Finds documents with both search terms in any word order, permitting "n" words as a maximum distance between them. Best choose between 15 and 30 (e.g. NEAR(recruit, professionals, 20)).
Finds documents with the search term in word versions or composites. The asterisk * marks whether you wish them BEFORE, BEHIND, or BEFORE and BEHIND the search term (e.g. lightweight*, *lightweight, *lightweight*).
The article addresses the challenge of energy planning in high-density urban contexts, where energy consumption for building space heating is significant. It emphasizes the need for reliable energy models and assessments at various scales, incorporating urban morphology and spatial characteristics. The study focuses on urban building energy modeling, particularly the assessment of natural ventilation at building and urban scales. It introduces a lumped parameter network-based multizone model to calculate the air change per hour (ach) in buildings, considering wind-driven and buoyancy effects. The research also employs a 2D CFD scheme to study wind and heat transfer phenomena within urban canyons, providing insights into the impact of crosswinds and thermal gradients on ventilation. The methodology is validated through comparisons with experimental data and CFD simulations, highlighting the importance of accurate modeling for energy efficiency in urban environments.
AI Generated
This summary of the content was generated with the help of AI.
Abstract
This work proposes a new model to evaluate the air changes per hour (ach) due to natural infiltrations in buildings. This modeling already exists at building scale, but the new model will implement the hourly ventilation load in a physical-based modeling for space heating and cooling in buildings at urban scale. The proposed improvement considers the wind and buoyancy effects in the calculation of hourly achs in a high-density urban context. A three-zone air flow lumped modeling is applied to describe the air flow in buildings; the air flow rate due to infiltrations is calculated depending only on leakages’ characteristics and pressure variations in various climate conditions. The non-linear equations system of mass and energy conservation is solved by an iterative procedure using the Newton-Raphson numerical method. Besides, two different methodologies are compared to evaluate the external dynamic and static pressure conditions on building façades: experimental values (pressure coefficients Cp) and CFD simulations. For the latter, the air flow field in the urban canyons is described by the windy conditions and by imposing a temperature gradient due to solar irradiation between the windward and leeward facades. This methodology is applied to three urban canyons in Turin, with typical aspect ratios and orientations for some local climate conditions considering both heating and cooling seasons. Comparing the results of hourly ach obtained from the Cp method, the CFD technique allows to modulate the ach considering the impact of the canyon dimension, wind and buoyancy effect of non-isothermal condition, in varying the wind speed on the façades of buildings for different scenarios. It also overcomes the limit of field of applications of Cp, especially in high-density built urban environments. The encouraging results of this work will lead to future developments of the three-zone lumped model and its numerical solution techniques.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
alt
Altitude m (asl)
ach
Air changes per hour 1/h
A
Area m2
Cd
Discharge Coefficient -
Cp
Pressure Coefficient -
DirV
Wind direction (undisturbed flow) 0°(N)
g
Gravity m/s2
H
Height of the canyon m
he
Convective exchange capacity W/m2K
H/W
Aspect ratio (Height-to-Width) -
K
Leakage coefficient -
Ib
Direct normal solar irradiation W/m2
Id
Diffuse solar irradiation W/m2
Iinc
Incident solar irradiation W/m2
ṁ
Air flow rate Kg/s
n
Type of flux motion (coeff.) -
Patm
Atmospheric pressure Pa
pdyn
Dynamic pressure Pa
ps
Static pressure Pa
ppot
Potential pressure Pa
Tair
Air temperature °C, K
Ts-a
Sol-air temperature °C, K
U
Wind velocity (undisturbed flow) m/s
v
Wind velocity (inside canyon) m/s
vol
Volume m3
W
Width of the canyon m
z
Height from the ground m
α
Absorption factor -
β
Sun incident angle on building facade °
ΔP
Pressure variation between nodes Pa
ΔT
Temperature variation inside canyon K
θ
Wind direction (undisturbed flow) 0°(N)
υ
Roughness parameters -
ρ
Air density Kg/ m3
Introduction
Energy planning is becoming crucial to face current challenges: crisis of energy prices, war, pandemic, and climate change (Perera et al., 2023). Many countries and cities around the world are developing plans and strategies to reach an ever-greater level of energy self-sufficiency and carbon-neutrality (https://resilientcitiesnetwork.org).
In, high-density urban contexts, where the energy consumption for buildings space heating predominantly contributes to GHG emissions, these goals are even more difficult to reach due to a spatial coexistence of high-energy intensity and low availability of renewable energy sources (RES) (Mutani et al., 2023). This challenge requires pursuing and boosting energy policies to reduce and optimize consumption, but also broadening the energy assessments at the territorial scale, including the spatial and temporal dimension.
Advertisement
The complexity of this issue consistently increases in the attempt of describing local phenomena and managing their mutual influence with larger scale phenomena, with many random factors as the one related to energy use (Perera et al., 2021). Reliable energy models and tools are necessary based on accessible databases to be easily replicable in any context and scale (Palusci & Cecere, 2022). In addition, to evaluate the impact of each intervention on the overall energy performance of a building, it is no longer useful to implement energy assessments for single buildings and their contexts, but rather to consider the interdependent system of buildings that make up homogeneous areas in the city as the object of investigation (Basu et al., 2019).
The assessment of urban ventilation is a clear example of a phenomenon that varies in relation to the scale and has a strong mutual influence with the spatial and geometric characteristics of urban obstacles (buildings). Urban morphology affects urban ventilation which reciprocally influences the ventilation inside or through buildings and consequently their energy demand (Rezaeiha et al., 2020).
State of the art
Urban building energy modeling
Many literature reviews (Ali et al., 2021), (Harish & Kumar, 2016) describe existing Urban Building Energy Modeling (UBEM) referring to their different approaches (bottom-up or top-down) and their modeling type (data-driven, process driven or hybrid).
Physical-based engineering models are used to assess the energy performance of buildings, evaluating separately how each thermal gain (or loss) affects the thermal energy balance equation for building space heating (or cooling). A topic of recent debate is their implementation with a place-based approach. This can help in defining proper solutions, suitable for each specific case study (Mutani et al., 2023). Its potentiality origins from relying on wide available geo-databases and interoperable tools (i.e., GIS) which facilitate the description of spatial relationship between elements and the interchange between the spatial scale of energy analysis: from the building to the block-district-city and territorial scales. In this way it is possible to evaluate the effect of each single intervention and its repercussions on systems correlated to it.
Advertisement
This work is part of a broader research activity whose main objective is the implementation of an already existing place-based engineering urban energy model for the assessment of the monthly-hourly space heating and cooling energy consumption of residential building both at building and urban scale, to which apply the hourly variation of ach (Mutani & Todeschi, 2020).
Ventilation assessment at building level
Regarding the heat flow rate by ventilation in the assessment of the thermal energy balance equation for the space heating and cooling of residential buildings, the main parameter is the air change per hour (ach). As reported in (Mutani et al., 2021), it mainly depends on the air flow rate through a building and its volume. Concerning only the air flow due to infiltrations of openings, the infiltration rate is caused by pressure difference generated by the incident wind on building façades and the thermal buoyancy inside building zones. It depends also on the airtightness of the building envelope and its components. In scientific literature, natural ventilation at building level has been deeply investigated for different studies concerning indoor air quality, including fire safety (Calì et al., 1997), HVAC, and energy performance efficiency.
The most frequent methods used in the scientific literature to assess the infiltration rate and the ach are:
measurements and field experiments, testing the permeability of single technological components; ach is then derived and tabular data are created for class of building typology and pressure difference (Mun et al., 2021);
network-based multizone models to compute the interaction of airflow between different zones on a whole-building scale. Knowing the local values for the input variables and assuming some stringent boundary conditions, it is possible to apply physical equations of fluid dynamics phenomena to determine the output parameters in all zones of the network. Model’s computational effort increases with the complexity of the network elements. The most used parametric models are CONTAM (Dols & Polidoro, 2020) and COMIS (Feustel, 2013);
Computational Fluid Dynamic models (CFD) are based on differential equations of energy, mass, and momentum to determine airflows over time on a detailed grid describing model geometry. High computational cost and high case-dependency (Najafi et al., 2023) make it less appropriate for large-scale building analyses.
In this work, a lumped parameters network-based multizone model is applied to calculate the ach at building level. It represents a good compromise for the description of the physical phenomena, the number of input variables, the detail of the characteristics of the building, whose schematic description is simple enough to apply the model's balance equations to all the buildings in an urban area.
Ventilation assessment at urban level
Ventilation within urban street canyon is acquiring importance in the scientific framework due to its impact in heat stress exposure, pollutants and increasing energy demand. Among different methods to study how the wind profile is influenced by the presence of roughness elements (buildings), in (Santantonio & Mutani, 2022) a GIS-based methodology and open-source QGIs plug-in are used to adjust the wind velocity above the displacement layers (Fig. 1a, b). The GIS tool is based on Digital Surface Modeling (DSM) that easily described the real urban built environment and spatial relationship between objects. The height of displacement layer zd is assessed as a function of morphometric parameters (i.e., Building Density, building height variability, Frontal Area Index), for each specified wind directions representative of the local climate; results are referred to a predefined grid at urban scale to describe the spatial distribution of zd. Knowing the height of the displacement layer zd in front of each building, a wind profile is assigned to every building of the examined area. In this way it is possible to indicate in which urban canyons turbulent flows are generated (Fig. 1b). Compared to parametric models based on tabular data with limited fields of application (i.e., υ roughness parameters), a GIS-based modeling can determine wind profiles at urban scale considering the real characteristics, size and geometry of all the objects (buildings) and the exact spatial relationships of urban canyons, for each examined wind direction. The displacement layer (zd) can be intended as a threshold value (Fig. 1a):
above zd the reference speed of the undisturbed wind is corrected by applying the logarithmic law and calculating it directly in GIS on an urban scale;
below zd the turbulent motion generates vortexes and eddies, which can only be investigated using CFD models to be applied to canyons with similar characteristics.
