Computational wind analysis of an open air-inflated membrane structure

Sherly Joanna Pool-Blanco; Krisztián Hincz

doi:10.1556/606.2023.00804

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Pollack Periodica

Volume/Issue:: Volume 18: Issue 3

Computational wind analysis of an open air-inflated membrane structure

Authors:

Sherly Joanna Pool-Blanco

Sherly Joanna Pool-Blanco Department of Structural Mechanics, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, Hungary

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sherlyjoannapoolblanco@edu.bme.hu https://orcid.org/0000-0001-7284-7540

and

Krisztián Hincz

Krisztián Hincz Department of Structural Mechanics, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, Hungary

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Pages:: 33–38

Online Publication Date:: 04 Jul 2023

Publication Date:: 25 Sep 2023

Article Category:: Research Article

DOI:: https://doi.org/10.1556/606.2023.00804

Keywords:: tensile membrane structure; air-inflated structure; wind action; computational wind engineering; pressure coefficient

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Abstract

The current research aimed to obtain mean pressure distribution over an air-inflated membrane structure using Computational Wind Engineering tools. The steady-state analysis applied the Reynolds-Averaged Navier-Stokes equations with the $k - ε$ standard turbulence model. The pressure coefficients were compared with former experimental results to validate the numerical solution. Significant errors were detected close to the critical flow separation points when comparing the numerical results with the wind tunnel tests. However, these errors are local, and the numerical methodology provides accurate results in those areas with minor turbulence motion influence. In general, the numerical solution provided good approximation of the pressure coefficient fields.

Abstract

1 Introduction

Membrane structures offer lightweight, environmentally friendly, and cost-effective construction solutions to cover large public spaces like concert halls or stadiums [1]. Moreover, lightweight houses can be built like the ones described by [2], representing cheap shelters for emergency situations. Membrane structures can be permanent or temporary buildings; some even possess the deployable characteristic that allows the change of their configuration whenever needed e.g., deployable umbrellas [3].

Tensile membrane structures are composed of flexible textile membrane and a tensioning system that might include arches, masts, rings, and cables [4].

Pneumatic membrane structures are supported and stabilized by the enclosed, compressed air; therefore, they are extremely light structures. Pneumatic structures can be divided into subgroups: air-supported and air-inflated [4–6]. In the case of air-supported structures, the covered air volume is closed and compressed; therefore, special entrances are built to enter or exit the construction. Air-inflated structures are tensioned by the enclosed, pressurized air in their walls; the structure and the covered space can be open, and no special entrances are needed.

The design procedure of membrane structures must consider the strong relationship between geometry and membrane forces. Special numerical methods are applied to determine the equilibrium shape according to the material properties, tensioning system, and external load actions. With their geometry and prestress, the membrane structures must carry downward and upward wind actions or any snow/rain load without wrinkling, ponding, or fluttering problem [1].

The structural design for wind requires knowledge about the pressure distribution on the structure, which can be given by the dimensionless pressure coefficient $(C_{p})$ . Because of the complex and unusual shapes, those parameters are not given in the Standards for membrane structures. The pressure coefficients can be obtained by experimental studies or numerical simulations. The Wind Tunnel test (WT) is the most reliable technique related to the wind engineering of structures; however, it is time-consuming and costly. Usually, this technique implies measurements on scaled, rigid models wherein material properties and deformations cannot be considered. Wind tunnel investigations of different membrane roofs are presented in [7–10].

Numerical approaches, also known as Computational Wind Engineering (CWE), apply the governing equations that describe the fluid eddy motions to solve the aerodynamic wind effects around the building [11–13]. This technique may include steady-state or time-dependent analysis where material properties and deformations can also be analyzed (fluid-structure interaction). It should be mentioned that CWE cannot be considered a completely reliable technique, so its validation with experimental results is strongly recommended. Numerical investigations to analyze the aerodynamic behavior of different tensile membrane structures are described in [13–15]. The current research validated the CWE analysis of an open air-inflated membrane.

2 Methodology

2.1 Former wind tunnel tests

The structure selected for the CWE analysis was previously tested in a wind tunnel [16]. The prototype structure consists of six inflated tubes with a diameter of 3 m (Fig. 1); its total length (L) and height (H) are 13 m; meanwhile, the width (W) is 26 m. The experiments were completed in the open-circuit wind tunnel with a test section of 1 × 1 × 1.5 m of the Autonomous University of Yucatan, Mexico. The 3D printed model had a scale ratio of 1:72.5. The pressure on the external and internal surface of the model was measured at 102 points for three wind directions 0°, 45°, and 90°.

