Symmetry

Research

14 pages, 1143 KiB

Open AccessArticle

On the Horizontal Divergence Asymmetry in the Gulf of Mexico

by Tianshu Zhou, Jin-Han Xie and Dhruv Balwada

Symmetry 2025, 17(1), 136; https://doi.org/10.3390/sym17010136 - 17 Jan 2025

Viewed by 314

Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compressibility in the Gulf of Mexico by analyzing drifter data (the Grand [...] Read more.

Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compressibility in the Gulf of Mexico by analyzing drifter data (the Grand LAgrangian Deployment (GLAD) experiment and the LAgrangian Submesoscale ExpeRiment (LASER)) based on the asymptotic probability density function of the angle between velocity and acceleration difference vectors in a strain-dominant model. The results reveal a notable divergence at scales between 10 km and 300 km, which is stronger in winter (LASER) than in summer (GLAD). We conjecture that the divergence is induced by wind stress with its curl parallel to the Earth’s rotation. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

15 pages, 6130 KiB

Open AccessArticle

Asymmetry of Two-Dimensional Thermal Convection at High Rayleigh Numbers

by Jian-Chao He, Yun Bao and Xi Chen

Symmetry 2024, 16(12), 1583; https://doi.org/10.3390/sym16121583 - 27 Nov 2024

Viewed by 520

Abstract

While thermal convection cells exhibit left–right and top–bottom symmetries at low Rayleigh numbers (

R a

), the emergence of coherent flow structures, such as elliptical large-scale circulation in Rayleigh–Bénard convection (RBC), breaks these symmetries as the Rayleigh number increases. Recently, spatial double-reflection [...] Read more.

While thermal convection cells exhibit left–right and top–bottom symmetries at low Rayleigh numbers (

R a

), the emergence of coherent flow structures, such as elliptical large-scale circulation in Rayleigh–Bénard convection (RBC), breaks these symmetries as the Rayleigh number increases. Recently, spatial double-reflection symmetry was proposed and verified for two-dimensional RBC at a Prandtl number of 6.5 and

R a

values up to

10^{10}

. In this study, we examined this new symmetry at a lower Prandtl number of 0.7 and across a wider range of Rayleigh numbers, from

10^{7}

to

10^{13}

. Our findings reveal that the double-reflection symmetry is preserved for the mean profiles and flow fields of velocity and temperature for

R a < 10^{9}

, but it is broken at higher Rayleigh numbers. This asymmetry at high

R a

values is inferred to be induced by a flow-pattern transition at

R a = 10^{9}

. Together with the previous study, our results demonstrate that the Prandtl number has an important influence on the symmetry preservation in RBC. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

24 pages, 6522 KiB

Open AccessArticle

Blood Damage Analysis within the FDA Benchmark Nozzle Geometry at Laminar Conditions: Prediction Sensitivities to Software and Non-Newtonian Viscosity Models

by Gautham Krishnamoorthy and Nasim Gholizadeh

Symmetry 2024, 16(9), 1165; https://doi.org/10.3390/sym16091165 - 6 Sep 2024

Viewed by 891

Abstract

There is a prevailing consensus that most Computational Fluid Dynamics (CFD) frameworks can accurately predict global variables under laminar flow conditions within the Food and Drug Administration (FDA) benchmark nozzle geometry. However, variations in derived variables, such as strain rate and vorticity, may [...] Read more.

There is a prevailing consensus that most Computational Fluid Dynamics (CFD) frameworks can accurately predict global variables under laminar flow conditions within the Food and Drug Administration (FDA) benchmark nozzle geometry. However, variations in derived variables, such as strain rate and vorticity, may arise due to differences in numerical solvers and gradient evaluation methods, which can subsequently impact predictions related to blood damage and non-Newtonian flow behavior. To examine this, flow symmetry indices, vortex characteristics, and blood damage—were assessed using Newtonian and four non-Newtonian viscosity models with CFD codes Ansys Fluent and OpenFOAM on identical meshes. At Reynolds number (Re) 500, symmetry breakdown and complex vortex shapes were predicted with some non-Newtonian models in both OpenFOAM and Ansys Fluent, whereas these phenomena were not observed with the Newtonian model. This contradicted the expectation that employing a non-Newtonian model would delay the onset of turbulence. Similarly, at Re 2000, symmetry breakdown occurred sooner (following the sudden expansion section) with the non-Newtonian models in both Ansys Fluent and OpenFOAM. Vortex identification based on the Q-criterion resulted in distinctly different vortex shapes in Ansys Fluent and OpenFOAM. Blood damage assessments showed greater prediction variations among the non-Newtonian models at lower Reynolds numbers. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

