Experimental Measurements of Wind Flow Characteristics on an Ellipsoidal Vertical Farm

Abstract

The rise of high-rise vertical farms in cities is helping to mitigate urban constraints on crop production, including land, transportation, and yield requirements. However, separate issues arise regarding energy consumption. The utilisation of wind energy resources in high-rise vertical farms is therefore on the agenda. In this study, we investigate the aerodynamic performance of an ellipsoidal tall building with large openings to determine, on the one hand, the threshold income wind that could impact human comfort, and on the other, the turbulence intensity at specific locations on the roof and façade where micro-wind turbines could operate. To this end, we calculate the wind pressure coefficient and turbulence intensity of two scale models tested within a wind tunnel facility and compare the results with a separate CFD simulation completed in the past. The results confirm that the wind turbines installed on the building façade at a height of at least z/h = 0.725 can operate properly when the inlet wind speed is greater than 7 m/s. Meanwhile, the wind regime on the roof is more stable, which could yield higher energy harvesting via wind turbines. Furthermore, we observe that the overall aerodynamic performance of the models tested best under wind flowing at angles of 45° and 60° with respect to their centreline, whereas the turbulence at the wind envelope compares to that of the free wind flow at roof height.

1. Introduction

1.1. Vertical Farms and High-Rise Buildings Wind Energy Study

The highly integrated, highly productive high-rise vertical farm is an agricultural facility that grows crops in urban buildings using vertically stacked cultivation, energised with artificial lighting and novel farming techniques such as soilless cultivation. The vertical stacking consists of plant racks distributed in layers, lined up near the exterior walls. This layout saves space, ensures the quality of agricultural products, while the food production benefits from its favourable geographical location within the city, shortening the supply chain and reducing transportation costs. The vertical farm can cultivate continuously throughout the year while supervised with an industrial IoT monitoring system and an environmental regulation (temperature, humidity, light, gas, etc.). Notably, the production capacity of the vertical farm could be 10–20 times higher than that of traditional cultivation per hectare [1].

However, since the production and cultivation system in a vertical farm require human intervention, their operating costs could be higher than those of open-field and greenhouse farming. Besides the cost of land, which is dominated by geographical advantages, the most important cost relates to energy in its various forms, e.g., temperature, humidity, lighting, gas supply, etc. that is required to regulate and monitor the environment for plant cultivation [2,3,4]. As a result, it has been established that the cost of vertical farming is high, which plays against sustainability core objectives. As we know, full transition to renewable energy is required in the coming decades [5], which poses a major challenge to the construction sector as, in the EU for example, it is responsible for about 36% of CO₂ emissions and 40% of total energy consumption [6]. For this reason, vertical farming must transition to renewable energy to be included in the blueprint of urban construction. The new paradigm of food production unveils questions around the transition to renewable energy for vertical farming which currently constrains its proper integration with urban developments.

In this context, this paper investigates the wind energy potential and wind aerodynamics of a 108 m-tall vertical farm prototype with an elliptical cross-section with major and minor dimensions of 80 m and 60 m, respectively. The most common methods for investigating the wind flow characteristics of buildings are full-scale real-time tests, numerical CFD analyses, and wind tunnel tests. Among them, CFD numerical simulation has successfully evolved to become the most popular method in wind engineering research [7]. Notwithstanding, CFD results still rely on wind tunnel testing since the latter enables validating simulation results while continually diversifying to include environmental studies in anthropogenically controlled environments, widely used in urban microclimate research, in addition to the classical wind aerodynamics [8]. Both CFD and wind tunnel testing are cost-effective, save time, and yield reliable results, which are useful qualities to have before the project is built and landed. For this reason, this study pairs CFD modelling with wind tunnel testing to calculate and validate aerodynamic pressure coefficients ($C_P$) that describe the flow regime at different locations on the façade, including through corridors and vents, by using the orifice equation to relate the flow rate to the wind velocity [9].

Since vertical high-rise buildings that populate cities provide good flow amplification effects, they appear suitable for wind energy generation [10]. There is abundant research on the wind flow characteristics of high-rise buildings undertaken in the past. For example, Vranešević et al. verified the large-eddy simulation and performance maps of turbulence intensity over the roof of a 1:3 prismatic building and proposed a strategy for quantifying its wind energy potential [10]. Avini et al. [11] studied the wind loads on high-rise buildings using a normative and computational wind tunnel (CWT) and determined the horizontal peak acceleration due to the wind acting on the top floor of the structure, allowing the evaluation of the impact of wind loads on occupants’ comfort. The results also showed that the CWT test is a relatively inexpensive and accurate tool that can be used to complement the experimental full-boundary-layer wind tunnel test. Lin and Yan [12] used the concentration effect of the building and the height of the building to increase the utilisation of wind energy in order to investigate the feasibility of using wind energy in high-rise buildings, which led to an increase in wind speed of 1.5 to 2 m/s, and a further increase in wind energy density of 3 to 8. Vita et al. [13] investigated the wind energy resources over high-rise buildings by experimentally testing a square prismatic building with a height-to-width ratio H/D = 3. The results of the study showed that improving the roof shape by tilting the roof is one of the viable ways to improve wind energy resources. Wang et al. conducted wind vibration response tests on tuned mass dampers (TMDs) for wind-sensitive chimneys, which are tall and slender structures. The adaptive–passive variable pendulum and adjustable eddy current pendulum TMD has a better control effect and robustness, as confirmed in simulations and wind tunnel tests [14,15]. Further research on wind energy performance of buildings using wind tunnel tests [16,17,18,19] and CFD simulations [20,21,22,23,24] is abundant, as it is the pairing of the two methods [10,25,26,27]. However, the majority of these studies target square and cylindrical prismatic buildings, with little to no studies on high-rise buildings with an elliptical cross-section. Therefore, this paper proposes to investigate and discuss the wind energy potential of a tall vertical farm with an elliptical cross-section.

