MAE 593 Applied Project Report:

Investigation on the sensibility of simulation of wind energy over roof of building in urban area

Tianze Peng

Abstract Wind energy is the fastest growing renewable energy source through past decades. Different

from the largescale wind energy, urban wind energy is innovative, environmentally friendly, but under development. The feasibility of integrating wind turbine to the buildings provides high potential for urban wind energy. Previous CFD research shows the possibility of yielding wind energy over the roof, but the fidelity of the results by various CFD package is not demonstrated. This report will give two investigations for sensitivity of mesh resolutions and turbulent models respectively under the ANSYS Fluent 15.0. The results of the investigations show the prediction of the region of acceleration is fairly independent from the selection of turbulence model and from mesh resolution, but different turbulent models yield diverse flow patterns.

1. Introduction With increasing awareness on fossil-alternative energy among the world, wind energy

becomes the fasted growing form among all renewable energy sectors. It was reported by World Wind Energy Market Update 2015 that installations grew by 42% year-over-year in 2014 to 51.2 GW of wind power and cumulative installed capacity climbed to 372 GW [1]. Among different sources of wind energy, built-environment wind energy shows advantages and potentials for less transmission issues and high integration of utilities of building. In 2011, the cumulative installed capacity of small turbine (<100 kW) in the U.S has reached 198 MW, deploying 151,300 turbines [2]. The growing trend of utilization of built-environment wind energy also shows a great potential in reduction of carbon emission, with saving in the range of 0.75 – 2.2 Mt carbon dioxide by 2020[3].

In practice, small wind turbines can be mounted or integrated in the built environment. For mounted wind turbines, there are two major types, Horizontal Axis Wind Turbines (HAWTs) and Vertical Axis Wind Turbines (VAWTs). For the buildings with specific design, integrated wind turbines can meet the requirements to fit the appearance and demands of utility of the buildings.

However, wind energy in built environment involves several challenges that are different from utility-scale wind farm, including lower average wind speeds, roughness of terrains, and higher level of turbulence. From various researching projects by B. Wang [4], Lin Lu [5], and Islam Abohela [6], research shows the feasibility to utilize the energy over roof of buildings is solid, because that disturbed flows over the roof can locally increase wind speeds, which increases the energy yield in cubic with velocity where the relation is derived from Bernoulli Equation. In addition, Klara Bezalcova [7], et al, claims the wind velocity in urban area increases with increasing height. This shows to capture more energy requires adequate height to reach the

optimal velocity zone. Also, this indicates the roof of building may be a preferable place to mount turbines and utilize wind energy.

In research aforementioned [4][5][6], to capture and investigate the feasibility of wind energy on top of the roof, the Computational Fluid Dynamics (CFD) simulation can be a good approach to model wind flows over buildings, and give guidance for the location and the design of wind turbines. For CFD simulation, meshing and turbulence modeling are the two most significant issues, which impacts the quality and reliability of the simulation. For most of recent research on urban wind flows, like Lu’s and Abohela’s research, ANSYS Fluent was used since its developed numerical solver and highly integrated tools for meshing and post-CFD. Historically, ANSYS is more preferred to be used in the application with domain in human scale with small size of mesh that resolves the most of details of flows. However, due to large domain involved in urban wind characterization, the domain always has the longitudinal dimension scales from 0.1 km to hundreds of km.

Widely used in ANSYS Fluent, Reynolds Averaged Navier-Stokes (RANS) models is a compromised model with ensemble-average form of the Navier-Stokes equations and specific turbulence modeling as the closure to the averaged equations. So in RANS model, the turbulence models and mesh resolutions are competing factors, where generally model with finer mesh structure will has less dependence on turbulence modelling, vice versa.

However, since in urban wind energy modelling, the domain size is much larger than common geometry dealt in Fluent. Fine meshing will also introduce huge running time for simulation, much beyond the capacity of general workstation or server. Thus, the efficient way in this series simulations is to generate coarser mesh in the ambient surrounding with refined mesh near the building.

Though this compromised approach has been adopted in many researching projects, the question that whether the results is fairly independent from the meshing resolution is still left opened. Actually, only a few research projects were performed to compare the sensitivity of the results based on perturbation on meshing resolution.

