Comparative metrics for computational approaches in non-uniform street-canyon flows

Building and Environment 158 (2019) 16–27

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Comparative metrics for computational approaches in non-uniform streetcanyon flows

T

Arash Nemati Hayatia, Rob Stolla,∗, Eric R. Pardyjaka, Todd Harmana, J.J. Kimb a b

University of Utah, Department of Mechanical Engineering, Salt Lake City, UT, 84112, USA Pukyong National University, Department of Environmental Atmospheric Sciences, 48513, 45, Yongso-ro, Nam-Gu, Busan, South Korea

A R T I C LE I N FO

A B S T R A C T

Keywords: Computational fluid dynamics Flow topology Street canyon Urban fluid mechanics

Three different computational fluid dynamics (CFD) methods are assessed for their ability to predict topological flow features in idealized street canyons with uneven building heights. Mean velocity-fields from step-up (i.e., a high-rise building downwind of a low-rise building) and step-down (i.e., a low-rise building downwind of a highrise building) street canyons are evaluated against high-spatial-resolution wind-tunnel data. Each method represents a different level of flow physics using: a mass-conserving model entitled Quick Urban & Industrial Complex wind model (QUIC-URB), a Reynolds-averaged Navier-Stokes (RANS) model, and a large-eddy simulation (LES) model. A new metric that represents the equally weighted trade-off between accuracy and efficiency is introduced to evaluate the CFD methods’ capabilities to capture major-flow topological features in uneven building height street canyons. For step-up street canyons, all three methods qualitatively predict primary topological features, however, none simultaneously capture all secondary features. For step-up street canyons and step-down street canyons with narrow-streets, QUIC-URB captures most of the primary flow topological features including stagnation and saddle points and rooftop recirculation zones. RANS captures primary vortices for stepup street canyons and step-down street canyons with wide-streets. LES is computationally costly but it is the only method that successfully predicts secondary flow topological characteristics for step-down street canyons with wide-streets. When examining our trade-off metric, QUIC-URB has the highest score for step-up street canyons, while QUIC-URB and RANS have equally high trade-off scores for step-down street canyons with narrow-streets, and QUIC-URB and LES have nearly equal trade-off scores for step-down street canyons with wide-streets.

1. Introduction Urban form and land use significantly impact microclimate, air quality, and water and energy use in cities [1,2], all of which can have deleterious effects on human health and quality of life [3]. When aggregated, microclimate impacts can manifest city wide as an urban heat island [4]. To reduce these harmful effects, it is necessary to understand the interaction of urban infrastructure elements, such as buildings and vegetation, with the surrounding environment by field measurements, full-scale and reduced-scale wind-tunnel experiments, and numerical simulations [5]. While experimental studies provide the most accurate source of data for urban microclimate studies, the challenges associated with momentum and dispersion measurements and the diversity of urban morphological parameters, make computational approaches an appealing and practical alternative [6,7]. Increasingly, different computational fluid dynamics (CFD) methodologies have been used for momentum and scalar transport

∗

quantification in urban micro-climate research, design, and applications [7–10]. The different methods use a wide range of approximations for the governing equations of motion on a discretized domain. Fast response techniques, Reynolds averaged Navier-Stokes (RANS), largeeddy simulation (LES), lattice Boltzmann method (LBM), and detachededdy simulation (DES) are typical methods each differing in the level of physical representation and computational expense [11–14]. The simplest method is the use of fast-response techniques that are rapid and often empirically-based mass-conserving approaches for quick turn-around modeling of environmental transport processes in urban areas. RANS approaches are less empirical and solve the Reynolds-averaged governing equations by decomposing an unsteady field into an ensemble average and a fluctuating quantity. Compared to fast-response and RANS approaches, LES is a relatively computationally expensive technique that models instantaneous flow dynamics by resolving large-scale turbulent motions and modeling only subgrid-scale motions. DES is a hybrid approach, where RANS is typically used in the

Corresponding author. University of Utah, 1495 E 100 S (1550 MEK), Salt Lake City, UT, 84112, USA. E-mail address: [email protected] (R. Stoll).

https://doi.org/10.1016/j.buildenv.2019.04.028 Received 4 January 2019; Received in revised form 11 April 2019; Accepted 12 April 2019 Available online 20 April 2019 0360-1323/ © 2019 Elsevier Ltd. All rights reserved.

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canyon length, respectively). Then, we synthesize the findings from step-up street canyons with those previously obtained for step-down street canyons [29]. We provide new information on the ability of different numerical approaches to capture flow regimes and topological characteristics for a broad range of street-canyon configurations.

