Large eddy simulation of thermal comfort and energy utilization indices for indoor airflows.
Computational Fluid Dynamics (CFD) has become an effective method for the design of a comfortable and energy efficient indoor environment. In general, CFD simulation of turbulent indoor flows can be divided into three types: Reynolds-averaged Navier-Stokes (RANS), large eddy simulation (LES) and direct numerical simulation (DNS). DNS solves Navier-Stokes equations without any turbulence model so the whole range of spatial and temporal scales of the turbulence must be resolved which leads to highest computational cost and thus limits its application in building simulations. RANS uses time-averaged equations of motion to calculate time-averaged air velocity and temperature. This method significantly reduces the need for computer memory and improves computational speed so many studies used RANS for indoor environmental modeling (Srebric et al. 1999; Zhai et al. 2007). Because LES solves the large scale turbulence motion directly whereas approximates the small scale motion by turbulence models, it predicts time-dependent turbulence flows faster than DNS but slower than RANS. To reach a flow at steady state, typical LES codes often take the time of more than two orders of magnitude longer than RANS modeling (Chen 2009) so most of the indoor environmental modeling uses RANS rather than LES. However, LES is useful in some aspects, e.g. prediction of time-accurate information. A few previous studies have used LES for indoor airflow modeling. Jiang (2002) modeled cross ventilations in buildings by an in-house LES code and found that the computational cost was around 50 times more than RANS for a typical building. The LES also seems more popular for predicting particle distributions in ventilated spaces, because particle predictions need detailed turbulent flow information (Chen 2009).
These previous studies often focused on modeling airflow itself but not on derived air parameters, such as indoor thermal comfort and energy utilization, which have been widely studied by RANS models (Ridouane 2011; Liu 2008). Meanwhile, the thermal comfort and energy utilization of room air distribution at a transient state can be of particular interests in the cases where indoor airflow is hard to be maintained at a steady state due to the on/off operation of air conditioners. Therefore, it is necessary to study how the transient indoor airflows affect the thermal comfort and energy utilization of room air by LES, and how a LES prediction is compared to the time-averaged simulation by RANS models, if the results at the steady state are obtained in LES. On the other hand, there are recently increasing cases of LES studies, among which an open-source LES code, fire dynamics simulator (FDS), developed by the US National Institute of Standards and Technology (NIST), is often used (McDermott 2012). FDS uses a direct Possion solver and predictor-corrector scheme to solve coupled partial differential equations, which significantly reduces the computational time when compared to a typical LES code. Therefore, an increasing number of studies were conducted using FDS (Sinclair 2011). Wang (2010) modeled multiple scenarios of a portable generator operated outdoors by FDS to predict CO concentrations near a home. With the help of FDS, Cho (2010) identified the correlation between the minimum airflow and discharge air temperature of an air conditioner outlet. FDS was developed for low-speed flows with an emphasis on smoke and heat transport from fires. Concerns are raised on how well a fire modeling code performs, and what adjustments should be made to adapt FDS to indoor simulations without fires. This study evaluated the capabilities of FDS for indoor environmental modeling, specifically the modeling of thermal comfort and energy utilization in a full-size chamber with a ceiling mounted air conditioner. No previous studies have used FDS for the simulations of transient thermal comfort. Two indices were added in FDS to characterize the thermal comfort by an air diffusion performance index (ADPI), and the energy utilization by an energy utilization coefficient (EUC). Different near-wall convection models were evaluated and the predicted results were compared with the experimental data, and the predictions from a RANS model. The ADPI and EUC values at both the steady and transient states were calculated and discussed.
The LES model in FDS is in a form of Smagorinsky model (Smagorinsky 1963). Due to page limit, the details of the FDS theory and numerical formulations were not provided here but can be found in the user guide (McDermott 2012). The RANS model was selected to be Realizable k-[epsilon] model and a commercial software package, FLUENT, was used. The details on the RANS simulations can be found in the study of Qi (2009). Here, we focus on how FDS can be adapted to indoor airflow modeling of thermal comfort and energy utilization. We are also concerned about the near-wall heat transfer because the building envelope cooling/heating load may significantly affect indoor temperature and thermal comfort condition. Since the numerics in FDS and FLUENT are different, it is also in our interest to compare the results of both models.
Near-wall heat transfer model
Because FDS is designed for modeling fire dynamics and the convection heat transfer in non-fire cases may be distinct from fire scenarios, it is necessary to evaluate the performance of the near-wall heat transfer model when FDS is used for modeling indoor airflows. The most recent version, FDS version 6 (FDS 6), has two near-wall heat transfer models: convection heat transfer model and wall function model. The convection heat transfer model is shown as follows (McDermott 2012):
q = h[DELTA]T; h = max[[C.sub.1][[absolute value of [DELTA]T].sup.1/3], [k/L] [C.sub.2] [Re.sup.4/5] [Pr.sup.1/3] (1)
The definitions and the units of [DELTA]T, [C.sub.1] and [C.sub.2] can be found in the nomenclature of this paper. For horizontal flow, [C.sub.1] = [C.sub.1H]; for vertical flow, [C.sub.1] = [C.sub.1V]. The near-wall velocity in this study is quite small so h = [C.sub.1][[absolute value of [DELTA]T].sup.1/3]. By default, FDS assumes [C.sub.1H] = 1.52 and [C.sub.1V] = 1.31. Musser et al. (2001) tested one of the very first versions of FDS and suggested [C.sub.1H] = 4.05 and [C.sub.1V] = 3.08 based on measured data. During the past ten years, FDS has been extensively revised, for example, a new near-wall LES logarithmic law model for heat transfer was recently added to FDS 6 (McDermott 2012). It is therefore necessary to revisit these constants when using the current version of FDS for indoor airflow modeling. Three models will be evaluated for FDS as shown in Table 1. The details on the new near-wall LES heat transfer model can be found in the FDS 6 user manual (McDermott 2012) to be published soon. With the help of NIST through personal contacts, we were able to test the new model in this study.
Thermal comfort and energy utilization model
Thermal comfort and energy utilization indices are important factors that are often considered for indoor environmental design (Fanger 1989; Yao 2009, 2010). Here, two commonly used indexes, ADPI and EUC, were selected and added to the FDS 6 source codes. ADPI is a single number rating of the air diffusion performance for a room based on air temperature and velocity at a number of evenly distributed nodes in the occupied zone (ASHRAE 2009). It is a ratio of the number of points satisfying specific thermal comfort conditions to the total number of points. An acceptable ADPI level is often higher than 0.7 (Ridouane 2011). In this study, ADPI index is calculated by the volume of air nodes, where the thermal comfort conditions are met, divided by the total volume of the occupied zone (Eq. 2).
ADPI = volume of occupied zone satisfying-1.7[degrees]C < [DELTA]ET < 1.1[degrees]C and v [less than or equal to] 0.35m/s/total volume of occupied zone (2)
For IP units, -3[degrees]F < [DELTA]ET < 2[degrees]F and v [less than or equal to] 70 fpm. [DELTA]ET is the effective draft temperature defined as: [DELTA]ET = ([T.sub.i] - [T.sub.av]) - 8([v.sub.i] -0.15) [degrees]C or [DELTA]ET = ([T.sub.i] - [T.sub.av]) - 0.07([v.sub.i] - 30) [degrees]F ([v.sub.i] IP unit is fpm) (3)
EUC represents the effectiveness of energy utilization supplied into the occupied zone (Gao 1995). A higher EUC value indicates better energy utilization. For a central air conditioning system, EUC higher than 1 indicates a good energy utilization.
EUC = [T.sub.s] - [T.sub.e]/[T.sub.s] - [T.sub.av] (4)
Where, the volume-weighted average temperature, [T.sub.av], is defined as:
[T.sub.av] = [summation][T.sub.i][[v.sub.i]/V] (5)
This study evaluated FDS by comparing the numerical results to the measured data in a full-size environmental chamber with a ceiling mounted air conditioner. The chamber is with four closed windows and two doors as shown in Figure 1. The cassette type air conditioner (AC) was installed in the center of the ceiling with four inlets at the edges (east, south, west and north) and one outlet in the center. A partition board is placed/removed in the chamber to create the cases with/without different partition locations relative to the AC. The temperatures were measured by Type T thermocouples with a precision of [+ or -]0.2 [degrees]C ([+ or -] 0.36 [degrees]F). Four thermocouples were distributed evenly on each wall and the floor, and two on each window to measure wall/window temperatures. For air temperatures, the thermocouples were distributed evenly at the height of 0.5 m (1.64 ft), 1.0 m (3.28 ft), 1.5 m (4.92 ft), 2.0 m (6.56 ft) and 2.5 m (8.20 ft). Air velocities were measured along the velocity direction of inlets (north and south inlets) by a handheld anemometer with a precision of [+ or -]10% at an interval of 0.5 m. The time-averaged temperatures of the supply air and the walls, as well as the inlet velocity were summarized in Table 2. Note that the supply air temperature was pretty high due to the limitation of the test chamber at the time of the test: the indoor temperature must be above 30[degrees]C (86[degrees]F) to achieve enough indoor cooling load to allow the steady operation of the compressor. However, for the sole purpose of the verification of FDS, the impact of this situation is trivial.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
FDS was developed with the intention that relatively coarse grids can be used (Musser et al. 2001). In this study, we choose the near inlet mesh size of either 0.02 m (0.066 ft) or 0.04 m (0.13 ft) and the near wall mesh size of either 0.07 m (0.23 ft) or 0.13 m (0.43 ft), which are typical grid sizes in FDS. The grid independence study in Figure 2 shows that the results from both meshes are reasonably close so the mesh of 0.02 m (0.066 ft) near the inlets and 0.13 m (0.43 ft) in the near-wall region was selected (with the total grid number of about 126,000). The FDS source codes were compiled by Intel FORTRAN compiler on a LINUX system running on an Intel Xeon 2.40 GHz processor and 4GB memory. As mentioned previously, FDS is faster than typical LES codes so it took about 72 hr for one FDS simulation compared to about 10 hrs for one FLUENT simulation. Because the measured data were collected at steady state, the FDS results need to be averaged over time for the comparison. We compared the results averaged over different periods of time and found that 100 seconds are enough to obtain the "steady state" values. Due to the page limit, the comparison was not shown here.
[FIGURE 3 OMITTED]
Figure 3 presents the air temperature profiles of different models compared to the experimental data at the center Y-Z plane of the room with Z = 1.5 m (4.9 ft). For case 1, the predicted temperature profiles were compared among the three models (Table 1) and the RANS model. Compared to the measurement, both Models 2 and 3 overestimate the air temperature, especially near the walls. Model 1 and the RANS model give better prediction which indicates that the coefficients [C.sub.1H] = 4.05 and [C.sub.1V] = 3.08 are more accurate than the default values. Similarly, the predicted temperatures in case 2 and 3 by Model 1 in FDS are also close to the RANS model. Model 2 and 3 were not simulated in case 2 and 3 so only the results by Model 1 are shown for case 2 and 3. Temperature at other locations were also compared and showed similar trends so they are not shown here. Measured at different locations from the temperatures, the air velocity were only available at the Y=5 m (16.4 ft) plane near the south and north inlets. Figure 4 compares the air velocity profiles of Model 1 and the RANS model to the experimental data for case 3. The time-averaged results of FDS by Model 1 are pretty close to those by the RANS model and the measured data. Similar results were observed for case 1 and 2 so they are not provided here.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
The predicted ADPI and EUC by LES with model 1 and RANS are shown in Table 3. Good agreement between LES and RANS is observed for both ADPI and EUC. The predicted values are close for case 2 and case 3 whereas they are relatively lower in case 1. In case 1, due to the existence of the partition, the supply air is blocked and "short circuited" directly to the return so the air is difficult to spread to the other side of the partition. Therefore, the ADPI and EUC of case 1 is the lowest: ADPI is near the minimum acceptable level of 0.7 and EUC is only about 0.6. In case 1, 2 and 3, the air supply temperature is around 40[degrees]C (104[degrees]F)-42[degrees]C (107.6[degrees]F), which are much higher than normal cases due to the reasons explained earlier. In order to study the predictions of these indices for practical situation, we calculated another case (case 1B) with the same layout as case 1 but with the air supply temperature of 23 [degrees]C (73.4 [degrees]F). The temperatures of windows, wall, floor and ceiling are 25 [degrees]C (77 [degrees]F), 19 [degrees]C (66.2 [degrees]F), 21 [degrees]C (69.8 [degrees]F) and 20 [degrees]C (68[degrees]F), respectively. Compared with case 1, ADPI and EUC in case 1B are improved: EUC is about 0.74. This is because the air supply temperature of case 1B is much lower than case 1 creating a lower thermal buoyancy so as to aid the air supply to spread to the lower portion of the room and the occupied zone. Since ADPI is a thermal comfort index for the uniformity of the air distribution of the space, the reduced thermal buoyancy contributes to a more uniform air distribution. Therefore, the ADPI of case 1B is also the highest among all the cases.
As a practical application, FDS can also provide transient information such as the variations of ADPI and EUC during the on/off operation of air conditioners. To consider the transient effect, ADPI and EUC are adjusted accordingly: [T.sub.av] for ADPI and [T.sub.e] for EUC were evaluated at the steady state. When time = 0s, the room air is at rest with a uniform initial temperature of 10[degrees]C (50[degrees]F) so the initial ADPI and EUC are zero according to Eq. (2) and (4). In case 1B, it took a while (> 600s) to heat the room from 10[degrees]C (50[degrees]F) to 21[degrees]C (69.8[degrees]F), during which the ADPI increases from 0 to 0.85 and EUC increases from 0 to 0.74 (Figure 5). The predicted variation of ADPI and EUC during the start-up of air conditioner could be used to optimize the control strategy of air conditioning. For example, Figure 5 shows that there was about a 10- min delay for the occupied zone to reach a desirable ADPI at the steady state and a 15-min delay for the EUC. The thermostat to control the on/off of the AC should be placed at a location which allows the AC to run at least 10 mins to achieve the desired thermal comfort (at least for the first time run of the AC based on the initial condition in this simulation). Meanwhile, a higher ADPI and EUC with shorter time delay should be always desirable for an efficient AC system. In this case, it took more time for the EUC to reach the steady state than the ADPI. To shorten the time of ADPI and EUC to reach the desirable values in the occupied zone, one of modifications of the system could be to change the ceiling supply to the side supply or the floor supply. Because the focus of this study is not system optimization but LES verification and demonstration, the modification of the current system was not investigated but should be a worthwhile subject to study in the future.
In this study, a fire dynamics simulation program, FDS, was used to simulate indoor airflow, thermal comfort and energy utilization effectiveness in terms of two indices, ADPI and EUC. FDS with different near-wall heat transfer models were evaluated and the results were compared to the predictions of the RANS by FLUENT and the experiments. We found that near-wall heat transfer model plays an important role in the simulation of indoor airflow using LES. For the modeled chamber with a ceiling air conditioner, the constant coefficients of natural convection model should better be set as: [C.sub.1H] = 4.05 and [C.sub.1V] = 3.08 to provide better temperature predictions. The newly added indices of ADPI and EUC in FDS can be used to predict thermal comfort in the occupied zone and energy utilization effectiveness of the air conditioner in the chamber modeled at both steady and transient conditions, thus providing useful information on the AC performance and effectiveness. Future research should be conducted to evaluate further the capabilities of FDS or LES models in general for indoor environmental modeling when compared to FLUENT or other RANS models.
T = air temperature, [degrees]C for SI unit and [degrees]F for IP.
h = enthalpy; heat transfer coefficient
[DELTA]T = temperature difference between the wall and the first grid near the wall
q = convective heat flux
[C.sub.1] = coefficient for natural convection, W/([m.sup.2] x [degrees][C.sup.4/3])
[C.sub.2] = coefficient for forced convection, W/([m.sup.2] x [degrees][C.sup.4/3])
Re = Reynolds number
Pr = Prandtl number
v = air velocity, grid volume
V = volume of occupied zone
av = average value
i = grid i
s = supply air
e = exhaust air
The authors acknowledge the financial support from the Discovery Grants of the Natural Sciences and Engineering Research Council of Canada (NSERC) (No. 402848-2012), and the Graduate Student Support Program (GSSP) of Faculty of Engineering and Computer Science of Concordia University.
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Dahai (Darren) Qi
Liangzhu (Leon) Wang, PhD
ASHRAE Member ASHRAE
Radu Zmeureanu, PhD
Dahai (Darren) Qi is a PhD student in the Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada. Liangzhu (Leon) Wang is an Assistant Professor in the Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada. Radu Zmeureanu is a Professor in the Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada.
Table 1. Near-wall heat transfer model Heat transfer model Near-wall heat transfer Model 1 Convective heat transfer model: [C.sub.1H] = 4.05, [C.sub.1V] = 3.08 Model 2 Convective heat transfer model: [C.sub.1H] = 1.52, [C.sub.1V] = 1.31 (default in FDS) Model 3 New near-wall LES logarithmic law model for heat transfer (McDermott 2012) Table 2. Boundary conditions. Temperature ([degrees]C [[degrees]F]) Case Inlet Window Wall Case 1 41.8 (107.2) 23.2 (73.8) 29.6 (85.3) Case 2 40.6 (105.1) 23.1 (73.6) 30.2 (86.4) Case 3 40.5 (104.9) 23.1 (73.6) 30.0 (86.0) Temperature ([degrees]C [[degrees]F]) Case Floor Ceiling Case 1 26.2 (79.2) 30.4 (86.7) Case 2 27.6 (81.7) 29.3 (84.7) Case 3 29.2 (84.6) 30.4 (86.7) Inlet air velocity (m/s [fpm]) Case East South West North Case 1 5.2 (1024) 5.7 (1122) 5.2 (1024) 4.8 (945) Case 2 5.2 (1024) 5.7 (1122) 5.2 (1024) 4.8 (945) Case 3 5.2 (1024) 5.7 (1122) 5.2 (1024) 4.8 (945) Table 3. ADPI and EUC of different cases Index Turbulence Case 1 Case 1B model 41.8[degrees]C 23.0[degrees]C (107.2[degrees]F) (73.4[degrees]F) ADPI LES 0.68 0.85 (Model 1) RANS 0.72 0.88 EUC LES 0.63 0.74 (Model 1) RANS 0.60 0.72 Index Case 2 Case 3 40.6[degrees]C 40.5[degrees]C (105.1[degrees]F) (104.9[degrees]F) ADPI 0.79 0.82 0.78 0.81 EUC 0.85 0.89 0.84 0.89
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|Author:||Qi, Dahai "Darren"; Wang, Liangzhu "Leon"; Zmeureanu, Radu|
|Date:||Jul 1, 2013|
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