Fig. 1.

Dimensions of the prototype structure and the wind directions considered during the CWE analysis

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

2.2 Numerical analysis

The 3D steady-state analysis followed the recommendations of [16–18]. The numerical simulations were based on the so-called Reynolds-Averaged Navier-Stokes (RANS) equations, which are suitable for analyzing mean pressure distribution, discarding any transient flow effect. The applied turbulence model was $k - ε$ standard [19], which was selected based on a previous grid sensitivity analysis. The preliminary results showed that the $k - ε$ standard turbulence model provides acceptable solutions, which are almost independent of the grid resolution.

The studied wind directions were 0°, 30°, 45°, 60°, and 90°. The CWE analysis was performed using ANSYS-Fluent 2019 R3 [20].

2.3 Domain size dimensions and mesh resolution

The creation of the flow domain with double inlet/outlet faces followed the suggestions presented in [21–23]. The double inlet/outlet allows a more straightforward application in the case of non-orthogonal wind directions. The distance from the structure to the inlet and to the top faces was 5H; to the outlet surfaces was 15H, based on [17, 18].

The semi-structured mesh integrated tetrahedral elements close to the structure and hexahedral elements in the rest of the domain (Fig. 2). Around the membrane surface, inflation layers were also considered. The minimum element size was 0.5 m, whereas the maximum was 5.0 m; the total number of nodes and elements were 5.0·10⁶ and 5.5·10⁶, respectively.

Fig. 2.

Semi-structured mesh: domain without top surface (left); tetrahedral and hexahedral elements (right)

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

2.4 Boundary conditions and convergence criterion

The following boundary conditions were applied:

a)Inlet face: the inlet velocity profile followed the power law equation (Eq. 1) to characterize a flat type terrain [23–25]:

U / U_{h} = {(Z / Z_{h})}^{α},

(1)

where

U

is the wind velocity at a certain point;

Z

is the point height;

Z_{h}

is a reference height; and

U_{h}

is the wind velocity at the reference height (15 m s⁻¹); finally,

α

is the velocity exponent that depends on the terrain roughness, based on [23],

α

= 1/9.5;

b)Outlet face: 0 Pa gauge pressure;
c)Walls: no-slip, free-slip, or symmetry condition. Additionally, the near-wall treatment was in accordance with scalable wall functions approximation. The lower y+ limit for those cells near the walls was 30.

For all wind directions, the membrane surface and the ground surface had the no-slip wall condition, whereas the top domain surface had the symmetry condition. The other abovementioned boundary conditions depended on the current wind direction. For example, for the 0° wind flow, the inlet boundary was the surface perpendicular to the Y-axis on the windward side of the structure. In contrast, the wall on the positive side of the Y-axis (and perpendicular to it) was the outlet boundary face. Additionally, for this wind direction, both boundary walls perpendicular to the X-axis followed the free-slip boundary condition.

Similarly, for the 90° wind direction, the inlet and outlet boundaries were the domain walls perpendicular to X-axis. Finally, for oblique wind directions, the X and Y components of the wind velocity vectors were set at the walls on the negative side of the X and Y axes; then, the outlet boundaries were the walls on the positive side. Figure 3 depicts the boundary conditions for orthogonal and oblique wind directions.

Fig. 3.

Domain dimensions and boundary conditions for all wind directions

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

The solution method involved the SIMPLEC scheme for the pressure-velocity coupling and second-order spatial discretization. The convergence criterion was a limit of $1 \cdot 10^{- 5}$ for all residuals, but the analyses were stopped if they reached 5,000 iterations.

3 Results and discussion

This section introduces the results based on CWE simulations and their validation with experimental results. The pressure distributions on the surfaces are described by dimensionless

C_{p}

values:

C_{p} = \frac{p - p_{0}}{ρ U^{2} / 2},

(2)

where

p

is the pressure at a specific point on the membrane surface;

p_{0}

is the upstream pressure;

ρ

is the air density; and

U

is the free-stream velocity. The notations

C_{p e}

and

C_{p i}

mean pressure coefficients on the external and internal surfaces of the structure, respectively (Fig. 1).