Fig. 1
The displacement layer zd as a threshold value to identify wind profiles and modeling type (a) at urban level, and and an example of the result of the spatial distribution of the parameter zd at an urban scale evaluated with a GIS-based model and plugin (b)
In the reference scientific literature of urban microclimate studies, numerical solutions relying on CFD simulations are acquiring importance. In the field of urban ventilation studies, they provide many advantages: variables are investigated in the entire computational domain, simulations explicitly perform the coupling of wind velocity and temperature fields, even at finer scales. A review on the CFD analysis of urban microclimate (Toparlar et al., 2017) reports several CFD studies at the building scales, concerning natural ventilation and wind flows around buildings: many of these adopt 2D modeling focusing on urban street canyons (Li et al., 2012), with the possibility of coupling CFD analysis and building energy simulations to evaluate the building energy consumption (Bartak et al., 2002). The mentioned review investigates and categorizes all CFD studies based on the type of urban area (real or generic) and the presence of validation. The result shows that the majority of studies concerns real urban areas conducted without validation, using RANS equations; generally, they consist of comparative studies among different configurations in the same urban area with the aim to optimize target variables. The lack of CFD validation is explained by the common difficulty in finding relevant or well-documented measured data: measurement campaigns on urban areas imply logistic challenges and data quality issues. Even if it requires further investigation, a possible solution to these difficulties may be represented by the great availability of data detectable by the Internet of Things, using low-cost environmental sensors with WiFi network, that are increasingly widely distributed in urban areas.
Many simplified models are used to compose building geometries forming urban structures. The choice between 2D or 3D urban canyon models is based on the features of the phenomenon investigated (i.e., wind speed, pollutant dispersion, etc.), and the scale of interests. It can imply specific morphometric parameters as input data: in 2D models the most used are the aspect ratio and building height or height variation, in 3D models length-to-width or length-to-high, and plan area density are fundamental (Palusci et al., 2022). Two-dimensional (2D) urban models have been applied to study the impact of the urban canyon aspect ratio on urban ventilation and pollutant dispersion (Di Bernardino et al., 2018). Most studies apply 3D CFD model on generic building geometries that form idealized urban structures (Ai & Mak, 2017). Studies on actual urban areas are still rare due to the complexity of describing the physical phenomena and the high level of detail required in modeling the built environment. More frequently the aim of these studies is to describe phenomena in specific contexts (Tsichritzis & Nikolopoulou, 2019), verify the accuracy of the computational settings (O’Neill et al., 2016) or evaluate the correlation between urban parameters and wind speed (Palusci & Cecere, 2022). (Javanroodi et al., 2022) highlighted the difficulty in generalizing the results of the 3D CFD simulations and propose two data-driven models to downscale climate variables at defined urban forms, considering extreme climate conditions. As described in the Best Practice Guidance (BPG) on CFD analysis for wind comfort and safety (Blocken et al., 2012), all buildings relevant for the wind should be modeled explicitly; but this requirement cannot be easily achieved for neighborhood-scale applications for a whole city. Nevertheless, the neighborhood scale is considered the best compromise for describing the entire physical process of natural ventilation and the actual urban configuration that influences it (Sanaieian et al., 2014).
A lack of investigation of CFD simulations regards the evaluation of urban airflows pattern in non-isothermal conditions, considering the combined effect of cross wind and thermal gradient in urban street canyons. (Mouzourides et al., 2022) deepen this topic through experimental investigation and corresponding 2D CFD analysis used to acquire velocity vector field in examined canyons of different aspect ratio. Results show that aspect ratio affects velocity field and vortical structure whose flow direction is influenced also by the presence of heated walls.
In this paper, the choice of the 2D CFD scheme is dictated by the aim to define a methodology at neighborhood scale to investigate the physical phenomena of crosswind driven and thermal gradient in the urban canyons (UC), with a sufficiently acceptable level of accuracy to apply the simulation results to similar areas within the city. The authors chose to analyze the ideal case of the urban canyon of infinite length to limit the number of parameters, as it alone allows to characterize the canyon geometry. In case of a dense, compact, and regular built environment, urban street canyons are easily assumed to be an infinite canyon; the 2D CFD scheme is a representative vertical section of the entire infinite canyon and is considered sufficient to describe the variables that influence the physical phenomena evaluated in the project study. In this study, 3D CFD modeling would add a higher level of description of reality, but in addition to the computational effort required, it would not solve the difficulty of making the results replicable at city scale.
Research objectives
The main objectives of this paper consist in:
2D CFD simulations to study the velocity field of wind inside urban canyons, describing relation between environmental conditions and canyon dimensions, considering combined cross natural wind and thermal gradient, and evaluating their contributions.
Describing the 3-zone air flow lumped parameter model to calculate the hourly air change per hour as a function of environmental conditions and building characteristics.
Comparing different results of hourly ach applying tabular data of pressure coefficient (Cp) or the wind velocity field inside urban canyon from CFD simulations in the calculation of the dynamic pressure incident on the building windward façade.
Materials and method
The input data regarding local climate, urban morphology and building characteristics have been harmonized using Q-GIS software and, then a unique geo-database has been created. It has been applied in the two main steps that made up the overall methodology of this work, as synthetized in Fig. 2: the investigation of the air flow at urban and building scale. In the first step, CFD simulations have been done to study the velocity field of wind and vortical structures in the domain of urban canyons; the final output is the wind velocity v, calculated as a function of the height (z) from the ground in the canyon and it is used as an input data in the 2nd step of analysis. The second step consists of the application of a 3-zone air flow model to calculate the ach in several environmental conditions. This model is then used to compare 2 different methods in the calculation of the dynamic pressure (Pdyn) incident on the building facades.
To investigate the phenomena involved in the ventilation assessment in the urban street canyon, a CFD model has been developed. The CFD model employed in this study utilizes the Star CCM+ software, version 2310.
The model is designed to investigate wind and heat transfer phenomena within an urban canyon. In the reference scientific literature, the RANS (Reynolds-Averaged Navier-Stokes) approach is the most widely used to conduct numerical simulations, assuming a steady state flow regime; it also considered an optimal compromise for efficiency and accuracy of building-terrain solving local climate studies (Javanroodi et al., 2022). The k-ω turbulence model has been selected for this study due to its effectiveness in capturing flow characteristics around buildings, offering good predictive capabilities for both the near-wall and free-stream regions (Ai & Mak, 2017). This model assumes a steady state flow regime, which is appropriate given the primarily steady conditions expected in the study area and the practical need for reasonable computational times.
Boundary conditions of the domain
The physical domain has been mapped using a combination of structured and unstructured elements; the structured mesh is employed in the regions where the geometry allows for a regular grid, such as the main urban canyon section. This structured mesh provides good resolution and efficient computation. However, specific urban canyon regions, characterized by high flow gradients such as corners, have been refined to capture the local flow complexity.
To study separately the contribution of thermal gradient and cross natural wind in determining the velocity field in the domain, the input parameters used are the following (also schematized in Fig. 2a, b):
the geometry of the urban canyon described by the aspect ratio parameter H/W, where H [m] is the average height of the buildings and W [m] is the width of the street; the canyon length is usually considered regular and infinite (Samsonov et al., 2015) and the main direction is here defined as θ [°] (0°N-clockwise);
the local climate condition of reference wind speed Uref [m·s-1], necessarily perpendicular to the canyon axis direction, and temperature variation (ΔT).
Validation of the model and grid convergence
To validate the CFD model, we reproduced test cases from an experimental campaign (Allegrini et al., 2013), and (Allegrini et al., 2014). In the experimental campaign, a wind tunnel setup was used to simulate the flow within an urban street canyon. The physical model had dimensions W×H×L=20×20×180, with the airflow directed perpendicular to the canyon's longitudinal axis. The canyon surfaces, made of aluminum, provided a smooth, low-roughness environment, allowing us to ignore surface roughness in the numerical model. The walls and ground were heated uniformly using mats, ensuring consistent temperature distribution due to aluminum's high thermal conductivity. Particle Image Velocimetry (PIV) was employed to measure flow characteristics, focusing on a central cross-section of the canyon.
For the grid convergence study, simulations were conducted with four different base mesh sizes (BS) under isothermal conditions (Uref 1.45 [m·s-1] Tref 23 [°C]). Figure 3a and b present the normalized vertical velocity along the horizontal centerline and the normalized horizontal velocity along the vertical centerline of the canyon, respectively. These figures compare the experimental data with numerical results from each mesh size. The normalized vertical velocity profiles (Fig. 3a) and the horizontal velocity profiles (Fig. 3b) showed minimal differences among the three finest meshes (BS 1, BS 2, and BS 4), indicating good agreement with experimental data.
