1、2009 ASHRAE 850ABSTRACT Airflows in confined spaces such as airplane cabins, animal enclosures, human occupied rooms, etc. are always characterized by low velocity and high turbulent intensity. The flow regime (laminar, transitional, and turbulent) is difficult to predict as it depends on many facto
2、rs such as the room geom-etry, ventilation rate, temperature, and humidity, etc. In this paper, large eddy simulation (LES) was applied to investigate the airflows in a full-scale room at different ventilation rates ranging from 0.1 ACH to 27.9 ACH (Air Change Per Hour), with the focus on the underl
3、ying flow physics such as flow regime, development of vortices, etc. It was found that, at the present room configuration, airflows were fully developed at ventilation rates equal to or higher than 19.5 ACH, which was supported by the investigation of mean velocity, spanwise vorticity, sub-grid cons
4、tant, and viscosity ratio distributions. Close examinations of the vortex structures inside the room showed that they were three-dimensional in most regions of the room except near the inlet. The sidewall effects were limited to wall regions and did not affect the flow patterns in the middle plane,
5、as shown by the vortex cores distributions and limiting streamlines on the ceiling and floor. Finally, the counter gradi-ent transport phenomena (CGT) were observed when the venti-lation rate was higher than 1 ACH. The existence of CGT partly explained the difficulties of some commonly used two-equa
6、tion Reynolds Averaged Navier-Stokes (RANS) turbulence models, which are based on gradient transport assumption, in the prediction of indoor room airflows. INTRODUCTIONThe health and comfort of building occupants are largely determined by the thermal conditions and the indoor air qual-ity. There are
7、 many factors that can compromise the indoor air quality, such as microbial contaminants (mold, bacteria), chemicals (such as carbon monoxide, radon), allergens, ther-mal and humidity discomfort. Airflow patterns and/or turbu-lent intensity distributions inside the building strongly affect the trans
8、port and deposition of harmful particulate matter and gases, and thermal conditions. Investigation of velocity and turbulence profiles inside the building provide important information necessary to characterize all indoor transport process. Airflow pattern and turbulence distributions strongly depen
9、d on the ventilation rates, as has been observed in smoke visualization (Timmons 1984a, 1984b), Laser Doppler Velo-cimetry measurements (LDV, Nielsen 1974), Hotwire measurements (Zhang 1991), Particle Image Velocimetry (PIV) measurements (Zhao 2000), and Volumetric Particle Streak-Tracking Velocimet
10、ry (VPSTV) measurements (Sun 2007; Jiang 2007). As the ventilation rate reaches a threshold value, which depends on room dimensions, location and size of inlet and outlet, temperature, etc., the normalized velocities and turbulent quantities of room airflows are independent of ventilation rates (Nie
11、lsen 1998). At this time, the room airflows are fully developed turbulence. However, airflows in confined spaces such as airplane cabins, animal enclosures, human occupied rooms, etc., are seldom fully developed and always characterized by low velocity and high turbulent inten-sity due to the low ve
12、ntilation rate. The widely used Reynolds Averaged Navier-Stoke (RANS) turbulence models in the study of indoor airflows are mainly developed based on the assumption of fully developed turbulence and their applica-bilities to indoor airflows at low ventilation rates need more specific validation. Dav
13、idson et al. (2000) conducted Large Eddy Simulation of Airflows in a Full Scale Room at Different Ventilation RatesJianbo Jiang, PhD Xinlei Wang, PhDAssociate Member ASHRAE Member ASHRAEJianbo Jiang is a postdoctoral fellow at Monell Chemical Senses Center, Philadelphia, PA. Xinlei Wang is an associ
14、ate professor in the Depart-ment of Agricultural and Biological Engineering, University of Illinois at UrbanaChampaign, Urbana, IL.LO-09-083 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2
15、. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.ASHRAE Transactions 851numerical simulations in a ventilated room where inlet flows were laminar while airflows inside the room we
16、re turbulent. Laminar model and the k- model were found to generate totally unreliable results. As k- models are superior to most of the other RANS turbulence models in dealing with flows that are close to being laminar (Wilcox 1998; Davidson et al. 2000), it was expected that other RANS turbulence
17、models would also fail in the prediction of these flows. Davidson et al. (2000) found the LES based on one equation dynamic model proved to give reasonable results. Jiang (2007) evaluated different RANS turbulence models and the Large Eddy Simu-lation (LES) with a dynamic sub-grid model (Germano et