Similarly, for turbulence modeling, RANS models compose with a series of models that are based on time-averaging of the equations [8]. Among several models, claimed by P. L. Davis’s research [9] with similar geometry, realizable k-ε model is more preferred. However, it is hard for a specific turbulence model or a method of solver to guarantee stability, accuracy, or convergence, when solving different non-linear partial differential equations. Therefore, the sensibility of turbulent model can be evaluated by applying different models on the same meshing file with same solution method.

This report attempts to address the investigation the sensibility of main factors affecting the installation location of roof mounted wind turbine by employing CFD simulation with two different inlet profiles (Uniform turbulence velocity profile, and turbulent shear flows) and two different heights of building.

2. Numerical modeling 2.1 Modelled Parameters

To test the response of different mesh resolution and turbulence model respectively, for each simulation, only one variable is perturbed. Since the project is aimed to investigate the specific of sensibility in ANSYS Fluent, the Fluent 15.0 was used to simulate all models.

There are two sets of geometry models, for the building with height of 6m and 12m respectively. To investigate how mesh resolution impacts the convergence of results, the general idea for simulation is based on Grid Confidence Index (GCI) analysis. In this project, the maximum stream-wise velocity on vertical axis of building is picked out for GCI analysis, and its relative height is also compared. For the same model, it is assigned at least three different meshes from relatively fine to relatively coarse. To investigate the impacts of different turbulence models, perturbations of turbulence model were applied on the same geometry models with intermediate meshing resolution, which has larger independence on meshing than the fine meshing, but lesser dependence on most coarse mesh.

2.2 Geometry settings Two sizes of buildings are used in this project. Define x, y, z directions present the

downstream direction, vertical direction, and lateral direction respectively. One building is a cubic building with edge of 6 meters, and the other one has height of 12 meters.

Table 1 Geometry Scenarios

Scenarios Building size ABL Domain dimension (x × y × z) Downstream Distance from inlet 6m 6m × 6m × 6m 126 m × 36 m × 18 m 21 m 12m 6m × 6m × 12m 100 m × 72 m × 36 m 10 m

In real world, the domain of urban area is approximately infinity if the effect from surrounding buildings is not considered. In this CFD simulation, the building has to be set in a limited domain like wind tunnel experiment. Limited atmospheric domain will introduce wall-bounded effect, where the lateral boundary effect cannot be discarded only if the vertical and lateral dimension is sufficiently large. As to vertical dimension of ABL domain, based on the guideline by J. Frank, et al [10], if we set the height of building as H, for small blockage 4H is recommended, and 10 H for large blockage. For lateral domain, it is reasonable to have 2H plus the building width [6] in order to prevent impacts from lateral boundary of the domain. For downstream direction, the distance depends on the type of boundary condition used at out flow [10]. In this project, only velocity profile above the building is considered, and there is no pressure difference between outlet and inlet. Thus the limit of downstream extension is considered around 8H. The dimensions are described in Table 1 and Figure 1.

Figure 1 Geometry of Scenarios of 6m (left) and 12m (right)

2.3 ABL profile In this project, the ABL profiles are set into two cases, and both case are steady wind

boundary conditions (SWBC). The first case is the uniform inlet flow. Since the acceleration is expected over top of the roof, if the model impose uniform inlet flow, the location with maximum stream-wise velocity must have maximum acceleration ratio, which is the parameter designed to be captured.

However, in reality, the profile is not uniform. Thus the second case imposes a power law profile, which is closer to the real atmospheric profile than the uniform profile. For this case, a study by Salim et al [11] provides a reasonable profile.

𝑢(𝑧) = 4.7 *

𝑧0.12.

/.0 (1)

where z is a dimensionless number as the relative height that can be expressed as

𝑧 =𝑦𝐻

(2)

The second case is plotted as the following figures, where the left one corresponds to geometry scenario A (6m), and scenario B (12m) for the right.

Figure 2 Inlet velocity profiles (Case 2), left: Scenario A (6m), right: B (12m)

For turbulent specification, the turbulent intensity is set as 10%, and turbulent viscosity ratio is set as 10.

