Experimental and numerical study of airflows in a full-scale room.
In recent years, indoor air quality has gained more and more attention as people begin to realize that indoor air quality is important to their health and comfort (Zhang 2005). In addition, intensive animal production and animal welfare in confined animal buildings have raised the issues related to indoor environmental control such as reduction of cold downdrafts, preserving thermal conditions and reduction of contaminants (Bennetsen 1999). The thermal comfort of animals and people are affected not only by temperature, but also air velocity (Boon 1978). Furthermore, the transport and distribution of particulate matter and gaseous pollutants are greatly affected by airflow patterns, especially turbulence. Thus, it is important to study the air distribution, turbulent characteristics, and contaminants distribution in the ventilated rooms.
It is worthwhile to briefly mention why airflows in ventilated rooms are important from the theoretical point of view. First, ventilated room airflows exhibit almost all the simple and complex flow phenomena that can possibly occur in incompressible flows, such as eddies, secondary flows, three dimensional flow characteristics, separation and reattachment, complicated particle motions, instabilities, transition, and turbulence. Second, the flow domain for a given ventilated room is unchanged and thus investigations are facilitated over the whole range of Reynolds numbers from zero to infinity. One of the most interesting aspects of fluid mechanics is the inherent instability of viscous flows and the related transition from laminar flow to turbulence with increasing Reynolds numbers. Given an appropriate disturbance, the flow characteristics, topological structures, symmetries or even time dependent nature in a mechanically ventilated room may be changed (Van Dyke 1982). Airflows in a ventilated room provide an excellent case for studying the behavior of the flow field dominated by three-dimensional vortical structures and undergoing unstable transitions.
The co-existence of low air velocities and high air turbulent intensities makes the measurement difficult in the ventilated rooms. Due to the secondary airflows resulting from thermal buoyancy around the sensor, thermally based sensors such as Hotwire are not suitable for low velocity measurements in indoor rooms. For most of the existing air velocity instruments, the inadequacy of being able to measure many locations simultaneously in a room limits their uses. Furthermore, velocity measurements with Hotwire and Laser Doppler Velocimetry (LDV) in the separated flow regions where instantaneous flow reversal occurs may be subject to errors caused by velocity bias (Adams and Eaton 1988). In order to understand airflow patterns and turbulent characteristics in large rooms, simultaneous and non-intrusive measurements are needed.
In recent years, Computational Fluid Dynamics (CFD) along with theoretical and experimental tests has become a powerful tool in the study of room airflows due to the increase in the computing power. Direct Numerical Simulation (DNS), which solves the entire Navier-Stokes equations directly, is theoretically the best tool to investigate the airflows and related quantities. But due to the formidably high costs, its use is limited to very low Reynolds number flows and is unfeasible in real engineering problems such as room airflows in the foreseeable future. On the other hand, Reynolds-Averaged turbulent models based on Navier-Stoke equations (RANS) are widely used in engineering applications due to their simplicity and low cost with comparably accurate results. The limitation related to the RANS models is that most of them are only applicable to fully developed turbulent airflows. In fact, airflows in real ventilated rooms, such as an office, are usually not fully developed turbulent flows due to their low ventilation rates. It has been the belief in recent years that the Large Eddy Simulation (LES), which is between DNS and RANS, is a promising tool in the study of room airflows, especially those at low ventilation rates.
Fully developed turbulent indoor airflows have been studied extensively during the past several decades. Different RANS models have been evaluated, but there is no complete evaluation of different RANS models in the same configuration (Voigt 2001). In addition, the effects of different inlet boundary conditions, the sidewall effects on the indoor airflows have not completely been understood (Chiang et al. 2000; Lee et al. 2002). On the other hand, only a few studies have been devoted to the indoor airflows at low ventilation rates (airflows are in the transitional regimes). There is a lack of experimental data in the non-fully turbulent indoor airflows. The applicability of the RANS models in non-fully turbulence airflows is also not well understood (Davidson et al. 2000). The present study attempts to fill this gap.
MATERIAL AND METHODS
To provide a real-time full-field view of airflow as an aid in understanding the complexities and provide corroborating evidence for the flow simulation results, a series of experiments using Volumetric Particle Streak-Tracking Velocimetry (VPSTV) were conducted in the Room Ventilation Simulator (RVS). The schematic of the RVS is shown in Figure 1. It consists of an insulated outer building (L x W x H = 12.2 m x 9.1 m x 3.6 m or 40 ft x 30 ft x 12 ft) and an inner room (L x W x H = 10 m x 7 m x 2.4 m or 33 ft x 23 ft x 8 ft). Through the use of its own heating, ventilating, air conditioning and humidifier/dehumidifier, temperature and relative humidity controls, the conditions in the outer room can vary in range (-27[degrees]C, 38[degrees]C or -17[degrees]F, 100[degrees]F) and (20%, 90%) respectively. The inner room can be adjusted to different room sizes by use of modular walls and is divided into two parts in the present experiments. One is a test room with a dimension of 5.5 m x 3.7 m x 2.4 m (or 18 ft x 12 ft x 8 ft, L x W x H) and the other is a camera room for image acquisition with a dimension of 5.5 m x 2.5 m x 2.4 m (or 18 ft x 8.2 ft x 8 ft). One sidewall of the test room is made of glass in order to permit optical access and all remaining walls were painted with flat-black paint to form a good optical background. The independent HVAC system for the inner room was used to provide constant conditioned supply air and the conditions around the inner room were maintained at the same temperature. The walls, ceiling and floor were built with plywood and batt fiber glass was used for insulation.
[FIGURE 1 OMITTED]
A sketch of the test room is shown in Figure 2. Both the inlet and outlet spanned the whole width of the test room and were put on the opposite walls. Two glass slits were installed on the two end walls (where the inlet and outlet were located with the purpose of transmitting the illumination light). The VPSTV system was set up in the RVS and consisted of two group projector lamps, two bubble generators and two digital cameras (Figure 3, Sun et al. 2001, 2004; Sun 2007). An air delivery system was used to provide ventilation air during the experiments. The system consisted of a flow rate measurement chamber, a centrifugal fan and a frequency controller. This system was calibrated using a fan test chamber designed and based on ASHRAE Standard (1985). Based on calibration curves, airflow rates can be obtained from any pressure drop, which is monitored using a manometer. The mean inlet air velocity was measured with a single-probe Hotwire anemometer (Model 8330, TSI Inc., St. Paul, MN) which has a detection limit of 0.025m/s (or 5 ft/min). In the experiments, 300W projector lamps were chosen as the lighting source due to the efficiency in illumination, stronger light intensity, and relatively even volume illumination. Sixteen 300W (1024 BTU/hour) projector lamps were installed on the outside two opposite walls of the inner room, with eight lamps on each side. A vertical glass window in the middle of each side wall was used to transmit the illumination light. Forced-air cooling systems were installed near the lamps for circulating air around the bulbs, thus, preventing heat accumulation. To further reduce the heat gain from the light beam radiation on the airflow, the lamps were switched on only when photos were taken. Thus, isothermal conditions were well maintained during the measurements.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Helium-filled soap bubbles were chosen as tracer particles due to their good neutral buoyancy. A SAI Model 5 Bubble Generator with two heads made by Sage Action Inc. (1995) was used to generate the helium filled soap bubbles. The diameters of the bubbles were in the range of 1.3 mm to 3 mm (or 0.004 ft to 0.01 ft) while film thickness was in the range of 0.1 [micro]m to 0.3 [micro]m (or 3.3e-7 ft to 9.8e-7 ft). Two digital cameras were selected as the image-capturing equipment in the experiments. Their resolution was 3072 x 2048 pixels. The distance between the cameras was about 5 m (or 16 ft) and they were 5.2 m (or 17 ft) away from the center plane of the flow field. The angle between the two camera's optical axes was 40[degrees] due to the limitation of the camera wide-angle lens, although an angle of 90[degrees] was preferred. More details about the principles of VPSTV are described in Sun et al. (2001, 2004) and Sun (2007).
