Experimental study of human thermal plumes in a small space via large-scale TR PIV system

International Journal of Heat and Mass Transfer 127 (2018) 970–980

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Experimental study of human thermal plumes in a small space via large-scale TR PIV system Jiayu Li a,c, Junjie Liu a,⇑, Jingjing Pei a, Krishna Mohanarangam b, William Yang b a

Tianjin Key Laboratory of Indoor Air Environmental Quality Control, School of Environmental Science and Engineering, Tianjin University, Tianjin 300072, China CSIRO Mineral Resources, Clayton, Victoria 3169, Australia c Institute for Energy Efficient Buildings and Indoor Climate, E.ON Energy Research Center, RWTH Aachen University, Mathieustr. 10, Aachen, Germany b

a r t i c l e

i n f o

Article history: Received 28 March 2018 Received in revised form 19 June 2018 Accepted 26 July 2018

Keywords: Unsteady airflow Vortex identification Instantaneous air distribution Turbulence scales POD analysis Limited space

a b s t r a c t In small occupied spaces such as vehicle cabins, in-depth information about human thermal plumes can be important for designing ventilation systems, especially in the case of displacement ventilation. In this study, large-scale time-resolved particle image velocimetry measurements were performed to reveal airflow characteristics of thermal plumes inside a small space with high temporal and spatial resolutions. The measured time-averaged velocity showed that the development of thermal plumes was limited by the small space, with maximum vertical velocity of 0.184 m/s above the head. The standard deviation of velocity and the turbulence intensity (TI) indicated high fluctuation characteristics, with TI of approximately 0.4 in the mainstream area. With these time-resolved data, the integral, Taylor and Kolmogorov scales were calculated, which provided recommended grid sizes and time steps for different numerical simulations. For investigation of instantaneous characteristics and vortex structures, three vortex identification parameters were compared. The vorticity index identified bulky attached and detached vortexes around the head; the Q-criterion revealed that the mainstream area was controlled mainly by deformation structures; and the kci criterion, which was the most effective means of identification, avoided the influences of deformation structures and focused only on the rotation structures with directions of rotation. Furthermore, multi-scaled characteristics of thermal plumes were revealed by proper orthogonal decomposition, and the period of ascending plumes was estimated as 5 s. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Small occupied spaces are vehicle cabins and similar confined spaces. In vehicle cabins with high occupant density, such as the cabins of cars, trains, and airliners, airflow patterns are essential for removing excess heat and diluting contaminants [1], which can be the result of interaction between conditioned air supplied by the environmental control system (ECS) and the human airflows, mainly thermal plumes from passengers [2,3]. Hence, the study of human thermal plumes in small spaces could provide fundamental support for the design of ventilation systems for vehicles, especially displacement ventilation (DV) systems, which are driven mainly by thermal plumes. A confined space, meanwhile, is defined by the Occupational Safety and Health Administration (OSHA) as a workplace with limited openings and unfavorable natural ventilation [4]. Although confined spaces are not intended for continuous ⇑ Corresponding author at: Room 228, Building 14, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (J. Liu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.138 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

employee occupancy, air distributions inside such spaces can play a decisive role in the heath of workers [5,6]. Moreover, because confined spaces typically lack mechanical ventilation systems, the airflow patterns are likely to be dominated by natural convection, especially by thermal plumes from workers themselves. Researchers have investigated human thermal plumes through both computational fluid dynamics (CFD) simulations and experiments. In comparison with numerical studies [7–13], fewer experimental investigations of human thermal plumes can be found in the literature because of the sophisticated measurement techniques needed for airflows that are low-speed and sensitive (easily influenced by instruments). However, numerical results are reliable only when they are validated by experiments under similar scenarios [14,15]. With the use of intrusive sensors such as ultrasonic anemometers and thermo-anemometers, Zukowska et al. [16] found that thermal plumes above a seated thermal manikin had asymmetrical distribution characteristics in a large room. In a subsequent study, Zukowska et al. [17] observed that the surroundings of a thermal manikin, such as the furniture in the room, influenced the air distributions of thermal plumes. These results

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

971

Nomenclature x, y, z U, V, W

Cartesian coordinates in m instantaneous velocity components in x, y, z directions in m/s u, v, w fluctuation velocity components in x, y, z directions in m/s, defined as u ¼ U  hUi; v ¼ V  hVi; w ¼ W  hWi rU ; rV ; rW standard deviation of U, V, W in m/s, defined in Eq. (1) TI turbulence intensity, defined in Eq. (2) Um magnitude of instantaneous velocity in m/s, defined in Eq. (2) um magnitude of fluctuation velocity in m/s, defined as ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi um ¼ u2 þ v 2 þ w2 x vorticity in s1, defined in Eq. (3) Q scalar in Q-criterion for vortex identification in s2, defined in Eq. (4) sn tensor of stretching deformation in s2, defined in Eq. (5) ss tensor of shearing deformation in s2, defined in Eq. (6) kci scalar in kci -criterion for vortex identification in s1 d velocity gradient tensor matrix in s1, defined in Eq. (7) Kci kci with the sign of vorticity in s1, defined in Eq. (8) R two-point spatial correlation coefficient, defined in Eq. (9) sl integral timescale in s, defined in Eq. (10) l integral lengthscale in m, defined in Eq. (11) sk temporal Taylor microscale in s, defined in Eq. (12) k spatial Taylor microscale in m, defined in Eq. (13)