2.4 Computational mesh Various resolutions were applied on two different geometry scenarios. For the 6m scenario,

the resolutions are set as 0.25m, 0.5m, 0.75m, and 1m of structured hexahedral mesh. For the 12m scenario, the resolutions are 0.4m, 0.6m, 0.8m, 1.0m, 1.2m, and 1.6m of structured hexahedral mesh. The independence study would be carried out among different resolutions.

2.5 Turbulence models and numerical solver To the independence of mesh resolution, realizable k-𝜖 model is selected to apply in the

simulation. To investigate the sensibility of turbulence model, realizable k-𝜖, standard k-𝜔 and transient SST were applied on geometry scenario of 12m building where mesh resolution is 0.75m.

The pressure velocity coupling scheme known as SIMPLEC (Semi Implicit Method for Pressure Linked Equations-Corrected) was used to solve the Navier-Stokes equations. Compared to SIMPLE algorithm, SIMPLEC algorithm omits terms that are less significant than those omitted in SIMPLE. Even though the algorithms of SIMPLE and SIMPLEC are closely related to each other, it is reported that SIMPLEC converges faster than SIMPLE with gains of 20-30% for many problems [12]

2.6 Validation Judgment of the iterative convergence is normally based on the residuals, which indicate how

far the present solution is away from the exact solution within each cell. The monitoring of the residuals is based on scaled norms of the residual vector for each conservation equation. [10] However, in this project, only the velocity filed on top of roof is highly concerned rather than the filed among the whole domain. Considering that the object of this project is to investigate the sensitivity on mesh resolution, scaled residual is a good reference but not an efficient way to judge the convergence of result. By putting forwards the criteria listed below, convergence for all simulations in this project is evaluated in a comprehensive way. Two criteria are introduced as the following:

To evaluate how much the impact of the building on the velocity acceleration, the acceleration ratio (‘AR’) is normalized by the velocity over top of the roof divided by the velocity in the same domain without building.

𝐴𝑅 =𝑈8𝑈8/

(3)

• The scaled residuals should be in the range of 10-4 – 10-6, except for the limit of continuity, which is set to 10-3.

• All scaled residuals are stable for at least 500 iterations, and the curves become sufficiently flat or periodically oscillating in a small range (±5% ).

Hence it requires additional simulations on the same domain for each geometry scenario and ABL inlet profile to get the value of𝑈8:. The location of AR also has great significance since it gives guidance for the locations where wind turbines should be applied above the roof. By plotting normalized 𝐴𝑅versus relative height𝑧, effect of acceleration can be evaluated qualitatively.

Moreover, meshing adaption was also applied to each geometry scenario with different ABL inlet cases. Based on the AR obtained in equation (3), the mesh was adapted by Iso-value method, with the limits from the velocity corresponding to around 90% of 𝐴𝑅;<8 to the velocity for𝐴𝑅=>?. After adaption, the results from additional simulation were compared with the non-building simulation at same mesh resolution, where interpolation was applied for those adapted grids.

Figure 3 Mesh patterns used in the project, (from left to right: uniform mesh), iso-value adapted mesh, and near-wall adjusted mesh

3 Result and discussion The project contains four groups of simulation, which are named as A, B, C, D, and E. The

object and detail of each group are listed in following table.

Table 2 Simulation Groups

Groups Building height Mesh Patterns Inlet Profile Perturbed variables # of simulations A 6m Uniform & adapted Uniform Mesh resolutions 7 B 6m Uniform & adapted Uniform Mesh resolutions 7 C 12m Uniform & adapted Power-law Mesh resolutions 11 D 12m Adapted Power-law Turbulent models 4 E 12m Near-wall adjusted Power-law Turbulent models 4

The results show a general flow pattern, which is universal among all simulations. However different setting of parameters will introduce the difference in detail. To investigate the sensitivity of mesh resolution, the change on flow patterns will be analyzed, and then acceleration ratio will be extracted from the simulation results and plotted to compare. Lastly, the GCI analysis will apply on each group. To investigate the sensitivity of the turbulent models, similar procedures were applied except for GCI analysis.

3.1 General flow patterns By plotting the contour of stream-wise velocity (Figure 4) and streamline (Figure 5) of the

geometry, the acceleration area over the roof can be observed. Also, from figures it can also

observed the negative stream wise velocity due to flow separation in the corner of the building as well as the top of the roof with small vortices.

