J. Cent. South Univ. (2012) 19: 733-739 

DOI: 10.1007/s11771-012-1065-7

Natural ventilation performance of single room building with

fluctuating wind speed and thermal mass

TAN Gang

Department of Civil and Architectural Engineering, University of Wyoming, Laramie, Wyoming, USA

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Natural ventilation is driven by either buoyancy forces or wind pressure forces or their combinations that inherit stochastic variation into ventilation rates. Since the ventilation rate is a nonlinear function of multiple variable factors including wind speed, wind direction, internal heat source and building structural thermal mass, the conventional methods for quantifying ventilation rate simply using dominant wind direction and average wind speed may not accurately describe the characteristic performance of natural ventilation. From a new point of view, the natural ventilation performance of a single room building under fluctuating wind speed condition using the Monte-Carlo simulation approach was investigated by incorporating building fa?ade thermal mass effect. Given a same hourly turbulence intensity distribution, the wind speeds with 1 min frequency fluctuations were generated using a stochastic model, the modified GARCH model. Comparisons of natural ventilation profiles, effective ventilation rates, and air conditioning electricity use for a three-month period show statistically significant differences (for 80% confidence interval) between the new calculations and the traditional methods based on hourly average wind speed.

Key words: natural ventilation; fluctuating wind speed; thermal mass; GARCH model

1 Introduction

Building energy accounts for a significant portion of the total energy that is consumed by the entire country in many nations around the world. As an example, in United States, almost 40% of the primary energy and approximately 70% of the electricity are used in buildings [1]. Since buildings contribute significantly to carbon emissions and therefore building energy efficiency is critical to guarantee a nation’s energy security, net zero energy buildings have become a hot topic in recent years, especially for new building development [2].

Natural ventilation is one of the technologies widely used to save building energy use as natural ventilation reduces cooling demand and mechanical ventilation needs. Natural ventilation uses stack effect and/or wind driven forces to achieve air changes between building spaces and outside environment when climate is moderate. Accurately quantifying the future performance of natural ventilation will help designers and engineers to design the appropriate structures and control mechanism.   However, this task is challenging due to the tremendous uncertainties in natural ventilation such as wind speed fluctuations, wind direction variations, and occupants’ interaction.

HORAN and FINN [3] used CFD to study the influence of variations in external wind speed and direction on the air change rate (ACH) for a two-storey naturally ventilated building. They examined the external wind speed varying from 25% to 250% of the mean site wind speed as well as maintaining the single wind speed to investigate the relationship between the wind direction and the ACH rate. However, their study was only focused on an atrium space. CHAPLIN et al [4] set up a series of idealized experiments to examine the ventilation flow through an opening in a chamber in which a simulation of the internal pressure responds to a sinusoidal external pressure variation.

Also, ETHERIDGE [5-6] conducted a theoretical study into the effects of unsteady wind pressures on the instantaneous flow rates, of which the main concern was to reduce the occurrence of instantaneous flow reversal through openings. The inertial and the compressibility of the air were examined and they recommended the use of long ducts instead of sharp-edged openings.

Researchers concern the wind fluctuation having two effects on the air change: 1) the pulsation flow, and 2) the penetration eddies. COCKROFT and ROBERSTON [7] studied the single-opening pulsation flow of an enclosure with a single opening, subjected to a turbulent impinging air stream from a mechanical device. SASAKI et al [8] considered the fluctuation of the airflow through the cracks to be influenced not only by the static resistance of the crack but also by the depth of the crack, the air volume behind the crack, and the dynamic feature of the wind pressure. SASAKI modeled a building using a mechanical system consisting of mass, resistance, and elastic forces. HAGHIGHAT et al [9-10] used a stochastic process composed by a mean value of the wind velocity superimposed by a fluctuating component.

However, the wind fluctuations (especially surrounding buildings) have unique dynamic features. The mechanical device driving air flow doesn’t match the dynamic characteristics of wind in few aspects [11]. One example is that wind has significant autoregressive behavior in volatility as ZHU et al [12] observed in the monitored wind velocity. Therefore, the sinusoidal variation model [4] and regular Gaussian stochastic model [9] may not represent the dynamic fluctuations of wind and may result in air change rates under mechanical forces instead of natural ventilation.

The previous research about the effect of wind fluctuations on infiltration rates generally was concentrated on high frequency variations, while investigation on the overall ventilation of building with fluctuating wind lacks. On the other hand, most of the current multi-zone models calculate bulk air infiltration rates based solely on average wind velocity and the complex wind fluctuations are not considered. A bridge approach is needed to address both wind fluctuations and the overall infiltration rates that directly determine the energy performance of buildings.

