Laminar to Turbulent flow transition complexity
Bernoulli's equation does not apply during flow transition. Bernoulli's equation is only applicable to steady, incompressible, and frictionless flows. It cannot be used when the flow is rotational, turbulent, or unsteady. Bernoulli's equation is no longer applicable when the flow becomes excessively viscous or compressible and when the Reynolds number is large enough that the flow transitions to turbulence. There are laws which don't strictly apply under the conditions we often use. They introduce errors. Darcy's law is an example. Darcy's law is invalid for turbulent flow, which can occur in very coarse-grained sediments or in pipes with a Reynolds number above 4000
Following changes occur during transition from laminar to turbulent flow.
Wall shear stress: The frictional force exerted by the fluid on a surface change. In laminar flow, wall shear stress is directly proportional to the velocity gradient near the surface. In turbulent flow, wall shear stress is more complex and varies with turbulent fluctuations.
Mixing: In laminar flow, there is little mixing between adjacent layers. In turbulent flow, mixing is highly
Flow separation
Turbulent flow is less likely to separate
Turbulent flow is more resistant to separation than laminar flow. This is because turbulent flow has better wall-normal momentum transport. Flow separation can occur when flow transitions from laminar to turbulent:
Transitional separation: This type of separation occurs when the flow transitions from laminar to turbulent, and then back to laminar. It's characterized by a more abrupt separation of the boundary layer from the surface than laminar separation
Laminar separation bubble: This occurs when the flow transitions from laminar to turbulent over a surface due to an adverse pressure gradient. The region between the laminar separation and turbulent reattachment is called a laminar separation bubble
Increase in flow velocity: The transition from laminar to turbulent flow is typically triggered by an increase in flow velocity. As the velocity of the fluid increases, the flow patterns become more chaotic and irregular, ultimately leading to turbulent flow.
Formation of eddies and vortices: In laminar flow, the fluid moves in smooth, orderly layers with little to no mixing between them. In turbulent flow, however, the fluid experiences non-linear, chaotic motion that results in the formation of eddies and vortices. These structures cause significant mixing of fluid particles and can enhance heat and mass transfer.
Increase in pressure drop: Turbulent flow is associated with higher pressure drops compared to laminar flow. This occurs because of the increased mixing and turbulence in the flow, which results in higher frictional losses.
Enhancement of heat transfer: Turbulent flow is more effective at transferring heat compared to laminar flow. The chaotic motion of fluid particles in turbulent flow results in better mixing and increased contact between the fluid and the heat transfer surface, leading to higher heat transfer coefficients.
Increase in energy dissipation: Turbulent flow is characterized by higher levels of energy dissipation compared to laminar flow. This is due to the formation of eddies and vortices, which require additional energy to maintain the chaotic motion of the fluid.
Overall, the transition from laminar to turbulent flow is accompanied by significant changes in flow behavior, including increased mixing, flow separation, pressure drop, heat transfer, and energy dissipation. These changes have important implications for a wide range of industrial and natural processes involving fluid flows.
Complexity
The transition from laminar to turbulent flow significantly increases the complexity and unpredictability of fluid behavior due to the following reasons:
Chaotic motion: Turbulent flow is characterized by chaotic, irregular motion of fluid particles. This chaotic motion leads to the formation of vortices, eddies, and swirling patterns, which constantly evolve and change in a seemingly random manner. The unpredictable nature of these flow structures makes it difficult to predict the behavior of the fluid at any point in time.
Increased mixing: Turbulent flow is highly efficient at mixing different fluid layers and particles, leading to rapid and thorough mixing of fluid components. This results in a loss of distinct layers and boundaries within the fluid, making it challenging to track individual fluid particles or predict their trajectories.
Energy dissipation: Turbulent flow is associated with higher levels of energy dissipation compared to laminar flow. The constant generation and dissipation of turbulent kinetic energy in the form of eddies and vortices contribute to the complexity and unpredictability of fluid behavior. This energy dissipation leads to fluctuations in flow properties such as velocity, pressure, and temperature.
Non-linear dynamics: Turbulent flow exhibits non-linear behavior, meaning that small changes in initial conditions can lead to significant changes in the flow patterns and behavior over time. This sensitivity to initial conditions, known as the butterfly effect, makes it challenging to accurately predict the behavior of turbulent flows over longer time scales.
Lack of universal laws: Unlike laminar flow, which can be described by simplified mathematical equations such as the Navier-Stokes equations, turbulent flow does not have universally applicable laws that can accurately predict its behavior under all conditions. The complexity and unpredictability of turbulent flow often require the use of computational fluid dynamics (CFD) simulations and empirical models to understand and predict fluid behavior.
Overall, the transition from laminar to turbulent flow introduces a high degree of complexity, variability, and unpredictability in fluid behavior, making it challenging to accurately predict and control turbulent flows in engineering and natural systems.