Figure 4 Contour of stream wise velocity of building (Group A, mesh size 0.25m)

Figure 5 Streamlines along the central plane for the building (Group A, mesh size 0.25m)

The case with power-law inlet profile has similar flow patterns, but the max streamwise velocity cannot recognize the acceleration. The acceleration effects can be observed by the gradient change over the roof (Figure 6).

Figure 6 Contour of streamwise velocity of the building (Group C, mesh size 0.4m)

3.2 Sensitivity on mesh resolution Three groups in this project were designed to test the sensitivity of mesh resolution. The

experimental table is listed in Table 3. In each group, adaptation was applied on each case. The flow pattern can be captured from the contour by the shapes and colors. Minimum and Maximum streamwise velocity were also recorded since the main factor affecting the energy yield is the wind velocity. The acceleration ratio listed below will be plotted versus relative height (Figure 7).

Table 3 Comparison between cases with different mesh resolutions

Groups Mesh Size (m)

Number of Cells

Building Height (m) UDF Adapt 𝑈8;@A

(m/s) 𝑈8;<8 (m/s)

AR Location of AR

Group A A-1 0.25 5211648 6 No No -3.432799 8.202964 1.2658 1.46H A-2 0.5 651456 6 No No -2.8294 8.081512 1.2388 1.50H A-3 0.75 193024 6 No No -1.853224 7.678425 1.2119 1.50H A-4 1 81432 6 No No -1.363215 7.433276 1.1674 1.50H

AA-2 0.5 910071 6 No Yes -2.840872 8.14145 1.2704 1.42H AA-3 0.75 765736 6 No Yes -2.724612 8.081512 1.2550 1.44H AA-4 1 276368 6 No Yes -2.686313 8.006049 1.2431 1.50H

Group B B-1 0.25 5211648 6 Yes No -3.608252 12.58511 1.1615 1.25H B-2 0.5 651456 6 Yes No -1.744909 12.53137 1.1134 1.33H B-3 0.75 193024 6 Yes No -2.230961 12.48119 1.1099 1.31H B-4 1 81432 6 Yes No -1.850638 12.4273 1.0968 1.46H

BA-2 0.5 883555 6 Yes Yes -1.777277 12.53504 1.1226 1.46H BA-3 0.75 942696 6 Yes Yes -3.043004 12.51615 1.1707 1.38H BA-4 1 241130 6 Yes Yes -2.019854 12.4408 1.1088 1.5H

Group C C-1 0.4 4447575 12 Yes No -4.684166 15.31087 1.2097 1.20H C-2 0.6 1380460 12 Yes No -3.789419 15.2893 1.1707 1.20H C-3 0.8 608556 12 Yes No -3.19466 15.27042 1.1346 1.26H C-4 1 323460 12 Yes No -2.214256 15.25305 1.1366 1.24H C-5 1.2 196235 12 Yes No -1.439075 15.23704 1.1103 1.29H C-6 1.6 177559 12 Yes No -1.247517 15.22566 1.1081 1.30H

CA-2 0.6 2270650 12 Yes Yes -3.828673 15.28949 1.1938 1.20H CA-3 0.8 994781 12 Yes Yes -3.122889 15.27049 1.1580 1.20H CA-4 1 518942 12 Yes Yes -2.189661 15.25299 1.1403 1.24H CA-5 1.2 559451 12 Yes Yes -1.437327 15.23715 1.1492 1.19H CA-6 1.6 252876 12 Yes Yes -1.283438 15.22556 1.1431 1.20H

The results show that with the increase of mesh size, the minimum value of 𝑈8 increases and the maximum value decreases. For example, by plotting the contours of 𝑈8 for non-adapted cases in group A (Figure 7). In the region above the roof, finer mesh predicts the larger value of streamwise velocity as the color above the roof is deeper than the color of coarser cases. Also in the corner regions both upstream and downstream, finer mesh captures larger intensity of flow separation as the color in the corner is ‘bluer’ in finer cases.

Figure 7 Contours of Group A. (mesh size for a, b, c, and d is 0.25m, 0.5m, 0.75m, and 1m respectively)

The trends of the minimum and maximum velocities are plotted in the following figures. From these figures, coarser mesh has less magnitude of both maximum and minimum values. This result can be considered as one factor of sensitivity of the mesh resolution on the magnitude of streamwise velocity.

