Air Change and Transfer Efficiencies within a Cross-Ventilated Room Model Sheltered by Urban-Like Block Arrays using RANS simulations

. Natural and cross ventilation is recognized as an important measure for introducing outdoor fresh air to indoor without the use of mechanical equipment. Plenty of fruitful studies for elucidating natural and cross ventilation mechanisms have been reported adopting experimental and computational methods. Field and wind tunnel experiments could provide substantial flow information on indoor-outdoor interaction in actual or reduced model conditions. However, these approaches were relatively costly and time-consuming and limited in terms of spatial and temporal resolutions. Computational fluid dynamics approaches are promising complementary technique to these methods. In this study, we performed isothermal CFD simulations for both airflow and concentration fields for cross-ventilation conditions sheltered by surrounding buildings with two different opening conditions. ANSYS/Fluent was utilized to perform CFD using RANS simulation. Heterogeneity of ventilation efficiencies determined by concentration distributions in cross-ventilated room model were quantitatively analyzed using ventilation efficiencies, e.g., age of air. The results showed that the location of the openings had a significant impact on the cross-ventilation rate, creating completely different concentration fields, and ventilation efficiencies indices could quantitatively demonstrate the formation mechanisms of scalar concentration distributions in an indoor space.


Introduction
Natural ventilation can dilute indoor generated contaminants by introducing "fresh" outdoor air and promote human body heat dissipation by introducing "cool" outdoor air without relying on mechanical power. For this reason, it is an attractive alternative as a response to energy conservation, to be used in conjunction with or instead of mechanical systems. In addition, natural ventilation and ventilation is a relatively easy and simple act for occupants to perform. However, because it uses passive driving forces such as natural wind, accurately estimating the amount of ventilation is a major challenge when introducing natural ventilation. The ventilation phenomenon in buildings has long been studied as a field of building engineering, originating in hygienics [1]. Since then, research results have been steadily accumulated, including the development of basic data on flow coefficient and wind pressure coefficient necessary for ventilation volume calculation [2,3], and the proposal of local dynamic similarity models for inflow opening pressure [4]. On the ground, however, atmospheric turbulence that develops on a flat surface has a significant impact on the energy and material circulation between the atmosphere and land, so the structure of atmospheric turbulence is extremely complex on land surfaces with canopies such as cities and forests. In particular, the urban turbulent boundary layer formed by a group of buildings shows a complex distribution of airflow fields in both horizontal and vertical directions due to the large shape resistance of the building group. For example, the average wind speed around buildings in the urban canopy layer shows a characteristic distribution called Flow Regime that differs with building density [5]. In addition, it is known that the incidence and intensity of weak and gusty winds within the canopy layer depends greatly on the arrangement of the building group [6]. The effect of such urban building clusters on indoor ventilation is called the Sheltering effect. In recent years, with the increasing precision of experimental instruments and the expansion of computing resources, many studies have been conducted using wind tunnel experiments (WTE) and numerical fluid dynamics analysis. In a pioneering study, Tominaga and Blocken [7] reported that mean wind velocity decreases due to the shelter effect and that the distribution of turbulent energy and concentration changes significantly for indoor airflow in stand-alone buildings and buildings under shielding conditions. Ikegaya et al. [8] found that the interior unsteady airflow distribution differs significantly among buildings and opening locations using the Particle Image Velocimetry (PIV) method, and later Adachi et al. [9] performed LES for a detailed comparison. Shizadi et al. [10] found that indoor airflow differs significantly with different wind directions by using RANS simulation. In addition, many cases have been reported that discuss local ventilation efficiency as well as volume flow and air exchange calculations. Fernandez et al. [11] conducted LES in a crossventilated model and evaluated it using age of air, purge flow rate, and net escape velocity. However, there are still many unknowns regarding the impact of outdoor airflow on indoor airflow. One of the reasons for this is that it is difficult to simultaneously observe fluid phenomena in the urban turbulent boundary layer, which consists of several kilometres in scale, and fluid phenomena in building ventilation, which are only a few meters in scale, because there is a large gap between the two phenomena. Given the above, basic research on urban turbulent boundary layer effects E3S Web of Conferences 396, 02015 (2023) https://doi.org/10.1051/e3sconf/202339602015 IAQVEC2023 on indoor airflow from a fluid dynamics perspective remains important. RANS, while less accurate than LES, has the advantage of a smaller computational load and the ability to perform steady-state analysis. Therefore, it is significant to use RANS for discussing natural ventilation airflow and ventilation efficiency. Against this background, this paper compares the changes in indoor airflow and indoor ventilation rate by using RANS to reproduce the wind tunnel experiment conducted by Ikegaya et al. [8] and the LES setup conducted by Fernandez et al. [11] for natural and cross ventilation phenomena in a group of urban buildings. We report the results of a quantitative analysis of the heterogeneity of ventilation efficiency determined from concentration distributions in a cross ventilated room model, using age of air [12] as an index of ventilation efficiency.