1.2. Research Gap

The urban integration and inner-city organisation associated with vertical farming equipped with micro-wind turbines addresses sustainability development goals 2, 3, 7, 9, 11, 12, and 13 [28]. Beyond the industrial and infrastructure innovation, it helps in tackling the shortage of fruits and vegetables caused by the reduction in urban cultivable land, and it encourages good health and wellbeing for more sustainable cities. However, as noted above, the operation of vertical farms demands additional power supply and technologies to constitute an emission-free production system [29,30]. For this reason, new ideas for supplying urban vertical farms with clean energy (nuclear and renewable) have started to develop, these being wind and solar energy sources, the most feasible alternatives given the existing technologies for energy harvesting [22,31,32]. The challenges associated with advancing vertical farming partially energised with solar panels and wind turbines lie in their variability both in time and space. For example, the current solar energy potential in the UK is concentrated in the south of England and Wales, where the average daily solar radiation exceeds 130 Wm⁻² [33,34], whereas the localised consumption of wind energy requires reducing the hourly mismatch between demand and production, as well as finding the best form of adaption to exogenous electricity markets [30].

At this stage, wind energy research on high-rise buildings focuses on commercial office buildings [13,35], residential buildings [16,36], campus buildings [37], and dense urban building clusters [38]. There are few studies on vertical urban farms, and most of the current studies focus on the structural form of buildings with square column structures [16,36,37,38,39], while fewer studies cover elliptical and cylindrical high-rise buildings. Therefore, this study systematically analyses and investigates the wind flow characteristics and wind energy potential of a vertical parking model with an elliptical column structure to be built in an urban area.

In this study, two methods, wind tunnel tests and CFD simulations, are employed to investigate the wind flow characteristics and wind energy potential of high-rise vertical farms. The collected data on wind speed, turbulence intensity, and the calculated wind pressure coefficients as well as the power generated by a wind turbine were compared for the operation of a wind turbine at two different locations. The discrepancy between the results of wind tunnel tests and CFD simulations is further discussed. The results of this study help to provide useful information for capturing renewable wind energy and its utilisation in vertical farms.

2. Methods

2.1. Modelling

The Council on Tall Buildings and Urban Habitat (CTBUH) developed the international standards for measuring and defining tall buildings, where a building of 14 or more stories—or more than 50 m (165 feet) in height—could typically be used as a threshold for a “tall building” [40]. This is in line with Cook’s [41] definition of a high building: when 2 H > D, the building is considered as a high-rise building. This research was carried out on a prototype ellipsoidal vertical farm building 108 m tall, 80 m wide, and with a chord of 60 m. The elliptical building shape was selected in this study mainly because it is expected to have better wind aerodynamics than those with corners, which tend to induce higher flow disturbances and occasionally generate vorticity. The elliptical prototype offers better energy harvesting since the flow is more uniform at the envelope, and at the same time it has a good inward and outward orientation, with inward convergence in the centre and outward uniformity, while insulation installed all around the perimeter reduces the energy demand for heating. In addition, the elliptical shape improves resilience against earthquakes and wind loading due to low changes in stiffness across its perimeter.

The testing prototype used in this study has six ventilation corridors of width equal to 5 metres, which was found to be the most appropriate corridor width in a previous investigation [42]. In that study, we compared the wind speed amplification effects of 3~6 m-wide ventilation corridors separately, concluding that 5 m ventilation corridors had the best wind flow characteristics, hence ensuring air circulation while allowing a significant planting shelf area. The six corridors are located at floors 3 F, 6 F, 9 F, 12 F, 15 F, and 18 F. To investigate the wind energy potential of the vertical farm, the test models were designed separately with two different wind turbine arrangements, as shown in Figure 1. Model A does not have turbines on the façades but on the roof, whereas for model B, the ventilation corridors were redesigned to allow distributing the wind turbines around the mid-height of the model. In model B, floors 3 F, 6 F, 9 F, 12 F, and 18 F have ventilation corridors with a width of 5 metres, whereas the perimeter of 14 F, 15 F, and 16 F simultaneously moved inwards by 5 m to allow for the installation of wind turbines, thus ensuring safety (comfort for pedestrians and avoidance of turbulence) while allowing sufficient light into the interior of the building. These three floors have a total height of 16.2 m, with a major axis of 70 m and a minor axis of 50 m. The wind regime at the roof is less disturbed; hence, it enables a speed of the flow like in free-flow conditions [22]. On the other hand, curved walls and recessed regions have the effect of amplifying the wind speed as much as 1.8 times that in the neighbourhood [43], that is, the roof and recessed regions on the façades have some wind acceleration. These aerodynamic features informed the decision to place the wind turbines at the specific heights z/h = 0.725 and z/h = 1.185.