boundary layer and LES is used in separated flow zones [15]. Compared to other approaches, LBM is relatively new to environmental fluid dynamics and uses a microscopic modeling approach in which fluid elements are represented by a finite number of particles streaming and colliding within a discrete mesh. One of the limitations of LBM is that it requires a massive number of particles to represent the correct flow features at different macroscopic scales [16]. Many studies have focused on the ability of CFD methods to faithfully model microscale urban flow dynamics. Most centered on evaluating performance for simulations of isolated building [e.g. Refs. [17,18]], street-canyon [e.g. Refs. [19–22]], and regular or heterogeneous building array [e.g., 23–27] flows. Typically, method performance is evaluated against wind-tunnel data or data from field experiments using various validation criteria including statistical analysis and pattern detection tests [28]. Statistical analysis has been extensively used in urban microclimate studies with evaluations focusing on wind vector diagrams, scalar concentration contour plots, and weighted average error metrics such as fractional bias and normalized mean square error [12,24]. Pattern detection tests are rarely used in urban CFD studies. One exception is Hayati et al. [29] who performed detailed analysis of flow topological patterns for step-down street canyon flows. They showed the strengths and weaknesses of various CFD methods in capturing different flow features and suggested the need for more studies on other urban flow regimes. Improved understanding of the performance of different methods using pattern tests has the potential to improve guidelines for choosing the most appropriate CFD method to capture desired flow features across different applications. For instance, Liu and Niu [15] showed that the wake region of a high-rise building is captured by DES with the same accuracy as LES but with less computing requirements. Hoof et al. [30] concluded that choosing a CFD method for urban flow simulations should be associated with the type of flow regions and topological features that are of interest. Despite numerous studies on urban flows, limited information is available on the trade-off between the computational efficiency and the physical accuracy of different approaches for various flow regimes and topological features. This knowledge gap primarily exists because detailed CFD comparisons of different flow characteristics require highspatial resolution wind-tunnel data-sets. Most evaluation studies are limited to discrete in-canyon vertical velocity profile comparisons and time-series analysis [e.g. Refs. [20,23,27,31]]. Additionally, many studies examine model performance for uniform street canyons with equal building heights and only include model sensitivity to geometric parameters such as the building length, the roof shapes, and the building facades [20–22,24,32]. While some studies do evaluate model performance for uneven buildings [e.g. Refs. [23,26,27]], they use complex full building arrays and include only standard point-based performance metrics. The complexities of spatial flow characteristics produced by different CFD methods and the methods' sensitivities to a broad range of non-uniform street canyon geometries with uneven building heights have not been sufficiently addressed. Here, we use three well-validated CFD models that are representative of the three primary levels of flow physics modeling: fast-response, RANS, and LES, to predict the flow structures in street canyons with uneven buildings. The DES method and the LBM are not included for brevity and because as yet, they are not widely used. We compare and evaluate the CFD results against each other and against high-spatial-resolution experimental data for step-up street canyons, which are defined as building arrangements with a high-rise building downstream of a low-rise building [33]. We focused on each method's ability to predict flow regime topological features in the mean velocity field including in-canyon vortices, rooftop recirculations, and stagnation points. Several canyon configurations are examined by varying the downwind-to-upwind building height ratio (Hd / Hu , where Hd and Hu are the downwind and upwind building heights, respectively), and building-width to canyonlength aspect ratio (W / S , where W and S are the building width and

2. Methodology Three main CFD approaches with different levels of physics representations are examined using well-validated CFD models including a fast-response mass-conserved semi-empirical solver, a mean momentum solver (e.g., RANS solver), and an instantaneous filtered momentum solver (e.g., LES solver). The specific models are briefly described below. For full descriptions of each model please see Ref. [29] and the references contained therein. 2.1. Description of the models The fast-response model used in this study is the Quick Urban & Industrial Complex (QUIC-URB) wind solver. It is a simple CFD model that uses a three-dimensional mass-consistent set of equations to compute mean-flow fields around buildings. The model includes empirical parameterizations for various flow patterns including upwind and downwind cavities and rooftop recirculation zones [34,35]. After initializing the velocity field based on these parameterizations, the variance of the difference between the initial and final velocity fields is minimized using the mass conservation constraint [36]. QUIC-URB is among the most well-published fast-response building-resolved wind solvers. Numerous studies have utilized QUIC-URB for urban applications [e.g. Refs. [37–41]]. To represent the RANS methodology, the renormalization group (RNG) k-ε turbulence closure scheme is used in a three-dimensional, non-hydrostatic, non-rotating, and Boussinesq RANS model with isothermal conditions [42,43]. A standard turbulent wall function is implemented to resolve near-wall effects [44]. The model has been used extensively for urban studies and shows good agreement with experimental data [43,45–48]. The LES model used in this study is Uintah:MPMICE, a massively parallel LES model developed within a generalized Eulerian-Lagrangian two-way coupled fluid-structure interaction code [49–51]. Uintah:MPMICE has recently been deployed for urban physics studies [29] and is representative of urban LES models used in past studies [e.g. Refs. [52,53]]. The Material Point Method (MPM) is the structural mechanics algorithm used to compute the evolution of the solids. Objects are discretized into a cloud of particles (i.e., material points) with specific material properties and particle interactions are tracked in a Lagrangian frame through a background mesh which is used to calculate the velocity gradients at each time step [54,55]. The evolution of the fluid is solved using the Implicit Continuous fluid Eulerian (ICE) algorithm, which is a multi-material, Eulerian, cell-centered, finite-volume, compressible fluid simulation code that includes different turbulence subgrid-scale models (the dynamic Smagorinsky model is used for this study) [56,57]. 2.2. Canyon configurations and experimental data The step-up street-canyon numerical simulations for all three CFD models are compared against high-resolution wind tunnel data from the literature [33]. The data was collected using two-dimensional (2D) particle imaging velocimetry (PIV) under isothermal conditions in a 7.9-m long boundary layer wind tunnel with a 0.91 × 0.61 m crosssection. For each tested building configuration, 1000 image pairs where collected and after interrogation the resulting velocity vectors had a pitch of ≈1.05 mm. All experimental results shown in Sec. 3 are averaged over all 1000 2D vector fields. All the building configurations examined experimentally by Ref. 17

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Fig. 1. Inflow parameters and geometric specifications used in step-up test cases: Hu : upwind building height, Hd (z ref ): downwind building height, u∞: freestream velocity, u Hd (uref ): streamwise velocity component at z = Hd , δ: boundary-layer height, S: street-canyon along-wind width, W: building cross-wind width, L: building along-wind length.

