Modelling the effect of an occupant on displacement ventilation with computational fluid dynamics

Energy and Buildings 40 (2008) 255–264 www.elsevier.com/locate/enbuild

Modelling the effect of an occupant on displacement ventilation with computational fluid dynamics M. Deevy a,*, Y. Sinai b, P. Everitt b, L. Voigt b, N. Gobeau c b

a Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN, United Kingdom ANSYS Europe Ltd., West Central 127, Milton Park, Abingdon, Oxfordshire OX14 4SA, United Kingdom c Direction des Risques Accidentels, INERIS, BP 2, 60550 Verneuil-en-Halatte, France

Received 21 November 2006; received in revised form 25 January 2007; accepted 16 February 2007

Abstract Displacement ventilation of a room with an occupant is modelled using computational fluid dynamics (CFD) and compared against experimental data. The geometry of the experimental manikin is accurately represented in the CFD model to minimise potential errors from using a simplified form. Modelling thermal radiation from the manikin is found to be important and calculations using a radiation model show good agreement with experimental data. The influence of turbulence modelling is considered and a comparative study is made between an unsteady Reynolds-averaged approach (URANS) and detached-eddy simulation (DES). The results show that the URANS and DES give similar predictions with the DES results in slightly better agreement with the experimental data. The realistic manikin geometry is required to give accurate heat transfer and contaminant exposure predictions; such geometries can be handled with relative ease using current grid generation tools and CFD solvers. # 2007 Elsevier B.V. All rights reserved. PACS : 47.27.Eq; 47.27.-i Keywords: Displacement ventilation; Occupant influence; CFD; Thermal radiation; Turbulence modelling; URANS; DES

1. Introduction CFD modelling is often used to assess the influence of heating, ventilation and air conditioning equipment on indoor air flows. Such modelling often does not account for the presence of the occupants of the room or building in question. The effect of people on the surrounding airflow can be significant and hence should be considered when assessing thermal comfort and exposure to contaminants. Computational fluid dynamics (CFD) is a useful tool in studying ventilation both for assessment of an existing configuration and in the design process. CFD studies can often be cheaper than experiments and they provide a wealth of data on the details of the flow in the room, which can be useful for flow visualisation. However, such simulations must use appropriate boundary conditions, geometrical detail and physical modelling. This

* Corresponding author. Tel.: +44 1298 218135; fax: +44 1298 218161. E-mail address: [email protected] (M. Deevy). 0378-7788/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2007.02.021

means that CFD must be validated against good quality experimental data for simple ‘benchmark’ indoor air flows. The present work arose from a contribution to a benchmark exercise aimed at investigating the above issues in modelling flow around an occupant [1]. The benchmark exercise involved a number of participants submitting computational work for two test cases involving indoor air flow around an occupant. The air flow around people has only relatively recently been modelled in detail following the recent significant increase in available computing power. Such models can be used to investigate exposure to contaminants and thermal comfort issues. Using experimental data from the benchmark exercise, the influence of different physical models and boundary conditions could be investigated. Two test cases were selected: a seated manikin in a room with mixing ventilation and a standing manikin in a room with displacement ventilation. The latter of these two test cases is considered in the present study. Further details of the benchmark exercise along with the work of some of the participants can be found at www.cfdbenchmarks.com.

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2. CFD modelling of the flow around a person An early application of CFD to this area was made by Murakami et al. [2] who studied the convective heat transfer between a model of an unclothed manikin and its environment. Five different scenarios for flow around a standing person were examined, including a number of uniform flows past the person and a displacement ventilation scenario. Nilsson and Holme´r [3] modelled the flow around a seated person in a room with displacement ventilation using the RNG k–e turbulence model [4]. The results were converted into thermal comfort indicators and compared with measurements. Murakami et al. [5] modelled the flow around a standing person in a room with displacement ventilation. A low-Reynolds number k–e turbulence model was used and thermal radiation was modelled using the method of Gebhart [6]. Murakami [7] made an in-depth study of the flow around a standing person in a room with displacement ventilation, emphasizing the importance of modelling thermal radiation in such flows. The influence of breathing on the thermal plume was considered using both thermal manikins and real people. A low-Reynolds number k–e turbulence model was used for the majority of the analysis of the mean flow around the person. In addition, large-eddy simulation (LES) was used to study the flow around a simplified rectangle used to approximate the standing person. However, results were only presented of velocity and temperature power spectra at specific locations. Sideroff and Dang [8] carried out simulations of the displacement ventilation test case proposed as part of the benchmark exercise. The standard k–e and v2 f turbulence models were used, and the v2 f model [9] was found to return better results in the thermal plume. However, a thermal radiation model was not used—a factor that may have a significant influence on the flow and hence the assessment of the predictions from different turbulence models. Recent work on the same test case [10] presented steady state results using a k–e turbulence model and a thermal radiation model. A simplified geometry made from four rectangles was used to represent the manikin head, torso and legs. In general, the results showed good agreement with the experimental data and the authors concluded that accurate boundary conditions for the body were more important than geometrical accuracy. 3. The displacement ventilation test case The aim of displacement ventilation is to achieve a stratified distribution of contaminants, with low concentrations at people’s breathing height. It is a potentially effective way of reducing exposure to contaminants. However, it can lead to local variations in temperature and low level draughts. Hence, a number of authors have considered the thermal comfort of occupants in rooms using displacement ventilation [11,12]. Fig. 1 shows the geometry used in the present test case. The flow consists of a three-dimensional wall jet from the rectangular inlet that approaches the feet of

Fig. 1. The geometry used in the CFD calculations. Table 1 Boundary conditions specified for the displacement case Boundary condition

Value used

Inlet velocity Inlet temperature Inlet turbulence intensity Inlet turbulent length scale Heat flux from manikin

0.2 m/s 22 8C 30% 0.1 m 76 W if using radiation model, otherwise 38 W Adiabatic

Heat flux from walls

the person, and a thermal plume above the head. Table 1 shows the boundary conditions given as part of the benchmark exercise. Experiments for this test case were carried out by the University of Tokyo [13]. The conditions in the experiments were designed to correspond with those of the definition of the benchmark exercise. There were two significant differences: the average inlet velocity used in the experiments was slightly lower (0.18 m/s rather than 0.2 m/s) and the outlet dimensions were different (0.3 m  0.3 m rather than 0.2 m  0.4m). In the present calculations, the boundary conditions from the benchmark exercise were used except for the size of the outlet, which was set at 0.3 m  0.3 m to correspond with the experiments. The heat flux from the manikin corresponds to a typical value for a standing person, with 50% of the heat loss due to radiation and 50% due to convection. 4. Simulation approach The commercial CFD code CFX-10 was used to carry out the CFD modelling. Using a turbulence model to calculate the eddy-viscosity, mt, the unsteady Reynolds-averaged NavierStokes (URANS) equations can be written as follows:

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@r @ðrU i Þ þ ¼ 0; @t @xi   @ðrU i Þ @ðrU i Þ @P @ @ðU i Þ 2 @k þU j ¼ þ ðm þ mt Þ  r þSM i ; @t @x j @xi @x j @x j 3 @xi    @ðrhÞ @ðrhÞ @ m @T þU j ¼ lþ t þ SE ; @t @x j @x j s t @x j where Ui are the velocity components, P the pressure, h the static enthalpy, l the thermal conductivity of the fluid and SMi and SE are source terms. The air is assumed to behave as an ideal gas. An unstructured grid was used to enable the resolution of the complex shape of the manikin. Prismatic cells were used near solid surfaces to resolve the wall-jet and thermally driven flow near the body of the person. A total of 222,116 nodes were used and the maximum y+ (wall units y+ = yut/n) on the near wall nodes near the body was 8 and the average y+ was 4. The surface mesh used to resolve the shape of the manikin is shown in Fig. 2 whilst Fig. 3 shows a cross section through the symmetry plane of the mesh. Ten prismatic cells were used next to solid surfaces to resolve the wall shear layers correctly. A grid-dependence test from an earlier study [14] suggested that this level of resolution is sufficient to achieve a reasonably grid-independent URANS solution, although ideally a slightly finer grid might be used in the region above the head of the manikin.