2.2. CFD Simulation

In the simulation setup, we place the model in the computational domain of length 20H + W, width 10H + L, and height 6H, where W, L, and H denote the length of the long axis, the length of the short axis, and the height of the model, respectively. The location of the model is shown in Figure 1c, which is intended to avoid the effect of backflow on the wind environment of the model. The blocking rates in the X and Y directions of the model are ${\rho }_{blocking-X}=1.15\%$ and ${\rho }_{blocking-Y}=0.45\%$, both of which satisfy the requirement that the blocking rate of the model should not exceed 3% [44]. In the simulation process, we compared the effects of fine, basic, and coarse meshes on the accuracy of the test, and we concluded that the use of a basic mesh for the simulation of the model is sufficient to meet the requirements of computational accuracy, speed, and convergence. We also compared the wind speeds at each height in the free-flowing basin with the theoretical values for each of the five turbulence models, the $k-\epsilon$ model, realizable $k-\epsilon$ model, RNG $k-\epsilon$ model, $k-\omega$ model, and SST $k-\omega$ model. The results are in good agreement, among which the SST model has the best agreement, and it is decided to adopt the SST $k-\omega$ model as the turbulence method. More on the CFD simulation setup can be found in our previous study [42].

2.3. Wind Tunnel Tests

2.3.1. Wind Tunnel and Measurements Setup

The experimental campaign was carried out in the boundary layer wind tunnel (BLWT) at the University of Birmingham, UK. This tunnel is 14 m long and has a working cross-section of 2 m. The experimental prototype and ABL profiles were designed with a 1:300 length scale turbulent boundary layer flow that develops over a long section of the upwind area. The turbulence is generated with spikes and a grid of cubes set at ground level, as shown in Figure 2. The maximum wind speed in the free flow was set to 10 m/s, and the 1:300 scale testing models were manufactured with aluminium alloy and plywood, were equipped with 64 pressure taps of 2 mm outer diameter and 0.2 mm wall thickness connected to a manifold, and were all assembled totalising 1.165 kg (model A) and 1.205 kg (model B). The pressure recording grid is shown in Figure 3.

The reference velocity and static pressure were monitored with a Cobra Probe (Turbulent Flow Instrumentation Pty Ltd., Tallangatta, Victoria, Australia, 2015) mounted at roof height on the building model. The probe measured 3D velocity data and was configured to record at a sampling rate of 1250 Hz, which was chosen as a compromise between temporal resolution and computational cost. The tip of the Cobra Probe was orientated to face the approaching airflow, i.e., directly upstream of the wind tunnel. The pressure was measured using a bespoke, 64-channel digital pressure measurement system (DPMS, Solutions for Research Ltd., Bedford, UK, 2014) connected to a pressure tap via a short piece of pipe with a restrictor.

The mean wind speeds at the reference height ranged from 3.622 to 7.32 m/s, and the mean wind speeds at the reference heights were calculated according to the wind profile power law, ranging between 6 and 12 m/s. Therefore, the speed scale was approximately 1:1.6, and the time scale can be derived as 1:187.5. For each measurement point, the 60 s pressure recording was divided into 20 segments of 3 s duration; hence, each segment corresponded to a duration of 10 min at full scale.

The downscaled calculations were performed at a scale of 1:300, and the wind speed and turbulence intensity were measured with a Cobra Probe at different heights above the turntable (testing area) in the wind tunnel. The collected data were then used to determine the mean wind speed profile, turbulence intensity profile, and the longitudinal wind power spectrum (see Figure 4). The results show that the simulated profiles are in good agreement with theoretical values, whereas the wind power spectrum at the reference height of 0.36 m above the turntable is consistent with the von Kármán spectrum.

2.3.2. Accuracy of Experimental Measurements

The experimental setup consisted of a 64-channel DPMS with sampling rate of 500 Hz, connected to SensorTechnics HCLA12 × 5DB pressure transducers with an operating differential range of 1250 Pa and maximum uncertainty of ±3 Pa (SensorTechnics UK, Rugby, UK, 2014). The pressure taps installed on the model connected to the DPMS via 1.35 mm (inside diameter) tubes of length 0.6 m. The pressure taps on the building are connected to the DPMS via 1.35 mm (inside diameter) tubes of length 0.6 m. To calibrate the transmission stability of the pressure signal, we followed the method proposed in Jesson et al. [45], which allows minimising resonance and noise effects in the pressure tubes. The refinement process included five simulation runs at an inlet wind speed of 5 m/s, after which we obtained pressure values with an error of 5%, which was considered acceptable. The Cobra Probe used to monitor the incoming flow was tested through ten pre-runs, by moving the probe holder subject to a 5 m/s inlet wind speed until it correctly registered the reference velocity at the height h = 360 mm. The average wind speed error obtained during this additional calibration was ±0.21 m/s, and we concluded that such differences could be due to the head of the probe deviating from the direction of the incoming flow. The experimental results in terms of wind speed and turbulence intensity shown in Figure 4a were collected by the Cobra Probe and found in good agreement with theoretical values.

