Navigating the complex landscape of fluid dynamics unveils a dichotomy between laminar and turbulent flow phenomena. This scholarly exploration delves into their distinct characteristics, spanning from the ordered trajectories of laminar flow to the chaotic eddies of turbulent flow. Investigating their implications across natural and engineered systems unveils the critical role of the Reynolds number in delineating flow regimes. Furthermore, we scrutinize the computational methodologies offered by ANSYS Fluent to simulate these phenomena, elucidating the nuanced intricacies of each viscous model.

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ToggleThis academic discourse aims to deepen our understanding of fluid dynamics and its computational simulations, fostering advancements in engineering and scientific domains.

## What is laminar flow?

In a **laminar flow**, fluid particles move along smooth, non-crossing paths in distinct layers. This type of flow is predictable and can be accurately modeled mathematically. Essentially, laminar flow is characterized by well-defined, orderly paths, with fluid particles moving in a structured manner.

Have you ever seen engine oil spilled? In some cases, you will encounter a situation like Figure 1. Even though you know the fluid is moving, it appears solid. This phenomenon occurs because the movement of the oil is a laminar flow, moving completely uniformly, so no change is seen in the flow, giving the illusion of solidity.

Figure 1. Laminar flow of engine oil.

In Figure 2, the fluid inside the tube exhibits laminar flow. The ink is injected into the flow by a syringe. Due to the laminar flow, the ink follows a specific path and does not mix with the fluid immediately. The ink may slowly mix with the fluid through diffusion.

Figure 2. Injecting ink into a laminar flow.

## What is Turbulent Flow?

In t**urbulent flow**, the fluid moves irregularly. This type of flow is characterized by disordered motion with eddies, swirls, and vortices, leading to high levels of turbulence and mixing.

Figure 3. Water vapor in this image exhibits turbulent flow.

In Figure 4, the fluid inside the tube exhibits turbulent flow. The ink is injected into the flow by a syringe. Due to the turbulent flow, the ink mixes quickly with the fluid.

Figure 4. Injecting ink into a turbulent flow.

Turbulent flow is chaotic in nature, making many of its details unpredictable. For instance, the speed of the flow at a specific point varies unpredictably over time. However, experimental tests reveal that the average speed over time remains constant.

## Example of laminar flow

**Honey dripping:**The slow, viscous honey flows smoothly in layers as it drizzles down, illustrating laminar flow.**Flow in microfluidic devices:**Laminar flow is commonly employed in microfluidic devices across fields like biotechnology and chemistry due to its predictability and limited fluid mixing.**Blood Flow in Capillaries**: Blood flow in the body’s small blood vessels, like capillaries, typically demonstrates laminar flow, driven by their low velocities and small diameters.

## Example of turbulent flow

**Car Exhaust:**When driving a car, the exhaust emitted from the rear is an example of turbulent flow. The exhaust gas contains particles in random motion.**Waterfalls:**The flow of water over a waterfall can transition from laminar to turbulent as it descends and interacts with the air and rocks below.**River Flow:**Rivers frequently demonstrate turbulent flow, attributed to the presence of rocks, bends, and fluctuations in depth that disturb the otherwise smooth movement of water.

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## Laminar flow Vs turbulent flow Reynolds number

Scientists and engineers use the dimensionless Reynolds number to determine whether a flow is in a laminar or turbulent regime.

Where *ρ* [Kg.m^{-3}] is the fluid density, *V* [m.s^{-1}] is the characteristic velocity of the flow, *L* [m] is a characteristic length scale of the flow (e.g., pipe diameter for flow in a pipe) and *μ* [Pa.s] is the dynamic viscosity of the fluid.

The Reynolds number is interpreted as the ratio of inertial forces to viscous forces. Although this number is not the exact ratio of these forces, as it increases, the influence of inertial forces relative to viscous forces also increases, leading to a rise in flow turbulence.

In the movement of any fluid, several factors contribute to irregular fluid flow, including surface roughness, the presence of obstacles, and variations in fluid properties at different pressures and temperatures. The irregularities in fluid flow are mitigated by viscosity and friction. However, as the Reynolds number increases and the inertia relative to viscosity rises, friction becomes less effective in suppressing these irregularities, leading to turbulent flow.

In a fluid phenomenon, such as fluid flow inside a pipe with a circular cross-section, the Reynolds number is increased from low to high values. Based on experimental results, researchers determine the Reynolds number at which the flow becomes turbulent.

For flow in a circular pipe, the critical Reynolds number that separates laminar and turbulent flow is generally accepted to be around Re = 2300. It is not the case that the flow regime suddenly changes at Re = 2300; rather, the flow regime changes gradually. For flow in a circular pipe, consider the flow as laminar when Re = 100 and as turbulent when Re = 4000. In the case where Re = 2100, be cautious with your numerical calculations; considering the flow as either turbulent or laminar will result in errors. In such cases, it is better to rely on experimental methods.

The Reynolds number is used in every fluid and heat transfer phenomenon where the flow regime is important. These phenomena include flow separation, drag force, convection heat transfer, and more.