2.3.1. QUIC-URB The distances from the buildings to the inlet, lateral, and outlet boundaries are 5L , 5L and 10L , respectively with the domain height fixed at 240 m for all cases. A uniform grid size of 3.2 m in all directions is used (1,890,000 total cells for the widest buildings test case). QUICURB velocity fields are strongly dependent on the empirical parameterizations used in the model [e.g., 36] and not on the chosen grid resolution. As a result, tests with the numerical grid refined to 1.6 m in all directions did not substantially impact the velocity field flow topological features produced by QUIC-URB. The inlet profile replicates the measurements from the wind-tunnel experiment in Ref. [33] where the mean wind profile at the inlet is specified by fitting a power-law to the experimental mean inlet velocity given by

[33] are used in this study. In the simulations, the experimental building geometries are scaled up by a factor of 1000 while velocity and fluid properties are not scaled. Inflow parameters and geometric specifications are shown in Fig. 1, with the origin of the coordinate system located at the mid-width of the upstream building's leading edge on the ground surface. Hu , Hd , u∞, u Hd (uref ), S, L, and W, represent upwind building height, downwind building height, upstream reference velocity, streamwise velocity at the height of the downwind building, streetcanyon along-wind width, building along-wind length, and building cross-wind width, respectively. The inflow profiles are similar to those described in Ref. [29] but with a different reference height (z ref = 96 m) and reference streamwise velocity (uref = 4.32 ms-1). The street-canyon along-wind width and the building along-wind length are fixed at S = L ≈ 32 m, with the downwind building height fixed at Hd ≈ 96 m for all cases (Table 1). Four different building-width to canyon-length aspect ratios (e.g., W / S ≈ 1,2,3,4 ) are considered by changing the building width from W ≈ 32 m (narrow buildings) to W ≈ 64 m (mid-width buildings), W ≈ 96 m (wide buildings), and W ≈ 128 m (very wide buildings). The width of the two buildings is always equal. For each aspect ratio, the downwind-to-upwind buildingheight ratio (Hd / Hu ) varies from Hd / Hu ≈ 3 (short upwind building) to Hd / Hu ≈ 1.67 (tall upwind building). All four cases W / S ≈ 1 − 4 are examined with the QUIC-URB and RANS models and two cases with W / S ≈ 1,3 are examined with the LES model. The test case configurations are summarized in Table 1.

z ⎞ u (z ) = uref ⎜⎛ ⎟ z ⎝ ref ⎠

2.3.2. RANS The grid size, the distances to the inlet, lateral, and outlet boundaries from the buildings, and the mean inlet wind profile are identical to those used for the QUIC-URB simulations (Sec. 2.3.1). Higher-resolution simulations at 1.6 m did not significantly alter the flow patterns and topological features observed in the numerical results. The governing equation set is numerically solved on a staggered grid system using the finite volume method with the semi-implicit method for pressure-linked equation (SIMPLE) algorithm [59]. For more details about the discretization methodology of the RANS CFD model see Ref. [42]. The inlet turbulent kinetic energy (k) and its dissipation rate (ε) are given by Ref. [58] as

A summary of the key parameters including Courant number, integration time, near-wall treatment, and convergence criteria for each approach is given in Table 2. Further description for each model are given in Sec. 2.3.1, 2.3.2, and 2.3.3. Table 1 Canyon configuration for all test cases.

k (z ) =

W/S

Hd/ Hu

W (m)

Hu (m)

S = L (m)

Hd (m)

1 2 3 4 5 6 7 8

1 2 3 4 1 2 3 4

3 3 3 3 1.67 1.67 1.67 1.67

32 64 96 128 32 64 96 128

32 32 32 32 57.5 57.5 57.5 57.5

32 32 32 32 32 32 32 32

96 96 96 96 96 96 96 96

(1)

where a, z ref , and uref represent the power-law exponent, reference height, and streamwise velocity component at z = z ref , respectively. Details about various algorithms, inlet parameters, and domain dimensions are given in Table 3.

2.3. Numerical setup

Test case

a

ε (z ) =

1 2 z 2 u ⎛1 − ⎞ and 0.5 * δ⎠ Cμ ⎝

(2a)

Cμ0.75 k1.5 κz

(2b)

respectively, where Cμ , κ, u * , and δ are the empirical constant (Cμ = 0.09), von Karman constant (κ = 0.4 ), friction velocity, and boundary layer height (taken equal to the domain height), respectively, in the RNG k − ε turbulence closure scheme under the assumption of local turbulence isotropy. At the top, lateral, and outlet surfaces, zero18

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Table 2 Summary of key configurations for the QUIC-URB, RANS, and LES simulations. Model

Courant number

Integration time (sec)

Near-wall treatment

Convergence criteria Mass-conserved velocity field with 10−3 threshold No significant change in flow topological features Same as above

QUIC-URB

–

–

Rooftop, sidewall and wake algorithms [34,35]

RANS LES

0.9 0.4

1800 1800

Turbulent wall function [58] Turbulence grid and surface roughness elements [29]

Table 3 Setup configurations for the QUIC-URB simulations.

Table 5 Setup configurations for the LES simulations.

Model/parameter

Type/value

Model/parameter

Type/value

Street-canyon algorithm Blended region algorithm Rooftop algorithm Upwind-cavity algorithm Wake algorithm Rooftop surface roughness length (z o ) Building sidewall recirculation Grid size Inlet parameters

Rockle with Fackrell cavity length [34,35] On [34,35] Recirculation [34,35] High-rise MVP model [34,35] Area scaled 0.1

Subgrid-scale turbulence model Inflow parameters Domain size (Lx × Wy × Hz )

Dynamic Smagorinsky uref = 4.32 m.s-1

On [29] 3.2 m uref = 4.32 m.s-1 , z ref = 96 m, a = 0.21

Domain size (Lx × Wy × Hz )

18L × (10 + W / S ) L × 7.5L

2.4. Performance metrics To quantify the accuracy of the CFD methods in the prediction of flow topological features, we use the mean relative error (εR ) defined as:

ε¯R = Table 4 Setup configurations for the RANS simulations. Model/parameter

Type/value

Turbulence model Wall function Grid size (sx × sy × sz ) Inlet parameters

RNG k − ε [58] Turbulent wall function [58] 3.2 m × 3.2 m × 3.2 m uref = 4.32 m.s-1, z ref = 96 m, a = 0.21, Cμ = 0.0845

Domain size (Lx × Wy × Hz )