3. Comparison of Results

The experimental results were cross-checked against a former CFD simulation on the vertical farm prototype [42] in terms of mean wind speed, wind speed spectral density, and turbulence intensity.

3.1. Wind Characteristics

Figure 4a shows the mean wind speed profile and turbulence intensity for an inlet velocity of 10 m/s, obtained with the wind tunnel test, the CFD simulation, and the wind profile power law. This figure illustrates the rate of increase in the wind profiles and reduction in turbulence intensity with the vertical coordinate. In either case, the experimental results and CFD simulations show consistency with theoretical values.

The target profile expressions for the mean wind speed and turbulence intensity were established with Equations (1) and (2):

$${\displaystyle \frac{U_z}{U_h}}={\left({\displaystyle \frac{Z}{Z_h}}\right)}^{\alpha }$$

(1)

$${\displaystyle \frac{I_z}{I_{10}}}={\left({\displaystyle \frac{Z}{10}}\right)}^{-\alpha }$$

(2)

where $U_h$ is the mean wind speed at the roof height, i.e., h = 108 m, which was set as the reference height in this investigation; $I_{10}$ is the turbulence intensity at a height of 10 m above the ground ($I_{10}=0.39$ for an urban environment, i.e., terrain IV [46]); $U_Z$ and $I_Z$ are the mean wind speed and the turbulence intensity at the reference height; and $\alpha$ is the wind speed contour index, which is $\alpha =0.3$ for terrain IV. The turbulence intensity at the top of the building model in the wind tunnel is 22.4% of the 108 m prototype height.

The operational efficiency of a wind turbine is highly dependent on the turbulence intensity, and the turbulence intensity is directly proportional to the output power of the wind turbine [47]. The observations that the turbulence intensity tends to decrease with increasing altitude are confirmed in Figure 4a. Thus, further research could be conducted to study the efficiency of wind turbines operating at various altitudes and different turbulence conditions.

3.2. Normalised Power Spectral Density of the Longitudinal Velocity Fluctuations

Figure 4b shows the wind power spectrum of the longitudinal wind speed at a testing height h = 360 mm, calculated in MATLAB 2023 with the Pwelch function. The theoretical von Kármán spectrum is also shown in this figure for comparison. The wind power spectrum of the longitudinal wind speed was fitted to the von Kármán spectrum in MATLAB using the polyfit function, where a cubic fit has a norm of residuals (the maximum value of the residual distance among all points) of 0.24, which was considered acceptable for the experimental simulation.

3.3. Reynolds Number

In a former study by the authors [42], the commercial CFD software ANSYS Fluent 2023 R1 was used to determine the aerodynamics of the vertical farm prototype. That study has been revisited with five turbulence models to compare the simulation results with the wind tunnel test. The five turbulence models were extended to investigate the changes in the flow regimes caused by the elliptical columnar outer profile of the building model B. The Reynolds number ($R_e$) was determined with Equation (3) to confirm that the maximum Reynolds number in wind tunnel tests and CFD simulation is about 1.06 × 10⁵.

$$R_e={\displaystyle \frac{\rho uL}{\mathsf{\mu }}}$$

(3)

where $\rho$ air density is 1.225 kg/m³, $u$ denotes the incoming wind speed, $\mathsf{\mu }$ denotes the dynamic air viscosity (m/s), and $L$ denotes the characteristic length (m), which was taken as the major dimension of the elliptical section.

4. Results

4.1. Wind Speed

To determine the amount of energy that could be harvested by placing micro-wind turbines on the building façade, it was deemed necessary to create a reasonable layout for placing those devices. Since the controlling factor for evaluating the amount of wind energy is the wind speed, measurements were taken at eight different levels that coincide with building corridors at 3 F, 6 F, 9 F, 12 F, 15 F, 18 F, 19 F, plus an additional recording point located at the roof area. To capture wind velocity levels at these locations, we installed the Cobra Probe facing the windward façade on each target layer, i.e., 10 mm (corresponds to full size 3 m) in front of taps nos. 1, 9, 17, 25, 33, 41, 49, and above the centre of the roof of the model. Figure 5 shows the average wind speed profiles inferred for each target level when varying the inlet velocity between 5 m/s and 12 m/s in (a) wind tunnel tests and (b) CFD simulations.

As expected, both the wind tunnel tests and the CFD measurements show that the wind speed increases with increasing building height, with the increase in wind speed reaching its maximum at h = 207 mm (i.e., at the actual height H = 62.1 m). Since six of the eight test levels set up in this paper are at the height of the ventilation corridor, the aim is to investigate whether the recessed ventilation corridor has an impact on the running wind speed, which is one of the most important factors for wind energy, and whether the Vestas V15 wind turbine can start operating when its cut-in wind speed is greater than 4 m/s. From Figure 5a, it can be found that the wind turbine with a height above z/h = 0.725 (the lowest position for wind turbine installation) can reach the cut-in wind speed when the inlet speed is greater than 7 m/s, which corresponds to the normal operation of the wind turbine. Similarly, in the CFD simulation (Figure 5b), this height value is reached as soon as z/h = 0.275, with an inlet velocity of 6 m/s.