The validation included error measurement methods that compared the WT-based and the CWE-based

C_{p}

values. The accuracy assessment included the Mean Absolute Error (

M A E

) and the Mean Square Error (

M S E

) calculation (Table 1):

M A E = \frac{1}{n} \sum_{i = 1}^{n} | C_{p, i (W T)} - C_{p, i (C W E)} |,

(3)

M S E = \frac{1}{n} \sum_{i = 1}^{n} {(C_{p, i (W T)} - C_{p, i (C W E)})}^{2},

(4)

where

n

is the total number of points to compare (n = 102 according to the number of measurement points during the WT experiments);

C_{p, W T}

and

C_{p, C W E}

are the pressure coefficients based on WT tests and CWE simulation, respectively.

Table 1.

Accuracy factors for different wind directions

Wind direction	Surface	MAE	MSE
0°	External	0.21	0.07
0°	Internal	0.18	0.07
45°	External	0.14	0.03
45°	Internal	0.23	0.08
90°	External	0.12	0.03
90°	Internal	0.19	0.04
Deformed structure (90°)	External	0.23	0.10
Deformed structure (90°)	Internal	0.09	0.01

Two sets of measurement points were selected for further comparison. Point set A represents six points on the top and on the bottom of the arches, in the symmetry plane that contains the central axis of the structure. Point set B corresponds to the points on the external and internal surfaces of the two central arches. Figure 4 depicts the pressure coefficients in these set of points on the external surface, and Fig. 5 on the internal one.

Fig. 4.

C_p on the external surface, a) 0°; b) 45°; and c) 90° wind direction

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

Fig. 5.

C_p on the internal surface, a) 0°; b) 45°; and c) 90° wind direction

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

Figures 4a and 5a show the $C_{p}$ in point set A for 0° wind direction. The most significant differences between the CWE and WT results were detected at the first arch, close to the flow separation area. CWE provided the best results at the last two arches.

Figures 4b and 5b represent the $C_{p}$ values in the set of points A for 45° wind direction. At most of the points on the internal surface, the numerical solution is accurate. Meanwhile, the most significant difference on the external surface was on the top of the first arch. The large turbulent eddy motions in that area are highly unpredictable.

Figures 4c and 5c depict $C_{p}$ in the point set B for the 90° wind direction. (The dashed lines represent the $C_{p}$ of the deformed structure shape; this analysis is introduced in the following section.) On the external surface, CWE gave highly accurate results at the windward side of the model; however, there are significant differences from the WT results at the top of the structure. On the internal surface, there is relatively small wind suction, and the numerical solution underestimated the $C_{p i}$ values.

Figure 6 and Table 2 give a more general view of the pressure distribution. Figure 6 includes the pressure coefficient fields based on CWE results for all analyzed wind directions. Table 2 summarizes the maximum and minimum $C_{p}$ values for every analyzed wind direction. The following conclusions are drawn.

Fig. 6.

Pressure coefficient distributions on the external (top) and internal (bottom) surface for all analyzed wind directions

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

Table 2.

Maximum and minimum $C_{p}$ values on the membrane surface based on WT tests and CWE approximations

Wind direction	Surface	WT		CWE
Wind direction	Surface	Max.	Min.	Max.	Min.
0°	External	−0.297	−1.228	−0.261	−1.139
0°	Internal	−0.069	−0.794	−0.306	−1.235
30°	External	−	−	0.260	−1.752
30°	Internal	−	−	0.471	−1.654
45°	External	0.770	−1.388	0.643	−1.515
45°	Internal	0.692	−1.196	0.705	−1.861
60°	External	−	−	0.782	−1.352
60°	Internal	−	−	0.785	−2.473
90°	External	0.731	−0.802	0.785	−1.039
90°	Internal	−0.039	−0.636	0.073	−0.344

On the external membrane surface, the most significant suction $C_{p e} = - 1.752$ was found at 30° wind direction, whereas the maximum positive $C_{p e} = 0.785$ was found at 90° wind direction. The critical wind direction for the inner membrane surface was 60°, which presented the most significant suction $C_{p i} = - 2.473$ and positive $C_{p i} = 0.785$ as well.

In the case of the 45° wind direction, the largest suction determined by CWE ( $C_{p i} = - 1.861$ ) was 56% larger than the $C_{p i}$ at the same point according to the WT ( $C_{p i} = - 1.196$ ), which represented the most significant error in the negative pressure coefficients. The most significant error in the positive pressure coefficients was much smaller, approximately 16%.