23 pages, 6132 KiB

Open AccessArticle

Local-Energy-Conservation-Based Decomposition Method for Wall Friction and Heat Flux

by Mingzhi Tang, Wenfeng Zhou, Yanchao Hu, Gang Wang and Yanguang Yang

Symmetry 2024, 16(9), 1147; https://doi.org/10.3390/sym16091147 - 4 Sep 2024

Viewed by 907

Abstract

A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this [...] Read more.

A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this method provides a clear physical and reliable interpretation suitable for arbitrary-curvature profiles. Utilizing this method, an analysis of the aerothermodynamic characteristics of the bistable states of curved compression ramp flows was conducted. The results reveal that the generation of undisturbed and peak

C_{f}

is dominated by viscous dissipation. Specifically, flow separation happens when all of the energy input from the work exerted by the adverse pressure gradient (APG) is insufficient to be entirely converted into local viscous dissipation and kinetic energy. Furthermore, the propensity for flow separation at higher wall temperatures is firstly elucidated quantitatively from the perspective of the work by the APG. The peak heat flux is predominantly triggered by the work of viscous stress, with the secondary contribution from energy transport playing a more significant role in the generation of the peak heat flux of the separation state than that of the attachment state. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

24 pages, 10930 KiB

Open AccessArticle

The Influence of Low-Frequency Oscillations on Trailing-Edge Tonal Noise with Symmetry Spanwise Source Regions

by Zhangchen Song, Peiqing Liu, Hao Guo, Yifeng Sun and Shujie Jiang

Symmetry 2024, 16(6), 710; https://doi.org/10.3390/sym16060710 - 7 Jun 2024

Cited by 1 | Viewed by 862

Abstract

For noise reduction at a low-to-moderate Reynolds number, airfoil trailing-edge tonal noise has multiple prominent tones. Among these tones, secondary tones are greatly influenced by external disturbances such as oscillations commonly in the environment. In previous experiments, the spatial movement of sources was [...] Read more.

For noise reduction at a low-to-moderate Reynolds number, airfoil trailing-edge tonal noise has multiple prominent tones. Among these tones, secondary tones are greatly influenced by external disturbances such as oscillations commonly in the environment. In previous experiments, the spatial movement of sources was found to be related to an inherent high-frequency oscillation. Therefore, the spatial influence of external low-frequency oscillations was investigated in this study. By using tripping tapes to construct different symmetry source regions on the pressure side with side secondary tones, a transient spatial analysis of an NACA0012 airfoil at 2 degrees was performed by microphone arrays when a 10 Hz pressure oscillation was significant at 24 m/s. Temporally, this 10 Hz periodic strength change became more intense at a broader frequency bandwidth for a longer source region. Furthermore, a substantial time delay, significantly larger than the sound propagating time difference between microphones, was observed exclusively along the spanwise direction. This delay led to a periodic directivity pattern, particularly when two 0.2 m source regions were separated by a 0.2 m or 0.4 m tripping region. This low-frequency oscillation introduces an asymmetric transient switching pattern for symmetric spanwise source regions. Consequently, the response of airfoils to external oscillations in field tests should be considered. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

18 pages, 63940 KiB

Open AccessArticle

Tomographic Background-Oriented Schlieren for Axisymmetric and Weakly Non-Axisymmetric Supersonic Jets

by Tong Jia, Jiawei Li, Jie Wu and Yuan Xiong

Symmetry 2024, 16(5), 596; https://doi.org/10.3390/sym16050596 - 11 May 2024

Cited by 1 | Viewed by 1602

Abstract

The Schlieren technique is widely adopted for visualizing supersonic jets owing to its non-invasiveness to the flow field. However, extending the classical Schlieren method for quantitative refractive index measurements is cumbersome, especially for three-dimensional supersonic flows. Background-oriented Schlieren has gained increasing popularity owing [...] Read more.