In this work, a stochastic model is adopted which captures the autoregressive behavior of wind speed to simulate wind fluctuations. With the generated wind speed, a multi-zone model coupling energy balance equations is applied to evaluating the bulk ventilation rates and thus the electric consumption of the air conditioner equipment is examined.

2 Methodology

2.1 Wind speed data generation

Instead of obtaining wind speed data from field monitoring, which may inherit special characteristics of individual site, this work uses a simpler but more general method: generating wind speed data from a validated stochastic model. The generalized autoregressive conditional heteroskedaticity (GARCH) model [13], with slight modification, has shown capability to capture the dynamic characteristic of wind velocity [14]. To implement the modified GARCH model, a logarithm change of wind velocity is defined:

                            (1)

where u_t is the wind speed monitored at time t, and u_r,t stands for the logarithm change of wind velocity from time t-1 to time t.

The modified GARCH model for wind speed regression is proposed as

                  (2)

where ε_t (the ARCH term) denotes the residuals of logarithm change of wind speed u_r,t and it is a function of the GARCH term ; z_t~i.i.d.N(0, 1) that is specified as a standard normal distribution with zero mean value and unit variance; T(u_t) is the turbulence intensity of the wind speed, which is the modification item to the general GARCH model. The turbulence intensity is to include the dynamic magnitude of the monitored wind speed into the model. Other items are either regression constants (e.g., c₀ and c₁) or regression coefficients (e.g., α₀, α₂, and α₃). To guarantee the non-negative value, the GARCH model requires the regression intersection c₁ non-negative too (?0). Meanwhile, to reduce the divergence probability, the addition of α₂ and α₃ is close to unit one but slightly smaller than one with α₂ greater than zero.

The hourly wind speed data from TMY2 for Denver, USA have been adopted as the ‘seeds’ to generate fluctuating wind velocities with one-minute frequency. Considering that weather stations are generally located in open areas, a wind profile power law has been applied to adjusting the TMY2 wind speed to localized wind speed at the objective building height:

                               (3)

where u_b is the wind velocity adjusted to building height, u_w is the velocity from TMY2 measured at weather stations, h_b is the building height, and h_w is the height of measurement location of weather station for wind speed, which is assumed 12 m in this work. Assuming a building located at a metropolitan area, the exponential coefficient g here (or so-called atmospheric boundary layer parameter) that reflects the roughness of the ground surface is chosen to be 0.25 in this work [15].

The adjusted TMY2 hourly wind speed is used as the outside fluctuating wind speed for the first minute of that particular hour. Then, two series of fluctuating wind velocity data are generated for the other 59 min with    1 min internal for that particular hour. In total, three months (June, July, and August) have been investigated in this work. The two series of wind speed data have different fluctuation magnitudes and turbulent intensities, which are determined by the GARCH model coefficients and constants as presented in Table 1. In Table 1, i.i.d. is the abbreviation of independent and identically distributed random variables, and U(a,b) is the uniform distribution in the range of a and b, while N(a, b) is the standard normal distribution with mean of a and standard deviation of b.

Table 1 Different GARCH model coefficients and constants for wind speed data generation

For a minute, once the logarithm change u_r,t has been calculated using Eq. (2), the wind velocity is thus interpreted as following Eq. (4). Figure 1 and Figure 2 show example generated wind velocity data for series 1 and series 2, respectively.

                            (4)

Fig. 1 Example generated wind speed for series 1

Fig. 2 Example generated wind speed for series 2

2.2 Ventilation rate calculation

A 5 m×6 m×2.8 m (L×W×H) single room building has been created to evaluate the natural ventilation performance under fluctuating wind boundary condition, as shown in Fig. 3. The flow network composed of opening’s resistance and zones for a multi-zone model is also sketched.

Fig. 3 Illustration sketch of single room building

Both buoyancy effect and wind pressure forces have been included into the multi-zone model calculation. For wind pressure estimate, a simple regression formula has adopted in order to reduce the computation [16]:

        (5)

where C_w is the pressure coefficient; z_h is ratio of the height of the opening to the height of the building; g is the ground roughness coefficient same as that in Eq. (3);  r_b is the ratio of height of the building to the average height of surrounding buildings; f_a is the ratio of the width of the windward wall to the height of the windward wall; s_a is the ratio of the width of the side wall to the height of the side wall; a_n is the wind direction angle (relative to north direction).