Currently, four complete criteria exist for assessing the wind comfort of pedestrians around buildings, namely, Isyumov and Davenport (1975) [48], Lawson (1978) [49], Melbourne (1978) [50], and NEN 8100 (2006) [51], respectively. Lawson’s and Melbourne’s criteria proved to be the most stringent, while Isyumov and Davenport’s criteria were most consistent with those of NEN 8100 [52]. Among these, the Lawson Comfort Criteria are clearly more sensitive to weaker wind conditions [53]. Consequently, the PWC was established by using the Lawson Comfort Criteria. These criteria have been evolving over time (LDDC, 2001, 1970, etc.); hence, past versions establish different probability values and associated wind speed thresholds. The latest Lawson 2001 Wind Comfort Criteria state that people’s activities are constrained due to physical discomfort when wind speeds exceed 8 m/s. Figure 5 shows that for an external wind velocity of 12 m/s, the average wind speed at the outdoor corridors does not exceed 7.5 m/s, being the critical condition at the corridor located at h = 315 mm.

Historical records show that the average hourly wind speeds in Birmingham, UK, fluctuate with the season. Data taken from [54] show that in 2023 the windiest month in Birmingham was January, when the average hourly wind speed reached 5.75 m/s. The calmest month of the year in Birmingham was July with an average hourly wind speed of 4.3 m/s. This means that opening outdoor corridors will not affect pedestrian comfort in normal weather conditions; however, some mechanisms to shut the building openings should be implemented to ensure a safe operational environment when the exterior wind exceeds 12 m/s.

4.2. Mean and Root Mean Square (RMS) Pulsating Wind Pressure Coefficients

In the wind-resistant construction of high-rise buildings, dimensionless wind pressure coefficients are generally used to determine the design wind loads on building façades and components. The comparison between wind pressure coefficients from wind tunnel tests and CFD simulations was carried out for two storeys, namely those at h = 261 mm and h = 360 mm (i.e., 15 F and the roof area, the height of the building in which the wind turbine is to be installed), for thirteen wind directions (θ = 0° to 165°, with 15° intervals). The numerical simulations were carried out using the coupled solver for fluid–solid coupling and with a residual of 10⁻⁴. For the wind tunnel tests, the wind pressure coefficients were determined based on segments at 3 s intervals, which corresponds to a duration of 10 min at full size.

The average RMS of the wind pressure coefficients is established according to Equations (4)–(6) [55]:

$$C_P={\displaystyle \frac{2(P-P_0)}{\rho U_z^2}}$$

(4)

$$C_{p,mean}={\displaystyle \frac{1}{T}}{\int }_0^T{C}_{pi}\left(t\right)dt$$

(5)

$$C_{p,RMS}=\sqrt{{\displaystyle \raisebox{1ex}{$\sum _{K=1}^N{(C_{Pik}-C_{P,mean})}^2$}\!\left/ \!\raisebox{-1ex}{$(N-1)$}\right.}}$$

(6)

in which $P$ is the static pressure at the point at which the pressure coefficient is being evaluated, $P_0$ is the static pressure in the freestream (i.e., remote from any disturbance), $\rho$ is the freestream fluid density (air at sea level and 15 °C is 1.225 kg/m³), $U_Z$ is the freestream velocity of the fluid, or the velocity of the body through the fluid, $T$ is the sampling time, and $N$ is the sampling length.

Figure 6 shows the variation in the mean and RMS fluctuating (standard deviation) wind pressure coefficients recorded from taps nos. 33~40 on the surface of the vertical farm building and from taps nos. 57~64 on the roof at an inlet velocity of 10 m/s. The results are compared with the results of the CFD simulation. The results of the wind tunnel test and the CFD simulation are compared and the numerical trends of the results of the two models in the two test environments are in good agreement. The main characteristic difference between the two circles of model A and model B is the height of the ventilation corridor at 15 F, which corresponds to taps nos. 33~40. Tap no. 33 is the measuring point on the windward side, facing the incoming flow, and tap no. 37 is the measuring point on the leeward side, furthest away from the incoming flow. From the numerical values, model A has a larger wind pressure coefficient for the frontal windward side compared to model B, while the wind pressure coefficient for the leeward side is not very different.

4.3. Turbulence Intensity and Flow Acceleration

Figure 7 depicts the turbulence intensity measurements along the downwind ($I_U$), crosswind ($I_V$), and vertical ($I_W$) directions at the height of the roof of the vertical farm. The turbulence intensities $I_U$, $I_V$, and $I_W$ are calculated according to Equation (7) for seven wind angles, namely, 0°, 15°, 30°, 45°, 60°, 75°, and 90° (see Figure 3). The turbulence intensity in the downwind direction is generally greater than that in the crosswind and vertical directions; therefore, we consider the downwind direction the main source of energy.

$$I_U={\displaystyle \frac{{\sigma }_U}{U}}, I_V={\displaystyle \frac{{\sigma }_V}{U}},I_W={\displaystyle \frac{{\sigma }_W}{U}}$$

(7)

where, ${\sigma }_U$, ${\sigma }_V$, and ${\sigma }_W$ are the standard deviations of pulsating wind speed in each direction.

