Buoyancy Effects on Mixed Convective Flow Past an Inclined Square Cylinder: A Numerical Study at Re=100

Core Concepts

This study uses direct numerical simulations (DNS) to investigate the impact of buoyancy on the flow field around a heated square cylinder inclined at 45 degrees, revealing a critical Richardson number (Ri) where the near-field flow transitions from unsteady to steady, while the far-field exhibits plume-like unsteadiness.

Abstract

• Bibliographic Information: Kabilana, K., Sen, S., & Saha, A. K. (2024). Numerical investigation of buoyancy-aided mixed convective flow past a square cylinder inclined at 45 degrees. Physics of Fluids. arXiv:2411.03124v1 [physics.flu-dyn].
• Research Objective: This study investigates the impact of buoyancy on the flow field around a heated square cylinder inclined at 45 degrees, focusing on the near-field and far-field dynamics.
• Methodology: The researchers employed direct numerical simulations (DNS) to model two-dimensional, incompressible, buoyancy-aided mixed convective flow of air past a heated square cylinder at a fixed incidence angle of 45 degrees. The study considered a Reynolds number (Re) of 100 and a range of Richardson numbers (Ri) between 0.0 and 1.0, with air as the working fluid (Prandtl number, Pr = 0.7).
• Key Findings:
  • The study identified a critical Richardson number (Ri) of 0.68, where the near-field flow transitions from unsteady (characterized by vortex shedding) to steady.
  • This transition coincides with the emergence of unsteadiness in the far-field, exhibiting plume-like behavior.
  • The study observed vorticity inversion in the flow field, influenced by the interplay of forced and natural convection.
  • Increasing buoyancy leads to a decrease in the momentum recovery distance and an increase in the Strouhal number.
  • The time-averaged Nusselt number increases with increasing Ri for flow-facing surfaces and decreases for wake-facing surfaces.
• Main Conclusions: The study highlights the complex interplay of forced and natural convection in mixed convective flows past an inclined square cylinder. The presence of buoyancy significantly influences the flow field characteristics, including vortex shedding, vorticity inversion, and heat transfer. The findings provide insights into the transition mechanisms and far-field dynamics of such flows.
• Significance: This research contributes to the understanding of mixed convective flows, particularly the influence of buoyancy on flow structures and heat transfer characteristics. The findings have implications for various engineering applications involving heat transfer from bluff bodies, such as heat exchangers, electronic cooling, and building aerodynamics.
• Limitations and Future Research: The study is limited to two-dimensional simulations at a fixed Reynolds number. Future research could explore the three-dimensional nature of the flow at higher Reynolds numbers and investigate the impact of varying cylinder inclination angles on the observed phenomena.

Stats

The blockage ratio in the investigation is 2%.
The critical Richardson number, determined using Stuart-Landau analysis, is 0.68.
For Ri ≥ 0.7, the momentum recovery occurs around Y = 5.
The domain size for the simulations is 120d x 50d, where d is the projected length of the cylinder.
The Reynolds number (Re) for the simulations is 100.
The Prandtl number (Pr) for air is taken as 0.7.

Quotes

Key Insights Distilled From

Numerical investigation of buoyancy-aided mixed convective flow past a square cylinder inclined at 45 degrees

by Kavin Kabila... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.03124.pdf

Deeper Inquiries

How would the findings of this study be affected by considering a different fluid with a significantly different Prandtl number?

Considering a fluid with a significantly different Prandtl number would substantially impact the findings of this study, particularly concerning the heat transfer characteristics and the interplay between the thermal and momentum boundary layers. Here's a breakdown of the potential effects:
Prandtl Number's Role:
The Prandtl number (Pr) signifies the ratio of momentum diffusivity to thermal diffusivity. A high Pr indicates that momentum diffuses more effectively than heat, leading to a thinner thermal boundary layer compared to the momentum boundary layer. Conversely, a low Pr implies that heat diffuses faster, resulting in a thicker thermal boundary layer.
Impact of Different Prandtl Numbers:

Heat Transfer Rates: Fluids with higher Pr would generally exhibit lower Nusselt numbers (Nu) for the same Re and Ri. This is because the thinner thermal boundary layer would create a steeper temperature gradient near the cylinder, impeding heat transfer. Conversely, fluids with lower Pr would likely experience enhanced heat transfer due to a thicker thermal boundary layer and a less steep temperature gradient.

Critical Richardson Number (Ric): The critical Ri, where vortex shedding is suppressed, might shift. A higher Pr fluid, with its reduced thermal influence, could potentially lead to a lower Ric. This is because the buoyancy-driven flow, primarily governed by thermal variations, would have a less pronounced effect on the flow field.

Vorticity Inversion: The location and behavior of vorticity inversion could be altered. A higher Pr fluid might exhibit a delayed or less pronounced vorticity inversion due to the weaker coupling between the thermal and momentum fields.