Net and gross ventilation rate
We used two ventilation rates (the net ventilation rate Qnet and the gross ventilation rate Qgross [14]) to evaluate the effect of sheltered and opening conditions on the building.
As shwon in sections 3.1, Qnet is equal to the ventilation rate calculated from the time-averaged air velocity orthogonal to the opening and the opening area. Therefore, the backflow in the opening is accounted for as a negative value, and if backflow is occurring, it is smaller than the total volume flow rate at the opening that actually occurs. Qgross is the ventilation rate which considers the contribution of temporally averaged reverse flow as the positive ventilations. As there are two openings in the indoor space, Qgross combines the incoming flow from both of these openings to serve as ventilation.

Age of air
Age of air, or SVE3, is the average time scale taken from the inflow of fresh air to reach a local area/point in a room [12]. The spatial distribution of the concentration field of a uniformly generated passive contaminant in space, expressed as where Cpm = ݉/ ܳ ௦௦ is the perfect mixing concentration (kg/m3). Fig. 1 shows a schematic diagram of the computational domain. The building blocks were cubes with H = 100 mm sides and had a wall thickness of 2 mm. The computational domain size was 4H × 4H × 4H in the x, y, z-directions, and the packing density of blocks on the floor was maintained at 25%. Only one block in each array comprised cross-ventilated openings with a fixed size of 10% of the wall area H2 m2, which were located at each center between two walls in the streamwise (hereafter, referred to as "STR," Fig. 1(a)) or lateral (hereafter, referred to as "LAT," Fig. 1(b)) directions.