indicated that thermal plumes in different surrounding environments could be different, and in limited small spaces thermal plumes would have special features. In a recent study, Koelblen and Bogdan [18] used thermo-anemometers to characterize thermal plumes above a manikin with different postures. However, the influence of intrusive methods with bulky sensors and traversing systems could be significant, especially in such small spaces. A non-intrusive method such as a particle image velocimetry (PIV) system, which allows the placement of all components outside the cabin, could be a means of measuring the thermal plumes in a small space. In a small room with DV, Marr [19] performed a series of PIV measurements to quantify human airflow with the use of a thermal manikin, and the results have been used repeatedly in the validation of other researchers’ numerical models [12,20,21]. However, these studies of human thermal plumes were conducted in ventilated environments. Thus, although the flow rates were kept very low, the thermal plumes in the studies were not driven only by thermal buoyancy, i.e., they were not socalled ‘‘pure” thermal plumes, but were also influenced to some extent by mechanical ventilation. In large or open spaces, by means of local seeding techniques, Craven and Settles [22] used a PIV system to measure thermal plumes without any ventilation, and Voelker et al. [23] utilized a particle streak tracking technique, which is similar to PIV, to characterize a microclimate created entirely by thermal buoyancy released from a seated thermal manikin. Licina et al. [24,25] conducted a series of PIV experiments to investigate human convection in a quiescent indoor environment with the use of local seeding techniques. They described the boundary layers of thermal plumes from a seated manikin and found that the thermal plumes had a significantly influence on contaminant transport. However, these local seeding techniques are not suitable for measuring thermal plumes in non-ventilated small spaces because the seeded particles accumulate quickly, and the concentration is not stable enough for a PIV experiment.

sg g e m un ain ðtÞ kn

temporal Kolmogorov microscale in s, defined in Eq. (14) spatial Kolmogorov microscale in m, defined in Eq. (15) turbulence dissipation rate in m2 s3, defined in Eq. (14) kinematic viscosity in m2 s1 the nth orthonormal bases of POD analysis, i.e., POD mode n temporal coefficient of mode n at ith instantaneous velocity field eigenvalue of un

Symbols hMi mean or expectation of M qðrÞ autocorrelation correlation function, defined in Eq. (10) Abbreviations ECS environmental control system OSHA Occupational Safety and Health Administration CFD computational fluid dynamics LES large eddy simulation DV displacement ventilation PIV particle image velocimetry TR time-resolved (U) RANS (unsteady) Reynolds averaged Navier-Stokes DNS direct numerical simulations POD proper orthogonal decomposition FoV field of view

In a very recent study, Li et al. [26] developed a PIV method to quantify the thermal plumes in an aircraft cabin mockup by means of pre-seeding techniques. However, the researchers were limited by the sampling rate of the large-scale PIV system, and they failed to characterize the unsteady and turbulent features of thermal plumes. According to the Nyquist-Shannon sampling theorem [27], the sampling rates of instruments, such as the timeresolved (TR) PIV system, are needed to further investigate the turbulent or unsteady characteristics. For investigation of the turbulent and unsteady characteristics of thermal plumes in a small space and to facilitate CFD simulation in related scenarios, a large-scale TR PIV system was utilized in this study to measure plumes from a thermal manikin inside a transparent cabin mockup. With the resulting high spatial resolution data, distributions of various statistics, such as time-averaged velocities, standard deviations and turbulent intensity, were obtained in order to characterize the human thermal plumes and also provide ideal data to numerical researchers for validation and improvement of their models. With these high-frequency data, turbulence scales were determined in order to provide more direct references for further simulation studies. Moreover, for further understanding of the airflow mechanism of human thermal plumes, spatial and temporal characteristics of thermal plumes were identified through three different vortex identification methods and proper orthogonal decomposition (POD) analysis. These characteristics could further support the study of thermal comfort and indoor air quality. 2. Experimental platform and set-up As shown in Fig. 1, the experimental platform in this study was a transparent airtight cabin inside a large air-conditioned space. The dimensions of the cabin were 1.50 m (x)
1.70 m (y)
1.80 m (z), and it was built on stilts to keep all the walls at approximately the

972

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

Fig. 1. Schematic of the experimental platform.

same temperature. Inside the cabin, a thermal manikin bound with resistance wires was seated on a simple chair without handrails. The manikin was used to mimic the natural sitting posture of a male adult. The geometrically symmetric plane of the manikin’s head was x = 0 m, but this plane was not the exact symmetrical plane of the body of the manikin because of the natural sitting posture. Before the start of the experiment, the manikin was preheated by a 75 W alternating current for more than one hour to ensure that thermal conditions had stabilized [26]. Thermal boundary conditions were measured with an infrared camera (i5, FLIR Systems, Inc., Wilsonville, USA). The infrared camera was factory calibrated within 2% accuracy, and the surface property and the emissivity of corresponding material were considered during the measureTable 1 Average surface temperatures in °C. Cabin walls Ceiling Ground Left Right Front Back

Manikin surfaces 21.9 21.1 21.6 21.5 21.3 21.3

Head Neck Chest Waist Thighs Calves

30.8 32.5 32.4 34.2 34.1 27.0

ments. The average surface temperature of each part of the manikin and the surface temperatures of the walls are listed in Table 1. The thermal boundary conditions are depicted in greater detail by the thermographs in Figure a1 in Appendix 1. To facilitate CFD simulation, a laser-scanned 3D numerical model of the sitting manikin is provided in Appendix 2. In this study, thermal plumes from the sitting manikin were investigated in the coronal and sagittal planes shown in Fig. 2. In the coronal plane, the manikin was approximately symmetrical along the x = 0 m plane, and thus only one zone above the head was measured, as shown in Fig. 2(a). However, because the head of the manikin blocked the laser, the tracer particles behind the head, i.e., on the other side of the laser light source, were not illuminated; this occlusion area is indicated in Fig. 2(a). Because the seated manikin was asymmetrical in the z-direction, two zones with 10% overlap were measured in the sagittal plane to reveal the difference in thermal plumes ascending behind and in front of the manikin. For the PIV experiment, the pre-seeding technique introduced by Li et al. [27] for quantifying thermal plumes without any ventilation in a small enclosed space was utilized in this study. Pre-seeded tracer particles were generated by a Laskin atomizer (PIVpart14, PIVTEC – GmbH, Göttingen, Germany), illuminated by a double-cavity Nd:YLF laser (LD30-527, Litron Lasers, Warwick-

Fig. 2. Measured locations on (a) coronal and (b) sagittal planes.