Data saved in the camera memory cards were first transferred to the computer in the format of JPG files. Then the image processing software WIP (whole image processing) developed by the Bioenvironmental Engineering (BEE) group at the University of Illinois at Urbana-Champaign was used to process the JPG files (Wang 2005). Several steps were involved in this image processing, including image preprocessing, discriminating simple and crossover streaks, and crossover streak recognition (Wang 2005). Once the image was properly processed, the centers, lengths, and angles of the streaks were obtained. After the raw image data were extracted during the image processing, the second image processing software VPSTV-BEE was used for post-processing, including system spatial calibration, image paring and 3-D velocity computation (Sun 2007). Interpolation was adopted for a clear view of the flow patterns (Sun 2007). The maximum measurement relative error was estimated to be below 30%.
A series of measurements were conducted to investigate airflows in the full-scale room. Three ventilation rates of 3 ach, 8.6 ach, and 19.5 ach were selected to represent a wide range of ventilation rates from smaller rooms such as laboratories, operating rooms, and airplane passenger cabins to larger animal production buildings (ASHRAE 2001). The corresponding Reynolds numbers (based on inlet mean velocity and inlet height) were 753, 2158, and 4895, which lied in the transitional and turbulent regions (Nielsen et al. 2000). All measurements were conducted under isothermal conditions and a summary of the measurements is provided in Table 1.
Table 1. Summary of Experimental Design Test Inlet Outlet Air Inlet Mean Reynolds Averaged Case Width Width Change Velocity, Number Velocity, U Rate [U.sub.d] (ach) Test 1 50 mm 200 mm 3 * 0.22 m/s 753 0.02 m/s (or (or (or 43 (or 3.9 0.16 ft) 0.66 ft) ft/min) ft/min) Test 2 50 mm 200 mm 8.6 0.63 m/s 2158 0.05 m/s (or (or (or 124 (or 9.8 0.16 ft) 0.66 ft) ft/min) ft/min) Test 3 50 mm 200 mm 19.5 1.43 m/s 4895 0.12 m/s (or (or (or 281 (or 23.6 0.16 ft) 0.66 ft) ft/min) ft/min) Test U/[U.sub.0.sup.+] Case Test 1 0.085 Test 2 0.077 Test 3 0.069 * Minimum airflow for experiments is 3 ach. [.sup.+][U.sub.0] is the maximum velocity at the inlet.
Governing Equations for Large Eddy Simulation. Assume the flow is isothermal and incompressible. The continuity and Navier-Stokes equations, in dimensionless and conservative form are:
[[[partial derivative][u.sub.i]]/[[partial derivative][x.sub.i]]] = 0 (1)
[[[partial derivative][u.sub.i]]/[[partial derivative]t]] + [[[partial derivative][u.sub.i][u.sub.j]]/[[partial derivative][x.sub.j]]] = -[[[partial derivative]p]/[[partial derivative][x.sub.i]]] + [1/[Re]] [[[[partial derivative].sup.2][u.sub.i]]/[[partial derivative][x.sub.j][partial derivative][x.sub.j]]] (2)
where [u.sub.i] are the velocity components, t is time, p is pressure. The variables are non-dimensionalized by the maximum mean inlet velocity [U.sub.d] and the inlet height h. The Reynolds number is Re = [U.sub.d]h/v. The basic idea of LES is to separate the turbulent field into large energy containing scales that would be solved explicitly, and small scales that would be modeled. Applying a spatial filter ("-") to continuity and momentum equations would generate the following equations:
[[[partial derivative][[bar.u].sub.i]]/[[partial derivative][x.sub.i]]] = 0 (3)
[[[partial derivative][[bar.u].sub.i]]/[[partial derivative]t]] + [[[partial derivative][[bar.u].sub.i][[bar.u].sub.j]]/[[partial derivative][x.sub.j]]] = -[[[partial derivative][bar.P]]/[[partial derivative][x.sub.i]]] + [1/[Re]] [[[[partial derivative].sup.2][[bar.u].sub.i]]/[[partial derivative][x.sub.j][partial derivative][x.sub.j]]] - [[[partial derivative][[tau].sub.ij]]/[[partial derivative][x.sub.i]]] (4)
[bar.Q](x, t) = [+[infinity].[integral].-[infinity]]Q(x, t)G(x - x')dx',
Q is u or P, and G is the filter. [[tau].sub.ij] is the sub-grid stress (SGS) and needs to be modeled.
Eddy viscosity assumption is commonly used in LES subgrid model and takes the following form:
[[tau].sub.ij] = -2[v.sub.t][[bar.S].sub.ij] + [1/3][[tau].sub.ll][[delta].sub.ij] (5)
[[bar.S].sub.ij] = [1/2]([[partial derivative][u.sub.i]]/[[partial derivative][x.sub.j]] + [[partial derivative][u.sub.j]]/[[partial derivative][x.sub.i]])
The most basic subgrid model developed by Smagorinsky (1963) and Lilly (1966) uses the following form:
[v.sub.t] = [L.sup.2][absolute value of [bar.S]] (6)
where [absolute value of [bar.S]] = [square root of [2[[bar.S].sub.ij][[bar.S].sub.ij]]] and L = [C.sub.s][V.sup.[1/3]],V is the volume of the cell. The commonly used value of [C.sub.s] is 0.1. Although this model (standard Smagorinsky model) has been widely used, the constant [C.sub.s] has to be adjusted according to specific flows.
In this study, the dynamic Smagorinsky model (Germano et al. 1991; Lilly 1992) was mainly used. In this model, [C.sub.s] is computed as a function of both time and space from the information contained in the resolved field. Thus, no ad hoc specification of [C.sub.s] is needed. Applying a second filter called test filter ("^") to subgrid stress generates
[T.sub.ij] = [^.[bar.[u.sub.i][u.sub.j]]] - [^.[bar.[u.sub.i]]][^.[bar.[u.sub.j]]] (7)
where [T.sub.ij] and [[tau].sub.ij] are related by Germano identity, that is
[L.sub.ij] = [T.sub.ij] - [[^.[tau]].sub.ij] (8)
The right side of (8) can be expressed by the Smagorinsky model and thus,
[L.sub.ij] = -(2C[^.[DELTA]][absolute value of [^.[bar.S]]][[^.[bar.S]].sub.ij] - 2[C.sub.S][^.[bar.[DELTA][absolute value of [absolute value of x]][[bar.S].sub.ij]]]) (9)
A least square method combining with contraction is used to evaluate the constant (Lilly, 1992)
[C.sub.S](x, t) = -[1/[2[[bar.[DELTA]].sup.2]]][[[L.sub.ij][M.sub.ij]]/[[M.sub.ij][M.sub.ij]]] (10)
[M.sub.ij] = [([^.[bar.[DELTA]]]/[bar.[DELTA]]).sup.2][absolute value of [^.[bar.S]]][[^.[bar.S]].sub.ij] - [^.[bar.[absolute value of [bar.S]][[bar.S].sub.ij]]] (11)
In this study, in order to avoid numerical instability, [C.sub.s] was plane-averaged in the homogeneous (spanwise) direction and then clipped at zero (Akselvoll and Moin 1995). The dynamical LES has other attractive features that are very suitable for investigating indoor airflows. As previously pointed out, indoor airflows are always a combination of turbulent, laminar and transitional flows, especially in a large full-scale room at low ventilation rates. In the dynamical LES, different flow regimes are reflected through [C.sub.s]: it vanishes in the laminar flows and increases in the transitional flows; in fully developed turbulence, it reaches a saturated value, which is dependant on the grid resolution and specific flows.