4 Deformed shape wind analysis

The large displacements of membrane structures and their effect on the pressure distribution cannot be considered during the conventional WT tests. Previous research proved that the impact of the displacements could be significant on the pressure distribution and on the according membrane forces as well [26].

In the current research, following the method presented in [26], the deformed shape of the structure according to 90° wind direction was determined by the Dynamic Relaxation Method (DRM). During the DRM analysis of the membrane structure the considered dynamic pressure was $= 1.52 k N / m^{2}$ , recommended by the Mexican Standard [24]. The internal pressure in the inflated arches was $p = 25 m b a r$ . The warp direction in the membrane was supposed to be “parallel” with the centerline of the inflated arches, and the fill direction was perpendicular to the warp direction. Linear elastic, orthotropic material model was taken into account with the same modulus of elasticity in warp and fill directions ( $E_{w} = E_{f} = 400 k N / m$ , $G = 10 k N / m$ ). The maximum displacement was approximately 2.7 m, and it was detected at the windward side of the structure. The deformed shape was 3D printed for a second WT test (Fig. 7).

Fig. 7.

Wind tunnel model of the deformed shape

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

The pressure distribution over the deformed shape was determined by WT test and CWE analysis following the methodology introduced at the analysis of the undeformed structure. MAE and MSE factors show that the CWE analysis provides a good approximation to the experimental results (Table 1).

Table 3 compares the maximum and minimum $C_{p}$ values, Fig. 8 shows the pressure coefficient fields based on WT test and CWE approach. The results show that there is a significant difference at the top of the structure between the numerical and the experimental results, but with the exception of that area, the CWE results give a good approximation. There is a very good agreement on the windward side of the model, and the results show positive pressure on a significantly larger area on the external surface compared with the undeformed surface (Fig. 5).

Table 3.

Maximum and minimum pressure coefficients on the deformed structure

Surface	WT		CWE
Surface	Max.	Min.	Max.	Min
External	0.591	−0.935	0.646	−1.693
Internal	0.000	−0.585	−0.038	−0.506

Fig. 8.

WT-based (left) and CWE-based (right) pressure coefficients on the external (top) and internal (bottom) surfaces of the deformed shape

Citation: Pollack Periodica 18, 3; 10.1556/606.2023.00804

5 Conclusion

This paper presented the pressure coefficient maps for an open air-inflated membrane structure based on 3D steady-state numerical simulation. The RANS equations with the $k - ε$ standard turbulence model were used to describe the turbulence flows. The pressure coefficients on the external and internal surfaces were determined for five wind directions. The CWE results were compared with experimental results and the error measurement, based on MAE and MSE factors showed that there is a good general agreement. However, significant, local discrepancies were found in some areas highly influenced by large eddy motions (close to flow separation regions). The analysis of the deformed shape according to one of the analyzed wind directions proved that the effect of the displacements could have a significant impact on the pressure coefficient maps.

Acknowledgements

This work was supported by NKFI under Grant K138615, and VEKOP-2.3.3-15-2017-00017 project “Establishment of an Atmospheric Flow Laboratory”.