Figure 7 shows the values at different inflow velocities for roof height and is compared for model A and model B, respectively. The results confirm that the turbulence intensity on the downwind side is generally larger than the turbulence intensity on the upwind side and the vertical turbulence intensity at the same inlet velocity. The experimental data show that in model A the values of turbulence intensity in $I_U$, $I_V$, and $I_W$ are highest in the 0° wind direction and lowest in the 15° wind direction, while in model B the values are highest in the 45° wind direction and lowest in the 0° wind direction. One possible reason for this phenomenon is that the geometry changes between 14 F–16 F for model B affects the airflow at the roof level, and such a concave profile increases the depth of the shear layer, leading to a decrease in turbulence intensity. It has been shown that building features such as roof geometry and balconies influence the turbulence intensity in the inflow. The presence of balconies, or otherwise façade misalignment by the section narrowing, reduces the turbulence intensity in the street canyon [56].

Figure 7 also shows that the three characteristic values of turbulence intensity at the roof level of model A subject to a wind direction flowing at 45° are similar to equivalent values calculated within the free flow (curve labelled ‘Fluid’ in the figure). In contrast, model B shows the best fit between the three-turbulence intensity values and those for free flow at the roof reference height for wind flowing at 60°. It can be concluded that the turbulence at both wind angles (45° and 60°) has similar characteristics to the free-flow values at the roof reference height, and therefore these two wind directions provide the most suitable flow patterns for wind energy harvesting.

4.4. Wind Energy Potential

4.4.1. Effect of Altitude on Wind Energy Potential

To further investigate the wind energy potential of the vertical farm, wind turbines were implemented in model A with a scaled height of Z/H = 1.185 (i.e., H = 128 m at full scale), and in model B with a building height of Z/H = 0.725 (i.e., H = 78.3 m). In these configurations, the hub centre of the wind turbine in model A extended outwards by 3 m as recommended in past research [31] to prevent high turbulence from interfering with the operation of the wind turbine. The wind speeds at these two heights were established for both the test and CDF simulations and the obtained results are shown in Figure 8a. At the same inflow speed, both the wind tunnel tests and CFD results show that the wind speed at model A height Z/H = 1.185 is 1.6~1.9 times higher than that at model B height Z/H = 0.725. As we know, the wind energy conversion is directly proportional to the air density, the area swept by the wind turbine, and the third power of the wind speed. This indicates that in either model, stations located on the roof have a better wind energy potential at the same wind speed.

Turbulence is of great importance in wind farms, even more when realising that it can also disturb the performance of installed wind turbines. For this reason, in Figure 8b we also compare turbulence intensity values calculated at two heights, before and after the models are added to the simulation space.

It can be seen from the results that the turbulence intensity increases significantly at the two heights z/h = 1.185 and z/h = 0.725 when the experimental model is placed in the wind tunnel. We also infer that the turbulence is negatively correlated with the power generation performance, because the turbulence affects the power curves of the wind turbine. Thus, the greater the turbulence, the worse the power generation performance. We already note that the turbulence level on power generation is low (about 1%) [57]; this is because when the value of $I_T$ is less than 10%, the turbulence intensity is relatively low, and when the value of $I_T$ is between 10% and 25%, the turbulence intensity is medium [55]. The value of $I_T$ is below 25% at either height, so we conclude that these two heights define the optimum range for the installation of wind turbines.

In Figure 9, we compare the turbulence intensity of $I_U$, $I_V$, and $I_W$ at the heights of model A z/h = 1.185 and model B z/h = 0.725, and it can be observed that the value of $I_U$ at the height of z/h = 1.185 is larger than that in the other two directions. Furthermore,

Table 1. Comparison of turbulence intensity in 0° wind direction wind tunnel test.

Inlet Velocity (m/s)	Model A at z/h = 1.185		Model B at z/h = 0.725		Fluid z/h = 1
	${\mathit{I}}_{\mathit{W}}/{\mathit{I}}_{\mathit{U}}$	${\mathit{I}}_{\mathit{V}}/{\mathit{I}}_{\mathit{U}}$	${\mathit{I}}_{\mathit{W}}/{\mathit{I}}_{\mathit{U}}$	${\mathit{I}}_{\mathit{V}}/{\mathit{I}}_{\mathit{U}}$	${\mathit{I}}_{\mathit{W}}/{\mathit{I}}_{\mathit{U}}$	${\mathit{I}}_{\mathit{V}}/{\mathit{I}}_{\mathit{U}}$
5	0.732	0.832	1.330	1.650	0.609	0.687
6	0.717	0.851	1.276	1.648	0.602	0.727
7	0.765	0.868	1.306	1.639	0.620	0.718
8	0.730	0.851	1.364	1.710	0.624	0.703
9	0.715	0.837	1.281	1.614	0.627	0.712
10	0.753	0.807	1.342	1.573	0.616	0.721
11	0.759	0.789	1.333	1.632	0.666	0.762
12	0.762	0.794	1.331	1.579	0.654	0.740

shows that the ratio of $I_W/I_U$ at the height of model A z/h = 1.185 is slightly larger than that of the free-flow domain and that the ratio of $I_V/I_U$ is slightly smaller than that of the free-flow domain. The possible explanation for this phenomenon is that the vertical wind direction of model A defines a domain, which increases the vertical obstruction compared to the open and unbuilt site, so the $I_W$ is relatively large and thus the $I_W/I_U$ value is slightly larger than the free-flow domain. As this recording point is distant from the roof, the horizontal wind is less obstructed by the presence of the building, so that $I_V$ is reduced and thus $I_V/I_U$ is slightly smaller than the free-flow area requirement.

