence models in predicting airflow and turbulence in enclosed environments by CFD: Part 2—Comparison with experimental data from literature. HVAC&R Res.
**2007**, 13, 871–886. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Wang, S.; Shen, Z.
Impacts of Ventilation Ratio and Vent Balance on Cooling Load and Air Flow of Naturally Ventilated Attics. *Energies* **2012**, *5*, 3218-3232.
https://doi.org/10.3390/en5093218

**AMA Style**

Wang S, Shen Z.
Impacts of Ventilation Ratio and Vent Balance on Cooling Load and Air Flow of Naturally Ventilated Attics. *Energies*. 2012; 5(9):3218-3232.
https://doi.org/10.3390/en5093218

**Chicago/Turabian Style**

Wang, Shimin, and Zhigang Shen.
2012. "Impacts of Ventilation Ratio and Vent Balance on Cooling Load and Air Flow of Naturally Ventilated Attics" *Energies* 5, no. 9: 3218-3232.
https://doi.org/10.3390/en5093218