The Schlieren technique is widely adopted for visualizing supersonic jets owing to its non-invasiveness to the flow field. However, extending the classical Schlieren method for quantitative refractive index measurements is cumbersome, especially for three-dimensional supersonic flows. Background-oriented Schlieren has gained increasing popularity owing to its ease of implementation and calibration. This study utilizes multi-view-based tomographic background-oriented Schlieren (TBOS) to reconstruct axisymmetric and weakly non-axisymmetric supersonic jets, highlighting the impact of flow axisymmetry breaking on TBOS reconstructions. Several classical TBOS reconstruction algorithms, including FDK, SART, SIRT, and CGLS, are compared quantitatively regarding reconstruction quality. View spareness is identified to be the main cause of degraded reconstruction quality when the flow experiences axisymmetry breaking. The classic visual hull approach is explored to improve reconstruction quality. Together with the CGLS tomographic algorithm, we successfully reconstruct the weakly non-axisymmetric supersonic jet structures and confirm that increasing the nozzle bevel angle leads to wider jet spreads. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

20 pages, 18983 KiB

Open AccessEditor’s ChoiceArticle

A Lagrangian Analysis of Tip Leakage Vortex in a Low-Speed Axial Compressor Rotor

by Jiexuan Hou, Yangwei Liu and Yumeng Tang

Symmetry 2024, 16(3), 344; https://doi.org/10.3390/sym16030344 - 13 Mar 2024

Cited by 4 | Viewed by 1326

Abstract

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent [...] Read more.

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent structures (LCSs). The computational method of the FTLE field in three-dimensional unsteady flow fields is discussed and then applied to the instantaneous flow fields at both the design and near-stall conditions. Results show that the accuracy of the particle trajectory and the density of the initial grid of the particle trajectory greatly affect the results of the FTLE field and, thus, the LCSs. Compared to the Eulerian Q method, which is calculated based on the symmetric and anti-symmetric components of the local velocity gradient tensor, the Lagrangian method has great potential in unraveling the mechanism of complex vortex structures. The LCSs show a transport barrier between the TLV and the secondary TLV, indicating two separate vortices. The aLCSs show the bubble-like and bar-like structure in the isosurfaces corresponding to the bubble and spiral breakdown patterns. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

12 pages, 505 KiB

Open AccessArticle

Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence

by Chensheng Luo, Ping-Fan Yang and Le Fang

Symmetry 2024, 16(2), 175; https://doi.org/10.3390/sym16020175 - 1 Feb 2024

Cited by 1 | Viewed by 1218

Abstract

In isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the literature. However, for two-dimensional isotropic turbulence, [...] Read more.

In isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the literature. However, for two-dimensional isotropic turbulence, they are still unclear. We derive rigorously the independent components for velocity gradient tensors of two-dimensional isotropic turbulence and give physical explanations. These theoretical results are validated using high-resolution direct numerical simulations (DNSs) of two-dimensional compressible turbulence. Results show that the present DNS setup is still not sufficient to capture the isotropy of third-order moments, suggesting that more investigations on determining the smallest scale and improving the numerical schemes for two-dimensional compressible turbulence are required. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

13 pages, 3998 KiB

Open AccessArticle

Symmetry Analysis of Mean Velocity Distribution in Stratified Atmospheric Surface Layers

by Yong Ji and Xi Chen

Symmetry 2023, 15(10), 1951; https://doi.org/10.3390/sym15101951 - 21 Oct 2023

Cited by 1 | Viewed by 1230

Abstract

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated here using the symmetry approach. Symmetry groups for the mean momentum and the Reynolds stress equations of ASL are searched under random dilation transformations, which, with different leading [...] Read more.

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated here using the symmetry approach. Symmetry groups for the mean momentum and the Reynolds stress equations of ASL are searched under random dilation transformations, which, with different leading order balances in different flow regions, lead to a set of specific scalings for the characteristic length

ℓ_{13}

(defined by Reynolds shear stress and mean shear). In particular, symmetry analysis shows that in the shear-dominated region,

ℓ_{13}

scales linearly with the surface height z, which corresponds to the classical log law of mean velocity. In the buoyancy-dominated region,

ℓ_{13} / L \sim {(z / L)}^{4 / 3}

for unstably stratified ASL and

ℓ_{13} / L \sim c o n s t

for stably stratified ASL, where L is the Obukhov length. The specific formula of the celebrated Monin–Obukhov similarity function is obtained, and hence an algebraic model of mean velocity profiles in ASL is derived, showing good agreement with the datum from the QingTu Lake observation array (QLOA) in China. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Applications Based on Symmetry/Asymmetry in Fluid Mechanics

Share This Special Issue

Special Issue Editor

Special Issue Information

Benefits of Publishing in a Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI