Knowing the Score

By Paulo de Mattos Pimenta, Professor, Polytechnic School at University of São Paulo, Brazil

Analyzing a World Cup stadium with ANSYS multiphysics tools takes one-tenth the time of wind-tunnel testing.

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Estádio Nacional Mané Garrincha,

In this case, validation had to be done in only 15 days, far less time than is required to build a scale model and test it in a wind tunnel.

Model of stadium
Geometrical model for CFD analysis

Estádio Nacional Mané Garrincha, a 70,000-seat football stadium in Brasília, Brazil, was rebuilt in 2013 and hosted seven games of the 2014 FIFA World Cup Brazil, including a quarter-final. Validating the design of a stadium of this size for wind loads normally requires wind-tunnel testing, which is time-consuming and costly, and runs the risk of scaling errors — a scale model that fits in a wind tunnel does not exhibit the exact same behavior as an extremely large building. With assistance from CFD simulation specialists at ESSS, the ANSYS channel partner in Latin America, the engineering consultant for the project used ANSYS multiphysics capabilities to verify the safety of the stadium. The ESSS team used CFD tools to predict airflow around the stadium and pressure on the stadium cover. Then the engineer (the author) performed a structural investigation to study the combined effects of wind, stadium infrastructure and the cheering crowd. Analysts recommended several changes, such as increasing the number of cables and cable tension. This is believed to be the first time that CFD analysis has been used to replace wind-tunnel testing in the design of a major stadium in Brazil. The analysis was completed in only two weeks. Simulation reduced costs by one-third and took one-tenth the time of wind tunnel testing.

MAJOR STADIUM RENOVATION PROJECT

CFD streamlines and air pressure
Streamlines and air pressure on roof as predicted by CFD
CFD streamlines and air pressure
Structural model
Structural model
Total deformation at 0.432 Hz
Von Mises stresses
Von Mises stresses
Modal simulation detail
Modal simulation detail
 

The stadium originally was built in 1974 and named after the famous Brazilian soccer player Mané Garrincha. Estádio Nacional was nearly demolished through an implosion in 2011 to make way for the current stadium, which includes a new facade, metal roof and stands — as well as a lowered pitch (playing field) that enables unobstructed views from every seat. The reconstruction involved dismantling the lower tier of seats and incorporating the upper tier into a new rectangular bowl. The size of the playing field was reduced to make the stadium into a single-use facility for football. The renovation cost approximately $500 million (U.S.).

NOVACAP, a Brazilian state company involved in construction in Brasília, contacted the engineer to validate the safety of the stadium design from a wind-loading perspective. Traditionally, this is done by building a scale model and testing it in a wind tunnel while measuring loads on the model. More recently, projects have been completed by using CFD to predict the loads on the structure, then using a wind tunnel to validate CFD simulation. However, stadium CFD simulation has progressed to the point that wind-tunnel validation is no longer mandatory, saving substantial time and money. In this case, the validation had to be done in only 15 days, far less time than is required to build a scale model and perform wind-tunnel testing.

Simulation reduced costs by one-third and took one-tenth the time of wind-tunnel testing.

CFD SIMULATION

NOVACAP provided an architectural model of the design. The stadium was designed as two independent structures. The roof is supported by columns and is independent of the stadium itself, which consists of seating, stairs and ramps. The roof is 309 meters in diameter, the largest circular roof in the world. The CFD design space was 6 km in both horizontal and vertical directions, which is about 20 times the size of the stadium. The model used quadrilateral, tetrahedral and pyramidal elements. The completed model has 20 million computational cells and 120 million degrees of freedom. The team iterated to remove details of the geometry that did not impact the flow, hence speeding up simulation without any loss in accuracy. Wind speeds were taken from Brazilian building code, which specifies a velocity of 35 meters per second. The team applied wind from two orthogonal directions as a boundary condition at the edge of the solution domain and employed the k-epsilon turbulence model.

ANSYS CFD simulation took about four hours to complete on a high-performance computing cluster with 12 nodes, 24 processors and 96 gigabytes of RAM. The results of the analysis provided the pressures, both positive and negative, exerted by the wind on the structure’s various elements.

Stresses in cables
Stresses in cables and trusses as predicted by structural analysis

STRUCTURAL ANALYSIS

The engineer converted the design into a finite element model with 100,000 beam and shell elements for structural analysis. The pressures predicted by the CFD model were transferred to ANSYS Mechanical using the ANSYS Workbench environment. The gravitational loads provided by spectators in the stands, lights and audiovisual systems were also incorporated into the model. The engineer first performed a static linear analysis with all loads applied. A dynamic analysis calculated the structure’s natural mode shapes and frequencies of vibration. Modal analysis was performed on the pre-stressed structure. The lowest frequency mode was a rotating mode at below 0.5 Hz. This mode was a problem because the original design did not have a lot of stiffness in the rotating direction. The lowest bending mode was at 0.8 Hz, which was acceptable. The engineer used hand calculations to determine the amplification factor of the structure.

The CFD model allowed evaluation of a number of different design changes to address the rotating mode problem. Simulation showed that by adding additional cables and increasing tensile force on some of the existing cables, the rotational stiffness of the structure increased and the frequency of the rotating mode was raised to above 0.8 Hz. The architectural design incorporated these changes, and the structure was completed in 2013. The stadium was used for the first time for the opening match of the Confederations Cup, in which Brazil defeated Japan. The stadium hosted seven matches of the 2014 FIFA World Cup Brazil; it will host some football games in the 2016 Summer Olympics to be held in Rio de Janeiro.

The work was performed under the auspices of Maruska Holanda (NOVACAP) and Pedro Almeida.

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