On the other hand, since the wind turbine installed on model B is located at its mid-height and this VF building has an elliptical cross-section, the transverse wind velocity component is very much influenced by the structure, and the transverse wind speed fluctuation is abnormally large, resulting in a large standard deviation, i.e., $I_V$, is much larger than $I_U$. At the same time, even if the hub centre of the wind turbine extends outwards by 3 m, it does not stick out of the façade sufficiently; hence, it can still be considered to lie inside the building, and the friction and obstruction caused by contact with the building surface is large, so the turbulence situation is chaotic, and therefore the increase in $I_W$ is much larger compared to $I_U$, which makes obvious the numerical increase of $I_W/I_U$.

4.4.2. Recording Stations with Higher Wind Energy Potential

The results presented above suggest that the wind energy potential varies across the building envelope. To identify the best stations, we defined eight measurement points at two reference heights, namely 20 m above the ring including taps nos. 57~64 in model A (above roof level z/h = 1.185) and 3 m distant from the ring formed by taps nos. 33~40 in model B (façade area z/h = 0.725). The average wind velocity and $I_T$ obtained at each recording point when the inlet wind speed equals 10 m/s are shown in

Table 2. Wind speed and $I_T$ value at hub height of wind turbine at different measurement points in 0° wind direction at 10 m/s.

Tap No.	WT		CFD		Tap No.	WT		CFD
	Velocity (m/s)	${\mathit{I}}_{\mathit{T}}$	Velocity (m/s)	${\mathit{I}}_{\mathit{T}}$		Velocity (m/s)	${\mathit{I}}_{\mathit{T}}$	Velocity (m/s)	${\mathit{I}}_{\mathit{T}}$
33	5.28	17.1	5.65	17.9	57	8.01	9.04	9.21	11.30
34	5.84	17.2	6.25	18.2	58	8.26	9.11	9.30	11.32
35	7.86	17.9	8.75	19.2	59	8.13	9.06	9.22	11.20
36	4.31	16.2	5.62	17.2	60	8.22	9.12	9.26	11.20
37	2.24	15.2	3.75	15.7	61	8.06	9.05	9.34	11.33
38	4.82	16.6	5.13	17.1	62	8.14	9.06	9.25	11.30
39	7.63	17.7	8.97	18.7	63	8.11	9.06	9.22	11.20
40	6.15	17.3	6.80	18.2	64	8.23	9.10	9.23	11.31

.

The data in Table 2 show that for model A above roof level the wind velocity and $I_T$ do not vary greatly across measurement points. This is because this height is already 20 metres from the roof of the vertical farm building, so that the wind turbine’s hub is little affected by the turbulence of the outer contour of the building. For model B at the façade area, the wind regime is less homogeneous. Since the selected points fall in the mid-height of the building, the boundary layer of the building shows variability in all directions. When the wind flows in the direction 0°, the wind speed and $I_T$ values of taps nos. 33, 34, and 40 (windward area) are significantly greater than those of taps nos. 36, 37, and 38 (leeward). Therefore, the hub of any planned wind turbines should operate as far as possible on the windward side of the building. We note that taps nos. 35 and 39 located on the side of the building are less affected by turbulence and the wind flow is less obstructed. As a result, in those recording stations the wind speed and $I_T$ are greater than those of the frontal wind, yet their blades could operate better by facing towards the incoming wind.

4.5. Wind Energy Harvesting

Equation (8) allows us to obtain the potential wind energy obtained using a wind turbine; the Vestas V15 wind turbine used in this study operates with a cut-in wind speed of 4 m/s and a rotor diameter of 15 m.

$$E={\displaystyle \frac{0.5\ast \rho \ast \mathrm{A}\ast U^3\ast \eta }{1000}}$$

(8)

where $E$ denotes the theoretical wind energy (KW), $\rho$ denotes the air density (1.225 Kg/m³), $A$ represents the effective area of the wind turbine blades (176.625 m²), $U$ denotes the wind speed of the turbine blades (data from Figure 5), and $\eta$ denotes the wind turbine coefficient; we take the Betz’s coefficients of 0.593.

Figure 10 shows the wind energy potential associated to a V15 wind turbine installed on model A at z/h = 1.185 (roof) and model B at z/h = 0.725 (façade), on both the experimental models tested in the wind tunnel tests through a previous CFD simulation [42]. According to these results, the total wind energy that can be harvested gradually increases as the inlet speed increases, with best results observed when the inlet wind speed exceeds 8 m/s. The rate of change on the experimental and numerical simulations could be due to the fact that the turbulence caused by the scaled-down wind tunnel test model is larger than in the CFD environment, and the wind speed is greatly affected by the profile of the building shape when it flows through the two heights, so that the wind speed and the growth of wind speed are suppressed, resulting in a decrease in the captured wind energy.