973

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980 Table 2 Key parameters of the large-scale TR PIV system. Laser

Laser source Laser power Thickness Divergence angle Time between pulses

Double cavity Nd:YLF Laser 30 mJ/pulse @1KHz 1–3 mm 31° 3 ms

Camera

Camera model Lens Resolution

Phantom V211 CMOS camera Sigma 20 mm F1.8 1280 pixel
800 pixel

Tracer particle

Model of atomizer Type of tracing particles Diameter of tracing particles

PIVpart 14 (PIVTEC – GmbH) Olive Oil 1 lm

Algorithms

Cross-correlation with highly accurate sub-pixel interpolation scheme Size of interrogation window 32 pixel
32 pixel Overlap of interrogation window 50% Processing software DynamicStudio v4.0

Overall parameters

Sampling frequency Sampling quantity Field of view (FoV)

shire, England), and recorded by a high-speed camera (Phantom V211, ViSion Research, New Jersey, USA). To avoid the influence of the momentum of seeding particles and to obtain homogeneous particle distributions, the tracer particles were seeded into the cabin 15 min before the camera started recording the particle images [26]. The key parameters of the large-scale TR PIV system setup are listed in Table 2. The system and its settings were technically supported by Dantec Dynamics A/S, Skovlunde, Denmark, which had been proved reliable for measuring low-speed airflows in previous studies, and the systemic error could be controlled at under 2% [28,29].

3. Results 3.1. Time-averaged air distribution and statistics Contour maps of the time-averaged velocity components are shown in Fig. 3. The distribution of time-averaged velocity components in the vertical direction (y-direction), defined as hVi, are shown in Fig. 3(a) and (c); the components in the transverse directions (x- and z-directions), denoted as hUi and hWi, are shown in Fig. 3(b) and (d), respectively. The streamlines on each figure were determined by the two velocity components on the corresponding plane, i.e., the streamlines on coronal planes were determined by hUi and hVi, and those on sagittal planes by hVi and hWi. According to the streamlines in the two planes in Fig. 3, the thermal plume was generated by the whole surface area of the manikin and moved upward while entraining ambient air. In the case of the plume around the manikin that ascended above the head, it first gathered together into the middle and then separated quickly when it reached the ceiling (at y = 1.7 m). The contour of the time-averaged velocity distributions in Fig. 3 indicates that the plumes in the initial regions (below the top of the head, as shown in Fig. 2) had strong characteristics of attached flow around the manikin. These characteristics were due to the Coanda˘ effect. In comparison to the velocity components hUi or hWi in the transverse directions, the velocity in the vertical direction hVi was two times larger, and it was considered as the mainstream direction of the thermal plumes. Because the space was limited, the plumes were not fully developed. The maximum vertical velocity hVimax was 0.184 m/s, in contrast with the measured maximum vertical velocities in previous studies, 0.24 m/s [22,26] and 0.27 m/s [23] in a large or open space with similar seated thermal manikins. The hVi was distributed asymmetrically in both the coronal and sagittal planes, as shown in Fig. 3(a) and (c), respectively. The hVi

250 Hz 8125 0.520 m
0.320 m

was distributed more asymmetrically in sagittal plane than that in coronal plane, shown in Fig. 3(a) and (c). In the coronal plane, this slight asymmetry was caused mainly by the natural sitting posture, in which a little larger portion of the body was on the x side, as detailed in Fig. 2. In the sagittal plane, more plumes generated by the body appeared in the area behind the manikin’s head because the head position was in front of the body in the natural sitting posture. By contrast, the transverse velocities (hUi and hWi) were distributed more symmetrically than vertical velocity hVi, as shown in Fig. 3(b) and (d). Although the transverse velocities were much smaller than the vertical ones, they clearly displayed the development of thermal plumes: in the initial region, the development of thermal plumes was determined by the geometry of the manikin due to the behavior of attached flows. Next, after the plumes detached from the head into the development region, the plumes around the manikin gathered together and then separated, as indicated by the distributions transverse velocity with opposite directions in Fig. 3(b) and (d). For statistical investigation of the unsteady behavior and fluctuation characteristics of the thermal plumes, the standard deviation (r, m/s) of the velocity components and the turbulence intensity (TI) for each data point were calculated according to Eqs. (1) and (2). The results are shown in Fig. 4. Note that, because of the limitations of 2-D measurements, there are two velocity components in each measured plane. For example, in the coronal plane, TI was calculated with the use of U; V; rU and rV , while W and rW were set as 0 in Eq. (2).

rU ¼

TI ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffi hðuÞ2 i;

rV ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffi hðv Þ2 i;

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðr2U þ r2V þ r2W Þ=2 Um

;

rW ¼

Um ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi hðwÞ2 i

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hUi2 þ hVi2 þ hWi2

ð1Þ

ð2Þ

In comparison to the large differences in time-averaged velocities between the vertical and transverse directions shown in Fig. 3, the fluctuation velocities in these two directions were in similar ranges, as shown in Fig. 4(a–d). In Fig. 4(a) and (d), it can be seen that the vertical fluctuations rV appeared to a greater extent in the outer layer of the main thermal plume stream; these fluctuations were due to the entrainment of ambient air. In contrast, the transverse fluctuations (rU and rW ) occurred to a greater extent in the area just above the head in both the coronal and sagittal planes, as shown in Fig. 4(b) and (e), respectively. The TI distributions in Fig. 4(c) and (f) indicate that the flow field of the thermal plumes was dominated by relatively high TI values; even in the

974

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

Fig. 3. Time-averaged airflow distributions in (a) & (b) coronal plane and (c) & (d) sagittal plane.

mainstream-controlled area with higher time-averaged velocities, the TI values could still be as high as approximately 0.4. In summary, the statistical results revealed that thermal plumes generated by a human body in a small space would be characterized by low velocity and high fluctuation. These unsteady characteristics required further study, and the following sections discuss instantaneous features and turbulent characteristics. In addition, these data on thermal plumes with high-spatial resolution would be ideal material for validation of related numerical models; therefore, the raw measured data along with the statistics are provided in Appendix 3 for interested readers.