Boundary Conditions for Large Eddy Simulation. In this study, four kinds of boundaries were used: wall boundary, inlet boundary, outlet boundary, and periodic conditions. When the flow is statistically homogeneous in the spanwise direction, periodic boundary conditions can be used (Akselvoll and Moin 1995).
At the walls, the wall function suggested by Werner and Wengle (1991) was used, which takes the following form:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
where A = 8.3, B = 1/7 . u is the velocity parallel to the wall and [DELTA]y is the vertical width of the grid volume next to the wall. One advantage of this wall approach is that it is applicable to both fully developed turbulence and unsteady laminar flow.
White noise approximation is commonly used when dealing with inlet boundary conditions for LES, in this method, a random number at every time step gives the desired turbulence level.
[[bar.u].sub.i] = <[[bar.u].sub.i]> + I[PSI][absolute value of [bar.u]] (13)
where I is the intensity of the fluctuation and [PSI] is the white noise.
At the outlet, a convective boundary condition was used for the velocity component [u.sub.i]. This method is suitable for vortical structures moving out of the computational domain.
[[[partial derivative][u.sub.i]]/[[partial derivative]t]] + [U.sub.c][[[partial derivative][u.sub.i]]/[[partial derivative]x]] = 0 (14)
where [U.sub.c] is the convection velocity, which is set equal to the mean streamwise velocity integrated across the outlet.
Initial Conditions for Large Eddy Simulation. At first two-dimensional initial flow fields were generated. Spanwise and vertical velocities were prescribed to be zero in the whole domain. Streamwise velocities at the inlet, which were either from experiments or assumed as uniform values, were distributed uniformly along the streamwise direction in the inlet region. In other regions, streamwise velocities were set to zero. This initial condition satisfied the global continuity requirement. A number of flow-through times were needed to remove the initial transients. For three dimensional calculations, if spanwise periodicity was assumed, 2-D velocity components were then duplicated for all the vertical planes. Otherwise, the following expression for streamwise velocity was used:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
where [U.sub.0] is maximal streamwise velocity at the inlet, W and w are the spanwise width of computational domain and the height of inlet, respectively. When experimental data is available [C.sub.2], can then be obtained by curve fitting. Otherwise, it is set as a constant. In this study, 0.35 was selected for the laminar flow case and 0.1 for the turbulent flow case. Finally, [C.sub.1] is the spanwise aspect ratio of the inlet (W/w), where W and w are the spanwise width and the vertical height of the inlet.
In order to initiate the turbulent flow, random disturbances with a zero mean were added to the initial flows. To avoid large fluctuations near the wall that can require small time steps for CFL restriction, the random disturbances in the near wall regions were damped after being multiplied with a small constant. In this study, the constant was set as 0.1.
The filtered time-dependent three-dimensional Navier-Stokes equations were discretized using a simplified marker and a cell method (Harlow and Welch 1965). A fractional-step method with viscous terms treated implicitly (Crank-Nicolson scheme) and nonlinear terms explicitly (3rd Runge-Kutta scheme) was used. A second order central differencing was used for spatial discretization. The Large Eddy Simulation with both standard and dynamical subgrid models was implemented into the homemade solver (RVS-SOLVER).
Governing Equations for Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models. Applying Reynolds averaging (i.e., Reynolds decomposition, [[~.u].sub.i] = [U.sub.i] + [u'.sub.i]) to the Navier-Stokes equations (1) and (2) and assuming steadiness generate the followings equations for mean quantities:
[[[partial derivative][U.sub.i]]/[[partial derivative][x.sub.i]]] = 0 (16)
[U.sub.j][[[partial derivative][U.sub.i]]/[[partial derivative][x.sub.j]]] = -[1/[rho]][[[partial derivative]P]/[[partial derivative][x.sub.i]]] + v[[[[partial derivative].sup.2][U.sub.i]]/[[partial derivative][x.sub.j][partial derivative][x.sub.j]]] + [[[partial derivative].sup.2]/[[partial derivative][x.sub.j]]](-[bar.[u.sub.i][u.sub.j]]) (17)
The term--[bar.[[u.sub.i][u.sub.j]]] is the so-called Reynolds stress. Due to the Reynolds stress, the above equations are unclosed; thus, the relationship between Reynolds stress and mean quantity is needed in order to solve the above equations. This is the closure problem and the task of turbulence modeling research is to devise reasonable approximations for the unknown Reynolds stress in terms of known flow quantities. Turbulence models used in this study include two categories: RANS (Reynolds-Averaged Navier-Stokes) models and Large Eddy Simulation models. For the RANS models, three families were considered: (1) k-[epsilon] family: k-[epsilon] model (Launder and Spalding 1974), RNG k-[epsilon] model (Choudhury 1993), realizable k-[epsilon] model (Shih et al. 1995), six low Reynolds number turbulence models: Abid (Abid 1993), Lam-Bremhorst (Lam and Bremhorst 1981), Launder-Sharma (Launder and Sharma 1974), Yang-Shih (Yang and Shih 1993), Abe-Kondoh-Nagano (Abe et al. 1995), Chang-Hsieh-Chen (Chang et al. 1995); (2) k-[epsilon] family: standard k-[epsilon] model (Wilcox 1998), k-[epsilon]-sst model (Menter 1994); (3) V2F model (Durbin 1991); and (4) RSM model (Launder et al. 1975). For Large Eddy Simulation, the standard Smagorinsky (Smagorinsky 1963) model was used for non-periodic cases while a dynamical version (Germano et al. 1991) was used for periodic cases. Table 2 summarizes the RANS models adopted in this study and their corresponding near wall treatment.
Table 2. Turbulence Models and Wall Treatments Turbulence Model Abbreviation Near-Wall Treatment k-[epsilon] SKE Wall Resolved RNG k-[epsilon] RNG Wall Resolved Realizable k-[epsilon] REAL Wall Resolved ABID ABID Wall Resolved Lam-Bremhorst LB Wall Resolved Launder-Sharma LS Wall Resolved Yang-Shih YS Wall Resolved Abe-Kondoh-Nagano AKN Wall Resolved Chang-Hsieh-Chen CHC Wall Resolved Low Re k-[epsilon] KW Wall Resolved k-[epsilon]-sst KWSST Wall Resolved V2F V2F Wall Resolved RSM RSM Wall Resolved
Boundary Conditions for Reynolds-averaged Navier-Stokes (RANS) Turbulence Models. At the walls the non-slip velocity conditions were used (Dirichlet conditions) in order to fully resolve the wall region (Table 2). The k-[epsilon] models (SKE, RNG, and Real) and the RSM are primarily valid for turbulent flows in the regions somewhat far from the walls. In order to resolve the wall region, the two layer model (Fluent User's Guide 2006) was used in the above four models. Two kinds of velocity inlet conditions were used: one was uniform velocity at the inlet; the other was profiled velocity, which was obtained from previous Hotwire measurements (Zhang 1991). The pressure outlet was used as an outlet condition to maintain the solution stability.