For each zone, no matter indoor or outdoor, a static pressure is used to represent its pressure condition. Therefore, the pressure difference between two zones j and i can be written as

                       (6)

where p_j and p_i are static pressures of two zones; p_s and p_w are the pressure differences induced by stack effect and wind forces, respectively.

In calculation, the Boussinesq approximation has been selected to quantify the density variation because of temperature change. The wind induced pressure is calculated using wind velocity u and wind pressure coefficient C_w:

                              (7)

Then, the mass flow rate between two zones through an opening is calculated using a power-law function:

                     (8)

where m_j,i is the mass flow rate between zone j and zone i, C_d is the discharge coefficient of the opening, A is the effective area of the opening, and ρ_{j or i} is the airflow’s density that depends on the airflow direction.

Besides the airflow balance for the room space, there are two energy balance equations, for thermal mass of building fa?ade and room air:

      (9)

where c_p is the specific heat of air, V is the space volume of the room, T is air temperature, Q_facade is the heat exchange between building facades (including walls and roof) and room air, Q_internal is the internal heat generation including occupants, lighting, cooking and miscellaneous equipment and “abs” stands for the absolute value. Herein, the subscript “1” stands for outdoor air at opening A1 height and the subscript “2” stands for room air.

The building facades are divided into two equally thick layers in calculation (see Fig. 4). The two layers have different materials and their thermal properties are listed in Table 2. The energy balance equations of these two building structure layers are

     (10)

      (11)

where c is the specific heat of building fa?ade material, V is the volume, T is the temperature, h is the convection heat transfer coefficient, and R is the conductivity thermal resistance. The subscript “o” stands for outside, the subscripts “a” and “b” stand for two layers of building facades, and the subscripts “1” and “i” stand for inside. The outside temperature in Eq. (10) is either outside air temperature or solar-air temperature if there is solar irradiation. These temperatures are either directly from TMY2 data or calculated from TMY2 data.

Fig. 4 Illustration sketch of building facades (a) and thermal resistance circuit (b)

Table 2 Thermal properties of building facades

2.3 Operation and control schemes

The single room in this work is designed to model a small size apartment. The occupants have regular business working hours from 9:00am to 5:00pm from Monday to Friday. The internal load profiles are assumed accordingly and shown in Fig. 5 and Fig. 6, for workday and weekend, respectively.

Fig. 5 Internal load profile of workday (i.e. Mon. to Fri.)

Fig. 6 Internal load profile of weekend day (i.e. Sat. and Sun.)

Natural ventilation would be possibly used if the outside weather condition allows, except that 1) outside ambient air temperature is lower than 16 °C, or 2) indoor air temperature rises above 30 °C. Once natural ventilation cannot meet the cooling requirement, a room air conditioner with 3.5 kW cooling capacity will be turned on and to maintain indoor air temperature at 24 °C. The control scheme is designed to switch between natural ventilation and mechanical cooling every 20 min. The air conditioner is rated at energy efficiency ratio (EER) of 9.4.

When the air conditioner is running, it may work under part load conditions. For the single stage unit, the part load rating is obtained by the cycling of the compressor. Research shows the ratio of electric consumption of the machine at part load working to the electric consumption at full load is a linear function to the ratio of the part load capacity to the full capacity at the same operative temperatures [17]. This elaborates a simple mathematical model and it can be used to estimate the electricity usage of air conditioner throughout the entire summer season:

                               (12)

where Z is defined as the ratio of the electric consumption of the machine at part load to that at full capacity, P_L is the ratio of the part load capacity to the fully capacity, and a and b are constants (a is used as 0.95 and b is quite small, about 0.05).

3 Results and discussion

This work borrows ideas of Monte-Carlo simulation to run the calculations for 15–20 times and statistical summary is thus obtained based on these runs for an 80% confidence interval.

3.1 Indoor temperature in natural ventilation

Natural ventilation can use ‘free’ cooling sources from outside air with relatively moderate temperature that can keep the indoor air temperature within the acceptable thermal comfort range. In this work, the room air temperature has been maintained approximately at 19-30 °C for natural ventilation. Due to the energy storage effect of building fa?ade thermal mass, the room air temperature varies in a smaller range than the outside air temperature, which is 9.0 °C of indoor environment compared to 13.0 °C of ambient environment (seeFig. 7).