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4.1. Thermal radiation modelling In certain indoor air flows in which even relatively small heat sources are present, thermal radiation may influence the flow. In the present study, the discrete transfer radiation model is used. Reference [15] is the paper which reported the discrete transfer model. This is one of the engineering-standard models for thermal radiation. Reference [16] is an example of the use of radiation in CFD simulations of HVAC. In the present study, predictions without a radiation model using a heat source of 38 W were compared with a calculation using the discrete transfer radiation model using a heat source of 76 W. Twelve rays were used and the air was treated as optically thin. 4.2. Turbulence modelling In the present study, the SST turbulence model [17] has been for the RANS calculations. This model has been shown to return good predictions for a wide range of turbulent flows and can be applied across the viscous sub-layer. The eddy-viscosity, mt, is calculated via transport equations for the turbulent energy, k, and turbulent frequency, v. The following source term is added to the k-equation to account for increased turbulence production due to buoyancy effects, m Pkb ¼ t bgrr; (2) rSct where Sct = 1, and the following source term is used in the vequation   Pkb Peb ¼ C 3 max 0; ; (3) 0:09k where C3 = 1.

Fig. 2. Surface mesh around the manikin.

Fig. 3. Cross-section of the mesh used for the displacement ventilation test case.

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Initial results suggested that there was some unsteadiness in the mean flow close to the body. Hence, unsteady (URANS) calculations were made to capture these effects. A timestep of 0.5 s was first of all tested and the results suggested the flow was unsteady. The timestep was then reduced and the results showed more unsteady behaviour close to the body. A timestep of 0.1 s was then used in the final URANS calculations. The flow was treated as transient in all of the calculations and a second-order Euler scheme was used for the time discretisation. An initial period of 480 s was simulated to ensure full convergence, and statistics were then averaged over the next 120 s. Fig. 4 shows contours of velocity magnitude at 10 s intervals, showing that the mean flow around the body is unsteady. The SST model uses an isotropic eddy-viscosity to describe the effects of turbulence on the mean flow. Such models can perform poorly in the strongly three-dimensional features that occur in this flow. For example, eddy-viscosity turbulence models are known to under-predict the spreading rate of threedimensional wall-jets such as the flow approaching the feet of the manikin [18]. In addition, buoyancy effects are difficult to capture correctly with eddy-viscosity models and the results can be strongly dependent on the values used for the empirical coefficients Sct and C3 [19]. In addition, air speeds indoors tend to be low and therefore parts of the flow may be turbulent or transitional whilst other regions may be laminar. These types of flows are difficult to model using RANS models. One way of avoiding some of the problems associated with RANS turbulence modelling is to use large-eddy simulation (LES), in which only the small scales of turbulence are modelled and the larger, energy-containing scales are resolved. At smaller scales turbulence is more isotropic and therefore easier to model. LES also gives more information on the flow than RANS, for example, giving peak levels of a transported contaminant, which can be useful for problems in occupational hygiene and for modelling exposure to toxic substances. However, LES calculations involve significantly increased

computational times and memory requirements. In addition, there can be difficulties in specifying appropriate turbulent fluctuations at inlets. An alternative is a hybrid approach between RANS and LES known as detached-eddy simulation (DES) [20] in which LES is used in areas of strong large-scale unsteadiness such as in the wake of a bluff body. The DES model used in CFX-10 [21] uses the SST model except for the turbulent lengthscale, lt, which is modified according to a formulation due to Strelets [22]. The model can be written as a modification to the destruction term in the k-equation. In the SST model, this term is equal to 0.09kv, whereas in the DES model it is written as:   lt 0:09 kvF DES with F DES ¼ max ;1 ; (4) CDES D where the turbulent lengthscale, lt, and the local grid spacing, D, are pffiffiffi k ; D ¼ maxðDi Þ: lt ¼ (5) 0:09v The model constant CDES is equal to 0.61 and Di is the local edge length. This means that CDESD is used as the turbulent lengthscale in regions where the grid is sufficiently fine, thus returning an LES region. Originally designed for application to high Reynolds number flows with massive separation, the idea behind DES is to modify the turbulent lengthscale in LES regions where the grid is sufficiently fine and revert to a RANS model elsewhere. This avoids the excessively fine resolution needed for LES of high Reynolds number boundary layers. In the present application, the aim was to use the DES model to capture more of the unsteadiness in the thermal plume and wake behind the manikin, without having to resolve the turbulent fluctuations in the wall jet coming from the inlet (as would be done with LES). The mean flow field and turbulence quantities were started from the Reynolds-averaged solution. Central differencing was used in the LES region whilst a second-order upwind biased scheme was used in the RANS region (see reference [21] for more details on the switching between the two numerical schemes). A timestep of 0.1 s (the same as that used in the URANS calculations) was used giving an average Courant number of 1.2, which should be sufficient to avoid dispersive errors in the LES region. An initial period of 480 s was simulated to allow the turbulent structures to develop, and statistics were then averaged over a further 480 s. The same grid was used for both the URANS and DES calculations. This reduces the computational times compared to using a fine grid for the DES. Moreover, it also allows for a useful comparison of URANS with DES as it is often applied in practice. A comparative study involving LES calculations using a much finer grid is planned for future work. 5. Results

Fig. 4. Contours of velocity magnitude (from a URANS calculation): (a) 0 s, (b) 10 s, (c) 20 s and (d) 30 s.

Three calculations were carried out to investigate the effects of using a thermal radiation model and the influence of different

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Fig. 5. Measurement locations.

turbulence models. Fig. 5 shows the locations in a plane in the centre of the room where measurements were made and the position of L3 corresponds to the location at which measurements were taken in the plume (1.74 m from the inlet). Fig. 6a and b show time averaged velocity magnitudes and temperatures, respectively, along L1. The results from a calculation in which only convection is modelled are compared with those from a calculation using the discrete transfer thermal radiation model. The velocity magnitudes from both

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calculations are in reasonable agreement with the experiments, although the velocity in the jet is slightly over-predicted. This may be because the inlet velocity specified in the benchmark exercise (see Table 1) and used in the calculation is 0.2 m/s, whereas the average inlet velocity was 0.18 m/s in the experiments. Also, it is unlikely that the measured velocity in the jet was actually the peak velocity. However, Fig. 6b shows that the calculation in which only convection is modelled predicts the wrong average temperature distribution. In contrast, when radiation is modelled there is reasonable agreement with the experiments. Fig. 7a and b show flow velocities and temperatures along L2. Fig. 7a shows that when a radiation model is used, a much ‘thinner’ wall-jet is predicted. This appears to be the result of radiation from the body heating the walls of the room, which in turn heats the nearby fluid and this increases mixing. Hence, the incoming air is cooler than its surroundings and the jet is negatively buoyant, resulting in a lower vertical spreading rate. Fig. 7b shows that the temperature stratification is quite well captured when a radiation model is used. Fig. 8 shows the time-averaged velocity magnitude in the plume above the head of the manikin. Although using a radiation model does improve the predictions, both calculations

Fig. 6. Time-averaged (a) velocity magnitude and (b) temperature along L1.

Fig. 7. Time-averaged (a) velocity magnitude and (b) temperature along L2.

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Fig. 8. Time-averaged velocity magnitude along L3 with and without a radiation model.