Fig. 3
In black the velocity measured in the experimental campaign. In green the results obtain with the numerical model for 4 different Base Size (BS). Both axes have been normalized
Given the results of the grid convergence, the BS 4 was chosen for subsequent simulations, providing a balance between accuracy and computational efficiency. Figure 4 provides a visual comparison of the normalized velocity fields inside the canyon, demonstrating the numerical model's capability to accurately represent the velocity distribution.
Fig. 4
Normalized velocity inside the canyon. On the left the experimental campaign. On the right the numerical model developed (Allegrini et al. 2013, 2014)
Further validation was performed for scenarios with a windward warm facade. Four different temperature differences were tested with Uref 2.32 [m·s-1], and normalized horizontal velocity were compered along the canyon centerline with experimental data (Fig. 5). The agreement between the simulated and measured data further corroborated the model's reliability in presence of a thermal gradient.
Fig. 5
In green the data obtained with the numerical model. In red the data obtained in the experimental campaign (Allegrini et al. 2013, 2014)
To assess the differences between steady-state (RANS) and unsteady (URANS) simulations, we performed a comparative analysis on the isothermal case, using identical boundary conditions and numerical settings across both models. The only variation was the introduction of temporal dynamics in the URANS model. The simulation has a dt of 0.04s and it is 20s long. The results shown represent the mean values and the standard deviation of the last 5s of simulation as in the first 15s of the simulation the transient phase was still affecting the results.
Figure 6 shows the velocity fields for the two approaches. The visual comparison reveals minimal differences between the steady-state and unsteady results, suggesting that the flow dynamics in this particular case exhibit quasi-steady behavior. This observation aligns with the expectations for predominantly steady flow in urban canyons under isothermal conditions.
Fig. 6
In black the velocity measured in the experimental campaign. In red the results obtain with the numerical model for BS4 in steady state and in blue the results with the same numerical setup but in unsteady condition
Figure 7 depicts the horizontal (Vx) and vertical (Vz) velocity profiles along the centerline of the canyon. For the URANS simulation, the ±3σ interval is shown as a shaded grey region around the mean values. The low standard deviation indicates that the fluctuations over time are minimal, further reinforcing the idea that the flow can be considered effectively stationary in this scenario. The steady-state results closely match the time-averaged URANS values, confirming the adequacy of the steady-state approach for this case.
Fig. 7
on the left the velocity field of the steady state case meanwhile on the right the velocity field of the unsteady case after the transient phase is completed
Overall, the comparison between RANS and URANS models reveals negligible differences in both the velocity field and the centerline velocity profiles. This suggests that, for the specific flow conditions analyzed here, the steady-state model is sufficient to capture the essential flow characteristics, with the unsteady model offering no significant additional insights.
Limits of the study
While the 2D simulations employed in this study provide a valuable and computationally efficient means of analysing flow and thermal phenomena within urban street canyons, it is important to acknowledge the inherent limitations of this approach. Specifically, 2D simulations cannot fully capture the three-dimensional nature of turbulence, which is a critical aspect of flow dynamics in real-world scenarios. As a result, certain complex turbulent interactions and vertical exchange processes may not be accurately represented. We recognize that this simplification could lead to discrepancies between the simulation results and actual 3D flow behaviour, particularly in areas where turbulence plays a significant role. Despite these limitations, the agreement with experimental data suggests that the key flow features relevant to our study are well-captured, making the findings useful for the intended analysis. Future work will consider 3D simulations to address these limitations and further enhance the model's accuracy.
Climate data
The local climate input data are the reference wind direction DirV [0°N-clockwise] and velocity Uref [m·s-1], the air temperature TC,air [°C], the direct normal solar irradiation Ib [W·m-2] and the diffuse solar radiation Id [W·m-2]. In this work, weather data has been collected from the weather station of the Living Lab of Polytechnic of Turin, located at 32m from the ground (https://smartgreenbuilding.polito.it). The climate data used is referred to the year 2022, selected as it has no missing or null values; the timespan is a quarter of an hour. To consider only the component incident to the buildings’ façade in the canyon, the incident solar radiation Iinc [W·m-2] has been calculated as Eq. (2), considering only the hours of the day in which the building façade is irradiated by the sun, depending on the height of the sun from the ground (β>0):
where: β [°] is the incident angle of the sun on the building façade in each hour of the day and Sky View Factor (SFV) is the portion of the sky visible for each specific point on building’s facade.
To simulate the non-isothermal condition in the street urban canyon, the delta of the air temperature (ΔT) in the canyon is determined, as according to Eq. (3), by considering the difference between the temperatures of the air layers adjacent to the façade not exposed to solar radiation (cold façade) and the one exposed to the incident radiation Iinc (warm façade). The first corresponds to the external air temperature TK,air [K], while the second to the sol-air temperature TK,s-a [K].
TK,s-a is a fictitious temperature that considers the conductive and convective heat exchanges contributions affecting the external surface of a building with the external air and the solar radiation received by the building facade (Lenin et al., 2022). Therefore, - the absorption factor of the building enevelope α [-], the convective exchange capacity he [W·m-2·K-1] and the incident solar radiation Iinc [W·m-2] are used in the definition of the sol-air temperature. Its complete definition is expressed by the three-components equation Eq. (4.1):
where: TK,air is air temperature, α is the absorption factor, he the coefficient of external adduction for horizontal heat flow, Iinc the incident solar radiation , ε is the emissivity of the surface (0.9 W·m-2), σ is the Stefan-Boltzmann constant (5.67·10-8 W·m-2·K-4), and TK,sky is apparent temperature of the sky.
Reference is made at the he UNI EN ISO 6946:2008 and UNI 10349-1:2016. In this paper, the absorption factor α is intended for walls with medium color (0.6), and the coefficient of external adduction he for horizontal heat flow is applied according to wind velocity (i.e., 25 W·m-2·K-1 for 4-5 m/s and 12.5 W·m-2·K-1 for 1 m/s).
The two-components equation Eq. (4.2) is a simplified version of the previous equation:
The example of the sol-air temperature reported in Table 2 starts from monthly air temperatures, water vapor pressure and incident solar radiation of the case-study and it is determined according to both the three-components equation (Ts-a,3) and the two-components equation (Ts-a,2); then the relative error [%] is calculated. For each month, the relative error is calculated as the discrepancy between the two results: in all months it represents less than 10%. Due to that, it is assumed the possibility to use the simplified two-component equation (4.2), for case-studies in which detailed information about sky conditions is not available.
Table 2
The sol-air temperature according to Eqs. (4.1) and (4.2)
The cases shown in Fig. 8 have been implemented in the Star CCM+ environment following methodology exposed previously. The CFD simulations aimed to investigate the velocity field within the canyon, weighting the different contributions provided by the cross wind and thermal buoyancy. This last has been generated by an imposed ΔT between the facades of the two buildings in the canyon.
Fig. 8
Cross section of the urban canyon (aspect ratio H/W), considering wind-driven velocity (U) and thermal buoyancy (ΔT= Tair-Ts-a) due to incident solar irradiation (Iinc) and concurrent effects on the windward warm façade (left scheme) and disjointed effects on the windward cold facade (right scheme). Tangential V(y) and normal V(x) components of the wind profile at probes located at 1% and 99% of the W dimension, generate entering (+ arrow) and outgoing (- arrow) air flows through facades
The simulations are organized considering three different aspect ratios representing: narrow, medium and large urban canyon. In addition, to highlight separately the contribution of the two natural phenomena in the creation of vortices structures and velocity field, the wind-driven and the buoyancy effect are evaluated considering extreme local climate condition, with respectively:
the hourly maximum value of wind speed (U max)
the hourly maximum values of incident solar radiation (Iincmax)
For each examined aspect ratios, the extreme climatic conditions U max and Iincmax are determined separately in three different bimestrial periods, representative of the winter, summer, and mid-season. Then, each simulation with define condition of urban canyon geometry and climate condition has been evaluated in two opposite scenarios:
the WWF scenario, where the windward building façade is also exposed to solar radiation (warm façade), and so the two effects are concurrent (Fig. 8, left scheme).
the WCF scenario, where the windward building façade is not exposed to solar radiation (cold façade), and so the two effects occur on opposite facades in the canyon (Fig. 8, right scheme).
The aim is to describe how concurrent or disjoined effects can impact on the vortical presence and structure in the domain field, also affecting the wind velocity field. The simulation campaign foresees 36 simulations, as schematized in Table 3.
Table 3
Criteria for CFD simulations campaign
Aspect ratio
Effect
Period
Scenario
Narrow Canyon (NC)
Wind-driven (U max)
Winter (WIN)
Windward Cold Façade (WCF)
Medium Canyon (MC)
Mid-season (MID)
Buoyancy (Iinc max)
Windward Warm Façade (WWF)
Large Canyon (LC)
Summer (SUM)
In order to evaluate the velocity law along the canyon, the model has foreseen two probes located near the two facades, recording the whole velocity profile at different heights from the ground. In detail: the 1% and the 99% probes refer respectively to the leeward and windward façades, calculated as the percentage of the canyon dimension (W) (Fig. 8) which varies in relation to the 3 proposed aspect ratio cases. For each point on the probe’s axis, both the tangential and normal component of wind velocity has been obtained.