The low-velocity, highly unsteady feature of thermal plumes was observed by means of a statistical method in the previous analysis. As described in the present section, the unsteady behavior of thermal plumes was further studied by characterizing the instantaneous air distributions of thermal plumes with three different vortex identification methods. The first identification index is vorticity (x), the most commonly used method to detect the tendency of the flow field to rotate, defined by Eq. (3).

@ v @u  @x @y

Q ¼ s2n þ s2s  x2

ð4Þ

where sn and ss represent stretching and shearing deformation, defined by Eqs. (5) and (6), respectively.

sn ¼

@u @ v  @x @y

ð5Þ

ss ¼

@ v @u þ @x @y

ð6Þ

The third vortex detector is swirl strength, or the kci criterion [32,33]. The kci is calculated by solving the eigenvalue problem of the constructed matrix of velocity gradient tensor (d) in Eq. (7).

3.2. Instantaneous air distributions and vortex identification

x¼

Weiss equation (Eq. (4)). An area will be controlled by deformation when Q > 0, while it will be dominated by rotation when Q < 0.

ð3Þ

The second method is the Q-criterion [30,31], which further distinguishes deformation from vorticity and is defined by the Okubo-

2

@u 6 @x d¼6 4 @v @x

3 @u @y 7 7 @v 5

ð7Þ

@y

In 2D cases, d will have either two real eigenvalues or a pair of complex conjugate eigenvalues. The kci is defined as the imaginary part the complex eigenvalue. In order to denote the sense of rotation, the sign of x is added to kci , which is defined by Eq. (8):

Kci ¼ kci signðxÞ ¼ kci

x

jxj

ð8Þ

Note that, for the sake of brevity, the equations listed above use the parameters in the coronal plane, and only the results in the

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

975

Fig. 4. Standard deviation and TI distributions in coronal plane (a), (b) & (c) and sagittal plane (d), (e) & (f).

coronal plane are presented in the main body of this paper. When the corresponding variables in the x direction are changed to those in the z direction, the parameters in sagittal plane can be obtained, and their distributions are shown in Figure a2 in Appendix 1.

As shown in Fig. 5, instantaneous velocity fields at three different time points were selected to investigate the transient behavior and vortex structures of the thermal plumes. When the instantaneous velocity vectors at the three selected times are compared,

Fig. 5. Instantaneous velocity vectors and distributions of x (a–c), Q (d–f), and Kci (g–i).

976

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

Fig. 6. Time-averaged distributions of Q and Kci .

it can be seen that the flow patterns were quite different from each other. Not only were the detailed local air distributions different at the three different times, but the thermal plumes swung in a large scale: at 2.000 s, most of the ascended plumes swung to the +x side as shown in Fig. 5(a, d and g), and at 10.000 s they swung to the other side, while they were relatively symmetrical at 6.000 s. This large-scale unsteady swing behavior is further demonstrated by the enclosed animations in Appendix 4. According to the contours of the three vortex detectors in Fig. 5, human thermal plumes displayed turbulence characteristics that were highly random and complex. The x with the simplest algorithm was already able to detect the attached vortex around the head and reveal the detachment above the head, as shown by the continuous vortex stripes in Fig. 5(a–c). However, the x mistakenly identified some non-vortex structures with high-velocity gradients and failed to describe the detailed structures of the vortex. The Q-criterion further distinguished between deformation and rotation, and revealed vortex structures. The deformation-controlled areas, with positive Q values, are displayed in purple1 in Fig. 5(d–f), while the rotationdominated areas, which were considered as vortex structures, had negative Q values and are displayed in green in the figure. The kci criterion, as shown in Fig. 5(g–i), identified vortex structures in similar areas to those marked green by the Q-criterion. Moreover, the sense of rotation was further distinguished as either anticlockwise or clockwise by marking a vortex red or blue, respectively. The distributions of Kci indicate that the attached airflows around the head were dominated by strong and stable attached vortexes, which are shown more clearly by the animation in Appendix 4. The thermal plumes that developed above the head on the x side were dominated by an unstable anti-clockwise vortex, and those on the +x side by a clockwise vortex. Next, the vortex structures of all 8125 measured instantaneous flow fields were identified by the Q and kci criterions, and then the statistics hQ i and hKci i, respectively, were calculated. The overall feature of the vortex distributions of the thermal plumes is shown in Fig. 6(a) and (b). According to the statistics for Q shown in Fig. 6 (a), the mainstream area of the thermal plumes was controlled by deformations for a longer time than rotations, whereas the boundary and outer layers of the thermal plumes were controlled mainly by rotations. Furthermore, the distribution of hKci i revealed the overall distribution feature of the rotation structures, shown in Fig. 6(b). The attached vortexes on both sides of the head are clearly visible, and, other than in these areas, most of the flow fields were controlled by two groups of vortexes that rotated in opposite directions. 1 For interpretation of color in Figs. 5 and 6, the reader is referred to the web version of this article.

3.3. Turbulence structures and microscales As discussed in this section, three different scales, an integral scale [34–36], the Taylor microscale [34,37,38] and the Kolmogorov microscale [34,39,40], were used to describe the turbulence characteristics of thermal plumes. The integral scale is defined here as the largest correlated temporal or spatial distance between velocity fluctuations, and it is considered to be the largest scale for description of vortexes in a flow field. The Kolmogorov scale is the smallest of the three, and it is considered to be the least discernible scale in turbulence flows. At the level of the Kolmogorov scale, the flows are dominated by viscosity, and the turbulent kinetic energy is dissipated into heat. The Taylor microscale, for which the spatial scale is also known as the turbulence length scale, is between the integral and Kolmogorov scales. Each of these three scales can be subcategorized into a temporal scale and a spatial (or length) scale. According to the Taylor frozen hypothesis, temporal and spatial scales can convert mutually. Furthermore, within the scope of these microscales, the assumption of isotropy could be made, and thus the magnitudes of the fluctuation pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi velocities (um ¼ u2 þ v 2 þ w2 ) were used in the subsequent calculations. With the high temporal resolution data obtained by the TR PIV system in this study, the temporal scales could be directly calculated on the basis of the autocorrelation functions, and the spatial scales were calculated in accordance with the Taylor frozen hypothesis, defined as Eqs. (9)–(14).