18L × (10 + W / S ) L × 7.5L

32L × (10 + W / S ) L × 7.5L

1 N

N

∑ i=1

num

⎛⎜ |x i ⎝

2

− x iexp | ⎞

x iexp

num

|z + ⎜⎛ i ⎠ ⎝

⎟

2

− z iexp | ⎞

z iexp

⎟

× 100

⎠

(3)

where ε¯R is the mean relative error in the prediction of each flow topological feature's location by different CFD methods with respect to the experimental data, N is the total number of test cases simulated by each method (i.e., N = 8 for QUIC-URB and RANS and N = 4 for LES), i indexes the test cases, x inum and z inum are the simulated x and z locations of the flow topology features for the ith test case, and x iexp and z iexp are the experimental x and z locations visually extracted from the streamline patterns observed in the PIV datasets following [29]. To quantify the trade offs of the different CFD methodologies for urban applications we apply two commonly used metrics: accuracy (A) and efficiency (E) with two new metrics that estimate the resource dependent computational cost (C) and trade-off between accuracy and efficiency (TM). These metrics are summarized in Table 6. The accuracy (A) of the approach is based on the local mean relative error (ε¯R ) (Eq. (3)) in the prediction of the physical location of the topological feature of interest. A is scaled between 0 and 0.9 with A = 0 indicating the failure of the model in predicting the target or ε¯R ≥ 100%, A = 0.3 (low) for 66 % ≤ ε¯R < 100 %, A = 0.6 (moderate) for 33 % ≤ ε¯R < 66 % , and A = 0.9 (high) for ε¯R < 33 %. If quantitative results are not available, accuracy is determined based on the model's ability to predict the feature. For instance, for the secondary vortex if a model captures the feature for all test cases, then A = 0.9 ; if it captures the features for more than half of the test cases, then A = 0.6; if it captures the feature for less than half of the test cases, then A = 0.3 ; and if it completely fails to capture the feature, then A = 0 . This approximate scaling has two

gradient, symmetry, and zero static pressure are applied, respectively. All simulations where run for a total physical duration of 3600 s with the mean velocity field integrated in time for the last 1800 s. Longer integration times and or spin-up times did not significantly change the flow topological features presented in Sec. 3. Table 4 provides specific configuration details for the RNG k − ε computations.

2.3.3. LES The grid size in all directions is 2 m for consistency with the stepdown street canyon simulations of Hayati et al. [29] which will be used in Sec. 3.4. For spatial and temporal discretization, second-order central difference and first-order Euler schemes were used, respectively. Resolution tests at coarser and finer grid sizes (3.2 m and 1 m) did not significantly change the flow patterns and topological features in the numerical result. The inlet profiles are generated using the grid-turbulence inflow method as described in Ref. [29]. In that method a rigid grid consisting of spanwise and vertical rectangular bars is placed at the inlet of the computational domain. As the flow passes the grid, the desired turbulence intensity is achieved at the downstream of the turbulence grid. For more details see Ref. [29]. The distances to inlet, lateral and outlet boundaries from the buildings are 15L , 5L , and 17L , respectively and the boundary conditions for outlet, lateral, top, and wall surfaces are local one-dimensional inviscid (LODI) [60], symmetry, zero-gradient, and no-slip, respectively. The turbulence model, reference velocity, and domain size are given in Table 5. The MPMICE rigid structure option is used for all building and roughness points and the mean velocity field is integrated over the last 1800 s of each 3600 s simulation matching the RANS simulations. Longer integration times did not significantly change the flow topological features in the numerical results.

Table 6 Non-dimensional metrics for the assessment of the performance of different CFD methods for flow topological features in street canyons. Metrics

Definition

Scale

Assumption

Accuracy (A)

Method's relative error for a target

0–0.9

A = 0 : 100 % ≤ ε¯R or Failure A = 0.3 : 66 % ≤ ε¯R < 100 % A = 0.6 : 33 % ≤ ε¯R < 66 % A = 0.9 : ε¯R < 33 %

0.3–1

⎧C = 0.3: QUIC−URB α = 0.07 C = 0.6:RANS ⎨ ⎩C = 1.0:LES – –

Computational cost (C) Efficiency (E) Trade-off Metric (TM )

19

C=

(

τ max (τ )

)

α

A / C × min (C )

A × E × max (C )−1

0–0.9 0–0.9

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Table 7 Computational cost for each testcase simulation. Method

τ (hours)

Clock time

QUIC-URB RANS LES

0.0014 20 28,800

5 seconds 5 hours 2.5 days

advantages, first it provides a consistent methodology to include both quantitative (using ε¯R ) and qualitative model assessments and second it removes the impact of small model changes (e.g., turbulence model, grid resolution) that have minimal impact on ε¯R in the calculation of A. The efficiency (E) is defined as the ratio of the model's accuracy to its computational cost

E=

A min (C ) C

(4)

and C is defined as

τ ⎞ C=⎛ max (τ ) ⎠ ⎝ ⎜

α

⎟

(5)

where τ is the computational cost of each simulation in CPU hours (Table 7). α is a weight constraint with a range of 0–1 with 0 indicating no constraint on computational resources and 1 indicating fully constrained computational resources. In most of our analysis we chose α = 0.07 corresponding to minimal computational constraints in terms of model efficiency and resource availability. A discussion of the impact of the choice of α is included in Sec. 3.4.2. For our primary choice of α, 0.3 ≤ C ≤ 1, with C = 0.3 indicating a “cheap” simulation, C = 0.6 indicating a moderate cost simulation, and C = 1 indicating an expensive simulation for simulations completed within ≈ seconds, hours, and days using QUIC-URB, RANS, and LES models, respectively. min (C ) = 0.3 is used to bound the metric between 0.3 and 1. Our last metric is a trade-off metric (TM ) that represents the equally weighted trade-off between accuracy and efficiency

TM =

min (C ) A×E A2 = × max (C ) C max (C )

Fig. 2. Contours of the normalized mean vertical velocity at the vertical plane for a step-up street canyon with short upwind building and wide buildings Hd / Hu ≈ 3, W / S ≈ 1 using different CFD methods (a) QUIC-URB, (b) RANS, (c) LES, with (d) Wind-tunnel data - Flow topological features I Primary vortex core, II: Secondary vortex core, III: Stagnation point, IV: Rooftop recirculation zone.

performance of the CFD methods. Three important aspects of the methods are explored including the accuracy, efficiency, and the tradeoff between accuracy and efficiency in Sec. 3.4 and finally recommendations are provided on the usage of the CFD methods to capture various flow regimes and topological features in street canyons.