We noticed in Figure 10 that as the inlet wind speed increases in both the wind tunnel and CFD simulations, the energy harvesting by the wind turbine located at z/h = 1.185 surpasses that of the wind turbine located at z/h = 0.725. The increase in power generation increases the power output, hence the economic benefit. According to [54], the probability of wind speeds below 9 m/s occurring at 10 m above the ground in Birmingham, UK throughout the year is about 80 percent, and the probability of wind speeds above 9 m/s is about 20 percent. The threshold of 9 m/s is used here because it induces the rated power of the wind turbine placed at z/h = 1.185. As the two wind turbines are located at H = 128 m and H = 78.3 m, respectively, the probability of wind speeds exceeding the 9 m/s threshold is well above 20 percent. This shows that wind turbines on the roof can operate at more sustained rated power than on building façades.

5. Discussion

In Figure 6, $C_{p,mean}$ ranged between −1.8 and 1.3, and the corresponding RMS of wind pressure coefficients fluctuated between 0 and 0.3, which aligns with results reported in Abraham et al. [58]. In the same figure, we observe that the maximum of $C_{p,mean}$ in the windward region appears within the interval of the wind flow direction limited by 0° and 90°, whereas the minimum value appears in the sides, most likely due to the deflection of the flow. This configures a pressure field whose magnitude gradually decreases from the windward sides, with a gradual return from the side elevations to the leeward area with suction as opposed to pressure. This pressure configuration is similar to the one established in BS EN 1991-1-4—Wind actions for circular buildings. Notwithstanding the quality of the results obtained, the following limitations require attention:

(1)

This study did not consider the probability distribution function (PDF) associated to wind energy harvesting. We consulted a study by Vita et al. [13] around the wind aerodynamics of urban buildings, which reported some positive bias of the PDFs at the corners and centres of building roofs. For the edge locations, the same study reports changes in shape of the PDF with the wind direction. This indicates that wind turbines placed at different operation points would be exposed to different wind regimes. Further research could be conducted to determine the power generation efficiency across various locations on the roof and façades;

(2)

The vertical farm prototype developed for this study does not allow the model to be placed in a complex urban environment. This is because, according to Juan et al., the density of buildings in the city, building contours, and wind direction all increase turbulence, hence lowering the running wind speed [38]. The subject could be investigated further as to determine the cost–benefit ratio of implementing vertical farms in highly populated areas;

(3)

The elliptical building prototype studied here has a fixed-ratio long-to-short axis of 4:3. Hence, the results presented could vary for a building whose plan view describes other elliptical trajectories.

6. Conclusions

This paper investigates the wind aerodynamics inside and outside a prototype vertical farm by experimentally testing two models in a wind tunnel facility, and by cross-comparing results against a separate CFD simulation reported in the past. The results obtained can be summarised as follows:

(1)

The testing prototypes allowed for measuring wind pressures around eight layers distributed along the façade, with the incoming wind flowing at speeds between 5 and 12 m/s. The results show that wind turbines placed at heights above z/h = 0.725 (the lowest position for the installation of the wind turbine) can reach a cut-in speed equivalent to the normal operation of the wind turbine at an inlet speed higher than 7 m/s;

(2)

The mean and RMS pulsating wind pressure coefficients were calculated at 64 measurement points varying the wind flow angle between 0° to 90° (15° intervals) at an inlet velocity of 10 m/s. Among these, 16 measurement points were located at a height of z/h = 0.725 and at roof level. There, the maximum positive mean wind pressure occurs at tap no. 33 for model A at 0° flow, and the maximum negative mean wind pressure occurs at tap no. 39 for model B at 45° flow. The largest wind pressure coefficient was recorded at the windward direction of model A, at a height of z/h = 0.725. No significant differences in wind pressure coefficients were detected in the leeward direction in that model;

(3)

The turbulence intensities of $I_U$, $I_V$, and $I_W$ at roof height calculated for seven wind angles show that the turbulence is similar to the free-flow domain values at roof height at 30° and 45° wind angles. Therefore, 30° and 45° wind direction angles provide a suitable flow pattern for energy harvesting in the vertical farm;

(4)

The turbulence intensity and radii $I_V/I_U$ and $I_W/I_U$ at 0° wind angle for model A at z/h = 1.185 and model B at z/h = 0.725 were below 25% in either case, the values of model A at z/h = 1.185 are closer to the free-flow domain, and in terms of total wind energy captured, z/h = 1.185 is significantly better than z/h = 0.725, suggesting that wind turbines installed on those levels have a better potential for generating wind energy.

Urban high-rise vertical farms address sustainable urban development food security, urban planning, construction, health, and well-being, hence touching on SDGs 2, 3, 7, 9, 11, 12, and 13. Notwithstanding, their progressive implementation requires a positive cost–benefit ratio, in many ways driven by the optimisation of higher energy needed for operation in comparison to residential buildings. For this reason, future research could focus on the impact of urban high-rise vertical farms of different geometries and heights, equipped with optimised energy harvesting systems. This requires parallel technological advances and strategies that can help us to devise a greener future.