Solution Method for RANS Models. All the calculations based on RANS models were done using Fluent (Fluent, Inc., Lebanon, NH), a general-purpose finite volume-based Computational Fluid Dynamics software package. The second order up-wind method was used for discretization of momentum, turbulent kinetic energy, turbulent dissipation, Reynolds stress, and specific dissipation rate. For discretization of the pressure, the standard method was adopted. The SIMPLE method was used for pressure-velocity coupling. A point implicit (Gauss-Seidel) linear equation solver was used in the present study. In addition, the Algebraic Multi-Grid (AMG) method was adopted to accelerate the computing speed. The under-relaxation parameters were adjusted to speed up the convergence.
Convergence Criteria for RANS Models. At first, the default convergence criteria in Fluent were chosen during this study, i.e. scaled residuals are less than [10.sup.-3]. The calculations show that the solutions by these criteria were not totally converged. Then global quantities such as wall shear stresses on the walls were monitored until they reached constant values. Calculation results showed that [10.sup.-4] of scale residual was enough to guarantee the solution convergence.
RESULTS AND DISCUSSION
Air Velocity Distribution. The original data saved in the camera was first processed using the WIP code (whole image processing, Wang 2005). The resulting raw data, including the centers, lengths, and angles of the streaks, were further post-processed with the VPSTV code (Volumetric Particle Streak-Tracking Velocimetry, Sun 2007). As described in Material and Methods, three ventilation rates of 3 ach, 8.6 ach, and 19.5 ach were used in the measurements. A total of 500 images were post-processed with 250 images from each camera for each ventilation rate. The maximum difference between the mean velocities from the 600 images (300 images from each camera) and those from the 500 images was less than 16% at the ventilation rate of 3 ach. At 8.6 ach and 19.5 ach, the maximum differences of mean velocities from 400 images and 500 images were less than 10%. Thus, the mean velocities averaged from 500 images were thought to be enough for post-processing and used for validating the numerical simulation results.
During these experiments, it was observed that the incoming air (jet flow) attached to the ceiling after entering the room because of the Coanda effect (Zhang 1991). The Coanda effect, which was caused by a large enough pressure difference between the upper and lower boundary of the jet, resulted in the deflection of the jet and reattachment to the ceiling. Due to the entrainment between the incoming air and the ceiling, the pressure in this region was reduced. Consequently, the incoming air was forced to deflect towards the ceiling and eventually attached to it. Beyond the Coanda effect region, the air then traveled along the ceiling for a certain distance and separated from the ceiling or reached the opposite wall. The jet entrained the air below the jet and a recirculation vortex was formed below the jet.
Figure 4a, Figure 4b and Figure 4c show the airflow patterns at the central symmetry plane of the room (z = 1.85 m or 6 ft) at the three ventilation rates. During the measurements, it was found that the particle paths were hard to record in the near wall regions due to the light reflection on walls. Only the results in an area of 4.5 m x 1.8 m (or 15 ft x 6 ft) were found to be credible (Sun 2007). At the lowest ventilation rate of 3 ach (Figure 4a), the small jet momentum could not maintain a stable flow across the whole room. The resultant room airflow was relatively stagnant with a very low velocity in the middle of the room. Three recirculation vortices were observed: one central (primary) recirculation vortex was found in the middle of the room, one weaker recirculation (second) vortex occurred near the lower and left corner, and one smaller recirculation (third) vortex was formed near the inlet. At the middle ventilation rate of 8.6 ach (Figure 4b), the inlet jet was much stronger than that of 3 ach and, thus, the resultant flow was more stable than that of the 3 ach rate. The central recirculation vortex was found to shift left to the middle of the room and expanded. In addition, the second recirculation vortex shifted towards the left corner and decreased in size. But the third recirculation vortex disappeared or shifted away from the measurement domain. At the highest ventilation rate of 19.5 ach (Figure 4c), a much stronger central recirculation vortex was observed in the middle of the room. The size of the recirculation vortex was even larger than the vortex of the 8.6 ach rate and as a consequence, the recirculation vortex near the lower, left corner became even smaller.
[FIGURE 4 OMITTED]
Figure 5a, Figure 5b and Figure 5c show the spatial distribution of the mean velocity magnitude in the middle plane of the room. Comparing the velocity distribution of the three test cases to the corresponding flow patterns, one can observe that relatively small velocities were present in the middle regions of the recirculation vortices. At the lowest ventilation rate of 3 ach, the larger velocities appeared in the top of the measurement domain, as is expected because of the entrainment of inlet jet flow. Larger velocities were also found in the region close to the bottom of the measurement domain. This is a result of the development of the wall jet near the floor, according to Jin and Ogilvie (1992). In the middle region (0.8 m < y < 1.8 m or 2.6 ft < y < 6 ft) of the measurement domain, mean velocities were also very low. At the middle ventilation rate of 8.6 ach, the mean velocities increased in most regions of the measurement domain. It was observed that the mean velocities near the lower, left corner of the measurement domain still remained very low, which resulted from the appearance of a second vortex (see Figure 4b). In addition, the middle region (0.8 m < y < 1.8 m or 2.6 ft < y < 6 ft) began to be contaminated by the wall jet flow from the floor. At the highest ventilation rate (Figure 5c) more portions of the middle region were populated by higher velocity flow from both the inlet jet and the floor wall jet. Low velocity regions were found near the left wall and below the inlet jet flow.
[FIGURE 5 OMITTED]
From the above results, it seems evident that the flow patterns and spatial distribution of the mean velocities inside the room were strongly affected by the ventilation rates. Table 1 also shows the averaged velocities (U) in the measurement domain for the three cases. It is clear that the averaged velocity (U) increases with the ventilation rates. However, the dimensionless averaged velocity (U/[U.sub.0]) decreases with the ventilation rates. Several researchers (Nielsen et al. 1978; Timmons 1984a, 1984b; Nielsen 1998) have shown that the flow patterns and dimensionless mean velocities (normalized by the inlet velocity) depended on the ventilation rates until one threshold value of the ventilation rate (inlet Reynolds number) was reached and then the flow was fully developed, i.e, the flow pattern and dimensionless mean velocities did not change with ventilation rates. It can be concluded from Figure 3 through Figure 5 that flows inside the full scale room were not fully developed when the ventilation rate was less than 19.5ach.