Fig. 9. Time-averaged velocity magnitude along L6 with and without a radiation model.

over-predict the velocity magnitude in the thermal plume, particularly close to the head of the manikin. Fig. 9 shows the velocity magnitude close to the mouth of the manikin along L6. Without a radiation model the shear layer is too thin and the velocity magnitude is under-predicted. However, when a

radiation model is included the results are in better agreement with the experiments. Fig. 10a and b show velocity magnitudes and temperatures along L4 (0.2 m behind the body). Fig. 10a shows that the velocity magnitude is not very well predicted by either calculation. However, Fig. 10b shows that using a radiation model improves temperature predictions at this location and agreement with the experiments is reasonable. Fig. 11a and b show velocity magnitudes and temperatures along L5 (near the outlet). As was discussed earlier, if radiation is not modelled the wall jet spreads too much in the vertical direction. As with the location further upstream, reasonable agreement is only obtained when thermal radiation is modelled. The results of the CFD calculation in which only convection is modelled shows a region above approximately 1 m from the floor in which the temperature is strongly stratified, below 1 m from the floor the temperature is close to that of the incoming air. This temperature distribution was not observed in the experiments. However, the CFD calculations using a radiation model show much better agreement with experimental data. Thermal radiation from the manikin appears to heat the solid surfaces causing natural convection to occur and thus increase mixing. Fig. 12a and b show these results on the symmetry plane. The velocity vectors in Fig. 12a show the thermal plume caused by the manikin and the wall jet that results from the incoming flow. The temperature contours in Fig. 12b show the vertical variation in temperature, the jet of cooler air coming from the inlet and the warmer air close to the manikin. The unsteady behaviour near the body of the person can be difficult to capture in a URANS simulation. URANS models can be used to simulate large-scale deterministic motion such as can occur in buoyancy driven flow or vortex shedding from a bluff body [23]. However, in a turbulent flow the distinction between large-scale coherent motion and smaller scale turbulent fluctuations is not always clear. Hence, it is useful to be able to compare URANS results with those of LES and DES (see reference [24] for a detailed study of modelling unsteady buoyant flows using RANS models). Fig. 13 shows the blending function used in the present DES calculations. The

Fig. 10. Time-averaged (a) velocity magnitude and (b) temperature along L4.

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Fig. 11. Time-averaged (a) velocity magnitude and (b) temperature along L5.

LES model is used in regions where this function is zero and where the value is one the RANS model is activated. The lighter grey above the head of the manikin (Fig. 13) suggests that the grid is somewhat too coarse to give an LES lengthscale throughout the thermal plume region.

Fig. 12. Time-averaged (a) velocity vectors and (b) temperature contours on the symmetry plane from the URANS calculations using the discrete transfer radiation model.

Fig. 14a and b show time-averaged velocity magnitude and temperature profiles along L2 with URANS and DES. The predictions with URANS and DES are similar, with some small differences in the upper half of the room. Fig. 15a and b show velocity magnitude and temperature profiles along L4 with URANS and DES. The predictions in the lower half of the room are very similar but in the region more than 1 m above the floor, the DES results are somewhat closer to the experimental data, although the temperature stratification is not fully captured in either case. Fig. 16 shows the time-averaged velocity magnitude along L3 in the plume above the head of the manikin. The DES predicts slightly lower velocity magnitudes and shows better agreement with the experimental data than the URANS. Fig. 17 shows velocity magnitude along L6. At this location, there is little difference between the DES and URANS predictions;

Fig. 13. Blending function used between LES and RANS regions in the DES calculation.

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Fig. 14. Time-averaged (a) velocity magnitude and (b) temperature with URANS and DES along L2.

Fig. 15. Time-averaged (a) velocity magnitude and (b) temperature with URANS and DES along L4.

both calculations slightly under-predict the peak in velocity magnitude but the DES results are slightly better near the mouth. Fig. 18a and b show turbulent kinetic energy (k) along L2 and L4, respectively, normalised by the inlet velocity squared.

The modelled k from the URANS calculation is shown along with the modelled and resolved turbulent kinetic energy from the DES calculation. The modelled k from the URANS and DES calculations are in reasonable agreement with the experimental data in the wall jet region close to the floor.

Fig. 16. Time-averaged velocity magnitude along L3 with URANS and DES.

Fig. 17. Time-averaged velocity magnitude along L6 with URANS and DES.