sl ¼

Z

þ1

qðrÞdr; qðrÞ ¼

0

* + um ðtÞum ðt þ rÞ um ðtÞ2

l ¼ sl
U m 

sk ¼  k¼2

2 q00ð0Þ

ð9Þ ð10Þ

1=2

hu2m i hð@um =@xm Þ2 i

ð11Þ

;

@um 1 @um ¼
Um @xm @t

ð12Þ

sg ¼ ðm=eÞ1=2 ; e ¼ 15mhð@um =@xm Þ2 i

ð13Þ

g ¼ ðm3 =eÞ

ð14Þ

1=4

As shown in Fig. 7(a) and (d), the integral timescale value in the thermal plume-controlled area was around 0.4 s, while the integral lengthscale values ranged from 0.07 m to 0.13 m; these were the largest temporal and spatial sizes, respectively, of the vortexes of the thermal plumes. In the ambient area, where velocities were

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

977

Fig. 7. Distributions of temporal turbulence scales (a–c) and spatial scales (e–f).

very low, the timescale was much larger. The Taylor scale, as shown in Fig. 7(b) and (e), provided similar distributions to those of the integral scale. In the plume-controlled area, the temporal and spatial Taylor microscale values were around 0.15 s and 0.003 m, respectively. These are very useful parameters for CFD simulation, as will be explained in greater detail in the Discussion section. As shown in Fig. 7(c) and (f), the Kolmogorov scale values ranged from 0.02 s to 0.1 s and from 3
104 m to 6
104 m for the temporal and spatial scales, respectively. These values were much smaller than those of the other two scales. Hence, in general, human thermal plumes, characterized as unsteady and lowvelocity free convection airflows, exhibited relatively large temporal turbulence scale values and small spatial scale values in comparison to those for forced flows in indoor environments [41,42]. 3.4. Proper orthogonal decomposition Through observation of the instantaneous flow fields in a time series in Section 3.2 and Appendix 4, one can see that the plumes ascended sometimes from the left side (x side) of the head, at other times from the right side (+x side), and sometimes from both sides at the same time. To further investigate this observation, proper orthogonal decomposition (POD) was introduced to characterize the fluctuation features and determine their corresponding temporal characteristics. POD is one of the principal types of component analysis, and it was first introduced into turbulence analysis by Lumley [43] to identify the coherent structures and their temporal features in complex instantaneous flow. In the present study, both temporally and spatially changing characteristics were analyzed by decomposing a series of fluctuation velocity fields ui ðx; y; tÞ into a spatial part, orthonormal bases un ðx; yÞ, a temporal part, and temporal coefficients, ain ðtÞ:

ui ðx; y; tÞ ¼

N X ain ðtÞun ðx; yÞ

ð15Þ

n¼0

where i represents the i th instantaneous velocity field, also known as a ‘‘snapshot” in the snapshot method [44,45], and n signifies the nth POD mode. The snapshot method is the most common approach to finding the orthonormal bases and corresponding temporal coefficients, and it was described in detail in our previous studies

[46,47]. By this method, the total number of POD modes that can finally be decomposed is equal to the total number of snapshots used (i.e., the sampling quantity, N = 8125). To reduce calculation efforts and extract all possible modes, a representative area (0.20 m
0.15 m) above the head of the manikin in the coronal plane was selected as the POD analyzing area, as shown in Fig. 2(a). The eigenvalue of each POD mode un , denoted as kn , represents the total kinetic energy of this mode. Hence, by reordering the decomposed POD mode un in the order of kn from large to small, we determined the coherent structures (POD modes, un ) in different scales from large to small and the corresponding energy contributions P kn = N1 kn , as shown in Fig. 8(a) and (b), respectively. For identification of the energy composition feature of the free convection of thermal plumes, we have included the energy composition of a typical forced convection flow, the jet flow from a multi-slot diffusor [47], in Fig. 8(b) for comparison. Whereas the energy of the jet flow has a relatively even distribution across modes, the first four modes of the thermal plumes together contributed more than 50% of the total energy. Hence, the first four modes could be the most important coherent structures of thermal plumes. Furthermore, as shown in Fig. 8(a), these four modes appeared in pairs, of which the first two, with vertical structures on the right and left sides, represent the discrete uptrend plumes ascending from both sides of the manikin; the latter two modes, with the structures towards the center, represent the interactions of the plumes from the two sides. In combination, these first four coherent structures encompass most of the important unsteady characteristics of thermal plumes. Then, with decreasing energy contribution, POD modes 5 to 10 exhibited smaller and irregular coherent structures, as shown in Fig. 8(a). After mode 10, the higher modes contributed less than 2% of the total energy, and their structures became increasingly random and irregular; this could be considered as background turbulence noise. The coherent structures in the POD modes represented the fluctuation features in different spatial scales. Furthermore, investigation of the corresponding temporal coefficient, as shown in Eq. (15), allowed the temporal characteristics of these specific structures to be analyzed. The temporal coefficients of the first four modes are shown in Fig. 9. Since mode 1 depicts rising plumes from the right side of the head, and mode 2 represents the left side, as shown in blue and red in Fig. 9, the positive peaks of corresponding temporal coefficients indicate the events of ascending plumes.

978

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

Fig. 8. POD modes (a) and corresponding energy contributions (b).

Fig. 9. Temporal coefficients of the first four modes.