Polynomial function
The velocity profiles obtained through the CFD simulations have been interpolated within the Matlab environment using a fifth-grade polynomial function, as Eq. (5). The wind velocity f(x) in the urban canyon was evaluated on the façade of the building as a function of its height x. This function depends on canyon dimension, climate data and vortical structure, considering the 36 conditions mentioned in Table 1. Then for each quota x, the wind velocity is represented by Eq. (5):
The coefficients obtained for each configuration under investigation have been used for the calculation of the wind velocity as it is one main variable influencing the ach.
Ventilation assessment at building level
Lumped parameter model
The lumped-parameter is a zero-dimensional model in which the building tridimensional structure is schematized as a simple network describing the motion of the air flow inside the building through a finite number of interconnected zones. Referring to a network model based on the theory of oriented graphs, the relationships between the different elements of the network system (nodes, links) can be described mathematically. The building is represented as a network of nodes (zones) connected by links, which describe the displacement of the air flow in space. The lumped parameters model is based on the following assumptions:
in each zone (node) the physical pressure, temperature, and air density conditions are constant throughout the relevant volume of the zone;
the air flow between the different zones occurs through the openings’ leakages, represented as one-dimensional connections (links) between the different volumes of the building (i.e., points of the network);
the air is supposed to be incompressible, and its motion, caused by the difference in pressure between zones, is due solely to natural causes. These are the surface pressure generated by the incident wind on the external envelope of the building (wind effect) and the spatial gradients of temperature that determine convective actions (stack effect).
In this work, a three-zone air flow model is studied, as schematized in Fig. 9, considering two heated zones, representing the apartments, one no-heated zone, representing the building shaft and the outdoor environmental conditions around the building’s facades. The air flows through openings’ leakages (Fig. 9, in pink) that contribute to the pressure variation between two zones due to the combined effect of incident wind and thermal buoyancy.
In each zone (node) are associated constant condition of physical pressure P [Pa], temperature T [K], air density ρ [kg·m-3] and height z [m a.s.l.]. For external nodes (Fig. 9, green points) pressures are known, for internal nodes in the barycenter of the zone’s volume (Fig. 9, red points) pressure is the unknown variable. Inside each zone, nodes at leakage level (Fig. 9, blue points) are positioned in the barycenter of the opening, and the local pressure is determined in relation to the pressure of the reference zone in the barycenter of the zone’s volume. At each link are associated the pressure variation ΔP between two nodes, the air flow ṁ [kg·s-1] and a direction. In this work, positive fluxes are the ones outgoing from a node.
Input data
The main input data for the 3-zones airflow model referring to the building scale are:
building geometry and dimension distinguish the volume of the heated zones and the shaft;
characteristics of the openings: two types are considered (window, door) with predefined dimensions and area Aop, the height zop from the ground level is calculated in the barycenter of each opening;
characteristics of the leakage whose height zleak coincides with zop and other important parameters that influence the type of air motion, described in the below paragraph.
Leakages’ characteristics
A typical leakage area At,leak is associated to each opening type, according to the air tightness of the component, reported in Table 4. It is used to calculate the equivalent leakage area Ae,leak as shown in Eq.(6).
Then, the discharged coefficient Cd for cracks in walls and floors has a range between 0.6 to 0.7: in this work Cd is fixed at 0.65. For each opening type, the flow coefficient K can be calculated according to Eq. (7); it is intended as the value of the flow rate induced by a unitary pressure difference.
The parameters n is the flow exponent that describe the type of motion of the fluid, depending on the dimension and characteristics of the cracks and theoretically varies between 0.5≤n≤1, from a fully turbulent flow to a laminar one (Allard & Herrlin, 1989). Table 5 reports some of the common values used in scientific literature to describe the airflow rate through different types of leakages.
Table 5
Typical values of the flow coefficient K and flow exponent n in scientific literature.
Referring to the environmental climate condition, the main input data are the wind velocity and the outdoor temperature, that respectively impact on the wind-driven and thermal buoyancy effects.
The outdoor air temperature TC,out corresponds to the hourly value of TC,air from the reference weather station. According to the local climate scenario, the indoor air temperature TC,in of the heated zones inside the building refer to a fixed set point temperature typical of heating and cooling seasons, respectively 20°C and 26°C. As the shaft is a no-heated zone, its temperature is calculated according to Eq. (8):
where: btr,u [-] is the correction factor for confined spaces with an external wall and windows, equals to 0.4 (Appendix A, UNI/TS 11300-1: 2014).
The air density [kg·m-3] is each specific zone is determined by Eq. (9), as it is function of the reference density (ρref = 1.29 kg·m-3) at the temperature TK,ref (-273.15 K), and the analyzed temperature TK (out, in or sh):
The velocity v [m·s-1] refers to the wind incident on the building in the barycenter of each opening both on windward and leeward facades; it varies according to climate conditions, urban obstructions, height, dimensions and number of the openings, and types of leakages.
In this work, two different methods have been used to correct the reference wind velocity Uref [m·s-1] from the meteorological station, considering the characteristics of the urban morphology, orientation and building geometry.
In the first method (Cp method), the pressure coefficients Cp have been determined for each external node in Fig. 9, considering its height and position on facades, specifying the windward and leeward ones. As in previous work (Santantonio & Mutani, 2022), the CpCalc software has been used considering tabular data, derived from experimental campaigns. A specific field of application is detailed for each input parameter. These are:
wind incident angle on windward façade (according to wind direction DirV and the azimuth of the building),
wind profile exponent (roughness parameter υ) according to the type of environment (0.10 – 0.33 – 0.45),
building orientation, geometry, Frontal Area Ratio FAR (0.5 – 4) and Side Area Ratio SAR (0.5 – 2) and
coordinates describing the position of openings on windward and leeward facades’ area.
The second method (CFD method) uses the output results of CFD simulations for given climate conditions, canyon geometry and vortical structure. The wind velocity at a specific height of an opening is obtained by the polynomial function in Eq. (5) for the conditions corresponding to the case study. So, for all external nodes in Fig. 9, the wind velocity obtained is derived directly from the CFD simulation.
Other input data are the gravity g [m·s-2] and the reference atmospheric pressure Patm,ref at 0 m asl, equals to 101325 Pa and the altitude alt in [m asl] of an examined case study.
Mass and energy conservation
Referring to the fundamental equations of mass and energy conservation, in each node in the network must exist a mass flow balance driven by a delta pressure and the algebraic sum of all the air flows is zero, according to Eq. (10) or written in vector form as Eq. (10.1):
where: i a generic node and Li, the number of links that flow into the node, ṁ [kg·s-1] the mass air flow rate entering (-) or outgoing (+) from the node through each link L.
$$f\left(\Delta P\right)=0$$
(10.1)
For the three-zone air flow model in Fig. 9, a system of 3 equations can be written Eq. (11):
For each link, the mass flow rate ṁ [kg·s-1] is described as a function of the pressure difference between two nodes, according to Eq. (12.1), considering the characteristic of the opening’s leakage (dimension and typology). Here, the exemplifying nodes a and c (Fig. 9) are considered:
where: Cd is the relative discharge coefficient [-], ρ the air density [kg·m-3], ΔP the pressure difference and Ae,leak is the effective flow area of the cracks [m2] between two zones (Equivalent leakage area in Eq. 6).
In most cases, a general law can be used, defined as Eq. (12.2); the mass flow rate ṁ [kg·s-1] is described as a function of the pressure difference between two, considering the characteristic of the leakages (K, n):
where: ΔPxy is the concentrated pressure drop due to the presence of the leakage. In determining the total pressure condition P, in each node both kinetic and potential pressure contributions are considered.
External nodes (P at nodes 1,2,3,4)
The dynamic pressure pdyn at each external node i (with i from 1 to 4) is generated by the effect of the natural wind on both the windward and leeward façade. It can be calculated according to Eq. (14.1) in application to the Cp-method and Eq. (14.2), in application to the CFD-method:
where: Uref is the undisturbed wind velocity [m·s-1] from the reference weather station, ρ [kg·m-3] is the outdoor air density, and Cp [-] is the experimental pressure coefficient at leakage’s position calculated with the tool CpCalc tool, as a function of the building dimensions and orientation, wind profile exponent and class of PAD.
where: v [m·s-1] is the wind velocity at leakage’s position inside the canyon, calculated from the CFD simulation, considering the effect of windward (+) and leeward (-) dynamic pressure on the façade, and ρ [kg·m-3] is the outdoor air density.
The pressure pi at each external node i is determined as Eq. (15) adjusting the reference atmospheric pressure Patmref, considering the local altitude alt [m asl] and the height of each node zi :
The potential pressure ppot at each external node i is determined as Eq. (16):
$${p}_{pot_i}=\rho \cdot g\cdot {z}_i$$
(16)
where: g [m·s-2] is the gravity, ρ [kg·m-3] is the outdoor air density and zi the height of each node.
As in the 3-zones airflow model the outdoor boundary conditions are known, in each external node i the total pressure Pi is defined according to Eq. (17):
$${P}_i={p}_{dyni}+{p}_i+{p}_{poti}$$
(17)
Internal nodes (P at nodes a,b,c)
In each internal node j (red nodes in Fig. 9) the boundary condition known are the indoor air density ρj [kg·m-3], and the height of each node zj [m]. It is not possible to directly determine the total pressure contribution Pj, according to Eq. (17), since the indoor dynamic contributions is not known, and only the potential contribution can be calculated, according to Eq. (16).
