Turbulent flow refers to a type of fluid flow characterized by chaotic changes in pressure and velocity. Unlike laminar flow, where the fluid moves smoothly in parallel layers, turbulent flow is irregular, with eddies, vortices, and unpredictable fluctuations.
In fluid mechanics, turbulence refers to the irregular, chaotic, and unpredictable motion of fluid particles. It is a flow regime characterized by rapid changes in velocity and pressure within the fluid, often involving swirling motions, known as eddies or vortices.
Re) is high, indicating the dominance of inertial forces over viscous forces.The Reynolds number is calculated as: Re = (ρ u L) / μ
ρ: Density of the fluidu: Flow velocityL: Characteristic length (e.g., pipe diameter)μ: Fluid viscosityWhen Re > 4000 (for pipe flow), turbulence usually develops.
The equation governing turbulent flow is complex and involves solving the Navier-Stokes equations, which are fundamental to fluid mechanics. However, due to the chaotic nature of turbulence, these equations are often approximated or simplified using models.
The Navier-Stokes equations describe the motion of fluid particles:
∂u/∂t + (u ⋅ ∇) u = -(1/ρ) ∇p + ν ∇²u + f
u: Velocity vector of the fluid (u, v, w).t: Time.ρ: Density of the fluid.p: Pressure.ν: Kinematic viscosity (μ / ρ).f: External force acting on the fluid (e.g., gravity).∇²u: Viscous term representing diffusion of momentum.For turbulence:
To deal with turbulence, the velocity and pressure are expressed as the sum of:
U, P).u', p').u = U + u', p = P + p'
Substituting this into the Navier-Stokes equations and averaging gives:
∂U/∂t + (U ⋅ ∇) U = -(1/ρ) ∇P + ν ∇²U - ∇ ⋅ ⟨u'u'⟩
The additional term ⟨u'u'⟩ is the Reynolds stress tensor, representing the effect of turbulence on the flow.
A simpler criterion to predict turbulence is the Reynolds number:
Re = (ρ u L) / μ
u: Flow velocity.L: Characteristic length (e.g., diameter of a pipe).μ: Dynamic viscosity.The flow regimes are:
Re < 20002000 < Re < 4000Re > 4000If the Reynolds number is larger than 3500 for external flow, the flow is turbulent.
The vast majority of industrial flows are turbulent. Turbulent flows, for example, are common in a water distribution system that transports potable water from a centralized treatment plant or wells to end-users.
The laminar-turbulent transition, in which a laminar flow becomes turbulent, is connected with the critical Reynolds number. This is a very sophisticated process that we don't fully comprehend right now.