0 0.05 0.1 0.15 0.2

-3.5

-3

-2.5

-2

-1.5

-1

relative mesh size (dx/H)

min

imum

ux [m

/s]

Comparison of min ux along different resolutions (Group A)

0 0.05 0.1 0.15 0.27.4

7.5

7.6

7.7

7.8

7.9

8

8.1

8.2

8.3

8.4

relative mesh size (dx/H)

max

imum

ux [m

/s]

Comparison of max ux along different resolutions (Group A)

w/o adaptionw/ adaption

w/o adaptionw/ adpation

Figure 8 Comparison of minimum (left) and maximum (right) of streamwise velocity of Group C

In each group, simulations were also run on adapted meshes. So all simulations with adaption in mesh have the same agreement on the trends of maximum and minimum velocities. Moreover, for specific cases, the adapted mesh weakens the trends of decreasing effects of those values. It is reasonable since finer meshes are better to predict high velocity gradient. But this effect only applies on the cases of uniform free stream inlet profile, where the region maximum velocity is overlapped with the region of large velocity gradient.

In addition, considering the boundary effect of the domain, coarser mesh presents thicker boundary layer than finer mesh due to its larger size of each cell. As long as the domain is sufficiently large compared to the building, this effect is negligible.

Acceleration ratio is a significant criterion to evaluate sensitivity of mesh resolution. It tells the effect of acceleration by the building up to wind. The figures regarding to AR are plotted in Figure 9. The left column in following figures gives the relation of AR versus relative height (from roof to the half-height domain), and the right column shows the location and the value of maximum AR in each case.

0 0.05 0.1 0.15 0.2-4

-3.5

-3

-2.5

-2

-1.5

relative mesh size (dx/H)

min

imum

ux [m

/s]

Comparison of min ux along different resolutions (Group B)

0 0.05 0.1 0.15 0.212.42

12.44

12.46

12.48

12.5

12.52

12.54

12.56

12.58

12.6

relative mesh size (dx/H)

max

imum

ux [m

/s]

Comparison of max ux along different resolutions (Group B)

w/o adaptionw/ adpation

w/o adaptionw/ adpation

0.02 0.04 0.06 0.08 0.1 0.12 0.14-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

relative mesh size (dx/H)

min

imum

ux [m

/s]

Comparison of min ux along different resolutions (Group C)

0.02 0.04 0.06 0.08 0.1 0.12 0.1415.22

15.23

15.24

15.25

15.26

15.27

15.28

15.29

15.3

15.31

15.32

relative mesh size (dx/H)

max

imum

ux [m

/s]

Comparison of max ux along different resolutions (Group C)

w/o adaptionw/ adaption

w/o adaptionw/ adaption

Figure 9 Maximum acceleration ratio (AR) of each case

From Figure 9, the AR has unimodal curve. It boosts over the top roughly between 1H to 1.5H, and it is constant as 1 and universal in far high from the roof. Negative AR shows the

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.41

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3Group A (H=6m, Uniform Inlet Profile)

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

mesh size 0.25mmesh size 0.50mmesh size 0.75mmesh size 1.00mmesh size 0.5m adaptedmesh size 0.75m adaptedmesh size 1.00m adapted

1.16 1.18 1.2 1.22 1.24 1.26 1.281.41

1.42

1.43

1.44

1.45

1.46

1.47

1.48

1.49

1.5

1.51

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

Maximum AR of Group A (H=6m)

mesh size 0.25mmesh size 0.50mmesh size 0.75mmesh size 1.00mmesh size 0.50m adaptedmesh size 0.75m adaptedmesh size 1.00m adapted

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.41

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

Group B (H = 6, Power Law Inlet Profile)

mesh size 0.25mmesh size 0.50mmesh size 0.75mmesh size 1.00mmesh size 0.50m adaptedmesh size 0.75m adaptedmesh size 1.00m adpated

1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.181.3

1.35

1.4

1.45

1.5

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

Maximum AR of Group B (H=6m)

mesh size 0.25mmesh size 0.50mmesh size 0.75mmesh size 1.00mmesh size 0.50m adpmesh size 0.75m adpmesh size 1.00m adp