An iterative calculation will be used to determine the output value of Pj : the initial values pj0 are needed and they are calculated as the sum of the internal pressure contributions Eq. (18), considering the following hypothesis:
$${p}_{j0}={p}_j+{p}_{dynj}$$
(18)
dynamic pressure pdyn j at each internal node j is calculated according to Eq. (19), as it is generated by the velocity of indoor air vint that is assumed to be the same for all zones,
where: vint [m·s-1] is the wind velocity at leakage’s position inside the zones (vint =3 m·s-1).
In this work, the stack-effect is considered separately inside the specific volume of each internal zone, and it considers the variation of nodes’ height between different nodes in the same zone that directly affects the contribution of the potential pressure to the total pressure. Assuming a constant velocity of the air flow and no pressure drop within each zone, it is possible to apply the Bernoulli’s equation to each couple of nodes, excluding the kinetic contribution in determining the pressures at the nodes. The relationship described by Eq. (20) is applied to each node j at the barycenter of the zone’s volume (red points in Fig. 9) and each correspondent node jn at leakages’ level (blue points in Fig. 9) for all the n openings in the same zone.
In the presented model, the stack-effect occurs only in the shaft (zone c), where the height zc in the barycenter of the zone’s volume is different from the height of the four nodes at leakage level (zc> zc’ , zc> zc”’,zc < zc” and zc< zc’v). Applying Eq. (20) between node c and each of the four nodes at leakage, it is possible to assign the following relations:
In both zones a and b, three nodes at leakage level exist (blue points in Fig. 9). Since their height corresponds to the height of the node in the barycenter of the zone’s volume, (za=za’=za”=za”’) and (zb=zb’=zb”=zb’v), and the local air density is the same within the volume of each zone, no stack-effects occur in these zones, and for each node at leakage, it is possible to affirm that: pa = pa' = pa” = pa”', in zone a, and pb = pb' =pb” = pb'v in zone b.
For zone a and b, there is no difference in calculating each of the three pressure contributions at leakage level jn or in the barycenter node j. Due to the stack effect in the shaft, it is necessary to consider the following relation Eq. (21), for each of the four (n) existing leakages:
where it is possible to rewrite \({p}_{dyn_c}+{p}_c={p}_{c_0}\), according to Eq. (18) and rename \({\rho}_cg\left({z}_c-{z}_{c_n}\right)={p_{stk_c}}_n\).The system of equations (11) can be re-written as Eq. (22a,b,c) that correspond to function F of the iterative calculation; reference is made to the nodes at leakages jn.
Then, the initial value pj0 of the iterative calculation, is assumed to be in a range whose lower (low) and upper (upp) limits are defined according to Eq. (23.1) and Eq. (23.2), respectively:
$${p}_{j0\_ low}={p}_j$$
(23.1)
$${p}_{j0\_ upp}={p}_j+{p}_{dynj}$$
(23.2)
Iterative procedure
Equations 22a,b,c cannot be solved analytically; therefore, numerical methods were used. To find the solution of Eq. 22a,b,c, numerical methods find the zeros of the functions: the solutions P for which f(P)=0.
In this work, Matlab software was chosen to automatize the iteration process to find the numerical solution using fsolve function. Fsolve provides several algorithms for solving non-linear equations with the Newton-Raphson method; among them, the trust-region (tr)has been used. Fsolve requires initial points as vectors; in this work in order to reach the convergence between the 3 solutions of the 3 unknown pressures at internal nodes (Pa, Pb, Pc), the iterative calculation has been set to consider different combination of the 3 initial points (pa0, pb0, pc0) that made up the starting vector. Each of the 3 initial points is defined in a range between the lower limit (pj0_low) and the upper limit (pj0_upp). Within the range of each initial point, ten values were selected at a regular distance, considering the width of each interval; each combination considered the variation of one initial value at a time: a total of 1000 combinations were applied in every iterative calculation. According to the accuracy of these values, the tolerance and stopping criteria applied for the trust region algorithm has been defined, as reported in Table 6; this choice is very important to achieve convergence and solve the non-linear system of three equations (Eq. 22a,b,c).
Table 6
Tolerance and stopping criteria of MatLab fsolve algorithms
Algorithm
Step Tolerance
Function Tolerance
Optimality Tolerance
Max iteration number
tr
1e-06
1e-09
1e-06
400
The choice of the correct solution of Eq. (22a,b,c) considers all the possible directions of the outgoing or entering mass flows at nodes of the 3-zone model (positive or negative signs of coefficients K), considering the mass conservation of the links entering in the same node. Then, for each simulation and each combination of the 3 starting points matrix A with 126 combinations of the signs of the mass flow rates at each of the ten links (ṁa1-ṁa3-ṁac at node a in Eq. (22a), ṁb2-ṁb4-ṁbc at node b in Eq. (22b,ṁca-ṁcb-ṁc3-ṁc4 at node c in Eq. (22c) was tested and the solution that minimizes the error was chosen:
The solution of the system is a triplet of the values of Pa, Pb and Pc which make each of the three equations of the system Eqs. (22a,b,c) closest to zero.
Air changes per hour calculation
The final output data of the presented methodology is the value of the Air Change per Hour (ach) calculated in the three indoor zones of the building: the two zones a and b heated at Tin and the shaft at Tsh. Ach is calculated according to Eq. (24),
where: the main related variables are the air flow rate ṁ [kg·s-1], the air density ρa [kg·m-3], and the volume vola [m3] of the zone a; the same calculation is applied to the other building’s zones (b and c).
The hourly variation of ach is related to the hourly variation of the environmental external condition: outdoor air temperature, and velocity of wind incident.
In this work, the 3-zone air flow model has been applied to a typical building (condominium with six floors in the center of Turin) for different scenarios of outdoor climate conditions, considering the same geometry and leakage characteristics.
Case study
The presented methodology has been applied to a case study in the city of Turin (Italy). The Crocetta district has a regular urban path, representative of the consolidated areas. Previous work (Santantonio & Mutani, 2022) defined it as a homogeneous zone. The main urban parameters to describe urban morphology are the Plan Area Density PAD (0.33), the average height of the building (20m), the typical H/W dimension (0.5) that considers internal courtyard of the block of buildings, and the wind profile exponent (0.4). These are also the main input parameters of the CpCalc software, used to assess the Cp values. The district has been chosen due to the presence of regular street canyons with different dimensions, and two prevailing orientations: +30°N (NE-SW) and -60°N (NW-SE) that correspond also the prevalent orientation of buildings. In addition, the weather station (LL, Fig. 10) used to collect local climate data is in the same district. In Fig. 10 and Table 7 are shown the 3 types of urban canyon in six streets of Crocetta district simulated in CFD analysis: fixing the height of the canyon to the average building height of the area (20m), 3 aspect ratio H/W are selected, according to the width of the street. Narrow urban canyons (NC) are representative of the internal streets in regular building blocks, while the medium (MC) and large (LC) canyons insist on the perimetral axis of blocks.
Fig. 10
Localization of the Crocetta district in the city of Turin (on the left) and urban canyons in Crocetta district (on the right) for selected aspect ratio: narrow (in blue), medium (in green) and large (in orange)
The extreme climate data conditions used in the CFD simulations are listed in Tables 8 and 9. The local prevailing wind direction (DirV in Fig. 11) is always considered from West-Northwest, (300°N, clockwise). Selected date from the year 2022, considering winter (WIN), mid-season (MID) and summer (SUM), for both extreme climatic conditions of highest hourly wind speed (U max) and hourly incident solar irradiation (Iinc max). In the first Umax three cases, the ΔT is low as the crosswind effect is prevalent, while in the second three cases (Iinc max), the ΔT is high due to the highest value of the incident solar irradiation on the facade, and the wind velocity is low.
Table 8
Extreme climate conditions of hourly wind (Umax) and solar irradiation (Iinc max) in winter (WIN), summer (SUM) and mid-seasons (MID) in the reference year 2022, applied in the CFD analysis
Extreme condition
Period
Date
(Year 2022)
Uref
[m· s-1]
Tair
[°C]
Ts-a
[°C]
Iinc
[W·m-2]
ΔT
[°C]
U max
WIN
02-07 08:00
6.8
9.8
15.0
215.8
5.2
MID
04-08 17:00
10.7
22.6
32.2
401.9
9.6
SUM
06-28 14:00
8.6
20.5
22.1
67.6
1.6
Iinc max
WIN
01-11 14:00
2.1
8.5
31.5
957.7
23.0
MID
04-10 16:00
1.4
16.6
36.9
844.4
20.3
SUM
06-10 17:00
1.6
31.0
51.1
839.5
20.1
Table 9
Typical climate winter and summer days (hourly data)
Period
Uref
[m· s-1]
Tair
[°C]
Ts-a
[°C]
Iinc
[W·m-2]
ΔT
[°C]
Winter
0.5
5.6
8.0
96.6
2.4
Summer
0.9
29.2
44.8
648.3
15.6
Fig. 11
Localization of the large urban canyon (LC) examined building with NE-SW axis, considering crosswind (DirV) and solar exposures (yellow dot) on the facades of building B1 and B2
To understand the typical meteorological seasons of the area of interest, two different seasons have been built using the typical meteorological days' approach (Hassan et al., 2021). The meteorological data gathered for Crocetta area has been clustered in three clusters using the k-means algorithm. Once the clusters have been assessed, the minimum and maximum centroids values have been assumed as winter and summer. The results obtained have been presented in Table 7.
According to the typical days, four different scenarios have been identified (Table 10), selecting four different dates from the reference year 2022, to be applied in the three-zones air flow lumped parameter model. It is possible to compare the resulting hourly ach in winter (WIN) and summer (SUM) seasons, considering for both cases low wind speed (no wind) and high wind velocity (windy) conditions.
Table 10
Climate hourly input data of the 4 scenarios applied in the 3-zone airflow model analysis
Scenario
Uref
[m· s-1]
Tair
[°C]
Tin
[°C]
Ts-a
[°C]
Iinc
[W·m-2]
ΔT
[°C]
WIN-windy
5.00
7.0
20
8.53
63.8
1.53
WIN-no wind
1.48
7.0
20
24.19
716.3
17.19
SUM-windy
6.17
28.0
26
33.98
249.2
5.98
SUM-no wind
2.18
28.0
26
42.36
598.3
14.36
The case study building for the application of the three zones airflow model is a simplified schematization of building B2, represented in Fig. 11. The main input data regarding the building geometry and opening types are listed in Table 11, while leakages’ characteristics are listed in Table 12. The period of construction of the building is before 1918, representative of the typical buildings in the selected area; this influences the tightness description of the openings and leakages (Table 11). The building has been chosen to respond to the application field of CpCalc software, used to calculate Cp at external nodes (P1, P2, P3 and P4). The openings are located at the lowest and highest parts of the building to observe different conditions of wind incident and to enhance the effect of buoyancy.
Table 11
Description of the case study: building dimension and opening characteristics
Building geometry
Openings characteristics
Zone
Type
Heated (a,b)
Shaft (c)
window w
door d
Dimension (LxHxW)
[m]
9x9x7.7
9x18x3.3
1.2x1.8
0.9x2.2
Number
[n]
3 floors
6 floors
8 w (per floor)
2 d (per floor)
Typical leakage area
[cm2/m2]
-
-
12
6
Table 12
Description of the case study: height and pressure coefficient of external and internal nodes
External nodes
Internal nodes
Internal nodes at leakage
1
2
3
4
a
b
c
a'
a”-c’
b'
b”-c”
c”’
c'v
Z
[m]
4.5
13.5
4.5
13.5
4.5
13.5
9.0
4.5
4.5
13.5
13.5
4.5
13.5
Cp
[-]
0.005
0.22
-0.03
-0.04
-
-
-
-
-
-
-
-
-
Results and discussion
In this section, the results of the two main steps of the work are described. In paragraph 5.1, results of the 2D CFD simulations describe: i) the comparison between the wind velocity profile in front of the leeward façade (probe at 1%), and the windward façade (probe at 99%), ii) the types of vortices that occur in the urban canyons, as a function of their H/W ratio and climate conditions, and iii) the equations that describe the wind velocity as a function of the height (z), considering the disjoined (WCF) or combined (WWF) effect of the cross-wind urban ventilation and non iso-thermal condition.
In paragraph 5.2, results of the 3 zone-air flow model at building scale are presented: i) the air mass flows and the air changes per hour for the four typical winter and summer conditions, in no wind and windy scenarios, ii) the comparison of the results of dynamic pressure, air flow rate, and ach, considering the two applied methodologies (CpCalc-method and CFD-method).
Results of the 2D CFD simulations
The wind flow profile is affected by the canyon geometry and the boundary conditions (i.e., climate inputs). In the following figures (Figs. 12, 13, 14, 15, 16), the results obtained for the large (LC), medium (MC), and narrow (NC) canyons will be presented, showing separately the contribution of the wind driven effect (Umax) in Figs. 12, 14, 16a, and the thermal gradient effect (Imax) in Figs. 13, 15, 16b, both during the winter and summer season, and for both considering the Windward Cold Facade (WCF) and Windward Warm Façade (WWF) scenarios. Considering the wind driven effect (Umax) in all canyon dimensions, the crosswind contribution is prevalent in determining a central vortex (Fig. 14a-f), and it is not affected by the presence of the irradiated wall; since no relevant differences occur between the WWF and WCF scenario, only results of the WWF scenario are shown.
Fig. 12
a-f. Wind driven (Umax) effect generating wind velocity profiles in large (LC), medium (MC), and narrow (NC) canyons, in front of leeward (1%) and windward (99%) façades, in WWF scenarios, during winter (a-c-d) and summer (b-d-f) seasons
a-n. Effect of the extreme condition of thermal gradient (Imax) in generating the wind velocity profiles in large (LC, a-d), medium (MC, c-h), and narrow (NC, i-n) canyons, , in front of the leeward façade (probe at 1%) and the windward façade (probe at 99%), during the winter (a-b-e-f-i-l) and summer (c-d-g-h-m-n) seasons, and Windward Warm Facade (WWF, a-c-e-g-i-m) and Windward Cold Facade (WCF, b-d-f-h-l-n) scenarios
a-f. Velocity field and vortical structures obtain from steady-state simulations, considering the extreme condition of the cross wind driven effect (Umax), in large (LC, a-b), medium (MC, c-d), and narrow (NC, e-f) canyons, in WWF scenarios, during the winter (a-c-d) and summer (b-d-f) seasons
a-n. Velocity field and vortical structures obtain from steady-state simulations, considering the extreme condition of the thermal gradient effect (Imax), in large (LC, a-d), medium (MC, c-h), and narrow (NC, i-n) canyons, during the winter (a-b-e-f-i-l) and summer (c-d-g-h-m-n) seasons, and Windward Warm Facade (WWF, a-c-e-g-i-m) and Windward Cold Facade (WCF, b-d-f-h-l-n) scenarios
a-b. Velocity field on windward façade (99%) for maximum conditions of wind-driven U max (a) and irradiation Iinc max (b) in the summer season WWF scenario, comparing the CFD results from the steady-state regime simulations (dotted lines) and the interpolated fitted curves with the fifth-grade polynomial function (straight lines), for the Narrow (blue dotted line), Medium (violet dotted line), and Large (green dotted line) canyons
Figures 12 and 13 show the wind velocity profiles of the steady flow regimeboth in front of the leeward façade (probe at 1%) and the windward façade (probe at 99%).
Figures 14 and 15 show the different contribution of the two extreme effects of the cross wind-driven and thermal gradient in creating the vortex structure in the domain of the urban canyons, as a function of their H/W ratio and climate conditions. Considering the undisturbed wind flow U (blue arrow), the windward façade of building B2 is always on the left of the scheme, and it is analyzed in both the Windward Cold Facade (WCF, in blue) and Windward Warm Façade (WWF, in orange) scenarios.
Regarding the cross wind-driven effect (Umax), in the Large Canyon (LC), a unique vortex occurs, and it has the same symmetrical behavior in all the two seasons analyzed. The same consideration can be done for the other canyons dimensions (MC and NC), but each one has a different intensity of wind velocity.
Regarding the thermal gradient effect, the contribution of the heated wall becomes tangible in the definition of the vortical structures. Oscillating solutions in the domain are obtained when the two effects (crosswind and irradiated wall) occur to the same facade, the flow on warm wall tries to flow upwards due to the buoyancy effect, but it conflicts with the vortex created inside the canyon and by the effect of the external upstreaming wind.
For all the three canyon dimensions, a single vortex is formed only in the case when the windward façade is not irradiated (WCF scenarios) in winter (Fig. 15b-f-l) and summer (Fig. 15d-h-n). Alternatively, when the windward façade is warm (WWF), crosswind and thermal buoyancy effects add up by thickening the mixing layer; one no longer traces a single vortex structure, but several recirculation zones in winter (Fig. 15a-e-i) and summer (Fig. 15c-g-m), and asymmetrical wind velocity profiles are obtained from all the probes in the canyon (Fig. 13a-n).
In all the WCF scenarios in Fig. 15, the vortex is even more symmetrical, and the air increases its velocity, especially near the vertical and horizontal surfaces. the same conditions (Iinc max and low U), in case of narrow urban canyon (NC), in each analyzed period,
The graphs in Fig. 16a-b describe the flow field of the crosswind near the windward façade (probe at 99%), in the summer season and WWF scenario (combined effect of wind and buoyancy on the windward façade), considering separately the extreme condition of maximum crosswind Umax (Fig. 14a) and maximum incident irradiation Iinc max (Fig. 14b). For each of the three urban canyons (narrow, medium, and large) the plotted curves describe the wind velocity as a function of the height in the canyon. In case of maximum wind Umax, for all canyons the velocity profile is symmetrical with the highest value at half height of the façade. In the large canyon (LC), the wind profile is lower than the ones in the medium and narrow canyons. This last consideration is valid also in Fig. 14b, where the effects of thermal gradient are evident. The warm air flows upwards due to the buoyancy effect, is increased by the presence of the vortex created inside the canyon, both circulating in the same direction.
Results of the 3-zones air flow model
In this paragraph are presented the results of the ach calculated for the case study building in the large (LC) and medium (MC) urban canyons. In both cases, the 3-zones air flow model is applied in 4 different climate scenarios of typical winter and summer days, both in windy and no-windy conditions. The two methodologies (Cpmethod and CFDmethod) have been applied to all scenarios and compared. The two methodologies differ for the calculation of the dynamic pressure pdyn that directly depends on the wind velocity incident on both windward and leeward facades for all the external nodes (1, 2, 3, 4 in Fig. 9).
In the Cpmethod the incident wind velocity has been calculated, adjusting the reference wind velocity (Uref) measured from the weather station according to the specific Cp evaluated at nodes’ height (z).
In the CFDmethod, the incident wind velocity vCFD (Table 13) is the results of the CFD analysis simulated separately for the large and medium canyons, extracted by the fitted curves (Fig. 16a-b) for each climate scenarios analyzed. For each of them, the associated equation that describes the velocity as a function of the quota has been directly used to determine the wind speed at the four height’s nodes. Reference is made to the equation of probe 99% for the two nodes (1,2) in the windward façade and to the equation of probe 1% for the two nodes (3,4) in the leeward façade.
Table 13
Results of dynamic pressure pdyn at the four external nodes’ height, comparing Cp and CFD methods on windward (WW) and leeward (LW) facades of a large (LC) and medium (MC) canyons
Scenario
Large Canyon (LC)
Medium Canyon (MC)
Façade
WW
LW
WW
LW
Node
1
2
3
4
1
2
3
4
z
4.5
13.5
4.5
13.5
4.5
13.5
4.5
13.5
[m]
Cp
0.005
0.223
-0.032
-0.041
0.005
0.223
-0.032
-0.041
[-]
WINT-windy
(Uref =5.0m/s)
vCFD
0.83
2.77
-0.17
-0.30
1.36
2.43
-1.06
-1.61
[ms-1]
PdynCFD
0.41
4.62
-0.02
-0.05
1.11
3.55
-0.67
-1.55
[Pa]
Cp·Uref2
0.23
10.31
-1.48
-1.90
0.23
10.31
-1.48
-1.90
[m2s-2]
PdynCp
0.14
6.25
-0.89
-1.14
0.14
6.25
-0.89
-1.14
[Pa]
WINT-no wind
(Uref =1.48 m/s)
vCFD
0.47
0.34
-0.17
-0.18
0.55
0.84
-0.36
-0.39
[ms-1]
PdynCFD
0.13
0.07
-0.02
-0.02
0.18
0.42
-0.08
-0.09
[Pa]
Cp·Uref2
0.01
0.57
-0.08
-0.10
0.01
0.57
-0.08
-0.10
[m2s-2]
PdynCp
0.00
0.34
-0.05
-0.07
0.00
0.34
-0.05
-0.07
[Pa]
SUM-windy
(Uref=6.17 m/s)
vCFD
2.06
3.20
-1.03
-1.70
2.31
3.51
-1.80
-2.68
[ms-1]
PdynCFD
2.54
6.14
-0.64
-1.73
3.21
7.38
-1.93
-4.30
[Pa]
Cp·Uref2
0.37
16.50
-2.37
-3.03
0.37
16.50
-2.37
-3.03
[m2s-2]
PdynCp
0.21
9.55
-1.37
-1.76
0.21
9.55
-1.37
-1.76
[Pa]
SUM-no wind
(Uref =2.18 m/s)
vCFD
0.75
1.13
-0.31
-0.57
0.87
1.32
-0.63
-1.14
[ms-1]
PdynCFD
0.34
0.85
-0.05
-0.26
0.45
1.05
-0.23
-0.78
[Pa]
Cp·Uref2
0.01
0.57
-0.08
-0.10
0.01
0.57
-0.08
-0.10
[m2s-2]
PdynCp
0.00
0.34
-0.05
-0.07
0.00
0.34
-0.05
-0.07
[Pa]
For each external node (1,2,3,4) and in all the four climate scenarios, Table 13 presents the result of pdyn at the nodes’ height z on windward (WW) and leeward (LW) facades for both the large (LC) and medium (MC) canyons, comparing the Cpmethod and CFDmethod, according to Equation 14.1 and 14.2, respectively.
In both methodologies, all the pdyn calculated at nodes (3,4) in the leeward (LW) façade have a negative sign related to the direction of the surface pressure. In all cases, pdyn at low height (4.5m for nodes 1,3) is always lower than pdyn at high height (13.5m for nodes 2,4), except the results of the CFD method for the leeward façade of the large canyon in the summer windy scenario (SUM-windy).
In all climate scenarios, pdynCFD in the medium canyon (MC) is greater than pdynCFD in the large canyon as shown in Fig. 16a-b, the vortex structure and the wind profile are similar for the 2 canyon dimensions, but in the MC the wind increases its magnitude. For this reason, in windy scenarios the increase is even more significant.
Comparing pdynCp and pdynCFD, they are of the same order of magnitude. The first is calculated only once, regardless of the size of the canyon, because it described pressure distribution along the façade at building scale. Therefore, for each scenario in Table 13, the same pdynCp result can be compared with pdynCFD of the large (LC) and medium (MC) canyons, and in both cases, it is always a lower value.
In windy scenarios, on the windward facade, the gap between pdynCp calculated at the two nodes at different heights is significant: at a lower height (node 1) pdynCp is always much lower than pdynCFD, while at a higher height (node3) pdynCp is always much greater than pdynCFD. This is closely related to the value of the Cp coefficients (Table 13) for the windward façade (WW).
The CFDmethod is very sensitive to the height of the observed points (nodes) related to the dimensions of the canyon (LC and MC), as it considers the vortex created by the combined effect of the wind and thermal buoyancy. The Cpmethod overestimates the incident speed (Cp·Uref2 in Table 13) on the facades because:
it describes the surrounding built context through tabular values of parameters (PAD, SbH, roughness parameter) without considering neither the presence nor the geometry of the canyon,
it only considers the effect of the incident wind and not the solar radiation which affects the convective motion of the air near the facades,
the limited field of application of the table parameters makes it difficult to apply the Cpmethod to typical buildings in Turin (closed condominiums with a central garden courtyard).
The resulting air flow displacement through the building zones is the same for the two methods applied and for the two canyon dimensions (large and medium) analyzed; it is schematized in Fig. 17, considering the winter (Fig. 17a-b) and the summer seasons (Fig. 17c-d), in windy (Fig. 17a-c) and no wind (Fig. 17b-d) conditions. Here, the outdoor airflow (fresh air) is represented by a green arrow while the indoor airflow (exhausted air) is represented by a red arrow. In all climate scenarios, the incident wind on the windward façade let the outdoor air enters and pass through the heated zones, reaching the shaft. The only exception is the winter no windy scenario (Fig. 17b): at the upper level (node2) the air flows from the heated zone to the outdoor space, due to the poor wind condition and the prevalence of buoyancy effect.
Fig. 17
a-c. Airflow displacement through buildings zones in both large (LC) and medium (MC) canyons, in winter-windy (a), winter-no wind (b), summer windy (c, only in MC) and summer no-wind (d) scenarios
Considering the shaft zone (node Pc), in all winter scenarios (Fig. 17a-b), the outdoor air enters from the ground level (node 3) and esc trough the leakages at higher level (node 4). In the summer scenarios it is the contrary: at the floor level (node 3) the air esc from the shaft, in both windy (Fig. 17c) and no wind (Fig. 17d) scenarios. In the summer no wind scenario, the outdoor air enters from the higher leakages (node 4) in the shaft, while in the summer windy scenario, at the upper level the exhausted air esc from the shaft. In winter the external air is colder than the internal one, the warmer air in the shaft tends to rise, and it is possible to assume that the thermal buoyancy effect is predominant, vice versa in summer.
For all scenarios, in Table 14 are compared the results of the ach for each of the three zones of the building: the upper zone (b), the lower zone (a) and the shaft (c). The ach* is calculated considering all the airflow entering the zone: the outdoor fresh air and the recirculation air from internal zones. So, the ach* is always greater than the ach in the shaft (c).
Table 14
Hourly ach [h-1] for upper (b) and lower (a) heated zones and the shaft zone (c) in the building, comparing results of Cp method and CFD method for the large (LC) and medium (MC) canyons
Scenario
Method
Canyon
ach(a)
ach(b)
ach(c)
ach(c)*
WIN-windy
Cp
LC-MC
0.05
0.08
0.18
0.28
CFD
LC
0.06
0.04
0.32
0.38
MC
0.08
0.03
0.41
0.57
WIN-no wind
Cp
LC-MC
0.01
0.02
0.07
0.08
CFD
LC
0.02
0.02
0.01
0.02
MC
0.03
0.04
0.03
0.05
SUM- windy
Cp
LC-MC
0.03
0.10
0.07
0.20
CFD
LC
0.06
0.07
0.28
0.42
MC
0.06
0.12
-
0.18
SUM-no wind
Cp
LC-MC
0.01
0.02
0.13
0.16
CFD
LC
0.01
0.03
0.06
0.09
MC
0.05
0.15
0.08
0.11
* Outdoor airflow plus airflow from zones a and b
The resulting ach values in each scenario are all lower than the fixed values used in the energy models (0.3-0.5), but this depends on the fact that this study only considers the airflow through the leakages of the openings. Considering only the results of the CFD method, in all zones the ach in the medium canyon (MC) is slightly greater than the ones in the large canyon (LC), due to the increasing air velocity related to canyon dimension. For each scenario, the ach resulting from the Cp method can be compared with the ones of the CFD method for both LC and M: the values are of the same order of magnitude. In all scenarios, the ach at lower zones (a) is lower than the ach at upper level (b), except in winter windy climate scenario, for both the CFD method’s application in large and medium canyons. In both winter and summer seasons the windy scenarios report higher ach values than the corresponding scenarios with no wind, due to the role of dynamic pressure in determining the passage of air in the areas of the building.