3.1. Vertical plane ( x − z plane)

(6)

where TM ranges from 0 to 0.9 and max (C ) = 1. Depending on the goal of the simulation, i.e., flow regime and topological feature, a CFD model with the best combination of accuracy and efficiency will score the highest on this metric with a maximum score of 0.9.

We begin exploring the simulations by examining the in-canyon mean vertical velocity (w¯ ) and streamline patterns on a vertical plane for the case of two narrow buildings where the upwind building is significantly shorter than the downwind building (Hd / Hu ≈ 3, W / S ≈ 1). The experimental data (Fig. 2d) indicate that the flow is in a non-classical skimming regime, where flow partially interacts with the street-canyon cavity in the in-canyon region, resulting in strong vertical motions, and partially separates from the rooftop of the upwind building [33]. Primary and secondary vortices occur in the middle of the canyon, with strong recirculation patterns over the downwind building rooftop and a stagnation point at the top of the canyon. In comparison with the experimental data, the QUIC-URB model strongly underpredicts the negative vertical motions in the in-canyon region (Fig. 2a), with the primary vortex core at the top of the upwind building but correctly predicts the rooftop patterns over both buildings. The defects in the QUIC-URB results indicate that these features are not associated with fluid kinematics and that the current street-canyon parameterization does not adequately transport momentum deep into the street canyon. The RANS model correctly captures the location of the primary vortex core but the rooftop flow patterns are not correctly predicted over either of the upwind or downwind buildings (Fig. 2b). The LES model captures the in-canyon vertical motions and rooftop recirculation patterns but it inaccurately predicts the primary vortex as attached to the upwind building. The defects in the LES results may be associated with the momentum exchange model near the buildings which assumes a linear stress rate-of-strain relationship (i.e., linear lawof-the-wall). All three models correctly capture the stagnation point but

3. Results and discussion Our analysis focuses on the evaluation of the street-canyon mean velocity fields from the three different CFD methods, the comparison of these velocity fields with reference experimental data, and an examination of the pros and cons of each method. We only consider the mean velocity field in our studies since the flow topological features consistently occur in the mean field but not in instantaneous velocity fields. Direct comparisons with experimental data are used to investigate the mean velocity field in step-up street canyons on a vertical plane at the middle of the canyon (i.e., x − z plane at y / S = 0 in Sec. 3.1), while on a horizontal plane when experimental data is not available inter-comparisons are used at the mid-height of the upwind building (i.e., x − y plane at z / S ≈ 0.5Hu in Sec. 3.2). Three different test cases are discussed, including a short upwind building with narrow and wide buildings (Hd / Hu ≈ 3, W / S ≈ 1, 3), and a tall upwind building with wide buildings (Hd / Hu ≈ 1.67 , W / S ≈ 3). The procedure for flow topology analysis in Sec. 3.3 is similar to that explained in Ref. [29] where different topological features are identified from the mean velocity contour plots and then tracked across building configuration cases. These new results are then combined with our prior evaluation of the models in step-down street canyons to evaluate the overall 20

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Fig. 3. Contours of the normalized mean vertical velocity at the vertical plane for a step-up street canyon with short upwind building and wide buildings Hd / Hu ≈ 3, W / S ≈ 3 using different CFD methods (a) QUIC-URB (b) RANS (c) LES, with (d) Wind-tunnel data.

Fig. 4. Contours of the normalized mean vertical velocity at the vertical plane for a step-up street canyon with short upwind building and wide buildings Hd / Hu ≈ 1.67 , W / S ≈ 3 using different CFD methods (a) QUIC-URB, (b) RANS, and (c) LES, with (d) Wind-tunnel data.

fail to capture the secondary vortex observed in the PIV data. For wider buildings (W / S ≈ 3) with a short upwind building (Hd / Hu ≈ 3), a similar flow regime occurs in the canyon but with stronger vertical motions, larger primary and secondary vortices, and a larger rooftop recirculation zone over the downwind building (Fig. 3d). QUIC-URB underestimates the vertical motions and fails to capture the primary vortex (Fig. 3a). This may be associated with incorrect parameterization of the street-canyon cavity for this case. The RANS model weakly resolves the rooftop recirculation over both upwind and downwind buildings (Fig. 3b) while both the QUIC-URB and LES models exaggerate these features to an extent where they create nonphysical rooftop structures over the upwind building (Fig. 3a, c). In contrast to QUIC-URB, both the RANS and LES models reproduce the intensification of vertical motions with wider buildings (cf., Figs. 2 and 3) with the caveat that the LES model clearly exaggerates the intensification. By increasing the height of the upwind building to Hd / Hu ≈ 1.67 while keeping W / S ≈ 3, a dominant counter-rotating vortex pair develops in the upper left-hand and lower right-hand corners of the canyon and a strong rooftop recirculation zone occurs over the upwind building as a result of the interaction of the elevated left-hand vortex with the upstream flow (Fig. 4d). Overall, the interaction of the rooftop and lateral flow with the in-canyon cavity results in a significantly more complex in-canyon flow pattern. RANS is the only model that predicts the vortex pair but only weakly captures the rooftop recirculation over the upwind building (Fig. 4b). Both the QUIC-URB and LES models incorrectly predict a single in-canyon vortex, but they do successfully capture the rooftop recirculation patterns (Fig. 4a–c). We can summarize the models' performances as follows. All three successfully predict the stagnation point while they differ significantly in the prediction of rooftop recirculations and in-canyon vortices. Both the RANS and LES models correctly capture the primary vortex while for the secondary vortices, surprisingly only RANS captures the feature for a number of cases. In contrast, RANS fails in predicting the rooftop recirculation patterns while both QUIC-URB and LES successfully capture them. Increasing the upwind building height or the buildings' widths, intensifies the strength of the secondary vortex in the canyons.

