Unsteady large-scale wake structure behind levitated freestream-aligned circular cylinder

Question

1. What is the model diameter in the wind tunnel test?

2. What is the purpose of the mirror system in the T-BART wind tunnel?

3. What components make up the MSBS at Tohoku University?

4. How was the stereo PIV measurement system developed to overcome optical access limitations?

Accepted Answer

The model diameter in the wind tunnel test is 50 mm, regardless of the value of /. This diameter is consistent for all cylindrical models used in the study, which include values of / = 1.0, 1.5, and 2.0. The model is made of machined polyoxymethylene and features permanent magnets inserted inside for magnetically levitated and support by MSBS. The magnets have an outer diameter of 40 mm, an inner diameter of 5 mm, and a length of 20 mm. The model's base is painted black to suppress reflections of the laser beam for PIV measurement, and a black band is present for measuring the model position by the sensor subsystem of the MSBS. The Cartesian coordinate system used in the study is based on the cylindrical model with an angle of attack to the freestream of 0 deg, and the cylindrical coordinate system is defined with the axis perpendicular to the circumference of the model from the origin. The positive part of the axis is set to 0 deg when viewed from behind.

Accepted Answer

The mirror system in the Tohoku University-Basic Aerodynamics Research Tunnel (T-BART) wind tunnel is used to build a laser sheet irradiation plane perpendicular to the freestream. This setup allows for accurate measurements and analysis of the airflow around the test object, such as the cylinder in the experiment. The mirror system helps to reflect the laser sheet and create a clear and focused view of the airflow patterns, enabling researchers to study the aerodynamic behavior of the object in detail. Additionally, the mirror system facilitates the use of stereo Particle Image Velocimetry (PIV) in the test section, which provides valuable data on the velocity and turbulence characteristics of the airflow. Overall, the mirror system plays a crucial role in enhancing the precision and effectiveness of the wind tunnel experiments conducted in T-BART.

Accepted Answer

The MSBS at Tohoku University consists of a sensor subsystem, a coil subsystem, and a control subsystem. The sensor subsystem includes five CCD line sensors, nine LED light sources, short-pass optical filters, plano-convex lenses, and half mirrors. The coil subsystem comprises eight iron-core coils and two air-core coils arranged around the test section. The control subsystem connects these two systems to control the position and attitude of the model using a proportional-integral control system with a double-phase advance compensator. The MSBS is capable of controlling the model's position and attitude in up to six degrees of freedom.

Accepted Answer

The stereo PIV measurement system was developed to overcome optical access limitations by introducing a mirror system, a traverser, and a seeding rake. The mirror system consists of two slender mirrors built into the bottom of the test section, which can be manually adjusted in angle. When the laser light sheet is illuminated, the laser head is placed at the bottom of the test section facing upwards and is reflected twice by the mirrors to set the measurement plane on the plane. The measurement plane is fixed to the test section due to the complex optical setup. To change the model position relative to the measurement laser plane, an MSBS traverser was introduced, consisting of a horizontal plate and two linear guides. The seeding rake, consisting of two main pipes and 17 sub-pipes, is installed in front of the wind tunnel inlet. Compressed air containing particles produced by the Ruskin nozzles passes through the main pipe and exits through holes in the sub-pipe in a spray pattern, uniformly introducing particles throughout the test section. This setup allowed for the measurement of the model position and attitude by the sensor system without clear problems caused by scattered light from the LED light source for MSBS.

Accepted Answer

The instantaneous velocity field is calculated using the CSC method by first obtaining particle images from each camera. A background image is calculated from these particle images to avoid error vectors near the model. The background image is subtracted, and a recursive correlation method is applied to the particle images to calculate the displacement of the particle group in each camera. The initial correlation window size is 32 px x 32 px, which is reduced to 8 px x 8 px. A two-dimensional three-component velocity field is obtained from the displacements of the particle group in each camera, and the results of calibration are used. Error vector processing is applied using velocity vectors at eight points around the inspection vector. The obtained velocity field is used as the instantaneous velocity field for further analysis. The distance between adjacent vectors in the velocity field is 1.27 mm.

Accepted Answer

In the software, the Cartesian coordinate system is defined for velocity field estimation. It is based on the calibration plate and the coordinate system derived from the levitated cylinder. However, due to the mismatch between these two systems, an origin correction is applied to obtain a Cartesian coordinate system centered around the cylinder. This correction is done by adjusting the origin based on the time-averaged streamwise velocity. The Cartesian coordinate system is essential for accurately representing the velocity field in the study.