From the coefficients of the first two modes, it can be estimated that the period of the plumes ascending from each side was approximately 5 s. A comparison of the first two coefficients indicates that there was no obvious correlation between the plumes from the two sides, i.e., the plumes ascending from one side were independent of those from the other side. The interactions of plumes from the two sides had a higher frequency and lower amplitude, as shown in the corresponding coefficients of modes 3 and 4, which were independent from each other and also from the first two modes. 4. Discussion The results of this study can be applied to similar scenarios, such as confined spaces and vehicle cabins. Hence, in this section, practical implications of the results will be discussed in two areas: 1. The use of this fundamental airflow information to facilitate CFD analysis. High spatial resolution statistical data for thermal plumes, such as distributions of time-averaged velocities and TI, provide ideal material for validation of the codes and numerical models used in CFD simulation of human thermal plumes. For

this purpose, detailed boundary conditions and a 3-D scanned numerical model of the manikin are included in Figure a1 in Appendices 1 and 2. Moreover, the turbulence scales in this study could guide researchers in choosing suitable mesh sizes and time steps for their numerical models [41,42]. For example, direct numerical simulations (DNS), which simulate all the scales in flow fields, require grid and temporal resolutions that are higher than those of the smallest scales, the Kolmogorov scales, in the flow fields. When the RANS model is used to calculate the time-averaged air distribution, grid sizes smaller than the largest length scale, the integral length scale, of the flow field are highly recommended for obtaining an acceptable prediction. The choice of time step for the unsteady RANS (URANS) model can also rely on the integral time scale. Because the grid size and time step for large eddy simulation (LES) should be between those for DNS and the RANS model, the Taylor scales could be the ideal references [34,41]. To summarize, the recommended grid sizes and time steps are listed in Table 3. Note that these recommended values are not suitable for boundary layers because the resolution of the PIV system used here was not sufficiently high, and laser reflection from the surface was inevitable.

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980 Table 3 Recommended grid sizes and time steps for numerical simulations.

Grid sizes in mm Time steps in s

(U-) RANS

LES

DNS

70–130 0.3–1

2–5 0.1–0.3

0.3–0.6 0.02–0.1

2. Investigation of contaminant transport and thermal comfort. As the airflows initiated by human bodies are always the control targets or objectives in occupied enclosed environments, these in-depth analyses of airflows could serve as important fundamental references in future studies of the control of contaminant transport and improvement of thermal comfort. The vortex structures introduced in Section 3.2 have a significant influence on contaminant transport: vorticitydominated locations are more likely than deformationcontrolled areas to ‘‘lock” contaminants [31]. Hence, for effective removal of pollutants from confined spaces, greater attention should be paid to the vorticity-dominated locations. For creation of a thermally comfortable space, the statistics in Section 3.1 can provide basic data. Furthermore, human thermal comfort is influenced by the unsteady characteristics of airflow [48–50], and the POD analyses in Section 3.4 provide unsteady characteristics of thermal plumes on different scales. Note that this discussion offers only some rough suggestions, which need to be further refined. This study also has some limitations. A high storage rate was required by the large-scale TR PIV system, whereas the data transmission speed of the system and the storage space of the camera were not sufficient to store many samples in a row. Moreover, the frequency of thermal plumes presented in Fig. 9 was relatively low, and thus the measurement time was not long enough for identification of an exact period by a mathematical method such as the fast Fourier transform. In addition, because turbulence is inherently random, the measured instantaneous velocity fields at different times could not be spliced together. Hence, under the limitations of the one-camera PIV system used in this study, the two measured zones in sagittal plane could only be spliced in statistical analyses. Another limitation is that this study focused more on the velocity distribution of the thermal plume, and only the surface temperature was provided. As a very important parameter, air temperature distribution is very important to characterize the plume, for example for calculating the buoyancy flux and the local Richardson number. However, in this confined small space, the intrusive methods for measuring the air temperature in previous studies [16,17] will inevitably influence this kind of very ‘‘sensible” low-velocity thermal plumes. Next, with the validating data and recommended grid sizes & time steps, CFD could be a promising solution to obtain more comprehensive data to push this analysis more theoretically. 5. Conclusions An experimental platform was built to investigate thermal plumes in a small space with the use of a large-scale TR PIV system. The resulting data with high spatial and temporal resolution not only can serve as ideal material for validation of CFD codes but has also revealed characteristics of human thermal plumes in the occupied enclosed environment. The main findings can be summarized as follows. 1. According to the statistical results, the thermal plumes in the limited space displayed the characteristics of low speed with high fluctuation. Limited by the small space, the thermal

979

plumes were not fully developed, with a maximum vertical velocity hVimax = 0.184 m/s in the area above and behind the head of the manikin. 2. Three vortex identification methods were compared. Vorticity identified the attached and detached vortexes around the head. The Q-criterion successfully distinguished the rotation and deformation structures and found that the mainstream area of the plumes was controlled mainly by deformation structures. The kci criterion, which was the most effective method, avoided the influence of deformation structures and focused only on the rotation structures and sense of rotation. 3. The integral, Taylor and Kolmogorov scales of thermal plumes were calculated, and they ranged, respectively, from 70 to 130, 2 to 5, and 0.3 to 0.6 in mm spatially and from 0.3 to 1, 0.1 to 0.3, and 0.02 to 0.1 in s temporally. On the basis of the calculated scales, recommended time steps and grid sizes were provided for numerical simulations. 4. POD analysis revealed the multi-scale characteristics of thermal plumes. In comparison with forced flows, fluctuations of thermal plumes were dominated to a greater extent by the first four POD modes. The first two modes characterized the discrete uptrend plumes ascending on each side of the head with a period of approximately 5 s. Conflict of interest We declare that no conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. Acknowledgments This study was supported by the National Natural Science Foundation of China (grant no. 51478301), the National Basic Research Program of China (the 973 Program) through grant no. 2012CB720100, and a scholarship from the China Scholarship Council (CSC) that enabled Jiayu Li to visit RWTH Aachen University. The authors of this paper would like to express their gratitude to Dr. Xiaodong Cao of Harvard University & Dr. Congcong Wang of Tianjin University for providing the thermal manikin and their kind help with this research and to Professor Dirk Müller & Mark Wessling of RWTH Aachen University for discussion about this paper. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.07.138. References [1] A. Mangili, M.A. Gendreau, Transmission of infectious diseases during commercial air travel, Lancet 365 (9463) (2005) 989–996, https://doi.org/ 10.1016/S0140-6736(05)71089-8. [2] M. Kühn, J. Bosbach, C. Wagner, Experimental parametric study of forced and mixed convection in a passenger aircraft cabin mock-up, Build. Environ. 44 (5) (2009) 961–970, https://doi.org/10.1016/j.buildenv.2008.06.020. [3] J. Li, X. Cao, J. Liu, C. Wang, Y. Zhang, Global airflow field distribution in a cabin mock-up measured via large-scale 2D-PIV, Build. Environ. 93 (2015) 234–244, https://doi.org/10.1016/j.buildenv.2015.06.030. [4] Occupational Safety and Health Administration (OSHA), Labor, Confined Spaces in Construction, Federal Register, 80(85) (2015) 25366–25526. . [5] D.C. Fuller, A.J. Suruda, Occupationally related hydrogen sulfide deaths in the United States from 1984 to 1994, J. Occup. Environ. Med. 42 (9) (2000) 939– 942. . [6] D. Burlet-Vienney, Y. Chinniah, A. Bahloul, B. Roberge, Occupational safety during interventions in confined spaces, Saf. Sci. 79 (2015) 19–28, https://doi. org/10.1016/S0167-6105(99)00088-4.