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Pollack Periodica

Print ISSN:: 1788-1994

Online ISSN:: 1788-3911

Editorial Board

Bálint Bachmann (Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Jeno Balogh (Department of Civil Engineering Technology, Metropolitan State University of Denver, Denver, Colorado, USA)
Radu Bancila (Department of Geotechnical Engineering and Terrestrial Communications Ways, Faculty of Civil Engineering and Architecture, “Politehnica” University Timisoara, Romania)
Charalambos C. Baniotopolous (Department of Civil Engineering, Chair of Sustainable Energy Systems, Director of Resilience Centre, School of Engineering, University of Birmingham, U.K.)
Oszkar Biro (Graz University of Technology, Institute of Fundamentals and Theory in Electrical Engineering, Austria)
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Matteo Bruggi (Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Italy)
Petra Bujňáková (Department of Structures and Bridges, Faculty of Civil Engineering, University of Žilina, Slovakia)
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Mirjana S. Devetaković (Faculty of Architecture, University of Belgrade, Serbia)
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Radomir Folic (Department of Civil Engineering, Faculty of Technical Sciences, University of Novi Sad Serbia)
Jana Frankovská (Department of Geotechnics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
János Gyergyák (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Kay Hameyer (Chair in Electromagnetic Energy Conversion, Institute of Electrical Machines, Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Germany)
Elena Helerea (Dept. of Electrical Engineering and Applied Physics, Faculty of Electrical Engineering and Computer Science, Transilvania University of Brasov, Romania)
Ákos Hutter (Department of Architecture and Urban Planning, Institute of Architecture, Faculty of Engineering and Information Technolgy, University of Pécs, Hungary)
Károly Jármai (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
Teuta Jashari-Kajtazi (Department of Architecture, Faculty of Civil Engineering and Architecture, University of Prishtina, Kosovo)
Róbert Kersner (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Rita Kiss (Biomechanical Cooperation Center, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, Hungary)
István Kistelegdi (Department of Building Structures and Energy Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Stanislav Kmeť (President of University Science Park TECHNICOM, Technical University of Kosice, Slovakia)
Imre Kocsis (Department of Basic Engineering Research, Faculty of Engineering, University of Debrecen, Hungary)
László T. Kóczy (Department of Information Sciences, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, University of Győr, Hungary)
Dražan Kozak (Faculty of Mechanical Engineering, Josip Juraj Strossmayer University of Osijek, Croatia)
György L. Kovács (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Balázs Géza Kövesdi (Department of Structural Engineering, Faculty of Civil Engineering, Budapest University of Engineering and Economics, Budapest, Hungary)
Tomáš Krejčí (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
Jaroslav Kruis (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic)
Miklós Kuczmann (Department of Automations, Faculty of Mechanical Engineering, Informatics and Electrical Engineering, Széchenyi István University, Győr, Hungary)
Tibor Kukai (Department of Engineering Studies, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Maria Jesus Lamela-Rey (Departamento de Construcción e Ingeniería de Fabricación, University of Oviedo, Spain)
János Lógó (Department of Structural Mechanics, Faculty of Civil Engineering, Budapest University of Technology and Economics, Hungary)
Carmen Mihaela Lungoci (Faculty of Electrical Engineering and Computer Science, Universitatea Transilvania Brasov, Romania)
Frédéric Magoulés (Department of Mathematics and Informatics for Complex Systems, Centrale Supélec, Université Paris Saclay, France)
Gabriella Medvegy (Department of Interior, Applied and Creative Design, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Tamás Molnár (Department of Visual Studies, Institute of Architecture, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Ferenc Orbán (Department of Mechanical Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Zoltán Orbán (Department of Civil Engineering, Institute of Smart Technology and Engineering, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Dmitrii Rachinskii (Department of Mathematical Sciences, The University of Texas at Dallas, Texas, USA)
Chro Radha (Chro Ali Hamaradha) (Sulaimani Polytechnic University, Technical College of Engineering, Department of City Planning, Kurdistan Region, Iraq)
Maurizio Repetto (Department of Energy “Galileo Ferraris”, Politecnico di Torino, Italy)
Zoltán Sári (Department of Technical Informatics, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Grzegorz Sierpiński (Department of Transport Systems and Traffic Engineering, Faculty of Transport, Silesian University of Technology, Katowice, Poland)
Zoltán Siménfalvi (Institute of Energy and Chemical Machinery, Faculty of Mechanical Engineering and Informatics, University of Miskolc, Hungary)
Andrej Šoltész (Department of Hydrology, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Slovakia)
Zsolt Szabó (Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Hungary)
Mykola Sysyn (Chair of Planning and Design of Railway Infrastructure, Institute of Railway Systems and Public Transport, Technical University of Dresden, Germany)
András Timár (Faculty of Engineering and Information Technology, University of Pécs, Hungary)
Barry H. V. Topping (Heriot-Watt University, UK, Faculty of Engineering and Information Technology, University of Pécs, Hungary)

POLLACK PERIODICA
Pollack Mihály Faculty of Engineering
Institute: University of Pécs
Address: Boszorkány utca 2. H–7624 Pécs, Hungary
Phone/Fax: (36 72) 503 650

E-mail: peter.ivanyi@mik.pte.hu

or amalia.ivanyi@mik.pte.hu

Indexing and Abstracting Services:

SCOPUS
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2023
Scopus
CiteScore	1.5
CiteScore rank	Q3 (Civil and Structural Engineering)
SNIP	0.849
Scimago
SJR index	0.288
SJR Q rank	Q3

Pollack Periodica
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