Accepted Answer

Modal decomposition combines azimuthal Fourier decomposition and proper orthogonal decomposition (POD) to analyze velocity data in a cylindrical coordinate system. It involves applying azimuthal Fourier decomposition to the velocity fields, forming a matrix of Fourier coefficients, and then using singular value decomposition to obtain spatial modes, square roots of eigenvalues, and mode coefficients. The process helps identify flow modes corresponding to fluctuations and large-scale vortex shedding. The azimuthal Fourier decomposition is applied using a fast Fourier transform, and the resulting Fourier coefficients are used to form a matrix. Singular value decomposition is then used to obtain spatial modes, square roots of eigenvalues, and mode coefficients. The weighting matrix W is calculated using the area responsible for each point, and it is used to weight the Fourier coefficients. This analysis is effective in discussing unexplained phenomena in the turbulent wake of a freestream-aligned circular cylinder.

Accepted Answer

The velocity profiles and turbulence statistics of the wake of a cylinder show similarities and differences compared to previous studies. The velocity in the freestream direction deviates significantly in the positive direction compared to previous studies, with a maximum difference of approximately 30% of the freestream velocity. The velocity profiles of the previous study show an unnatural high-wavenumber oscillation due to measurement issues. The turbulence statistics, such as 3C, decrease rapidly in the freestream region and become linear from a curve with a large change from the freestream region to the wake. The presence or absence of flow reattachment switches at / = 1.5, with intermittency observed for / = 1.5. The radial velocity fluctuations differ from the previous study for / > 0.6, while the profiles are consistent for other positions and cases. The streamwise velocity fluctuations are larger at locations where the change in the time-averaged streamwise velocity is greater. The turbulent kinetic energy distribution downstream becomes more gradual, resulting in a linear distribution. These findings provide insights into the flow behavior and turbulence characteristics of the wake of a cylinder.

Accepted Answer

The eigenvalues become smaller as / increases. This trend is similar to that of 3C shown in the figure, corresponding to the large velocity fluctuations in the nonreattaching flow and the smaller fluctuations in the reattaching flow. Regardless of / and -position, the dominant mode is the = 1 mode, which is larger than the other azimuthal modes, especially for / = 1.0 and 1.5. For / = 2.0, the magnitudes of the eigenvalues of = 1 and the second contributor, = 2, are comparable. The order of contribution of azimuthal modes other than = 1 depends on / or /. The contribution order of the axisymmetric mode = 0 varies with / or /. The contribution order of the axisymmetric mode for / = 1.0 is fifth after = 4 at / = 1.0, sixth after = 5 at / = 1.4, and seventh after = 6 at / = 2.0. The eigenspectra integrated in the frequency direction show that the m=0 mode contributes third after the = 2 mode at / = 0.1 and fourth after the = 3 mode at / 1.0. The distance between / = 0 and 1.0 differs by 0.34, but this difference is not considered significant. The result of Nidhan et al. (2020) at / = 2.0 is compared with that of / = 1.0 at / = 1.0, with the same distance from the leading edge. The order of contribution of the azimuthal modes for a disc is 1-2-3-0-* * *, whereas for a cylinder the order is 1-2-3-4-0-* * *. The = 1 mode is considered to represent large-scale vortex shedding, and the = 0 mode is considered to represent recirculation bubble pumping. The = 2 mode is considered to correspond to the double-helix structure reported by Johansson & George (2006b) and Nidhan et al. (2020) for the disc wake or the streak-like fluid structure reported by Nekkanti et al. (2023) and Zhang & Peet (2023) for cylinders. The spatial distributions of modes are discussed together with the eigenspectra in SS.

Accepted Answer

The dominant mode in the eigenvalue spectra is the = 1 mode, which is consistent across different cylinder diameters (1.0, 1.5, and 2.0). This mode is dominant regardless of the cylinder diameter and is observed within the recirculation region. The relationship between the dominant mode and vortex shedding has been discussed, and it aligns with the findings of Meliga et al. (2009). Further clarification of this relationship is desired in future research.

Unsteady large-scale wake structure behind levitated freestream-aligned circular cylinder

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Most frequently asked questions

1. What is the model diameter in the wind tunnel test?

2. What is the purpose of the mirror system in the T-BART wind tunnel?

3. What components make up the MSBS at Tohoku University?

4. How was the stereo PIV measurement system developed to overcome optical access limitations?

5. How is the instantaneous velocity field calculated using the CSC method?

6. How is the Cartesian coordinate system defined in the software?

7. How is modal decomposition applied?

8. How do the velocity profiles and turbulence statistics of the wake of a cylinder compare to previous studies?

9. What is the trend of eigenvalues as / increases in the eigenspectra for velocity fluctuation fields?

10. What is the dominant mode in the eigenvalue spectra?

References

Digital Particle Image Velocimetry

Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability

An Experimental Study on Aerodynamic Drag of Rectangular Cylinders

Bifurcations and symmetry breaking in the wake of axisymmetric bodies

Global mode interaction and pattern selection in the wake of a disk: a weakly nonlinear expansion

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