Aerodynamic and thermal interference between two building models

the paper considers aerodynamic and thermal interference of separated flows between two square prisms arranged at a short distance from each other. It is shown how relative positions of the square prisms affect the specific phenomena caused by the airflow interactions. This work is the experimental study of aerodynamic and thermal interference effects on two square prisms or building models depending on their relative positions. A strong difference is shown between aerodynamic and thermal interferences observed in the airflow behind two tandem models. The thermal interference effect turns to be rather conservative as compared to the aerodynamic. Using the interference parameters one can easily analyze the extreme values of the pressure and thermal flows interfering with the building models depending on many factors, including relative model positions.


Introduction
In civil engineering in Russia, great attention is paid to high-rise building. The advantage of this type of buildings is a large amount of space per square meter of the site. As a result, it is possible to more compactly distribute living and working spaces in the municipal area. Building is a complex structure which unifies all design and construction solutions. In Russia, there is no yet experience in design and continuous servicing high-rise buildings as, for example, in the USA. Thus, there is broad scope for new investigations in the field of high-rise construction with regard to climatic conditions of the country.
One of the most successful methods of investigating building parameters is physical modeling. In comparison with numerical, this method is the most reliable as it completely excludes the human factor affecting the accuracy of set parameters. The significant drawback of this method is the necessity to create precise and often complex models. Moreover, this method requires purchasing large and expensive equipment.
When designing a building, it is important to be aware of many factors. Among them, wind loading is one of the most important.
It is worth noting that engineers and researchers have always shown a lot of interest in the problem of wind loading. The learning potential and technical feasibility promote opportunities to study the wind flows and their effect on different objects. The recent years are characterized by remarkable advances in the knowledge acquirement concerning the wind effect on such objects as prisms, CAEST 2019 IOP Conf. Series: Materials Science and Engineering 775 (2020) 012140 IOP Publishing doi:10.1088/1757-899X/775/1/012140 2 pyramids, cylinders, etc. In each case, the air motion has specific features. Similar methods have been used for several objects, including their mutual effect on the airflow and its turbulence.
There are two main research trends of the wind loading. The first is the wind loading on a building, which is an integral action resulting in multiple phenomena, such as static load which includes air pressure and rarefaction; dynamic load which includes airflow pulses causing vibrations of an object; and many others. Second, the air motion is a source of the convective heat exchange of a building. The latter also includes many research trends among which are heat loss and heat exchange between several objects.
Interference of separated flows is the best example of changes in the dynamic airflow and the rate of heat transfer in the studied arrangement of the building models (beyond the disturbing barrier). The interference effect allows evaluating the turbulence impact from the front barriers on the fields of pressure and heat exchange.
The literature review in the area of the airflow interference between two or more models in tandem shows that both Russian [1−4] and foreign [5−20] researches are involved in the problem. In recent years, the numerical simulation of the interference effect has become very popular [21 −29]. Numerical and experimental simulation of interference of separated flows is presented, for example, in [30−32].
The results of numerous experiments on this issue achieved for the past years and their comparison with those of other authors allow highlighting general behavior of aerodynamic and thermal interference factors.
It is found that the separated flow which occurs near a group of buildings affects both the heat loss and wind loadings which, in turn, govern the internal microclimate of building, its operating parameters and safety.
Determination of the direct dependence between the heat loss and the wind pressure is still a complicated and multiple-factor problem that can be solved through the analysis and comparison of aerodynamic and thermal interference effects based on the systematic experimental studies.
This work aims at the experimental study of aerodynamic and thermal interference effects on two building models or square prisms depending on their relative positions.

Research Tasks. Pilot Model and Measuremet Technique
Research tasks were based on the experimental data on the wing loads and convective heat exchange. The results of multiple experiments being collected for the last few years and their comparison with those obtained by other researchers [1-32] allowed distinguishing general tendencies in the behaviour of the interference factor. At the first stage, the building models were prepared to explore the fields of pressure applied to different sides and the local and average heat transfer coefficients in the conditions of the forced convection. The second stage included the combined exploration of the wind (aerodynamic) load and thermal flows and finding common changes caused by the relative positions of the building models. Due to the large data volumes [33][34][35], we present the experimental results under the following conditions: • The square prisms have the relative height H/а = 6, where а = 50 mm is the size of the cross-section.
• The square prisms are arranged on the axis of the relative airflow ( Figure 1).