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.41

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

Group C (H = 12m, Power Law Inlet Profile)

mesh size 0.40mmesh size 0.60mmesh size 0.80mmesh size 1.00mmesh size 1.20mmesh size 1.60mmesh size 0.60m adaptedmesh size 0.80m adaptedmesh size 1.00m adaptedmesh size 1.20m adaptedmesh size 1.60m adapted

1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.241.18

1.2

1.22

1.24

1.26

1.28

1.3

1.32

Acceleration Ratio (Ux /Ux0)

Rela

tive

Heig

ht (y

/H)

Maximum AR of Group C (H=12m)

mesh size 0.40mmesh size 0.60mmesh size 0.80mmesh size 1.00mmesh size 1.20mmesh size 1.60mmesh size 0.60m adaptedmesh size 0.80m adpatedmesh size 1.00m adaptedmesh size 1.20m adaptedmesh size 1.60m adapted

separation of flow due to boundary effects. Generally speaking, the maximum values of AR in each group have a fairly acceptable agreement and the locations of maximum AR does not vary in a large scale.

In the right column, when plotting the maximum AR with its location, finer mesh gives higher AR while coarser mesh predicts smaller maximum values. For the location of maximum AR, qualitatively, coarser mesh predicts the height higher than finer mesh. This is because the discrete points are less when mesh size is large. Unless the maximum value locates right on the grid point, in coarser mesh, the detail of true max AR cannot be captured.

Different groups of simulation have different agreement in either location of max AR or the maximum value. Group A and group C, which have similar inlet profile, have AR value around 1.1 to 1.2, and both have good agreement on the location of maximum AR. But in group A, the location is universal for coarser cases, while in group C the location is universal among finer cases. For group A and group B, which share same geometry model but differ in inlet profile, the location and

For adaption of mesh, considering the effects that increasing resolution will give higher AR value as aforementioned, from the figures above, the adaption process does increase the AR value, but the effects of adaption is not efficient by increasing AR less than 3%. But with more grids near the roof, the lost detail in coarse mesh can be captured again. This is the reason for lower location of max AR for adapted cases.

Generally speaking, the results presents that different cases with various mesh resolution in each group has similar acceleration effect qualitatively. But the sensitivity of mesh resolution still exists. To quantify the independency of mesh resolution, GCI methods are yielded as following.

GCI analysis applies on uniform mesh where the mesh size of coarser mesh is double to the finer mesh. And the analysis is presented as following [13].

r=2 Determine order of convergence p

(where f is AR)

Richardson extrapolation with 2 finest grids to estimate solution at ∆𝑡 =0:

𝑓EFG/ ≅ 𝑓I +𝑓I − 𝑓L𝑟N − 1

Grid Convergence Index 𝐹PQR = 1.25

𝜖@T =𝑓@ − 𝑓T𝑓@

𝐺𝐶𝐼LI = 𝐹PQR|𝜖LI|𝑟N − 1

𝐺𝐶𝐼0L = 𝐹PQR|𝜖0L|𝑟N − 1

Therefore, the following table gives the results of GCI methods on AR for group A, B, and C. The table shows only group A has good fidelity which has error band within 2%, but the group B and C have negative GCI value, which means the tested cases are under oscillatory convergence [14].

Table 4 GCI analysis

Groups Building height 𝐺𝐶𝐼L0 𝐺𝐶𝐼IL A 6m 0.0438 0.0162 B 6m -0.0285 -0.0790 C 12m -0.0451 -0.1199

From GCI analysis, the convergence of results depends on different mesh and inlet flow profiles. Thus quantitatively, the results vary on different mesh resolution. From Figure 9, since all AR have universal trends in the same scenario, if we consider qualitatively and introduce the method of modification, the simulation could be independent from mesh resolution.

3.2 Investigation on sensitivity of turbulence models Two groups of simulation were designed to test sensitivity of turbulence models. For each

group, the turbulence models are selected as realizable k-𝜖, SST k-𝜔, transient SST, and standard k-𝜔, which are belong to Reynolds Averaged Navier-Stokes models. In this investigation, the geometry scenario is the 12m building case. Based on results from the previous part, the mesh of one group are chosen based on 0.8m adapted mesh, and the other group is based on 1.6m near-wall adjusted mesh. The information each simulation is listed in table 5.