Reattachment Length and Jet Penetration. The reattachment length and the jet penetration were measured by determining the reattachment point where the air jet reattached to the ceiling after leaving the inlet and the separation point where the wall jet separated from the ceiling. The reattachment length is the distance of the reattachment point from the inlet wall. On the other hand, the jet penetration length is the distance of the separation point from the inlet wall (Adre and Albright 1994). During the experiments, only the lamps located in the inlet wall were turned on when the reattachment points were recorded, in order to avoid the light reflection from the opposite wall. On the other hand, only the lamps in the right walls were turned on when the separation points were recorded. The reattachment length and the jet penetration for the three test cases are listed in Table 3. Several higher ventilation rates were also tested and the results were included for a comparison. It is clear from Table 3 that these two parameters show dependence on the ventilation rates and become constants once the ventilation rate is larger than the threshold value rate of 19.5 ach. Table 4 shows the comparison of the constant values of these two parameters at higher ventilation rates with experimental and theoretical data reported in the references of wall jet. As can be seen, there is agreement between this present study and those in the references for the jet penetration (JP). On the other hand, the value of left reattachment length (LR) in the present study is smaller than those reported in Nasr and Lai (1998) and Timmons (1984b). That difference can be mainly ascribed to the different inlet offset ratio ([h.sub.1]/h, Figure 2). Inlet offset ratio is a measure of relative distance of inlet from the ceiling. The larger values indicate longer distance between inlet and ceiling, and as a consequence, result in larger values of left reattachment (LR). Table 4 also shows that the effect of inlet offset ratio on the jet penetration is negligible.
Table 3. Reattachment Length and Jet Penetration Test Case Reattachment Length Jet Penetration 3 ach 0.7m[+ or -]0.06m 4.3m[+ or -]0.03m (or 2.3ft[+ or -]0.2ft) (or 14.1ft[+ or -]0.10ft) 8.6 ach 0.6m[+ or -]0.05m 4.5m[+ or -]0.03m (or 2.0ft[+ or -]0.16ft) (or 14.8ft[+ or -]0.10ft) 19.5 ach 0.5m[+ or -]0.05m 4.8m[+ or -]0.03m (or 1.6ft[+ or -]0.16ft) (or 15.7ft[+ or -]0.10ft) 24.5 ach 0.5m[+ or -]0.07m 4.8m[+ or -]0.03m (or 1.6ft[+ or -]0.23ft) (or 15.7ft[+ or -]0.10ft) 66 ach 0.5m[+ or -]0.05m 4.9m[+ or -]0.05m (or 1.6ft[+ or -]0.16ft) (or 16.1ft[+ or -]0.16ft) 80 ach 0.5m[+ or -]0.05m 4.7m[+ or -]0.05m (or 1.6ft[+ or -]0.16ft) (or 15.4ft[+ or -]0.16ft) 100 ach 0.5m[+ or -]0.05m 4.8m[+ or -]0.03m (or 1.6ft[+ or -]0.16ft) (or 15.7ft[+ or -]0.10ft) Table 4. Comparisons of Reattachment and Jet Penetration References Room Inlet Offset Left Jet Dimension Ratio, Reattachment, Penetration, (L x H x [h.sub.1]/h LR JP W), m (ft) Walter and Chen 0.116 x 0.5 N/A 0.88L (1992) 0.111 x 0.022 (0.38 x 0.36 x 0.07) Timmons (1984b) 2.44 x 25 50h 0.85L 1.22 x N/A (8.01 x 4.00 x N/A) Yu et al. 1 x 0.5 x 0.5 N/A 0.84L (2006) N/A (3.28 x 1.64 x N/A) Adre and 1.6 x 0.6 11 N/A 0.9L Albright (1994) x N/A (5.25 x 1.97 x N/A) Jean and Flick 13.3 x 2.5 0.5 N/A 0.82L (2003) x 2.46 (43.64 x 8.20 x 8.07) David (1994) 0.3 x 0.15 0.5 N/A 0.93L x N/A (0.98 x 0.49 x N/A) Nasr and Lai 0.25 x 0.2 7.2 14h N/A (1998) x 0.15 (0.82 x 0.66 x 0.49) Present Study 5.5 x 2.4 6.5 llh 0.87L x 3.7 (18 x 8 x 12)
Comparisons with Previous Results. The experimental data from the single probe Hotwire measurements (Zhang 1991) in a wider full-scale room (prototype I), 1/4 scale model room and the PIV results (Zhao 2000) in the same room (prototype II) as the present VPSTV measurements were compared with present measurements. The total uncertainties of the mean velocities for the Hotwire measurements were estimated within 0.025 m/s (or 5 ft/min, Zhang 1991) and those for the PIV measurements (Zhao 2000) were estimated at less than 18%. Corresponding dimensions of the three test rooms are listed in Table 5.
Table 5. Dimensions of the Three Test Rooms Inlet h, m Outlet t, m Length L, Height Width W, (ft) (ft) m (ft) H, m m (ft) (ft) Prototype I 0.05 (0.16) 0.2 (0.66) 5.5 (18) 2.4 (8) 7.3 (24) (Hotwire, Zhang) (Abbr. HP) One-quarter 0.0125 (0.04) 0.05 (0.16) 1.375 (5) 0.6 (2) 2.4 (8) scale model (Hotwire, Zhang) (Abbr. HS) Prototype II 0.05 (0.16) 0.2 (0.66) 5.5 (18) 2.4 (8) 3.7 (12) (Zhao) (Abbr. PIV) Prototype II 0.05 (0.16) 0.2 (0.66) 5.5 (18) 2.4 (8) 3.7 (12) (Present) (Abbr. VPSTV)
Three different Reynolds numbers (Re = 2458, 5735 and 8193) were used in the Hotwire measurements in both the full scale (prototype I) and the 1/4 scale model rooms (Zhang 1991). The Reynolds numbers were defined based on the mean velocity at the inlet and the inlet height. In the PIV measurements, the three ventilation rates (8.6 ach, 19.5 ach, 66 ach, which correspond to 2458, 5735 and 11941) were adopted. The comparison of the mean velocity from the VPSTV with the previous measurements from the Hotwire and PIV are shown in Figure 6a and Figure 6b for the low and medium Reynolds numbers. Three lateral positions along the streamwise directions were chosen, i.e., x/L = 0.125, 0.5 and 0.875. At the low Reynolds number (Re = 2458, 8.6ach), the mean velocity at x/L = 0.125 from VPSTV is smaller than that from the Hotwire measurements and is also smaller than the PIV measurements. At x/L = 0.5, a better agreement between these three measurements is achieved, but a relatively big difference is found in the region of y/H > 0.6. The VPSTV measurements are smaller than the PIV measurements, but larger than the Hotwire measurements. At x/L = 0.875, a good agreement is found between the PIV and the VPSTV; both of them are bigger than the Hotwire measurements in the region y/H > 0.7. At the medium Reynolds number (Re = 5735, 19.5ach), the VPSTV measurements agree better with the Hotwire measurements than the PIV measurements. The PIV measurements are the largest in most of the regions at x/L = 0.125. The Hotwire measurements agree with each other perfectly. At x/L = 0.5, a good agreement is found in the region of y/H < 0.7. In the upper regions (y/H > 0.7), the VPSTV measurements agree more with the PIV measurements than the Hotwire measurements. In addition, the HS (Hotwire measurements in the 1/4 scale model) measurements are much larger than the HP (Hotwire measurements in prototype I) measurements in this region. At x/L = 0.875, while a good agreement continues between the PIV measurements and the VPSTV measurements, the differences between the HP and HS become larger in the upper region (y/H > 0.7). The PIV measurements and the VPSTV measurements are close to the HS measurements.