3.2. Horizontal plane ( x − y plane) Examination of the mean flow field in a vertical plane at the canyoncenterline is instructive because it allows for direct comparisons to experimental data and for clear identification of prominent topological flow features. To understand how these features link to lateral-flow interactions into and out of the canyon, in this section we explore horizontal planes at the mid-height of the upwind building (z / S ≈ 0.5Hu ). Since experimental data are not available on horizontal planes, only comparisons among the three CFD methodologies are made. To begin, we start with the case of two narrow buildings where the upwind building is short (i.e., Hd / Hu ≈ 3, W / S ≈ 1). In the LES velocity field, two counter-rotating vortex pairs, one inside the canyon, and one in the wake of the downwind building can be identified (Fig. 5c). These features are an indication of strong lateral flow interactions between the fluid inside and outside of the canyon. In contrast, the RANS model velocity field has only a single counter-rotating vortex pair in the wake of the downwind building with significantly thinner sidewall boundary layers (Fig. 5b). The QUIC-URB model has a larger vortex pair zone inside the canyon and in the wake of the downwind building compared to the other two models (Fig. 5a). In total, more mean momentum is transported into the canyon in the LES results (Fig. 5c) compared to the RANS and QUIC-URB results (Fig. 5b, a). If the building widths are increased to W / S ≈ 3 while the upwind building height is kept short (Hd / Hu ≈ 3), the LES model predicts the same two vortex pairs as discussed for the narrow buildings but with a much larger wake region downwind of the downwind building with the vortex cores shifted to x / S ≈ 4.5. This is consistent with wind-tunnel results for isolated buildings with increasing building width [61] and QUIC-URB's isolated building parameterization [36]. Additionally, the wall-normal vortex pair in the canyon remains attached to the lateralcanyon edges where it interacts with the upwind-building sidewall lateral boundary layer (Fig. 6c) reducing the lateral flow into the canyon-cavity center. The reduction of flow into the canyon center also explains the larger vortex and rooftop recirculation zones observed from the vertical plane analysis in Sec. 3.1 (Figs. 3 and 4) where enhanced flow is forced into the canyon from the freestream below the 21

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Fig. 5. Step-up street canyon with short upwind building and narrow buildings Hd / Hu ≈ 3, W / S = 1 using different CFD methods (a) QUIC-URB, (b) RANS, and (c) LES.

stagnation point. This flow pushes laterally outward fixing the location of the wall-normal vorticies at the lateral canyon edges. The other two models also have decreased lateral penetration of flow from outside the canyon at the canyon lateral edges but with some important differences. The RANS model does not produce wall-normal vorticies at the canyon edges and as a result, lateral flow is almost entirely out of the canyon. The RANS model also differs from the other models in its representation of the wake-zone downwind of the downwind building generating a significantly wider wake zone with the counter-rotating wall-normal vortex pair vortex cores moving to x / S ≈ 5.5 (Fig. 6b). The QUIC-URB velocity field on the horizontal plane has flow features that are somewhat closer to the LES velocity field than the RANS one (Fig. 6a). It produces a similar wake zone to the LES model downwind of the downwind building but is slightly narrower in

horizontal extent and has weaker in magnitude vertical velocity deviations. Within the canyon, QUIC-URB exhibits similar coupling between vertical flow down into the canyon and lateral flow in and out of the canyon as the other two models with the primary difference that because of its generally weaker vertical velocity, interactions are damped. The horizontal plane results can be summarized as follows. For narrow buildings, the models predict different numbers of vortex pairs. Specifically, QUIC-URB and LES capture two, one inside the canyon and the other in the wake region, but RANS predicts only the one pair in the wake region. When the buildings’ widths are increased, the interaction of the lateral flow with the canyon cavity is modified in all three models by vertical flow into the canyon center from the freestream above the upwind building. This vertical flow intrusion decreases lateral flow into the canyon and enhances lateral flow out of the canyon. The effect is

Fig. 6. Step-up street canyon with short upwind building and wide buildings Hd / Hu ≈ 3, W / S = 3 using different CFD methods (a) QUIC-URB, (b) RANS, and (c) LES. 22

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Fig. 7. Stagnation point and primary vortex core position for step-up street canyons with different building width-to-canyon length aspect ratios (a) W / S ≈ 1.0 (narrow buildings), (b) W / S ≈ 2.0 (mid-width buildings), (c): W / S ≈ 3.0 (wide buildings), and (d): W / S ≈ 4.0 (very wide buildings) with downwind-to-upwind building height ratio decreasing from Hd / Hu ≈ 3 to.Hd / Hu ≈ 1.67 .

results increases with εR ≈ 85, 6.6, and 30.5 % for QUIC-URB, RANS, and LES, respectively, quantifying the surprisingly good performance of the RANS model.

strongest in the RANS model with the result that the horizontal extent of the wake region (containing the counter rotating vortex cores) downwind of the buildings is the widest and is shifted up to one building length further downwind than the other two models.

3.4. Synthesis of model performance in non-uniform street canyons 3.3. Flow topological features In section 3.3 we quantified the accuracy of each method in reproducing topological features in step-up street canyons. We can combine this analysis with previous work in step-down street canyons [29] using the metrics from Sec. 2.4 and Table 6.

