The effect of indoor heating system location on particle deposition and convection heat transfer: DMRT-LBM
Introduction
Over the years, researchers and engineers have been using Lattice Boltzmann Method (LBM) to simulate different flow fields such as magnetohydrodynamics, immiscible fluids, multiphase flows, non-Newtonian fluids, convective heat transfer problems and flows through porous media [1], [2], [3], [4], [5], [6], [7], [8]. Some researchers have previously used a single relaxation time (SRT) lattice Boltzmann model based on the well-known Bhatnagar–Gross–Krook (BGK) collision operator [9], [10], [11], [12], [13], [14], [15]. Due to its simplicity and acceptable efficiency, SRT model has become an attractive model among scholars as a collision operator, in spite of some known problems such as viscosity dependence of boundary locations and numerical instability [16]. So, to overcome these deficiencies d’Humières [17] proposed the multiple relaxation-time (MRT) LBM. Luo et al. [18] performed a comparative study and evaluated different models for the collision step to simulate various flows like SRT, the two-relaxation-time (TRT), the entropic lattice Boltzmann equation (ELBE) and MRT. With respect to their results the MRT and TRT models are preferable to be used for the collision step in terms of computational efficiency, stability and accuracy.
Recently, Sajjadi et al. [19], [20], [21] employed the MRT-LBM model to simulate various flow fields in different geometries. They illustrated that the MRT-LBM model can predict the results more accurately in comparison to the earlier works. Sajjadi et al. [22] investigated the convective heat transfer in a cavity and considered the effect of heater location on the heat transfer rate and concluded that the convective heat transfer reaches its maximum value when the heater is in the middle of the cavity.
Due to several applications of natural convection in an enclosure such as nuclear reactor design, solar energy collectors and building insulation, this type of heat transfer is an interesting research field. Numerical, analytical and experimental methods are used to consider the process of heat and mass transfer in the above-mentioned configurations [23]. For solving the flow field and natural convection, several numerical methods have been successfully used [24], [25], [26], [27]. Sharif and Liu [28] investigated the effect of angles of inclination on heat transfer in a two-dimensional (2-D) cavity. Their results showed that the rate of heat transfer decreases with increasing the angle of inclination. Baïri et al. [29] used finite volume method (FVM) to simulate a two dimensional free convection in an enclosure filled with air for various aspect ratios. By means of experimental results, they showed that the difference between simulated and measured data is negligible, namely less than 6%. Arpino et al. [30] proposed an algorithm to obtain precise results for free convection flows at high Rayleigh numbers in different cavities. Varol et al. [31] used experimental and numerical methods to simulate the free convection in an enclosure which had two hot and cold horizontal walls while the other walls were adiabatic. Kuznetsov and Sheremet [32] considered 2-D free convection in a cavity which had a heat source with fixed heat flux located on the internal part of the left wall. They reported the results for various Grashof numbers from 106 to 108. Nithyadevi et al. [33] used a numerical method to investigate magneto convection in a cavity with partially thermally side walls. They captured the results for various non-dimensional numbers such as Grashof number, Hartmann number, and Prandtl number. They concluded that the maximum Nusselt number was seen for the middle–middle thermally active positions while the minimum heat transfer rate is observed for the bottom cooling and top heating active positions.
The heat transfer rate declines by augmentation of magnetic field and enhances with an increase in Grashof and Prandtl number. Teamah et al. [34] used a numerical method for simulating a double-diffusive convective flow in a cavity with segmental heat sources for different non-dimensional numbers like Prandtl number, Rayleigh number and dimensionless heater lengths. Their results illustrated that the heat transfer rate () and average Sherwood number were enhanced by increasing Prandtl and Rayleigh numbers. as well as non-dimensional heater length. Huelsz and Rechtman [35] applied the LBM to solve the laminar free convection in an inclined enclosure with four fixed walls, namely two adiabatic walls and two heated walls. They presented that for a constant inclination angle, the Nusselt number had a power-law dependence with respect to the Rayleigh number.