Fig. 7 Comparison of room air temperature (RAT) and outdoor air temperature (OAT) for a naturally ventilated day

To enhance understanding of the comparisons between difference calculations, several parameters are defined:

T_0.5=(Number of natural ventilation hours in which RAT’s variation exceeds 0.5 °C for that particular hour)/(Total hours of natural ventilation)

T_1.0=(Number of natural ventilation hours in which RAT’s variation exceeds 1.0 °C for that particular hour )/(Total hours of natural ventilation)

Because of the fluctuating wind speed, coupling with other effects such as internal load variation, the   20 min interval indoor air temperature fluctuates too. The above defined two parameters, T_0.5 and T_1.0, tell us the percentage and strength of the fluctuations. Table 3 compares the 80% confidence interval (CI) of T_0.5 and T_1.0. It can be seen that there are a significant number of hours in which the room air temperature varies exceeding 0.5 °C, about 14% for both series of wind speed. In contrast, if the natural ventilation was calculated using hourly average wind speed instead of fluctuating wind speed, there is no obvious room air temperature variation in that particular hour even if we use the same control strategy of switching natural ventilation and air conditioning every 20 min.

Table 3 T_0.5 and T_1.0 parameter comparison for two series of fluctuating wind speed data

As indoor air temperature is one of the factors that impact occupants’ thermal comfort, the room air temperature variation in a short period (e.g. 1 h here) is noticeable. Calculations based on fluctuating wind speed provide detailed information of room air temperature variation which will help fully evaluate indoor thermal environment for a naturally ventilated building.

3.2 Ventilation rates

Before examining the variation of ventilation rates within 1 h period, it is worthy to look at the total number of natural ventilation hours for the entire summer from June to August. If evaluating natural ventilation performance using the average wind speed of each hour, the hours suitable for natural ventilation are greater than those if we use one-minute fluctuating wind speed to evaluate the wind pressure forces, as shown in Table 4. The ‘fluctuating’ in Table 4 refers to calculating natural ventilation using the one-minute fluctuating wind speeds while the ‘hourly average’ means using the hourly average wind speed.

Table 4 Natural ventilation hours for two series of fluctuating wind speed data

Similarly, two new parameters are introduced to help understand the ventilation patterns under different calculation modes:

V_10%=(Number of natural ventilation hours in which variation of ventilation rate exceeds 10% for that particular hour)/(Total hours of natural ventilation)

V_20%=(Number of natural ventilation hours in which variation of ventilation rate exceeds 20% for that particular hour)/(Total hours of natural ventilation)

Table 5 lists the comparison between V_10% and V_20% for the calculation modes using the two generated series of fluctuating wind speed data. The ventilation rates present much higher variations compared to room air temperature. The Series 2 wind data also create stronger variations in ventilation rates than those of the Series 1 wind data. As airflow speed is another factor that impacts occupant thermal comfort, it needs further investigation if in summer, 40% or over 50% of the natural ventilation hours exhibit 10% variations in ventilation rates and over 20% natural ventilation hours demonstrate 20% variations in ventilation rates.

Table 5 V_10% and V_20% parameter comparison for two series of fluctuating wind speed data

Three parameters are introduced here to evaluate the difference between natural ventilation rate calculations using fluctuating wind speed and that using hourly average wind speed:

R_10%=(Number of natural ventilation hours in which the ventilation rate calculated from fluctuating wind speed is 10% greater or smaller than the ventilation rate from hourly average wind speed for that particular hour)/(Total hours of natural ventilation)

The R_20% and R_50% parameters are defined similarly with 20% and 50% criteria, respectively. Table 6 lists the comparison between these three parameters. The ventilation rate for an individual hour is significantly different with that using the fluctuating wind speed compared with using the hourly average wind speed.

Table 6 R_10%, R_20%, and R_50% parameter comparison for two series of fluctuating wind speed data

3.3 Air conditioner electricity use

An air conditioner has been assumed to provide additional cooling capacity when the room air temperature rises beyond 30 °C and thus natural ventilation is not suitable for indoor environment control.  As the first step, the total electric consumption throughout three months is compared. From Table 7, the difference of total air conditioner electric consumption between the calculations based on fluctuating wind speeds and those based on hourly average wind speeds seem not very great, about 4.4% for the Series 1 data. However, it is noticeable that for Series 2 data this difference becomes 11.7%.

Table 7 Total air conditioner electric consumption for three months

Next, details of the electric use of air conditioner for individual hours are compared. A new parameter is defined:

E_10%=(Number of air conditioning hours in which A/C electric use from fluctuating wind speed is 10% greater or smaller than that of A/C electric use from hourly average wind speed for that particular hour)/(Total hours of air conditioning)

The E_20% and E_50% parameters are defined similarly with 20% and 50% criteria, respectively.