When using CFD as a design tool, it can be just as important to get the general flow features right as it is to have a low level of absolute error. In particular, it is of great importance to understand how different methods respond to changes in the flow geometry and how this matches experimental data. For our step-up street canyon simulations, this can be accomplished by examining how flow topological features vary with changes in street-canyon geometry i.e., downwind-to-upwind building height ratios (Hd / Hu ) and building width-to-canyon length aspect ratios (W / S ). The variation in the two most prominent flow topological features in the vertical plane, the stagnation point and the primary vortex core, for various building widths covering the range 1 ≤ W / S ≤ 4 is illustrated in Fig. 7. Note that the LES results are only available for two aspect ratios, W / S ≈ 1 and W / S ≈ 3. The experimental data indicate that the stagnation point and vortex core both shift upward as the upwind building height increases (smaller Hd / Hu ) regardless of the building width (Fig. 7a). All three CFD models correctly predict the dynamics of the stagnation point, while for the vortex core, QUIC-URB predicts the wrong trend for the feature, indicating a fundamental defect in the model rather than a tuning issue for W / S ≥ 2 (Fig. 7b–d). The RANS results have a higher level of agreement with the experimental results than the LES model, which overestimates the vertical location of the vortex core for wide buildings (W / S ≈ 3) (Fig. 7c). Error quantification for the step-up street canyon velocity fields closely tracks the general conclusions drawn from Fig. 7 and indicates that the QUIC-URB, RANS, and LES models all accurately capture the location of the stagnation point with εR ≈ 4.6, 2.6, and 2.1 %, respectively. However, for the vortex core, the discrepancy in the numerical

3.5. Flow regimes for non-uniform street canyons Three major street-canyon flow regimes exist in non-uniform street canyons, namely non-classical skimming, wake-dominated, and deepcanyon skimming which occur in step-up, wide step-down, and narrow step-down street canyons, respectively (Fig. 8) (see Sec. 3.1 [29], and [62] for a detailed description of the flow regimes). The non-classical skimming flow regime in non-uniform street canyons is a more complex version of the classical skimming flow regime that occurs in uniform street canyons and has been extensively studied with QUIC-URB, RANS, and LES [36,63–65]. In the non-classical flow regime, in addition to classical street canyon vortices inside the canyon, other flow patterns exist including a stagnation point and rootftop recirculation zones. The wake-dominated regime's unique defining characteristic is the interaction of the taller up-wind building with the shorter downwind building resulting in the formation of an elevated saddle point where the velocity field is in equilibrium. The deep-canyon skimming regime occurs when the interaction between the down-wind building and the up-wind building becomes strong enough to move the equilibrium point out of the canyon. 3.5.1. Model performance In the non-classical skimming flow regime (Fig. 8a), the RANS model has the best accuracy for the primary and secondary vorticies but 23

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RANS with QUIC-URB performing best on the reproduction of the saddle point, and RANS performing best for the reproduction of the primary vortex. For the deep-canyon skimming flow regime (Fig. 8c), QUIC-URB has the highest accuracy score and is the most efficient at predicting the primary features, resulting in it having the highest trade-off score for primary vortex predictions. RANS is by far the best option for predicting the secondary vortex (Fig. 11). The target-dependent trade-off score for the topological features examined in Figs. 9–11 is summarized in Table 8 for each CFD method. In general, if the goal is to capture the primary vortex for the nonclassical skimming and wake-dominated flow regimes, RANS offers the best combination of accuracy and efficiency while QUIC-URB has the superior combination for the deep-canyon skimming flow regime. LES is the only method that properly captures secondary vortices and separation points in the wake-dominated flow regime while in other flow regimes, RANS performs reasonably well for secondary vortex features. Across all regimes, primary flow-topological features including saddle and stagnation points, and rooftop recirculations are well-captured by QUIC-URB. Finally, to summarize the overall capability of the three CFD methods for different flow regimes we calculate the average of the methods’ trade-off metrics (TMO ) for different flow-topological features in street canyons (Fig. 12). QUIC-URB has the best overall trade-off score for the non-classical skimming and wake dominated flow regimes with QUIC-URB doubling the RANS score (Fig. 12). QUIC-URB and RANS have equally high TMO in the deep-canyon skimming flow regime, and QUIC-URB and LES have about equal scores in the wakedominated flow regime. The impact of our choice of α = 0.07 is also illustrated in Fig. 12. A few interesting observations can be made from the figure. First, in the limit of very small α values (i.e., no computational constraints) only in the deep-canyon skimming regime is LES clearly the superior methodology. This is consistent with the surprisingly strong performance of the RANS method in predicting the vortex core and QUIC-URB's good performance in predicting the stagnation point (Fig. 7). Second, in the non-classical skimming flow regime the RANS method is surprisingly the superior method as α approaches zero. The RANS model's ability to predict the secondary vortex for this case, and LES's failure, is the primary contributing factor to this. Last, no matter the flow regime for α > 0.07 QUIC-URB has the best overall trade-off score with values

Fig. 8. Schematic of three major flow regimes occurring in street canyons (a) non-classical skimming, (b) wake-dominated, and (c) deep-canyon skimming all from LES results with data used in (b) and (c) from the simulations of Hayati et al. [29].

only weakly predicts the rooftop recirculation (i.e., it fails) across all the step-up test cases with different building widths (Fig. 9a). QUICURB is the most efficient model in predicting the stagnation point and rooftop recirculation (Fig. 9b) and thus, based on the trade-off metric, it is the best option for capturing the stagnation point and rooftop recirculation. The usage of LES is not necessary for predicting any of the flow topological features in the non-classical regime (Fig. 9c). For the wake-dominated flow regime (Fig. 8b), LES is the only method that predicts the secondary flow features, including the secondary vortex and the separation point. Therefore, despite its low efficiency and extremely-high computational costs (Fig. 10a and b), LES is the only applicable model for secondary-flow features in this regime. The other topological features are captured well by QUIC-URB and

Fig. 9. Performance of different CFD methods for specified targets in the non-classical skimming flow regime occurring in step-up street canyons (a) accuracy, (b) efficiency, and (c) accuracy vs. efficiency trade off. Results are compiled from eight QUIC-URB and RANS simulation runs (Hd / Hu≈ 1.67 and 3 with W / S ≈1, 2, 3, and 4) and four LES runs (Hd / Hu≈ 1.67 and 3 with W / S ≈1 and 3). 24