[FIGURE 6 OMITTED]
The above measured mean velocities indicate that there are differences among Hotwire measurements in prototype room I and the 1/4 scale room, the PIV and VPSTV measurements in the prototype room II at the same Reynolds number. In the PIV measurements, the entire cross section (middle symmetry plane) of the room was divided into 10 sub-areas according to flow characteristics and the camera view frame. Images in each sub-area of the flow field were sequentially recorded three times. However, for the ventilation rates considered, the flows inside the room were highly unsteady and, thus, the velocities recorded in the PIV measurements were instantaneous velocities. The fluctuation, due to unsteady flow structures in the flows field, made the instantaneous velocities change strongly with time. Some kind of averaging techniques should be adopted to get the mean velocities. In Hotwire measurements, the averaging technique used was long-time averaging. In the PIV measurements or VPSTV measurements, the appropriate one should be ensemble averaging. Thus, 250 pictures were adopted in the VPSTV measurements to obtain the mean velocities. The differences between the PIV and VPSTV should be due to the insufficient number of images of PIV measurements (only three pictures, Zhao 2000). On the other hand, the reasons for the differences between the Hotwire measurements (HP and HS) and VPSTV are more complicated. One reason was proposed to be the different inlet dimensionless jet momentum and, thus, different flow regimes in these rooms at the same flow rates (Zhang 1991). However, a close examination of the flow pattern, mean velocity and turbulent kinetic energy in the Hotwire measurements shows that the airflows in both prototype room (I) and the 1/4 scale room were fully developed turbulence for Re = 5735, but not for Re = 2458. As shown in previous sections (see Figure 4a through Figure 4c, Table 3 and Figure 6c), the airflows in prototype room II is fully developed at the flow rate of 19.5ach (Re=5735). It should be noted that the spanwise aspect ratios (room width: room height) are different in the two prototypes and the 1/4 scale model (prototype I = 3; prototype II = 1.55; 1/4 scale = 4). It is well known that two-dimensional flows can only happen in large enough aspect ratio domains (Chiang and Sheu 1999). In addition, the critical Reynolds number for transition and fully developed turbulence in large aspect ratio cases are larger than those in a smaller aspect ratio (Timmons 1984a, 1984b). Even for fully developed flows, normalized mean quantities are different for different aspect ratio flows (Papadopoulos and Otugen 1995; Li and Michael 2006). Thus, it is highly possible that the differences between the Hotwire measurements (HP and HS) and the VPSTV measurements result from the different spanwise aspect ratios of the three test rooms (Prototype I, 1/4 scale room, and Prototype II).
Different turbulence models were evaluated by comparing airflow patterns, velocity distributions and velocity magnitude to the VPSTV measurements at the cross section (symmetry-plane) of the room (Figure 2). In addition, experimental observation of the positions of separation and reattachment points on the ceiling by flow visualization was also used as a criterion for the model evaluation.
The agreement between the predicted and the experimental values at each measurement location was evaluated by calculating the normalized square error (NSE) (ASTM 2002):
NSE = [[([V.sub.c] - [V.sub.m]).sup.2]/[[[absolute value of V].sub.c] * [absolute value of [V.sub.m]]]] (18)
where [V.sub.c] and [V.sub.m] are calculated and measured velocities respectively. For example, [V.sub.c] and [V.sub.m] differ by 50%, the NSE value will be close to 0.2; for differences of 100%, the NSE value will be near 0.5.
A comparison of velocity at 810 measurement locations (uniformly distributed across the middle section of the room) was conducted. Taking the potential consequences of the measurement uncertainties into account, a NSE value of 0.25 or less was chosen as an indicator of adequate model performance (ASTM 2002). Lower NSE values indicated a closer agreement between prediction and measurement.
A grid independence study was carefully performed for both RANS and LES simulations to make sure that the solutions were not dependent on the number of grid nodes. The grids near the wall were very dense in order to resolve the wall region and the wall unit values ([y.sup.+] = [u.sub.[tau]]y/v, where [u.sub[tau]] is the wall friction velocity and y is the distance from the wall) were less than 1 for both RANS models and LES. The final grids adopted were about 2 millions for RANS simulation and 4 millions for LES simulation. Every LES simulation was run long enough to make sure that the initial conditions had been flushed out before sampling the statistics. About 10 characteristic time units (10L/[U.sub.0]) were needed for this purpose. Then the statistics were sampled over 30 more characteristic time units.
Comparison of Airflow Patterns and Air Velocity Distributions. The airflow patterns predicted by the RANS turbulence model SKE and Large Eddy Simulation with dynamical sub-grid model are shown in Figure 7a to Figure 7c. A significant difference can be found between the VPSTV measurements and the SKE prediction on airflow patterns with the lowest ventilation rate of 3 ach. In the experiments, a second vortex was clearly observed in the bottom left of the measurement domain (0.09 < x/L < 0.32, 0.13 < y/H < 0.5). In contrast, the SKE predicted a much smaller second vortex in the region near the bottom left corner (0 < x/L < 0.09, 0 < y/H < 0.17). In addition, the prediction of SKE showed a much larger central vortex than the measurements. By increasing the ventilation rate from 3 ach to 8.6 ach, a slightly fuller central vortex was observed in the measurements. Correspondingly, the second vortex in the bottom left of the measurement domain became smaller and moved toward the bottom left corner. The decrease of the second vortex was also predicted by SKE, however, its size and location were very different from the measurements. At the maximum ventilation rate of 19.5 ach, both the measurement and the SKE showed a larger central vortex. However, a relatively small second vortex still existed in the bottom left of the measurement domain in contrast with the disappearance of the second vortex in the SKE prediction.
[FIGURE 7 OMITTED]
The other turbulence models in the k-[epsilon] family behaved similarly as the SKE except that YS did not converge at the lowest ventilation rate of 3 ach. More importantly, the difference between measurement and prediction decreases with an increase in the ventilation rates. In other words, those models are more effective for the predictions of high Reynolds number flows. This finding agrees with previous studies (Bjerg et al. 1999; Chen and Glicksman 2003; Sun 2007).
At the lowest ventilation rate of 3 ach, the KWSST model predicted a flow pattern closer to the measurement than the SKE although a much bigger second vortex was found in the prediction of KWSST. The model KW did not generate a converged solution at this ventilation rate. The prediction of V2F was similar to the KWSST in terms of size and locations of the central and second vortices. Among the models investigated in the present study, RSM and LES predicted the flow pattern that was closest to the measurement.
Similar to the SKE, the predicted flow patterns of KWSST, V2F, RSM, and LES reflected the change as the ventilation rate was increased to 8.6 ach; the central vortex became larger and the second vortex began to shrink. The most significant change of flow patterns was found in the prediction of the V2F model in that the second vortex became much smaller than the measurement. In contrast, both KW and KWSST predicted a relatively larger second vortex than the measurement. RSM and LES again performed better than other models in the predictions of flow pattern at this ventilation rate. At the highest ventilation rate of 19.5 ach, KWSST and KW predicted a very different flow pattern from the measurements; the second vortex occupied about half the room. On the other hand, the second vortex in the prediction of V2F almost disappeared, as in the case of the SKE prediction. A better agreement between the prediction and the measurement was found for RSM and LES predictions.
Comparison of Air Velocity Magnitude. In the experiments, measured data were located in the cell center of the uniform planar mesh. Correspondingly, numerical simulation results should also be taken at the cell center of the grids. For RANS simulations with Fluent, the "cell-center" option was selected when velocities were exported. For LES, the mean velocities at the cell center were evaluated through the linear interpolation that was second order accurate. The use of linear interpolation implied the use of a filtering procedure. In the present study, the corresponding filtering was based on the trapezoidal rule to approximate the filter.