Table 5 Comparison between cases with different turbulence models

Groups Mesh Size (m)

Number of Cells

Building Height (m)

Turbulent Models Adapt 𝑈8;@A

(m/s) 𝑈8;<8 (m/s)

AR Location of AR

Group D D-1 0.8 adp 630592 12 Realizable k-𝜖 Yes -4.078 15.275 1.1400 1.26H D-2 0.8 adp 630592 12 SST k-𝜔 Yes -3.402 15.279 1.1620 1.20H D-3 0.8 adp 630592 12 Transient SST Yes -3.486 15.280 1.1626 1.20H D-4 0.8 adp 630592 12 Standard k-𝜔 Yes -2.980 15.284 1.1521 1.20H

Group E E-1 1.0 adp 264090 12 Realizable k-𝜖 Yes -4.371 15.224 1.2484 1.18H E-2 1.0 adp 264090 12 SST k-𝜔 Yes -5.690 15.231 1.2987 1.18H E-3 1.0 adp 264090 12 Transient SST Yes -4.521 15.231 1.2504 1.20H E-4 1.0 adp 264090 12 Standard k-𝜔 Yes -4.178 15.232 1.2316 1.20H

From the above table, in each group, the results of 𝑈8YZ[ has better consistency than 𝑈8Y\]. Since the two groups here has non-uniform inlet profile, the consistency in maximum streamwise velocity cannot be evidence of either sensitivity or stability. Considering the negative velocity only occurs when there is boundary layer separation, it indicates different turbulent models have different characteristics in solving boundary layer separation. By plotting the contours (Figure 10 & 11) on the central plane for each simulation, the region over roof also has better consistency than the vortex regions in the corner.

Figure 10 Contours of Group D

(From left to right, first row: realizable k-𝜖, SST k-𝜔; second row: transient SST, and standard k-𝜔)

Figure 11 Contours of Group E

(From left to right, first row: realizable k-𝜖, SST k-𝜔; second row: transient SST, and standard k-𝜔)

In Figure 10 and 11, the blue regions that represent vortex regions vary a lot by different turbulent models. Since the large vortex lies in the wake, over-estimate or under-estimate of this region will affect the simulation with multiple buildings. However, above the roof, the results are almost consistent. By plotting the value and location of maximum AR, it shows the prediction does not change much by changing turbulent models.

Figure 12 Maximum acceleration ratio (AR) of each case in group D & E

In Figure 12, except for realizable k-𝜖, the locations of maximum AR for all cases are almost uniform. However, for the value of AR, the range of different results is much larger than the cases in Figure 9.

The results from this part can be addressed that various turbulence models gives different flow patterns as well as maximum AR values. However, the qualitative trend of wind acceleration as well as the locations of AR is consistent.

4 Conclusion From the investigation on mesh resolution, mesh resolution has impact on the detail of results

but independent from the qualitative and general trends of solution. Different mesh resolution have universal flow patterns and AR values far from the building in the domain, and have similar trends of max AR over the roof. The cases with refined mesh can boost the AR value due to coarser mesh.

1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.31.16

1.18

1.2

1.22

1.24

1.26

1.28

Acceleration Ratio (U/U0)

Rela

tive

Heig

ht (y

/H)

Maximum AR of Group D (mesh size 0.8m) and Group E (adjusted mesh)

D: Realizable k-eD: SST k-wD: Transient SSTD: Standard k-oemgaE: Realizable k-eE: SST k-wE: Transient SSTE: Standard k-oemgaC: Realizable k-e

From the investigation on turbulent models, even though, based on same mesh the location of AR are consistent, different models has diverse flow patterns especially in the vortex regions. Also, the diversity of maximum AR is more obvious than the cases of different mesh resolution.

In conclusion, both sensitivities of mesh resolution and turbulent models exist quantitatively. But considering more consistent the flow pattern and more concentrated distribution of max AR, qualitatively sensitivity on mesh resolution is less than turbulent models.

5 Recommendation Several recommendations can be addressed:

1) Since AR is shown to have universal value far away from the roof, the mesh can be coarse at the majority part of domain but fine near the building in order to increase the efficiency with the ability to predict the detail near the building.

2) Since all cases have similar curve of AR, it is possible to find a function to match the curve, and interpolate the AR values near the off in coarser mesh.