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Fig. 10. Performance of different CFD methods for specified targets in the wake-dominated flow regime occurring in wide step-down street canyons (a) accuracy, (b) efficiency, (c) accuracy vs. efficiency trade off. Results are compiled from eight QUIC-URB and RANS simulation runs (Hd / Hu≈ 0.08–0.69 with W / S ≈ 0.4) and five LES runs (Hd / Hu≈ 0–0.69 with W / S ≈ 0.4). Table 8 Target-dependent accuracy vs. efficiency trade off of different CFD methods for major flow topological features in street canyons. Flow topological feature

Best trade-off metric score

Considerations

Primary vortex

RANS

LES

For non-classical skimming/wakedominated flow regimes For deep-canyon skimming flow regimes . For wake-dominated flow regime For deep-canyon/non-classical skimming flow regimes –

QUIC-URB

–

QUIC-URB Secondary vortex LES RANS Separation point Stagnation point Saddle point Rooftop recirculation

building. We then combined these results with the results of [29], which focused on step-down (a high-rise building followed by a low-rise one) street canyons, to provide an overall, generalized evaluation for 3D street canyons. We evaluated model performance based on the following metrics: accuracy (quantified agreement with experimental data), efficiency (accuracy with respect to resource dependent computational cost), and the trade off between accuracy and efficiency (appropriateness for a specified target). Finally, we used our target-dependent trade-off metric to determine which model had the best combination of accuracy and efficiency for different flow-topological features in street-canyon flows. The interrogated CFD methods include a fast-response mass-consistent model with empirical parametrizations (QUIC-URB), a Reynoldsaveraged Navier-Stokes (RANS) model with a two-equation turbulence closure model (RNG k − ε ), and an instantaneous filtered Navier-Stokes modeling approach (LES). For step-up street canyons, eight different test cases were examined by varying the downwind-to-upwind building height ratio (Hd / Hu ) and the building-width to canyon-length aspect ratio (W / S ), resulting in street canyons with narrow/wide buildings and a short/tall upwind building. Overall, our anaylsis of step-up street canyon flow topological features and the dynamics of these futures with changes in building configuration indicates that all three models capture the primary flow features (stagnation point and primary vortex) with reasonable accuracy, while none of them correctly predict secondary flow features,

Fig. 11. Performance of different CFD methods for specified targets in deepcanyon skimming flow regime occurring in narrow step-down street canyons (a) accuracy, (b) efficiency, (c) accuracy vs. efficiency trade off. Results are compiled from eight QUIC-URB and RANS simulation runs (Hd / Hu≈ 0.08–0.69 with W / S ≈ 1) and five LES runs (Hd / Hu≈ 0–0.69 with W / S ≈ 1).

larger than 0.07 quickly resulting in a significant TMO gap between QUIC-URB and the other two methods. This is an indication of the superiority of methodologies like QUIC-URB when computational efficiency is critical.

4. Conclusion We investigated the ability of three different CFD methods to predict complex mean-flow topological features in non-uniform street canyons. The simulations were compared against each other and evaluated with high-spatial-resolution 2D wind-tunnel data. First, we focused on stepup street canyons, where a low-rise building is followed by a high-rise 25

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Fig. 12. Overall accuracy vs. efficiency trade off of different CFD methods for non-classical skimming, wake-dominated, and deep-canyon skimming flow regimes in non-uniform street canyons (a) summary for α = 0.07 , (b) non-classical skimming regime as a function of α, (c) wake-dominated regime as a function of α, and (d) deep-canyon skimming regime as a function of α.

momentum exchange between building elements and the fluid, and code optimizations are primary targets for improvement. Overall, improving these approaches will enhance the utility of CFD for urban design applications and for the current CFD codes that use the studied methodologies. Our results provide guidance on the application of these tools toward decision-making strategies in urban design and city planning.

including the secondary vortices and rooftop patterns across all the test cases. When we synthesize these results with those from step-down street canyons presented in Hayati et al. [29], we can identify three major street-canyon flow regimes including non-classical skimming, wake-dominated, and deep-canyon skimming occurring in step-up, wide step-down, and narrow step-down street canyons, respectively. Despite the overall high accuracy of LES for street-canyon flows, our results suggest that when efficiency and accuracy are equally weighted it may not always be the best choice. Because of LES's relatively low efficiency compared to RANS and fast-response models (e.g., QUICURB), its usage is only necessary when capturing secondary-flow structures, including secondary vortices and separation points in the wake-dominated flow regime. For the other flow regimes or when only the primary features are of interest in the wake-dominated flow regime, QUIC-URB and RANS models do an adequate job of efficiently capturing both primary and secondary flow features as measured by our trade-off metric. Between these two methods, RANS performs best at representing the primary vortices and QUIC-URB has the best performance for rooftop recirculation, stagnation, and saddle points. In summary, QUIC-URB has the best overall performance for the nonclassical skimming flow regime, QUIC-URB and RANS perform equally for the deep-canyon skimming flow regime, and QUIC-URB and LES perform almost equally for the wake-dominated flow regime. Future studies are required to expand the applicability of various CFD methods. For example, quantitative comparisons were not made for deep-canyons with equal-height buildings even though appropriate data for these cases can be found in the literature [66,67]. In addition, more complex street-canyon configurations, such as rotated buildings, non-uniform building widths, non-uniform building arrays, thermal effects, and full-scale cities should be investigated. Accomplishing this will require new high-quality experimental data for model validation and subsequent model improvements. The results from this study can be used to improve the examined models for non-uniform street canyon flows. For QUIC-URB, new parametrizations are required to account for flow separation, secondary-flow features, and sidewall flow interactions with the canyon cavity. For the tested RANS model, the reproduction of secondary vorticies, roof-top recirculation zones, and canyon separation points in the non-classical skimming and wake-dominated flow regimes would be beneficial. For the tested LES model, the surface boundary conditions,

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