## Difference between laminar, turbulent, and transitional flow

In various sources discussing fluid flow regimes, a transitional zone is introduced to improve accuracy between laminar and turbulent zones. In this region, the fluid gradually becomes more turbulent as the Reynolds number increases until it reaches a state of complete turbulence.

For flow in a circular pipe, Re < 2300 is considered the laminar zone, 2300 < Re < 4000 is the transition zone, and Re > 4000 is the turbulent zone.

## Laminar vs turbulent flow in lakes and rivers

In lakes and rivers, the distinction between laminar and turbulent flows shapes the dynamics of water movement and profoundly influences aquatic ecosystems. Laminar flow, characterized by smooth and orderly movement of fluid particles, is relatively rare in natural water bodies due to the typically low velocities and high viscosities required.

It may occur in calm, shallow waters or engineered channels with low flow rates, impacting sediment transport and nutrient distribution. In contrast, turbulent flow, with its chaotic and irregular motion, dominates in rivers, especially in fast-moving streams, rapids, and areas with obstacles. Turbulent flow facilitates sediment transport, enhances mixing for nutrient distribution, and dissipates energy through friction. Understanding these flow regimes is essential for managing and conserving aquatic environments.

## What is Rayleigh number?

The Rayleigh number (Ra) is a dimensionless number in fluid mechanics that helps predict natural convection in fluids. It plays a crucial role in determining whether natural convection in a fluid will be laminar or turbulent. It is defined as:

Where *g* [m.s^{-2}] is the acceleration due to gravity, *β* [1.K^{-1}] is the thermal expansion coefficient of the fluid, *x* [m] is the characteristic length scale, *α* [m^{2}.s] is the thermal diffusivity of the fluid, *ν* [m^{2}.s] is the kinematic viscosity of the fluid, T_{S }[K] is the surface temperature and T_{∞} [K] is fluid temperature.

The Rayleigh number is expressed as a measure of the ratio of the buoyancy force to the viscous force. It should be noted that it is not the exact ratio of these two forces, but it indicates that as the Rayleigh number increases, the ratio of the buoyancy force to the viscous force also increases.

Figure 5. Free convection boundary layer transition on a vertical plate, from “Fundamentals of heat and mass transfer” by Frank P. Incropera et al.

**In natural convection, the flow regime is determined by the Rayleigh number, not the Reynolds number.** Figure 5 shows natural convection flow on a vertical plane. As can be seen, the flow regime changes at Ra = 10^{9}, which is called the critical Rayleigh number. Natural convection currents are created due to the temperature difference in the fluid, which causes a density difference and the resulting buoyancy force.

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## The flow regime in ANSYS Fluent

In Ansys Fluent, the user determines the flow regime by calculating the Reynolds number (or Rayleigh number in case of natural convection) outside the software. Based on this calculation, it is determined whether the flow simulation is laminar or turbulent.

There are several methods in Fluent to simulate turbulent flow. Each of them has its advantages and disadvantages and is suitable for specific applications.

Under the title of “Viscous Models” in the software, all the simulation methods for the fluid flow regime available in the software are:

- Inviscid: In this model, it is assumed that fluid has no viscosity.
- Laminar: There is just one model for viscous laminar flows and it solves ordinary Navier-Stokes equation. The following models are for simulating turbulent flow
- Spalart-Allmaras: It is a Reynolds-Averaged Navier-Stokes (RANS) model, suitable for aerodynamics applications.
- k-epsilon: It is a Reynolds-Averaged Navier-Stokes (RANS) model, suitable for general-purpose turbulence modeling in various applications.
- k-omega: It is a Reynolds-Averaged Navier-Stokes (RANS) model, suitable for modeling near-wall and low-Reynolds number turbulence.
- Transition k-kl-omega: It is a Reynolds-Averaged Navier-Stokes (RANS) model, suitable for modeling transitional flows from laminar to turbulent.
- Transition SST: This model is a combination of the k-epsilon and k-omega turbulence models.
- Reynolds Stress it is a RANS model suitable for simulating highly anisotropic turbulent flows.
- Scale-Adaptive simulation: A hybrid RANS-LES model suitable for resolving different turbulent scales.
- Detached Eddy Simulation: A hybrid RANS-LES model suitable for resolving eddies near walls.
- Large Eddy Simulation(LES): A method resolving large turbulent structures, suitable for high-resolution simulations. It is
**not**a RANS model.

The details of each viscous model can be adjusted in the software. For example, for the k-epsilon model, there are three modes: standard, RNG, and realizable.

Figure 6. Viscous models, ANSYS Fluent

## Conclusion

In conclusion, our exploration of laminar and turbulent flow phenomena reveals their fundamental importance across various disciplines, from fluid dynamics to engineering and beyond.

By understanding the distinctions between these flow regimes and the critical role of the Reynolds number in their delineation, we gain valuable insights into complex fluid behavior. Moreover, the computational simulations offered by ANSYS Fluent provide powerful tools for modeling and analyzing these phenomena with precision.

As we continue to delve into the intricacies of fluid dynamics, this knowledge serves as a cornerstone for advancements in research, engineering design, and technological innovation.

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