3) Selection of turbulent model is critical to yield correct flow pattern, and the suitable turbulent model need to be studied before conducting numerical simulation.

Reference [1] NAVIGANT Research, World Wind Energy Market Update 2015, 2015 https://www.navigantresearch.com/research/world-wind-energy-market-update-2015

[2] AWEA, 2011 U.S. Small Wind Turbine Market Report, 2011 http://awea.files.cms-plus.com/2011_AWEA_Small_Wind_Turbine_Market_Report.pdf

[3] A G Dutton, J A Halliday, M J Blanch, The Feasibility of Building-Mounted/Integrated Wind Turbines (BUWTs), Energy Research Unit, 2005

[4] B. Wang, L.D. Cot, L. Adolphe, S. Geoffroy, J.Morchain, Estimation of wind energy over roof of two perpendicular buildings, Energy and Buildings, 2014

[5] Lin Lu, Kan Yan Ip, Investigation on the feasibility and enhancement methods of wind power utilization in high-rise buildings of Hong Kong, Renewable & Sustainable Energy Reviews, 2007

[6] Islam Abohela, Nevven Hamza, Steven Dudek, Effect of roof shape, wind direction, building height and urban configuration on the energy yield and positioning of roof mounted wind turbines, Renewable Energy, 2012

[7] Klara Bezpalcova , Zbynek Janour , Viktor M. M. Prior , Cecilia Soriano and Michal Strizik, On wind velocity profiles over urban area, 8th Int. Conf. on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, 2003, http://www.harmo.org/conferences/Proceedings/_Sofia/publishedSections/Pages239to243.pdf

[8] ANSYS Turbulence Modeling, http://www.ansys.com/staticassets/ANSYS/staticassets/resourcelibrary/brochure/ANSYS-Turbulence.pdf, 2011

[9] P. L. Davis , A. T. Rinehimer , and M.Uddin, A Comparison of RANS-Based Turbulence Modeling for Flow over a Wall-Mounted Square Cylinder, Cd-adapco, 2012, http://www.cd-adapco.com/sites/default/files/technical_document/pdf/PRU_2012.pdf

[10] Jörg Franke, Antti Hellsten, Heinke Schlünzen, Bertrand Carissimo Best practice guidline for the CFD simulation of flows in the urban environment, Brussels, 2007, https://www.mi.uni-hamburg.de/fileadmin/files/forschung/techmet/cost/cost_732/pdf/BestPractiseGuideline_1-5-2007-www.pdf

[11] S. M. Salim, A. Chan, R. Buccolieri and S. Di Sabatino, “Numerical simulation of atmospheric pollutant dispersion in an urban street canyon: Comparison between RANS and LES,”Journal of Wind Engineering and Industrial Aerodynamics, vol. 99, pp. 103-113, 2011. [12] Jayathi Y. Mutty, Variants of SIMPLE: SIMPLER & SIMPLEC, Purdue University, 2010, https://engineering.purdue.edu/ME608/webpage/Variants%20of%20SIMPLE.pdf,

[13] NASA, Examining Spatial (Grid) Convergence, 2008, http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html

[14] Ismail B. Celik Urmila Ghia Patrick J. Roache Christopher J. Freitas Hugh Coleman Peter E. Raad, Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications, Journal of Fluids Engineering, 2008

Appendix A1. User Defined Function

A2. GCI Analysis Code

#include "udf.h"

DEFINE_PROFILE(inlet_x_velocity,thread,position)

{

float x[ND_ND];

float y;

face_t f;

begin_f_loop(f,thread)

{

F_CENTROID(x,f,thread);

y=x[1];

F_PROFILE(f,thread,position) = 4.7*pow(y/12/0.12,0.3);

}

end_f_loop(f,thread)

}

clear K=[1.1081 1.1346 1.2097]; r=2; p=log((K(3) - K(2))/(K(2) - K(1)))/log(r); f0 = K(1) + (K(1)- K(2))/(r^p - 1) Fsec=1.25; eps12=(K(1)-K(2))/K(1); eps23=(K(2)-K(3))/K(2); GCI12=Fsec*abs(eps12)/(r^p - 1) GCI23=Fsec*abs(eps23)/(r^p - 1)