980

J. Li et al. / International Journal of Heat and Mass Transfer 127 (2018) 970–980

[7] S. Murakami, J. Zeng, T. Hayashi, CFD analysis of wind environment around a human body, J. Wind Eng. Ind. Aerodyn. 83 (1) (1999) 393–408, https://doi. org/10.1016/S0167-6105(99)00088-4. [8] S. Murakami, S. Kato, J. Zeng, Combined simulation of airflow, radiation and moisture transport for heat release from a human body, Build. Environ. 35 (6) (2000) 489–500, https://doi.org/10.1016/S0360-1323(99)00033-5. [9] D.N. Sørensen, L.K. Voigt, Modelling flow and heat transfer around a seated human body by computational fluid dynamics, Build. Environ. 38 (6) (2003) 753–762, https://doi.org/10.1016/S0360-1323(03)00027-1. [10] N. Gao, J. Niu, CFD study on micro-environment around human body and personalized ventilation, Build. Environ. 39 (7) (2004) 795–805, https://doi. org/10.1016/j.buildenv.2004.01.026. [11] N. Gao, J. Niu, Transient CFD simulation of the respiration process and interperson exposure assessment, Build. Environ. 41 (9) (2006) 1214–1222, https:// doi.org/10.1016/j.buildenv.2005.05.014. [12] M. Salmanzadeh, G. Zahedi, G. Ahmadi, D.R. Marr, M. Glauser, Computational modeling of effects of thermal plume adjacent to the body on the indoor airflow and particle transport, J. Aerosol Sci. 53 (2012) 29–39, https://doi.org/ 10.1016/j.jaerosci.2012.05.005. [13] Y. Liu, Y. Zhao, Z. Liu, J. Luo, Numerical investigation of the unsteady flow characteristics of human body thermal plume, Build. Simul. 9 (6) (2016) 677– 687, https://doi.org/10.1007/s12273-016-0296-1. [14] W.L. Oberkampf, T.G. Trucano, Verification and validation in computational fluid dynamics, Prog. Aerosp. Sci. 38 (3) (2002) 209–272, https://doi.org/ 10.1016/S0376-0421(02)00005-2. [15] Q. Chen, J. Srebric, A procedure for verification, validation, and reporting of indoor environment CFD analyses, HVAC&R Res. 8 (2) (2002) 201–216, https:// doi.org/10.1080/10789669.2002.10391437. [16] D. Zukowska, Z. Popiolek, A. Melikov, Determination of the integral characteristics of an asymmetrical thermal plume from air speed/velocity and temperature measurements, Exp. Therm. Fluid Sci. 34 (8) (2010) 1205– 1216, https://doi.org/10.1016/j.expthermflusci.2010.04.009. [17] D. Zukowska, A. Melikov, Z. Popiolek, Impact of personal factors and furniture arrangement on the thermal plume above a sitting occupant, Build. Environ. 49 (2012) 104–116, https://doi.org/10.1016/j.buildenv.2011.09.015. [18] B. Koelblen, A. Bogdan, Impact of clothing, breathing and body posture on the shaping of a thermal plume above a human, Int. J. Vent. 13 (4) (2015) 397–410, https://doi.org/10.1080/14733315.2015.11684063. [19] D. Marr, Velocity measurements in the breathing zone of a moving thermal manikin within the indoor environment, Mechanical and Aerospace Engineering, Syracuse University - Dissertations, 2007, p. 15. . [20] X. Jia, J.B. McLaughlin, J. Derksen, G. Ahmadi, Simulation of a mannequin’s thermal plume in a small room, Comput. Math. Appl. 65 (2) (2013) 287–295, https://doi.org/10.1016/S0140-6736(05)71089-8. [21] A.M. Abdilghanie, L.R. Collins, D.A. Caughey, Comparison of turbulence modeling strategies for indoor flows, J. Fluids Eng. 131 (5) (2009) 051402, https://doi.org/10.1115/1.3112386. [22] B.A. Craven, G.S. Settles, A computational and experimental investigation of the human thermal plume, J. Fluids Eng. 128 (6) (2006) 1251–1258, https:// doi.org/10.1115/1.2353274. [23] C. Voelker, S. Maempel, O. Kornadt, Measuring the human body’s microclimate using a thermal manikin, Indoor Air 24 (6) (2014) 567–579, https://doi.org/ 10.1111/ina.12112. [24] D. Licina, J. Pantelic, A. Melikov, C. Sekhar, K.W. Tham, Experimental investigation of the human convective boundary layer in a quiescent indoor environment, Build. Environ. 75 (2014) 79–91, https://doi.org/10.1016/j. buildenv.2014.01.016. [25] D. Licina, A. Melikov, C. Sekhar, K.W. Tham, Transport of gaseous pollutants by convective boundary layer around a human body, Sci. Technol. Built Environ. 21 (8) (2015) 1175–1186, https://doi.org/10.1080/23744731.2015.1060111. [26] J. Li, J. Liu, C. Wang, N. Jiang, X. Cao, PIV methods for quantifying human thermal plumes in a cabin environment without ventilation, J. Visualization 20 (3) (2017) 535–548, https://doi.org/10.1007/s12650-016-0404-4. [27] A.J. Jerri, The Shannon sampling theorem—its various extensions and applications: a tutorial review, Proc. IEEE 65 (11) (1977) 1565–1596, https:// doi.org/10.1109/PROC.1977.10771. [28] X. Cao, J. Liu, J. Pei, Y. Zhang, J. Li, X. Zhu, 2D-PIV measurement of aircraft cabin air distribution with a high spatial resolution, Build. Environ. 82 (2014) 9–19, https://doi.org/10.1016/j.buildenv.2014.07.027.