•
The longitudinal pitch is accepted to be L1/а = 0; 0.5; 1; 1.5; 3, 4.5 and 6.  The final data processing and the analysis of results were based on a comparison of the identical parameters. The initial parameters of the air pressure and rarefaction Cp and the heat transfer Nu did not allow comparing properly the changes in these parameters because of the difference in the units of measurement. On that basis, we used the interference factors IF(Cp) and IF(Nu) as parameters describing the rate of the aerodynamic and thermal interaction.
where Cp and Nu are respectively the pressure coefficient and the Nusselt number for one of the sides of the downstream Model 2; Cp0 and Nu0 are respectively the pressure coefficient and the Nusselt number for the whole surface of the Model 1 in front. Figure 2 illustrates two prismatic models with the different structure for measurements of the pressure and the heat transfer coefficients. On the side of the model for the pressure measurement there are channels for the air motion that was recorded with the multichannel pressure sensor switch. A set of thermocouples was placed at the respective points on the side of the model for measuring the heat transfer coefficient.
The measurements of the static pressure and the heat transfer coefficient as well as a study of the air motion are performed on a specific aerodynamic test bench. This test bench consists of the wind tunnel, the multichannel pressure sensor switch for recording changes in the heat transfer coefficient using the downstream model and the model of interest.
The wind tunnel is an open exhausting tube, the schematic view of which is presented in Figure 3. The range of speeds in the working chamber is 1−30 m/s; the turbulent stream rate is 0.5 %. The working chamber of the wind tunnel is 1200 mm long, its cross section is 400400 mm 2 . One of the lateral sides of this chamber has two windows made of organic glass. One window is intended for the model assembling and the other is for observations and locates above the model. The chamber housing is made of steel.
The gages are placed in the working chamber via an aperture at the bottom of the channel. The aperture is sealed with a fluoroplastic band. Branch tubes are connected to the type VО-5U2 mine fan with a 7.5 kW motor. The airflow speed is varied by the speed control system using a converter. The velocity profile in the flow core is uniform; the thickness of the boundary layer at the model placement is ~20 mm frequency.   Figure 3. Schematic of the wind tunnel for static pressure measurements: 1wind tunnel; 2building models; 3 -Pitot static tube; 4pressure differential gage DMTs-01М; 5multichannel pressure sensor switch; 6working chamber.
Air in the wind tunnel is supplied from the outer space through the laboratory rooms. During the experiment, the air temperature is rather constant (~20С).
A multichannel differential pressure sensor (1 mm graduation) is manufactured to vary the difference in pressure (Figure 4). The readout of information from the differential pressure sensor is provided by a digital camera, and the results are digitized in a GetData Graph Digitizer. The reference value is selected to be static pressure in the channel of the undisturbed flow. The order of calculation of the pressure coefficient Ср is as follows: 1. The airflow velocity U0 is detected first: where Р is the pressure sensor readings, Pa; k is the slope coefficient;  is airflow density; P is the air pressure, mm Hg; T = t0 + 273 is the airflow temperature, о С.  where Рi is the static pressure at the i-th surface point, Pa; P0 is the static pressure in the center of the channel, upstream, Pa; 1/2(ρU0 2 ) is the dynamic pressure of the oncoming flow; ρ is the density of the oncoming flow, kg/m 3 ; U0 is the flow density, m/s. Electric current passes through a nichrome coil to provide the surface heating in the model for the heat transfer measurements. Thermocouples were placed on one side of the model covered with a stainless steel plate 1 mm thick. The thermal boundary condition on this surface matches the stable thermal flow, i.e. q = const. In order to reduce the heat flow along the model, a number of slots are made as shown in Figure 2. The model is subsequently rotated to the proper angles for the heat transfer measurements on other sides.
The following equation defines the average Nusselt number for the whole surface of the model: where  is the average heat transfer over the square model surface, W/(m 2  о С); а is the crosssection of the square model, m;  is the thermal conductivity of the airflow, W/(m о С).
As a result of these measurements, we obtained the coefficients of the pressure distribution and the heat transfer, which were used to calculate the Nusselt number. Besides mean values, the aerodynamic component of the wind loading allowed detecting the maximum and minimum values of the resulting parameters. Thus, the interference factor was calculated using not only mean but also maximum and minimum values of Cp and Nu.

Results and Discussion
At the first stage, we obtain information on the separated flow structure using the oil flow visualization of the wind tunnel surface. The results of this visualization are illustrated in Figure 5. All the models are made of organic glass 5 mm thick.
The oil flow visualization is used to detect the correlation between the obtained visible flow patterns and the distribution factor of aerodynamic and thermal interference as well as to evaluate the hydrodynamic structure of separated flows, their size and behavior. Let us now discuss aerodynamic and thermal interference in the system of two building models. Firstly, the effective analysis is necessary for grouping the diagrams by the model sides and types of measurements (aerodynamic and thermal). Secondly, the individual analysis of medium, maximum and minimum values is required. Thirdly, the mutual analysis should be conducted for aerodynamic and thermal interference depending on the distance L1/a between the wind tunnel models at the airflow angle of attack. Let us discuss the results obtained.
According to Figure 6, the aerodynamic interference factor on the front side A-B of Model 2 strongly depends on the relative position of the models (Figure 6a). The interference factor is higher for the lowest values of the pressure coefficient Ср than for the mean (integrated) or maximum values. This is because the air rarefaction enabled by the model in front. The highest interference factor is observed at a relative distance L1/а = 4.5, when the measuring model is exposed to the horseshoe vortex.
Unlike aerodynamic, thermal interference effect shown in Figure 6b is less dependent on the distance L1/а between the models. At the same time, their mean, maximum and minimum values do not significantly differ from one another. The highest values of IF(Nu) are observed for the integrated value of the interference factor. The effect of aerodynamic interference observed along the sides В-С and D-A of Model 2 (Figure 7а) is higher at L1/а = 0.5…3. This is caused by the accelerated airflow along the sides of Model 2. At L1/а = 3… this effect is lower. According to Figure 8, the interference effect on the back side C-D of Model 2 is less dependent on L1/а distance and seems not to be significantly changed. It should be only mentioned that interference changes at L1/а = 1.5 (Figure 8a), when the vortex zone formed by the front Model 1 affects the side of Model 2 and is strengthened by the separated flows from edges В and А.

Conclusion
This study showed that the factors of aerodynamic and thermal interferences observed beyond the disturbing building model differed strongly. The thermal interference effect was rather conservative as compared to the aerodynamic. The highest values of the thermal interference effect were observed on the back side C-D in the vortex zone beyond the model.
Based on the description of aerodynamic and thermal interference effects it can be concluded that aerodynamic interference is more subjected to changes depending on the distance between the building models, i.e. at L1/а > 3 the changes occurred on А-В side, and at L1/а < 3 they were observed on other sides.
Using the interference parameters one can easily analyze the extreme values of the pressure and thermal flows on the model surfaces depending on many factors, including their relative positions.

Acknowledgement
This work was carried out within the state contract N АААА-А17-117030310010-9 and financially supported by Grant N 18-08-01025 from the Russian Foundation for Basic Research.