Table 15 reports the results (errors) of the three non-linear equations in the system Eq. (22a,b,c), considering the solutions of the iterative calculation. Errors closer to zero means that the solutions of the iterative calculation are more accurate and that the mass conservation law is verified in each node. The order of magnitude is similar between the various scenarios for the two methodologies applied.
Table 15
Errors of the three non-linear equations in the system Eq. (22a,b,c), corresponding to the mass conservation law balance at each node in the internal zones (a,b,c), comparing results of Cp-method and
CFD-method for the the large (LC) and medium (MC) canyons
In this work a three-zones air flow lumped model has been described and used to assess the hourly variation of the number of air changes per hour (ach). The air displacement in a building is determined, considering only the air flow rate due to infiltrations, depending on leakages’ characteristics and pressure variation due to the wind and buoyancy effect. The fsolve function has been used to solve the non-linear equations of mass conservation, through an iterative procedure.
The outdoor environmental condition of dynamic and static pressure on building façades have been determined by experimental values (Cp) and CFD simulations on urban canyons. Different climate scenarios have been considered to investigate the velocity field in the domain, evaluating the contributions of cross wind flow and thermal buoyancy in urban canyons with different dimensions. Then, polynomial function is interpolated to obtain the description of wind speed as function of the elevation.
The three-zones air flow lumped model can find the solutions with the numerical methodology for the case studies analyzed both with the Cp and the CFD outdoor data. The Cp data were used even if their field of application is not respected in environments with high building density. The CFD results can estimate the outside pressures and then airflow rates; in addition, it allows to modulate the ach at the building scale in different climatic scenarios, as the wind speed varies in relation to the canyon dimension and geometry.
Further developments of this work can improve the calculation of the outside pressures on buildings’ facades at urban level. Finally, some progress could improve to match the numerical method with the physical-based modeling of space heating and cooling for the buildings within a city.
Acknowledgment
Authors thank Prof. Franco Pellerey and his research group for their precious contribution in the definition of the numerical solution of air changes per hour modeling.
Declarations
Conflict of interest
The authors have no conflict of interest.
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Ai, Z. T., & Mak, C. M. (2017). CFD simulation of flow in a long street canyon under a perpendicular wind direction: Evaluation of three computational settings. Building and Environment, 114, 293–306. https://doi.org/10.1016/j.buildenv.2016.12.032CrossRef
Ali, U., Shamsi, M. H., Hoare, C., Mangina, E., & O’Donnell, J. (2021). Review of urban building energy modeling (UBEM) approaches, methods and tools using qualitative and quantitative analysis. Energy and Buildings, 246. https://doi.org/10.1016/j.enbuild.2021.111073
Allegrini, J., Dorer, V., & Carmeliet, J. (2014). Buoyant flows in street canyons: Validation of CFD simulations with wind tunnel measurements. Building Environment, 72, 63–74. https://doi.org/10.1016/j.buildenv.2013.10.021CrossRef
Blocken, B., Janssen, W. D., & van Hooff, T. (2012). CFD simulation for pedestrian wind comfort and wind safety in urban areas: General decision framework and case study for the Eindhoven University campus. Environmental Modelling & Software, 30, 15–34. https://doi.org/10.1016/j.envsoft.2011.11.009CrossRef
Calì M., Arena P., Borchiellini R., Mutani G. and. Vannelli G. (1997). Methods of analysis and verification of the performance of numerical codes aimed at energy and fluid dynamics calculations in civil and industrial buildings, Energy Dep. of Polytechnic of Turin, ITAG - Italian Technical Gas Association.
Dols, W. S., & Polidoro, B. J. (2020). CONTAM User Guide and Program Documentation Version 3.4. National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1887r1CrossRef
Harish, V. S. K. V., & Kumar, A. (2016). A review on modeling and simulation of building energy systems. Renewable and Sustainable Energy Reviews, 56. https://doi.org/10.1016/j.rser.2015.12.040
Hassan, M. A., Khalil, A., & Abubakr, M. (2021). Selection methodology of representative meteorological days for assessment of renewable energy systems. Renewable Energy, 177. https://doi.org/10.1016/j.renene.2021.05.124
Javanroodi, K., Nik, V. M., Giometto, M. G., & Scartezzini, J.-L. (2022). Combining computational fluid dynamics and neural networks to characterize microclimate extremes: Learning the complex interactions between meso-climate and urban morphology. Science of the Total Environment, 829. https://doi.org/10.1016/j.scitotenv.2022.154223
Lenin, G., Krishnan, P. E., & Ramkumar, R. (2022). Effect of various parameters on sol-air temperature. International Journal of Mechanical Engineering.
Li, X.-X., Britter, R. E., Norford, L. K., Koh, T.-Y., & Entekhabi, D. (2012). Flow and Pollutant Transport in Urban Street Canyons of Different Aspect Ratios with Ground Heating: Large-Eddy Simulation. Boundary-Layer Meteorology, 142-2, 289–304. https://doi.org/10.1007/s10546-011-9670-9CrossRef
Mouzourides, P., Marakkos, C., & Neophytou, M. K.-A. (2022). Urban street canyon flows under combined wind forcing and thermal buoyancy. Physics of Fluids, 34–37. https://doi.org/10.1063/5.0090642
Mun, J., Lee, J., & Kim, M. (2021). Estimation of Infiltration Rate (ACH Natural) Using Blower Door Test and Simulation. Energies, 14(4), 4. https://doi.org/10.3390/en14040912CrossRef
Mutani G., Santantonio S., and Todeschi V., (2021). Evaluation of ventilation loads in buildings energy modelling at urban scale, in 2021 IEEE 4th International Conference and Workshop Óbuda on Electrical and Power Engineering (CANDO-EPE). doi: https://doi.org/10.1109/CANDO-EPE54223.2021.9667547.
Mutani, G., Vocale, P., & Javanroodi, K. (2023). Toward Improved Urban Building Energy Modeling Using a Place-Based Approach. Energies, 16(9), 9. https://doi.org/10.3390/en16093944CrossRef
Najafi, Z. N., Cook, M., & O’Sullivan, P. D. (2023). The effect of airflow guiding components on effective ventilation rates in single-sided ventilation applications. International Journal of Ventilation. https://doi.org/10.1080/14733315.2023.2198793
O’Neill, J. J., Cai, X.-M., & Kinnersley, R. (2016). Stochastic backscatter modelling for the prediction of pollutant removal from an urban street canyon: A large-eddy simulation. Atmospheric Environment, 142, 9–18. https://doi.org/10.1016/j.atmosenv.2016.07.024CrossRef
Palusci, O., & Cecere, C. (2022). Urban Ventilation in the Compact City: A Critical Review and a Multidisciplinary Methodology for Improving Sustainability and Resilience in Urban Areas. Sustainability, 14(7), 3948. https://doi.org/10.3390/su14073948CrossRef
Palusci, O., Monti, P., Cecere, C., Montazeri, H., & Blocken, B. (2022). Impact of morphological parameters on urban ventilation in compact cities: The case of the Tuscolano-Don Bosco district in Rome. Science of the Total Environment, 807. https://doi.org/10.1016/j.scitotenv.2021.150490
Perera, A. T. D., Javanroodi, K., Wang, Y., & Hong, T. (2021). Urban cells: Extending the energy hub concept to facilitate sector and spatial coupling. Advances in Applied Energy, 3. https://doi.org/10.1016/j.adapen.2021.100046
Rezaeiha, A., Montazeri, H., & Blocken, B. (2020). A framework for preliminary large-scale urban wind energy potential assessment: Roof-mounted wind turbines. Energy Conversion and Management, 214. https://doi.org/10.1016/j.enconman.2020.112770
Samsonov, T., Konstantinov, P., & Varentsov, M. (2015). Object-oriented approach to urban canyon analysis and its applications in meteorological modeling. Urban Climate, 13. https://doi.org/10.1016/j.uclim.2015.07.007
Sanaieian, H., Tenpierik, M., van den Linden, K., Mehdizadeh, S. F., & Majid Mofidi Shemrani, S. (2014). Review of the impact of urban block form on thermal performance, solar access and ventilation. Renewable and Sustainable Energy Reviews, 38, 551–560. https://doi.org/10.1016/j.rser.2014.06.007CrossRef
Santantonio S. and Mutani G., (2022). QGIS-based tools to evaluate air flow rate by natural ventilation in buildings at urban scale, in 5th Building Simulation Applications Conference (BSA 2022), Proceedings ISSN 2531-6702, Bolzen (IT), June 29th – July 1st 2022, doi: https://doi.org/10.13124/9788860461919.
Toparlar, Y., Blocken, B., Maiheu, B., & van Heijst, G. J. F. (2017). A review on the CFD analysis of urban microclimate. Renewable and Sustainable Energy Reviews, 80, 1613–1640. https://doi.org/10.1016/j.rser.2017.05.248CrossRef
Tsichritzis, L., & Nikolopoulou, M. (2019). The effect of building height and façade area ratio on pedestrian wind comfort of London. Journal of Wind Engineering and Industrial Aerodynamics, 191, 63–75. https://doi.org/10.1016/j.jweia.2019.05.021CrossRef