In Figure 8a to Figure 8c, the air velocity magnitude predicted with SKE and LES was compared with the VPSTV measurements using the normalized square error (NSE) value calculated at 810 sampling locations across the middle section of the test room. As mentioned before, a NSE value of 0.25 or less is an indicator of adequate model performance. Table 6 summarizes the percentages of NSE that exceeds 0.25 for different RANS models and Large Eddy Simulation at the three ventilation rates. It was observed that the NSE was not uniformly distributed in the middle plane and that values of NSE larger than 0.25 were mainly located in the vortex regions (both central and second vortices) for RANS models. These regions were characterized with low velocities (stagnant regions).
Table 6. Percentage of Mean Velocities with Normalized Square Error (NSE) Greater than 0.25 Model SKE REAL RNG ABID AKN CHC LB LS YS V2F KW 3 ach 50 41 42 48 48 46 45 48 N/A 54 N/A 8.6 ach 53 51 50 52 52 51 52 52 47 51 40 19.5 ach 36 36 36 36 35 35 36 37 44 39 40 Average 46 43 43 45 45 44 44 46 46 * 48 40 * Model KWSST RSM LES 3 ach 49 39 18 8.6 ach 42 37 23 19.5 ach 41 33 24 Average 44 36 22 * Average between 8.6 ach and 19.5 ach cases.
[FIGURE 8 OMITTED]
One reason for the difference between prediction and measurement can be ascribed to the limitations of RANS models. As it is known, RANS models have difficulties simulating the low Reynolds number turbulent flows. Another reason is related to the measurement error. In fact, in the low velocities regions, small errors in either measurement or predictions can result in relatively larger NSE values.
The performance of different RANS models became better with increasing ventilation rates, as observed in Table 6. Among the RANS models investigated, RSM gave better predictions than the other models; the NSE values of RSM larger than 0.25 were 39%, 37% and 33% of the measurement domain for the lowest, medium and highest ventilation rates respectively. However, the computational cost and time of RSM is more expensive than the other RANS model used in this study. The performance of V2F model is disappointing as it is more expensively computationally than the two-equations models while not predicted better (if not worse). It is difficult to say which two equation models perform better than the others among the two equation models. For example, the k[omega] model gave the better prediction than the other two equation models at 8.6ach, but performed worse than most of the others except kwsst and YS at 19.5ach. In addition, it did not generate a converged solution at 3ach. If only accuracy was considered, obviously LES performed better than the RANS models investigated; the NSE values of LES larger than 0.25 were less than 25% of the measurement points (see Table 6). The overall performance of the different models at the three different ventilation rates was also tabulated in Table 6. For each model, the average value is the algebraic average of the percentages of NSE's values that exceed 0.25 at the three ventilation rates. LES gave the best predictions among the models investigated and RSM performed better than the other RANS models.
Separation and Reattachment Points. The flow patterns predicted by the different RANS turbulence models and LES with dynamical sub-grid model in the room at different ventilation rates can be roughly classified as three categories: SKE type, RSM/LES type and KW/KWSST type. Separation and reattachment points on the walls together with recirculation vortices were used to precisely characterize the differences between the three types of flow patterns. One important result was that these parameters predicted by the models varied with the ventilation rates, which indicated that all the models investigated have certain capabilities in predicting either low or high Reynolds number flows. But only LES and RSM preformed better than the other models at the low ventilation rates (low Reynolds number flows). Figure 9 showed the comparison of reattachment length and jet penetration length between predictions and measurement. Note that the distance of the reattachment point on the ceiling (CS) from the inlet wall is the reattachment length. In addition, the jet penetration is the distance of the separation point on the ceiling (CS) from the wall. By increasing the ventilation rates, the predictions of the RANS models agreed better with the measurement for the reattachment length. On the other hand, the predictions of the jet penetration differed more from the measurements with an increase in the ventilation rates. More attention should be paid to the LES predictions of the jet penetration: it predicted smaller values than measurement. Furthermore, it showed a different trend from measurements when the ventilation rate increased from 3 ach to 8.6 ach.
[FIGURE 9 OMITTED]
The performance of different turbulence models in the prediction of reattachment length and jet penetration is quite confusing when compared to their performance in the prediction of velocity in the region (measurement domain) away from the wall. As shown in Table 6, LES is the most accurate model for the velocity prediction which predicts very different values and trends of the jet penetration from the experimental data (Figure 9b). Furthermore, LES prediction of reattachment length at the 3ach is not as good as the KWSST model. At present, it is hard to pinpoint the exact reason for the different performances of turbulence models in the regions away from and near the walls. Further study is needed to investigate this point.
The Effects of Inlet Conditions. In real experiments, the detailed inlet boundary conditions are very difficult to measure and specify. In numerical simulations it is common to use a uniform velocity and constant turbulent quantities at the inlet. However, several researchers (Weathers and Spitler 1993; Lee et al. 2002) have reported that the assumption of uniformity at the inlet deteriorated the accuracy of the prediction and using profiled velocities generated from measurements produced positive agreement with the experimental data. Other researchers reported that the profiled inlet velocities did not show major differences from the uniform ones (Chen 1995, 1996; Muller et al. 2000).
Three calculations were conducted to investigate the effects of the inlet boundary conditions on the predictions of airflows: (1) Uniform case: constant velocity (1.43m/s or 281 ft/min) and constant turbulent intensity (10%); (2) Profile case A (Proto): profiled velocity and turbulent kinetic energy from the Hotwire measurement in prototype room I (Zhang 1991); (3) Profile case B (Scale): profiled velocity scaled from the Hotwire measurement in a 1/4 scale room (Zhang 1991) and constant turbulent intensity (10%).
The results of mean velocity and turbulent kinetic energy showed that the inlet conditions affected the flow only in the vicinity of the inlet region. On the regions away from the inlet, effects of inlet conditions were very small and could even be negligible. Similar observation was found in the LES predictions. It should be noted that the measured mean velocities (Zhang 1991) were very close to uniformity except near the diffuser edges. This partly explains the negligible effects of the small differences in this study to the inlet boundary conditions. Two additional reasons are the small ratio of the inlet width (h) to the height of wall (H) and the approximate two-dimensionality of airflow inside the room. The airflows in the study of Weathers and Spitler (1993) and Lee et al. (2002) were totally three-dimensional, which was due to the use of much larger inlets. As a consequence, the effects of the inlet boundary conditions were significant, not only in the jet regions, in their study.
The Effects of Sidewall. The ratio of the inlet length (W) to the inlet height (h) in the test room was 74, much larger than 20. According to Foerthmann's suggestion (Foerthmann 1934), the jet flows at the inlet were practically two-dimensional. During the measurements, relatively good two-dimensionality was found in the inlet and outlet along the spanwise directions. However, it should be noted that the two-dimensionality of inflows does not guarantee that the flow throughout the whole room is two-dimensional. In fact, Bjerg et al. (1999) and Jones and Whittle (1992) observed three-dimensional flow patterns inside a room, although the inlet boundary conditions were two-dimensional. Through simulation with the turbulence k-[epsilon] model and experiments, Bjerg et al. (1999) showed that the three-dimensional effects were small only when the ratio of room width to height was less than 1.