From Table 8, the hourly air conditioner electric consumption is quite different between using the fluctuating wind speeds and using the hourly average speeds, all above 10% for three ER parameters.

Table 8 E_10%, E_20%, and E_50% parameter comparison for two series of fluctuating wind speed data

4 Conclusions

1) Thermal mass maintains indoor air temperature varying less than the variations of outdoor air temperature even under natural ventilation mode.

2) Calculation based on fluctuating wind speed introduces 4%-7% less natural ventilation applicable hours than that from the hourly average wind speed.

3) The 8%-23% of the hourly ventilation rates obtained from fluctuating wind speed are at least 10% different compared with those from the hourly average wind speed.

4) Air conditioner uses 4%-12% more electricity if using the fluctuating wind effect than if using the hourly average wind speed.

5) It should be pointed out that these differences may interact with other factors such as wind direction variation, building structural thermal mass, HVAC system type and size, and internal loads. More research is needed to further investigate these impacts in order to obtain more general results assisting architectural and engineering design/operation for naturally ventilated buildings.

References

[1] EIA (U.S. Energy Information Administration), Annual energy review 2009 [EB/OL]. [2011-6-20]. http://www.eia.gov/emeu/aer/ contents.html.

[2] TORCELLINI P, PLESS S, DERU M, CRAWLEY D. Zero energy buildings: a critical look at the definition [EB/OL]. [2011-6-20]. http://www.nrel.gov/docs/fy06osti/39833.pdf.

[3] HORAN J M, FINN D P. Sensitivity of air change rates in a naturally ventilated atrium space subject to variations in external wind speed and direction [J]. Energy and Buildings, 2008, 40: 1577-1585.

[4] CHAPLIN G C, RANDALL J R, BAKER C J. The turbulent ventilation of a single opening enclosure [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2000, 85(2): 145-162.

[5] ETHERIDGE D W. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-mean flow rates [J]. Building and Environment, 2000, 35(2): 111-133.

[6] ETHERIDGE D W. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design-instantaneous flow rates [J]. Building and Environment, 2000, 35(2): 321-337.

[7] CROCKROFT J P, ROBERSTON P. Ventilation of an enclosure through a single opening [J]. Building and Environment, 1976, 11(1): 29-35.

[8] SASAKI T, HAYASHI M, ARATANI N. On the ventilating characteristics of the space under the fluctuating wind pressure [C]// Proceedings of ROOMVENT ‘87, Air Distribution in Ventilated Spaces. Stockholm, Sweden, 1987.

[9] HAGHIGHAT F, FAZIO P, UNNY T E. A predictive stochastic model for indoor air quality [J]. Building and Environment, 1988, 23(3): 195-201.

[10] HAGHIGHAT F, RAO J, FAZIO P. The influence of turbulent wind on air change rates–A modeling approach [J]. Building and Environment, 1991, 26(2): 95-109.

[11] OUYANG Qin, DAI Wei, LI Hong-jun, ZHU Ying-xin. Study on dynamic characteristics of natural and mechanical wind in built environment using spectral analysis [J]. Building and Environment, 2006, 41(4): 418-426.

[12] ZHU Ying-xin, OUYANG Qin, DAI Wei. Literature review of airflow fluctuations in building environments [J]. Journal of Tsinghua University: Science and Technology, 2004, 44(12): 1622-1625.

[13] BOLLERSLEY T. Generalized autoregressive conditional heteroskedasticity [J]. Journal of Econometrics, 1986, 31: 307-327.

[14] TAN Gang. Use of a stochastic regression model GARCH for wind fluctuation study [J]. International Journal of Ventilation, 2010, 9(2): 177-189.

[15] ASHRAE. 2009 ASHRAE Handbook–Fundamentals [M]. Atlanta, USA: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc, 2009: 24.3.

[16] WANG Yan-ling, GAO Fu-sheng. Main factors having effect on wind pressure coefficient used for infiltration calculation [J]. Journal of Harbin University of Civil Engineering and Architecture, 2001, 34(4): 87-90. (in Chinese)

[17] BETTANIN E, GASTALDELLO A, SCHIBUOLA L. Simplified models to simulate part load performances of air conditioning equipment [C]// Proceedings of 8th International IBPSA Conference. Eindhoven, Netherlands, 2003: 107-114.

(Edited by YANG Bing)

Received date: 2011-07-26; Accepted date: 2011-11-14

Corresponding author: TAN Gang; PhD, Assistant Professor; Tel: +1-307-766-2017, E-mail: gtan@uwyo.edu