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Fig. 18. Time-averaged turbulence kinetic energy along (a) L2 and (b) L4. Table 2 Measured temperatures on the surface of the manikin Region

Temperature (8C)

Head Hands Forearms Shoulders Chest Back

32.7 32.4 32.7 32.7 32.7 32.8

However, the DES results show much higher turbulence levels in the middle and upper parts of the room. Unfortunately, measurements were not taken in the upper part of the room but the available data do suggest that the DES over-predicts k in the middle of the room. This result is somewhat surprising since

mean velocities and temperatures from the DES are in better agreement with the experimental results than the URANS. However, it is not clear whether large-scale fluctuations around the body were included in measurements of turbulent kinetic energy. More detailed experimental data are needed to find the source of the discrepancies in the results. Table 2 shows the measured temperatures on the torso and head of the body. Values for hands, forearms, etc., are averages of the left and right sides. These values can be compared with Fig. 19, which shows contours of temperature on the surface of the manikin. The URANS and DES results are very similar since they both use the near wall treatment from the SST model (Fig. 12 shows that the DES model switches to a RANS treatment very close to the body). Overall the agreement with the experimental data is reasonable, although it is difficult to make precise comparisons without more detailed data.

6. Conclusions

Fig. 19. Contours of time-averaged temperature on the surface of the manikin with URANS and DES.

This paper has assessed a number of modelling considerations for applying CFD to a flow around a thermal manikin in a room with displacement ventilation. The CFD results were compared with experimental data of time-averaged velocities, temperatures and turbulence intensities. The geometry of the manikin used in the calculation accurately represents that used in the experiments. Good agreement was obtained with experimental data provided a thermal radiation model was used and coupled with the calculation of the hydrodynamic field. Thermal radiation from the body appears to heat the walls and hence causes natural convection and increased mixing in the bulk of the room. This increased mixing results in a more gradual stratification in agreement with observations. Although steady boundary conditions were used, the mean flow around the body was observed to be unsteady, hence URANS calculations were used. In order to obtain an improved representation of the unsteady flow close to the manikin, DES calculations were also made. The time-averaged results from the two approaches were quite similar, although the DES results were in slightly better agreement with the experimental data.

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Improved predictions might be obtained by using LES to resolve more of the turbulent structures in the room: a comparative study involving LES calculations using a much finer grid is planned for future work. LES and DES can be used to give improved predictions of the flow around a realistic geometry of a person and are particularly advantageous if peak exposure levels to a particular contaminant are needed. In the authors’ opinion, such calculations would be most useful for an in-depth study, adding information to a number of RANS calculations for a given problem, perhaps by clarifying the physics of a particular scenario. Another way to improve CFD predictions of the present flow might be to refine the heat transfer boundary conditions on the walls and the manikin. More generally, to improve predictions of the effect of occupants on indoor air flow one would need to consider more sophisticated boundary conditions, accounting for effects such as movement, breathing, variation in skin temperature, thermo-regulation and evaporation from the body. Acknowledgements The authors would like to thank Dr. Jeong-Hoon Yang and Prof. Shinsuke Kato of the University of Tokyo for providing the experimental data and an electronic file containing the data for the manikin geometry. Mike Deevy would also like to thank the Health and Safety Executive (UK) for sponsoring his contribution to this work. References [1] P.V. Nielsen, S. Murakami, S. Kato, C. Topp, J.-H. Yang, Benchmark Tests for a Computer Simulated Person ISSN 1395-7953R0307, 2003. [2] S. Murakami, S. Kato, J. Zeng, Flow and temperature fields around a human body with various room air distributions: CFD study on computational thermal manikin—part I, ASHRAE Transactions 103 (1997) 3–15. [3] H.O. Nilsson, I. Holme´r, Comfort climate evaluation with thermal manikin methods and comouter simulation models, Indoor Air 13 (2003) 28–37. [4] V. Yakhot, S.A. Orszag, Renormalization group analysis of turbulence. I. Basic theory, Journal of Scientific Computing 1 (1986) 3–51. [5] S. Murakami, S. Kato, J. Zeng, Combined simulation of airflow, radiation and moisture transport for heat release from a human body, Building and Environment 35 (2000) 489–500. [6] B. Gebhart, A new method for calculating radiative exchanges, ASHRAE Transactions 65 (1959) 321–323.

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