[29] M. Raffel, C.E. Willert, S.T. Wereley, J. Kompenhans, Particle Image Velocimetry: A Practical Guide, second ed., Springer, 2013. [30] J.C.R. Hunt, A.A. Wray, P. Moin, Eddies, streams, and convergence zones in turbulent flows, Studying Turbulence Using Numerical Simulation DatabasesI1, 1988, p. 193. . [31] F. Li, J. Liu, J. Ren, X. Cao, Y. Zhu, Numerical investigation of airborne contaminant transport under different vortex structures in the aircraft cabin, Int. J. Heat Mass Transf. 96 (2016) 287–295, https://doi.org/10.1016/j. ijheatmasstransfer.2016.01.004. [32] J. Zhou, R.J. Adrian, S. Balachandar, T.M. Kendall, Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech. 387 (1999) 353–396, https://doi.org/10.1017/S002211209900467X. [33] C.D. Tomkins, R.J. Adrian, Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech. 490 (2003) 37–74, https://doi.org/10.1017/ S0022112003005251. [34] S.B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, 2001. [35] P.A. Durbin, B.P. Reif, Statistical Theory and Modeling for Turbulent Flows, second ed., John Wiley & Sons, 2011. [36] P.L. O’neill, D. Nicolaides, D. Honnery, J. Soria, Autocorrelation functions and the determination of integral length with reference to experimental and numerical data. In 15th Australasian Fluid Mechanics Conference, vol. 1, The University of Sydney, 2004, pp. 1-4. [37] A. Segalini, R. Örlü, P. Schlatter, P.H. Alfredsson, J.D. Rüedi, A. Talamelli, A method to estimate turbulence intensity and transverse Taylor microscale in turbulent flows from spatially averaged hot-wire data, Exp. Fluids 51 (3) (2011) 693. . [38] G.I. Taylor, Statistical theory of turbulence (September), Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 151, no. 873, The Royal Society, 1935, pp. 421–444. https://doi.org//10. 1017/S002211209900467X. [39] D.C. Wilcox, Turbulence Modeling for CFD, third ed., DCW Industries, La Canada, California, USA, 2006. [40] A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers (February), Dokl. Akad. Nauk SSSR, vol. 30, no. 40, 1941, pp. 299–303. http://www.jstor.org/stable/51980. [41] C. Wang, J. Liu, J. Li, Y. Guo, N. Jiang, Turbulence characterization of instantaneous airflow in an aisle of an aircraft cabin mockup, Build. Environ. 116 (2017) 207–217, https://doi.org/10.1016/j.buildenv.2017.02.015. [42] S. Lestinen, S. Kilpeläinen, R. Kosonen, J. Jokisalo, H. Koskela, A. Melikov, Flow characteristics in occupied zone–an experimental study with symmetrically located thermal plumes and low-momentum diffuse ceiling air distribution, Build. Environ. 128 (2018) 77–88, https://doi.org/10.1016/j. buildenv.2017.11.020. [43] J.L. Lumley, The structure of inhomogeneous turbulent flows, Atmospheric turbulence and radio wave propagation, vol. 790, 1967, pp.166–178. [44] L. Sirovich, Turbulence and the dynamics of coherent structures. I. Coherent structures, Q. Appl. Math. 45 (3) (1987) 561–571. [45] L. Sirovich, Turbulence and the dynamics of coherent structures. II. Symmetries and transformations, Q. Appl. Math. 45 (3) (1987) 573–582. [46] J. Li, J. Liu, X. Cao, N. Jiang, Experimental study of transient air distribution of a jet collision region in an aircraft cabin mock-up, Energy Build. 127 (2016) 786– 793, https://doi.org/10.1016/j.enbuild.2016.06.039. [47] J. Li, J. Liu, C. Wang, M. Wesseling, D. Müller, PIV experimental study of the large-scale dynamic airflow structures in an aircraft cabin: swing and oscillation, Build. Environ. 125 (2017) 180–191, https://doi.org/10.1016/j. buildenv.2017.07.043. [48] Y. Zhu, M. Luo, Q. Ouyang, L. Huang, B. Cao, Dynamic characteristics and comfort assessment of airflows in indoor environments: a review, Build. Environ. 91 (2015) 5–14, https://doi.org/10.1016/j.buildenv.2015.03.032. [49] L. Huang, Q. Ouyang, Y. Zhu, Perceptible airflow fluctuation frequency and human thermal response, Build. Environ. 54 (2012) 14–19, https://doi.org/ 10.1016/j.buildenv.2012.02.004. [50] X. Zhou, Q. Ouyang, G. Lin, Y. Zhu, Impact of dynamic airflow on human thermal response, Indoor Air 16 (5) (2006) 348–355, https://doi.org/10.1111/ j.1600-0668.2006.00430.x.