Far-Field Unsteadiness: The characteristics of the far-field unsteadiness might be modified. The strength and frequency of the plume-like structures could be influenced by the different thermal diffusion rates associated with varying Pr.
In summary: Changing the fluid's Pr would necessitate a comprehensive re-evaluation of the flow and heat transfer phenomena. The balance between inertial, viscous, and buoyancy forces would be altered, leading to potentially significant changes in vortex shedding, heat transfer rates, and the overall flow structure.

Could the observed far-field unsteadiness be an artifact of the numerical simulation, or is it a physically realistic phenomenon?

While numerical simulations are inherently susceptible to artifacts, the observed far-field unsteadiness in this study is more likely a physically realistic phenomenon rather than a numerical artifact. Here's why:
Evidence Supporting Physical Realism:

Consistent with Previous Research: The presence of far-field unsteadiness in buoyancy-aided flows past bluff bodies has been reported in previous studies, particularly by Dushe (2017), lending credibility to the current findings.

Physical Mechanism: A plausible physical mechanism, the emergence of plume-like structures due to the interplay of buoyancy and inertial forces, explains the far-field unsteadiness. This suggests a physical basis for the observed behavior.

Domain Independence Test: The authors conducted a domain independence test, indicating that the observed unsteadiness is not merely a consequence of the chosen domain size or boundary conditions.
Addressing Potential Numerical Artifacts:

Outflow Boundary Condition: The choice of outflow boundary conditions can sometimes induce spurious reflections or unsteadiness. However, the authors employed a convective boundary condition, which is generally considered suitable for minimizing such artifacts.

Spatial Resolution: Inadequate grid resolution can lead to numerical instabilities or inaccurate representation of flow features. However, the authors performed a grid independence study, suggesting that the chosen grid is sufficiently refined to capture the relevant flow physics.
Further Validation:
To solidify the claim of physical realism, additional validation efforts could be beneficial:

Comparison with Experiments: Comparing the simulation results with experimental data, if available, would provide the most compelling evidence for the physical existence of far-field unsteadiness.

Sensitivity Analysis: Conducting a sensitivity analysis by varying numerical parameters, such as the time step size or the convective velocity in the outflow boundary condition, can help rule out numerical artifacts.
In conclusion: While acknowledging the possibility of numerical artifacts, the evidence strongly suggests that the observed far-field unsteadiness is a physically realistic phenomenon driven by the complex interaction of buoyancy and inertial forces in the flow.

How can the insights gained from this study be applied to optimize heat transfer in practical engineering applications, such as designing more efficient heat exchangers?

The insights from this study, particularly regarding the interplay of buoyancy, vortex shedding, and heat transfer, can be directly applied to optimize heat exchanger designs for enhanced efficiency. Here are some specific strategies:
1. Exploiting Vortex Shedding for Enhanced Mixing:

Optimal Spacing: The study highlights how vortex shedding enhances heat transfer by promoting fluid mixing. In heat exchangers with tube bundles, optimizing the spacing between tubes can promote beneficial vortex shedding, leading to thinner thermal boundary layers and improved heat transfer coefficients.

Turbulence Promoters: Introducing carefully designed turbulence promoters, such as fins or dimples, on heat transfer surfaces can induce controlled vortex shedding, even at lower Reynolds numbers, enhancing mixing and heat transfer.
2. Harnessing Buoyancy-Driven Flow:

Orientation Optimization: The study demonstrates the significant impact of buoyancy on flow patterns. In natural convection-dominated scenarios, optimizing the orientation of heat exchanger surfaces to align with the direction of buoyancy forces can enhance natural convection currents and improve heat transfer.

Mixed Convection Design: For applications involving both forced and natural convection, designing heat exchangers to leverage the synergistic effects of both mechanisms can lead to significant efficiency gains. This might involve optimizing flow channel geometries and flow rates to maximize both forced convection and buoyancy-induced mixing.
3. Tailoring Designs Based on Prandtl Number:

Fluid Selection: The study emphasizes the influence of the Prandtl number on heat transfer. Selecting fluids with lower Pr for heat exchanger applications can be advantageous, as they generally exhibit enhanced heat transfer due to thicker thermal boundary layers.

Surface Modifications: For fluids with higher Pr, where heat transfer is limited by the thin thermal boundary layer, employing surface modifications like micro-fins or rough surfaces can increase the effective heat transfer area and enhance heat transfer rates.
4. Utilizing Numerical Simulations for Design Optimization:

Parametric Studies: Conducting comprehensive numerical simulations, similar to the study, allows for parametric studies to investigate the influence of various design parameters, such as tube diameters, fin geometries, and flow conditions, on heat exchanger performance.

Optimization Algorithms: Integrating numerical simulations with optimization algorithms can enable the automated design of heat exchangers with optimized geometries and operating parameters for maximum heat transfer efficiency.
In essence: By understanding the intricate relationships between buoyancy, vortex shedding, and heat transfer revealed in this study, engineers can make informed design decisions to optimize heat exchanger performance, leading to more efficient and sustainable energy systems.