18、al. 1991; Lilly 1992) using the experimental data from the VPSTV measurements at three ventilation rates. It was found that the LES provided the best predictions while the Reynolds stress model (RSM, Launder et al. 1975) predictions were closest to the measurements among the RANS models. The main ob
19、jective of this paper was to investigate the underlying flow physics in a full scale room at different venti-lation rates using the LES with the dynamic sub-grid model. The maximum velocity decay, airflow boundary layer growth, velocity and turbulent quantity distribution, vortex dynamics, etc., wer
20、e investigated and analyzed. PROBLEM FORMATIONGeometryThe dimensions of the full-scale room are 5.5 2.4 3.7 m (or 18 8 12 ft, LHW). The room geometry is shown in Figure 1. The inlet width (h) is 0.05 m (or 0.16 ft), and the outlet width (t) is 0.2 m (or 0.66 ft). The ratio of inlet length to height
21、is more than 20; thus, the flow within the room is practically two-dimensional, according to Forthmanns suggestions (Forthmann 1934). Experimental data were collected at the middle symmetry plane (Figure 1) by using VPSTV to measure the air velocity distributions (Jiang 2007).Large Eddy SimulationAs
22、sume the flow is isothermal and incompressible. Appling a spatial filter to the Navier-Stokes equations gener-ates the governing equations of LES:(1)(2)whereQ = velocity (u) or pressure (P) G = the filter. The variables were non-dimensionalized by the maximum inlet velocity U0and the inlet height (h
23、). ijis the sub-grid stress (SGS) and needs to be modeled.The sub-grid model used in this study was the dynamic Smagorinsky model (Germano et al. 1991; Lilly 1992) and implemented in the homemade code (RVS-solver). In this code, the governing equations were discretized in an orthog-onal coordinate s
24、ystem with a staggered grid. For spatial discretization, a central second-order finite-difference was Figure 1 Schematic drawing of the full scale room (H = 2.4 m, W = 3.7 m, L = 5.5 m, h = 0.05 m, h1=2.05 m, t = 0.2 m, t1=1.29 m or H = 8ft, W = 12ft, L = 18ft, h = 0.16ft, h1=6.725ft, t = 0.66ft, t1
25、=4.23ft).uixi- 0=uit-uiujxj-+Pxi-1Re-2uixjxj-ijxi-+=Q x t,() Q x t,()Gx x()xd+=852 ASHRAE Transactionsused. A fractional-step method with viscous terms treated implicitly (Crank-Nicolson scheme) and non-linear terms explicitly (3rdRunge-Rutta scheme) was used. Total energy was conserved in the limit
26、 of an inviscid case with free-slip conditions assumed. A direct non-iterative FFT-based solver (Sweet 1973) on the staggered grid was applied as a pressure solver. During the time advancement, the pressure at the previ-ous step was used in the momentum equations and, thus, the intermediate velocity
27、 field was non-solenoidal. This non-sole-noidal velocity field was projected onto a solenoidal one by use of scalar quantity. The maximum value of Courant-Fried-rich-Lewis (CFL) could be 1.7. The Neumann condition at all boundaries, except the outlet, was applied for pressure. At the outlet, a conve
28、ctive boundary condition was used for the velocity component. At the inlet, random perturbations were superimposed on every velocity component in order to account for the stochastic characteristics of inflow. Near the wall, wall functions (Werner and Wengle 1992) were used when the mesh was too coar
29、se to resolve the viscous sublayer. All simulations assumed the isothermal conditions and a summary of simulated cases is provided in Table 1.Uniform velocity and constant turbulent quantities at the Figure 2 Airflow patterns measured (Left) and predicted (Right) at 3 ACH (Top), 8.6 ACH (Middle), an
30、d 19.5 ACH (Bottom).Table 1. Summary of Simulated CasesAir Change Rate (ACH) Inlet Mean Velocity, UdInlet Turbulent Intensity Reynolds Number (Udh/)0.1 7.33E-03 m/s or 1.44E+00 ft/min 10% 250.5 3.67E-02 m/s or 7.22E+00 ft/min 10% 1251 7.33E-02 m/s or 1.44E+01 ft/min 10% 2503 2.20E-01 m/s or 4.33E+01
31、 ft/min 10% 7538.6 6.31E-01 m/s or 1.24E+02 ft/min 10% 215819.5 1.43E+00 m/s or 2.81E+02 ft/min 10% 489527.9 2.05E+00 m/s or 4.04E+02 ft/min 10% 7000ASHRAE Transactions 853inlet are commonly used in the numerical study of indoor airflows. To investigate the effects of the inlet boundary conditions (
32、BC) on the predictions of airflows, two calcula-tions based on different inlet BC were conducted at the venti-lation rate of 19.5ACH: (1) constant velocity (1.43m/s or 281 ft/min) and constant turbulent intensity (10%); and (2) profiled velocity and turbulent kinetic energy from Hotwire measurement
33、(Zhang 1991). The comparison of mean flow pattern, velocity and turbulent kinetic energy profiles showed that the differences were negligible in the region away from the inlet region (x/L0.02). Thus, all the results shown in the present paper were based on constant velocity and constant turbulent in