The comparisons of the mean velocity and turbulent kinetic energy between 2-D and 3-D calculations by the use of SKE showed that the differences between the two-dimensional and three-dimensional simulations were negligible. The differences between predictions of periodic LES and those of non-periodic LES were also found negligible except in certain small regions. The possible reason for these differences may be the different models used in the two LES: the standard Smagorinsky sub-grid model was used in non-periodic LES, while a dynamical version was used in the periodic LES.
SUMMARY AND CONCLUSION
The room air movement has a direct and profound effect on the transport and distribution of airborne pollutants in ventilated airspaces. In this work, experimental and numerical studies of airflows at different ventilation rates in the Room Ventilation Simulator (RVS) were presented, which provided information that
is critical for the fundamental understanding of the underlying flow physics and evaluating different turbulence models.
The Volumetric Particle Streak-Tracking Velocimetry (VPSTV) developed in the BEE group (Wang 2005; Sun 2007) was applied to measure the velocity distribution in the middle plane of the room. Seven ventilation rates were tested during the experimental measurements. Three ventilation rates (3 ach, 8.6 ach and 19.5 ach) were chosen for post-processing and analysis. A total of 500 images were post-processed with 250 images from each camera for each ventilation rate. It was found that the measured velocities in the near wall regions were unreliable because the light reflection on the walls made particle paths hard to record. As a result, an area of 4.5 m x 1.8 m (or 15 ft x 6 ft) far from the walls was selected as the post-processing domain.
Among the three ventilation rates investigated, it was observed that one main central recirculation vortex was formed in the middle of the room and one relatively small vortex existed in the bottom left of the measurement domain. The size and positions of both vortices in the measurement domain varied with the ventilation rates. The central vortex became fuller and moved towards the center of the room with increased ventilation rates; at the same time, the second vortex became smaller and moved toward the bottom left corner. The averaged velocity and dimensionless averaged velocity in the measurement domain showed different trends; the averaged velocity increased with an increase of the ventilation rates, while the dimensionless averaged velocity decreased.
The measurements of separation and reattachment points on the ceiling showed that the reattachment length and the jet penetration were strongly dependant on the ventilation rates and they became relatively constant once the ventilation rate reached a threshold value. Comparisons with previous PIV measurements (Zhao 2000) in the same room (prototype II) and the Hotwire measurements (Zhang 1991) in a wider full-scale room (prototype I) and a 1/4 scale room, showed that the present VPSTV measurements were closer to the PIV measurements and the Hotwire measurements (HS) in a 1/4 scale room than the Hotwire measurements (HP) in the wider full-scale room (prototype I).
The experimental data from the VPSTV measurements under the three ventilation rates (3 ach, 8.6 ach, and 19.5 ach) were used to evaluate the performance of thirteen turbulence models based on the Reynolds-Averaged Navier-Stokes (RANS) method and Large Eddy Simulation with a dynamical subgrid model. It was found that among the models investigated, the Large Eddy Simulations gave the best predictions for all three ventilation rates. The RSM model performed best among RANS turbulence models but not as good as the Large Eddy Simulation. It was also found that the predictions of the RANS models agreed better with the measurements at the ventilation rate of 19.5 ach, than the other two lower ventilation rates (3 ach and 8.6 ach). At the ventilation rate of 19.5 ach, all the RANS models except YS, KW and KWSST were almost equally as good and had reasonable agreement with the measurements. The two equation models such as SKE were acceptable for the highest ventilation rates with much less cost than RSM;, thus, they were recommended for the predictions of indoor airflows at high ventilation rates (Reynolds number). The applicability of the RANS models was limited at low (3 ach) and medium (8.6 ach) ventilation rates, where the flows were characterized with low Reynolds numbers. Although some RANS models investigated have functions to simulate the low speed flows, such as RNG, low Reynolds number k-[omega]? etc, further improvement is needed to enhance their prediction applicability in the low Reynolds number flows. If high accuracy is needed for the prediction, the Large Eddy Simulation is recommended.
The reattachment length and jet penetration measured in the experiments were used to further evaluate the models. Consistent with previous finding, the RANS models gave better predictions of reattachment lengths at the higher ventilation rates. In contrast, the predictions of jet penetration differed more from measurements at higher ventilation rates rather than lower ventilation rates. One finding that needs special attention is that the LES predicted relatively smaller values of jet penetration than measurements.
The effects of the inlet conditions and sidewall on the airflows inside the room were numerically investigated and the results showed that: (1) the effects of inlet boundary conditions were confined to the regions near the inlet; (2) the sidewall did not affect the flows in the middle plane of the room.
In this study, only velocity measurements are available for the present VPSTV system. The measurement errors for velocity, which result from image sensor resolution and distortion, lens aberrations, image processing, data processing, and interpolation procedure, etc., make the calculation of standard deviation for velocity unreliable. Further information about turbulence quantities, such as fluctuation of the velocity and the turbulent kinetic energy, are valuable for understanding flow physics and evaluating the numerical models. Thus, the VPSTV system needs to be further improved to take the turbulent quantities into consideration. To this end, digital cameras with higher resolution and speed are necessary (Sun, 2007).
[C.sub.s] = subgrid constant
[C.sub.w] = throat constant
h =height of inlet diffuser
[h.sub.1] = offset distance of the ceiling from centerline of the inlet
H = height of the room
L =length of the room or mixing length
[L.sub.ij] = resolved turbulent stress tensor
p = any one of the 11 camera parameters or instantaneous pressure
[bar.P]= mean pressure
Re = Reynolds number
[S.sub.ij] = strain rate
t = height of the outlet
[t.sub.1] = distance of the outlet from the floor
[T.sub.ij] = subgrid Scale Stress tensor at the test level
[u.sub.i] = instantaneous velocity components, i = 1, 2, 3
[[bar.u].sub.^i] = mean velocity components, i = 1, 2, 3
[[bar.u].sub.i] = velocity components filtered at both the grid-filter and test-filter level
[U.sub.0] = maximum velocity at the inlet diffuser
[U.sub.d] = mean velocity at the inlet diffuser
U = mean velocity in the x direction
V = particle velocity or mean velocity in the y direction
W = width of test room or mean velocity in the z direction
x, y, z = space coordinates of a particle
[[tau].sub.ij] = subgrid scale stress tensor at the grid-filter level
[[tau].sub.w] = shear stress at the walls
[[delta].sub.ij] = Kronecker delta
[mu] = dynamical viscosity of fluid
v = kinematical viscosity of fluid
[v.sub.t] = turbulent viscosity
[DELTA] = filter width
[bar.[DELTA]] = filter width at the grid-filter level
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = filter width at the test-filter level
[rho] = density
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Jianbo Jiang, PhD
Associate Member ASHRAE
Xinlei Wang, PhD
Yigang Sun, PhD
Yuanhui Zhang, PhD
Jianbo Jiang is a postdoctoral fellow at Monell Chemical Senses Center, Philadelphia, PA. Xinlei Wang is an associate professor, Yigang Sun is a senior research engineer, and Yuanhui Zhang is a professor in the Department of Agricultural and Biological Engineering, University of Illinois at Urbana-Champaign, Urbana, IL.
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|Author:||Jiang, Jianbo; Wang, Xinlei; Sun, Yigang; Zhang, Yuanhui|
|Date:||Jul 1, 2009|
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