Because of considerable industrial and environmental applications, engineers and scientists have been interested in particle motion in indoor and outdoor flows [37], [38], [39], [40]. Lately, because of the importance of dust motion and deposition in air pollution as well as the associated health problems, this issue has received a significant attention [41]. Li et al. [42] developed a computational scheme to simulate aerosol particle motion in turbulent flows. They concluded that the deposition rate decreases significantly as the shape of the obstruction becomes more streamlined. Wang et al. [43] used experimental data for two cases, namely one steady-state case and one transient case, so that they can investigate the efficiency of several models. With respect to their results, the Eulerian method with Reynolds average Navier Stocks (RANS) model was efficient and accurate for the steady case, but for the transient one the Lagrangian method with large eddy simulation (LES) models was the most efficient and accurate choice. Zhang et al. [44] proposed a self-developed numerical wind tunnel model to investigate the pollutant dispersion around an urban building. They found that the position of emission did not affect the concentration of haze fog. Recently, Sajjadi et al. [45], [46], [47] investigated the particle motion in a modeled room by means of the LBM. They reported that the LBM is able to capture the features of particle dispersion and deposition reasonably well. Yet, as those authors have been focused on investigating flow field, energy equation is not solved so prospective temperature effects on particle motion are disregarded.
Few guidelines and standard are available for the Total Suspended Particle (TSP) in the world (Table 1) [36]. For instance, Kuwait EPA (Environment Public Authority) has suggested 0.23 mg/m for average exposure in 24-h periods, Australian NHMRC (National Health and Medical Research Council) has stipulated 90 g/m for 1-year exposure period, and US OSHA (Occupational Safety and Health Administration) has recommended 15 g/m for an average 8-h period.
Air temperature is an important factor to maintain an acceptable thermal comfort level in a building’s indoor environment. Table 2 illustrates standards and guidelines for air temperature in summer and winter.
The literature points to MRT-LBM as a powerful tool to simulate problems in either science or engineering [18], [19], [20], [21], but this numerical method needs more attention when applied to virtualize various flow fields. In this work, DMRT-LBM is used to investigate the particle deposition and dispersion for the first time, and particular attention is given to the effect of indoor heating system location on particle deposition and heat transfer in a modeled room. Furthermore, different particle sizes are considered and the effect of particle size on particle transport and deposition is discussed.
Section snippets
Present geometry
In this work, a cubic office room has been modeled where H is the edge length (Fig. 1). To investigate the effect of indoor heating system position, a 2-D heater with H/3H/3 dimension has been used at six various positions on the left wall (X 0) of the modeled room (Fig. 1). The temperature of the heater is constant at 1 () in the non-dimensional form, the dimensionless temperature of the right wall (X 1) is fixed at 0 () and all other walls are adiabatic. No-slip boundary
DMRT-LBM
In the literature, DMRT-LBM is known as a stable and powerful method to investigate the heat transfer and flow field [19], [20], [21]. therefore, in the present work, this new method is used to simulate the flow and temperature fields.
Particle motion equation
The governing equation for small particle motion [48]: here the lift force is neglected. In Eq. (17), is the particle velocity and is the fluid velocity at the particle location. is defined as the particle relaxation time . Here, S is particle-to-fluid density ratio, d is the particle diameter, is the kinematic viscosity of the fluid, and is the Cunningham slip correction defined as:
In Eq. (18), = 7
Code validation and grid independence analysis
To implement the LBM code, FORTRAN home-made programming is used for this study. To check the grid independence, the average Nusselt numbers on the heater (H/2YH, 0ZH/3 and 104) are reported for various grid resolutions as in Table 3. With respect to Table 3, the amount of average Nusselt number did not change significantly when the grid resolution (number of lattices) increases from (707070) to (808080), so the former grid resolution is chosen.
The present results for various
Conclusion
In the present study, using the Double Multi Relaxation Time Lattice Boltzmann method , the temperature and flow field inside a three-dimensional modeled room for two Rayleigh numbers, 104 and 105, are investigated. Different locations are considered for the heating system and their impact on heat transfer rate is analyzed. In order to understand the behavior of particles and pollutants in the modeled room, 50 000 particles with sizes of 1 and 10 m are randomly injected into the room and the
Acknowledgment
This work was supported by the Iran National Science Foundation: INSF, Iran [grant number: 97/s/5426].
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