34、tensity.Simulations were performed on several meshes in order to guarantee the grid independence of the results. The ventilation rate of 27.9 ACH was selected for the basis of the grid-inde-pendence study. It was found that the maximal relative differ-ence between the results from the Fine grid (3.8
35、 million) and Finest grid (7.3 million) was about 6.3% for mean velocity and 9.5% for the turbulent kinetic energy. Based on these results, the Fine grid was selected for all the simulations based on the rationale that a mesh adequate for higher ventilation rates would also be adequate for lower ven
36、tilation rates. For exam-ple, at the ventilation rate of 19.5ACH, it was found that the maximal relative differences between the Fine grid and the Finest grid were reduced to 3.8% and 5.3% for mean velocity and the turbulent kinetic energy respectively.Each Large Eddy Simulation was run long enough
37、to ensure that the initial conditions had been flushed out before sampling the statistics. About 10 characteristic time units (10L/U0, where U0is the maximal velocity at the inlet) were needed for this purpose. Then the statistics were sampled over 30 more characteristic time units. All the computat
38、ions were carried out on NCSA Tungsten Xeon Cluster and Cobalt SGI Altix Cluster at the University of Illinois at Urbana-Cham-paign, Urbana, IL. The time step used for LES was 0.03 h/U0and the time interval used for the statistical evaluations was 0.3 h/U0, which corresponded to approximately a 0.00
39、3 charac-teristic time unit. One entire simulation took about 1200 CPU hours on one node of the parallel machines at the ventilation rate of 19.5ACH.ValidationThe LES models described above were validated with the VPSTV measurements (Jiang 2007) in the same room at three different ventilation rates
40、(3ACH, 8.6ACH, and 19.5ACH). In the experiments (Figure 2, left column), it was observed that one primary central recirculation vortex was formed in the middle of the room and one secondary small vortex existed near the left bottom corner. The sizes and positions of the two vortices varied with the
41、ventilation rates; the central vortex became fuller and moved towards the center of the room with increasing ventilation rates and the secondary vortex became smaller and moved toward the left bottom corner. The LES simulations (Figure 2, right column) correctly predicted the velocity distributions
42、and variation of main recirculation vorti-ces with ventilation rates. RESULTS AND DISCUSSIONThe Large Eddy Simulation was used to investigate the flow physics of airflows inside the room at seven ventilation rates: 0.1 ACH, 0.5 ACH, 1 ACH, 3ACH, 8.6 ACH, 19.5 ACH, and 27.9 ACH. The flow physics were
43、 analyzed by studying the following physical quantities: (1) maximum velocity decay along the ceiling and floor, (2) airflow boundary layer growth, (3) velocity profiles and velocity distribution, (4) turbulent kinetic energy distribution, (5) vortex dynamics, and (6) spectral analysis. Finally, the
44、 existence of counter gradient transport (CGT) of momentum in the jet region was shown. Maximum Velocity DecayThe maximum (centerline) velocity first slightly increased in the inlet region when the air jet left the inlet, then decreased with the extent of the air jet travel towards the ceil-ing. Aro
45、und the point where the air jet was reattached to the ceiling, the maximum velocity of the air jet first increased and then decreased with the extent of the wall jet extending along the ceiling. It can be observed in Figure 3a that normalized maximum velocity profiles at the ceiling behaved similarl
46、y when the ventilation rate was larger than 8.6 ACH. Similarly, the normalized maximum floor velocity became independent of the ventilation rate once it was higher than 8.6 ACH (Figure 3b).The region of ceiling length below 3h (h is the height of inlet) was the potential core region that was charact
47、erized by constant velocity. The region along the ceiling between 3 h and 41 h was the development region. Following the development regions was the developed region (characteristic decay region). The terminal region started at about 82 h.The maximum velocity decay in the developed region had the fo
48、llowing form:(3)The estimated throw constant CWwas about 2.35, which was well within the ranges of other studies (Rajaratnam 1976; Albright 1990; ASHRAE 2005; Yu et al. 2006).Airflow Boundary Layer GrowthThe streamwise development of the half maximum wall jet velocity positions along the ceiling is
49、shown in Figure 4. For ventilation rates higher than 8.6 ACH, the growth rate of the wall jet agreed well with results of fully developed turbu-lence (Rajaratnam 1976).Velocity Profiles and Velocity DistributionsFigure 5a and Figure 5b show the dimensionless vertical velocity profiles at the ceiling and floor. The profiles were extracted at x/L = 0.5 (x/h = 55) for the different ventilation UUmax- CWhx-=854 ASHRAE Transactionsrates from 0.1 ACH to 27.9 ACH. The universal wall jet
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