Numerical set up
In the flow direction, the inlet boundary condition is implemented with the LES profile of Fernandez et al. [11] for the flow velocity and turbulent kinetic energy conditions, and the outlet boundary condition is given by zero gradient at the outlet boundary surface. In the spanwise direction, on the other hand, periodic boundary conditions were imposed to reproduce the situation where the same model array is infinitely aligned on the floor. The free-slip and no-slip boundary conditions were applied to the top of the numerical domain and on the block and ground surfaces, respectively. A hexahedral structured mesh generated by ANSYS/Fluent was employed, and the number of mesh were set to 2,841,124 after careful mesh independence check. Wall units at the first grid in indoor space was less than 3. A series of Steady RANS was performed using ANSYS/Fluent 2021R2. SST k-model [13] was adopted as a turbulence model and SIMPLE algorithm was employed as the coupling method between the continuity and the Navier-Stokes equations. A secondorder upwind scheme was employed for advection term. After the calculation of the steady flow field, the Age of air distribution was calculated.  Fig.2 presents the comparison of the streamwise and spanwise velocity profile u and v, respectively, within the ventilation block at z/H = 0.5 for each case. The experimental data [8] and LES data [11] are also  Fig.2 (a), the RANS velocity in the both x and ydirections have larger discrepancies with respect to WTE than the LES results near the window inlet and near the center. The RANS and LES velocities for the LAT case in Figure 2(b) are both in good agreement with the experimental data, although RANS is not much more accurate than LES. Fig.3 presents the vertical profiles of u at the spanwise center for the STR conditions. The experimental data and LES data were compared (in the experiments, values were interpolated between 0.3<z/H<0.4 and 0.6<z/H<0.7 because of experimental error). Discrepancies in upwind velocity are found between CFD simulation data (both RANS and LES) and experimental data.   4 shows the flow fields in the horizontal plane within the ventilation model for STR condition for RANS data, LES data [9] and experiment data [8]. In this plane, streamwise wind speed and velocity vector within the plane are indicated by a colour contour and vector, respectively. In the RANS, unlike the LES and experiments, a relatively oblique inflow is observed at the upwind opening and a large backflow in the center of the block. This is due to the fact that RANS solves by averaging the turbulence components through ensemble averaging, while LES solves by averaging turbulence on scales smaller than the grid size through spatial averaging and directly computing large turbulence. Therefore, near the upwind openings where the turbulence component is large, RANS reproduced a slightly different flow field with LES and WTE. Fig.5 presents the flow fields in vertical plane. In Fig.5, as can be seen from Fig.4, RANS shows a discrepancy with the LES results due to the poor reproduction of the turbulence component near the upwind openings. As reported in previous studies of isolated blocks [15], the jet spread was smaller in RANS than in LES and experimental results. Fig.6 presents the flow fields in the horizontal plane for LAT cases. In the LAT case, RANS did not show vortices near the downwind openings as seen in the LES and experiments. These are small vortices created by momentary fluctuations, which RANS could not reproduce because it models all flows. But, in the LAT case, unlike the STR case, RANS agreed well with the LES and the experimental results. This is due to the fact that the turbulence component near the openings is smaller than in the STR case. From these results, it can be said that the overall speed reproducibility and flow distributions of RANS is inferior to LES, but still somehow captured the general relevant characteristics of the flow field.  Comparing RANS and LES for normalized Qgross, RANS was underestimated by 7.1% for STR cases and overestimated by 19% for LAT cases, respectively. Due to the ventilation rate for LAT case is very low, particularly the order of magnitudes of the ventilation rates for RANS and LES are too small (for instance exponent of -5). We expected to have relatively high discrepancies.  Fig.8 presents the age of air distributions for the STR and LAT cases. Due to the asymmetry of the analysis domain, a heterogeneous distribution in SVE3 was observed for both the STR and LAT cases. For the STR case, the SVE3 was generally low near the openings and generally high at the central regions. This is due to the fact that near the opening, contaminants are difficult to accumulate due to the high velocity, whereas near the centre, contaminants are difficult to remove due to the low velocity. In the LAT case, SVE3 was low at window openings and high at the downwind wall (x/H = 1.0). This is because fresh outdoor air is easily supplied near the openings, and the higher velocity of the air causes the removal of contaminants, and as shown in 3.1, fresh air is not supplied near the downwind wall because the RANS can not reproduce vortices that reach the downwind side due to the limitations of the model.

Conclusion
This study reported the RANS results of air change and transfer efficiencies within a cross-ventilated room model sheltered by urban-Like block arrays. The objectives of this study were 1) to reproduce the wind tunnel experiment conducted by Ikegaya et al. and the LES setup conducted by Fernandez et al. for natural ventilation phenomena in a group of urban buildings by using RANS simulation, 2) to compare the ventilation rate of RANS and LES and 3) to evaluate ventilation efficiency. Mainly near the openings, RANS reproduced poorer results than LES because it modeled all turbulence components. However, it is not a significant error, and most of the other flow fields can still be reproduced. In terms of ventilation, RANS underestimated and overestimated ventilation in the STR and LAT cases, respectively, compared to LES. However, our sturdy was able to generate more similar ventilation rate to LES and WTE compared to previous studies [10,16]. Lastly, we evaluated the heterogeneity of ventilation efficiency using the age of air.