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A Two-Layer Turbulence Model for Simulating Indoor Airflow Part I

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A Two-Layer Turbulence Model for Simulating Indoor Airflow Part I Energy and Buildings 33 +2001) 613±625 A two-layer turbulence model for simulating indoor air¯ow Part I. Model development Weiran Xu, Qingyan Chen* Department of Architecture, Massachusetts Institute of Technology, 77 Massachusetts Avenue, MA 02139, USA Received 2 August 2000; accepted 7 October 2000 Abstract Energy ef®cient buildings should provide a thermally comfortable and healthy indoor environment. Most indoor air¯ows involve combined forced and natural convection +mixed convection). In order to simulate the ¯ows accurately and ef®ciently, this paper proposes a two-layer turbulence model for predicting forced, natural and mixed convection. The model combines a near-wall one-equation model [J. Fluid Eng. 115 +1993) 196] and a near-wall natural convection model [Int. J. Heat Mass Transfer 41 +1998) 3161] with the aid of direct numerical simulation +DNS) data [Int. J. Heat Fluid Flow 18 +1997) 88]. # 2001 Published by Elsevier Science B.V. Keywords: Two-layer turbulence model; Low-Reynolds-number +LRN); k±e Model +KEM) 1. Introduction This paper presents a new two-layer turbulence model that performs two tasks: 1.1. Objectives 1. It can accurately predict flows under various conditions, i.e. from purely forced to purely natural convection. This Energy ef®cient buildings should provide a thermally model allows building ventilation designers to use one comfortable and healthy indoor environment. The comfort single model to calculate flows instead of selecting and health parameters in indoor environment include the different turbulence models empirically from many distributions of velocity, air temperature, relative humidity, available models. and contaminant concentrations. These parameters can be 2. It can be more efficient than available turbulence obtained by using the computational ¯uid dynamics +CFD). models, such as LRN models and RSMs. On the other hand, indoor air¯ow have the impact on building energy consumption. For example, it is well-known that displacement ventilation can save energy because of the 1.2. Earlier work temperature strati®cation in a room. In addition, different ¯ow patterns can result in very different heat transfer Purely forced and natural convection can be viewed as coef®cients on building enclosures. The corresponding heat two extreme cases of mixed convection. Mixed convection is gain and loss will not be the same. more complicated than forced convection and natural con- Many indoor air®ows involve all three types of convec- vection since it combines the complexity of both. Turbulent tion: forced, natural and mixed convection. Accurate simu- forced convection has been extensively studied and most lation of these ¯ows is essential for building ventilation turbulence models are developed for forced ¯ows. A review system design. The CFD simulations often use turbulence of the studies on turbulent natural convection can be found in models, since most ¯ows encountered indoors are turbulent. [2]. This section reviews the state-of-the-art studies of However, the existing turbulence models are either inaccu- turbulent mixed convection and identi®es the problems with rate, such as the standard k±e model +KEM), or inef®cient, the existing turbulence models. such as low-Reynolds-number +LRN) KEMs and Reynolds Studies on turbulent mixed convection fall into three stress models +RSMs), to predict all three types of convection. categories: theoretical analysis, experimental investigation and numerical simulation. Theoretical studies include those by Nakajima and Fukui [4], Chen et al. [5] and Aicher and * Corresponding author. Martin [6]. Nakajima and Fukui [4] and Chen et al. [5] 0378-7788/01/$ ± see front matter # 2001 Published by Elsevier Science B.V. PII: S 0378-7788+00)00129-8 614 W. Xu, Q. Chen / Energy and Buildings 33 92001) 613±625 Nomenclature Superscript Ð time-averaged quantities Am, Ae constants used in the one-equation instantaneous quantities models non-dimensionlized by wall-friction 2 Arb bulk Archimedes number, gbDTL=Ubulk quantities 2 Ary local Archimedes number, gbDTyn/U C1e, C2e, C3e constants used in the e equation Subscripts Cm constant used for calculating nt i, j spatial coordinate indices dk diffusion of turbulent kinetic energy nb neighbor points gi component i of the gravitation vector ref reference conditions G gravitational acceleration t turbulent quantities Gk gravity production of turbulent kinetic energy +Àbgiuit) independently proposed damping functions similar to Van 3 2 Grx local Grashof number +bgDTx /n ) Driest's [7] to enable the mixing-length model to count the h convective heat transfer coefficient buoyancy effects. They also conducted an experiment in a k turbulent kinetic energy +uiui=2) long channel to study basic turbulence and heat transfer L characteristic length characteristics of mixed convection. Aicher and Martin [6] Nux local Nusselt number +hx/lair) proposed two heat transfer correlations for the mixed con- p fluctuating pressure vection in a tube. These studies provided some physical Pk shear production of the turbulent kinetic insights to understand the mixed convection. For example, energy +Àuiuj@Ui=@xj) Nakajima and Fukui found that the heat transfer in the Pt total pressure boundary layer of a plate was decreased when the plate Pr Prandtl number was slightly heated. Aicher and Martin [6] suggested that the Prt turbulent Prandtl number decrease was due to the reduction of the turbulent energy in 2 Ra Rayleigh number +bgDTL /nl) the boundary layer. Re Reynolds number Experimental investigations on turbulent mixed convec- t fluctuating temperature or time tion that can be directly used for validation of numerical T mean temperature simulations, i.e. those with simple geometry and boundary Ta ambient temperature conditions, are very few. The only notable contributions are u, v fluctuating velocity component in x, those by Schwenke [8] and Blay et al. [9]. Schwenke con- y direction ducted a series of measurements in a ventilated room with a ui component i of fluctuatingp velocity heated wall. He measured the penetration length, which is the ut friction velocity, tw=r length of how far the air stream from a diffuser can propagate uiuj Reynolds stress against the buoyancy-induced wall jet. He found that the uit turbulent heat flux energy imposed on the heated wall had a signi®cant impact Ui component i of the mean velocity on the air¯ow pattern. This case can represent the air¯ow in a U, V, W mean velocity component in x, y and typical ventilated room with a hot window. Blay et al. z direction p measured the mixed convection ¯ow in a two-dimensional Vc characteristic velocity, bgDTL cavity. Their measured quantities include velocities, tem- x, y, z spatial coordinate peratures and velocity ¯uctuations at mid-width and mid- yn normal distance to the nearest height plane of the cavity. Both studies have been selected to wall validate the model developed in this paper. y, yÃ, yà dimensionless wall distance, y u =n; n p p n t Numerical simulations of mixed convection are widely yn k=n; yn vv=n available in literature. Nielsen et al. [10] used the standard KEM with the wall functions and calculated the ¯ows in a Greek symbols ventilated room with ¯oor heating some 20 years ago. b thermal expansion coefficient À+1/r)+@r/ Though the prediction agreed reasonably with the experi- @T) mental data, it is well known that the wall functions cannot dij Kronecker delta calculate buoyancy effects accurately. In addition, their e turbulent energy dissipation results do not agree well with Schwenke's experimental l thermal conductivity data [8]. In spite of these, this early attempt showed the great n molecular viscosity potential of numerical simulation and it was considered as a nt turbulent viscosity milestone in applying the CED technique to indoor air¯ow r fluid density simulations. sk, se Prandtl number of k and e Many other researchers have applied LRN KEMs to tw wall shear stress calculate mixed convection ¯ows in vertical pipes [11], W. Xu, Q. Chen / Energy and Buildings 33 92001) 613±625 615 vertical channels [12,13], vertical boundary layers [14], and cavities [9,15]. These computational results have been compared with the corresponding experimental data and the agreement was reasonably good. However, the comput- ing costs in these applications were very high. For example, To and Humphrey [15] found that at least ®ve grids are needed in the viscous sublayer and 17 in the buffer layer to produce acceptable results. Chen [16] systematically compared the performance of several KEMs on indoor air¯ow simulation and found that the performance of various turbulence models was so Fig. 1. The configuration used in the DNS study [3]. diverse that no model can be used universally. For example, he found the RNG KEM performed best in mixed convection but very poor in forced convection ¯ows. 2.1. Brief description of the DNSdata Very few researchers have attempted to apply the RSMs on indoor air¯ow simulations. One contribution is due to Kasagi and Nishimura [3] conducted a DNS study for the Chen [17]. He found that the performance of the RSMs in con®guration shown in Fig. 1 under various Grashof num- mixed convection is less satisfactory than that in forced and bers. The free stream ¯ow in the channel is heated at one side natural convection. and cooled at the other. So far, only one DNS study has been performed towards Table 1 summarizes the ¯ow conditions under which the turbulent mixed convection [3]. This DNS was performed DNS was performed. The table also includes the conditions for fully developed channel ¯ows with small buoyancy for the DNS data from Versteegh and Nieuwstadt [18] as a effects. This paper has employed their data to develop a comparison. The table shows that cases 1±4 have a similar one-equation turbulence model. Reynolds number while the Grashof numbers varies from In summary, for turbulent mixed convection, few theore- 0±1:6  106.
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