來源：Reynolds Number calculation
https://www.nuclear-power.com/nuclear-engineering/fluid-dynamics/reynolds-number/

What is the Reynolds number?

The Reynolds number represents the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It is defined as a characteristic length multiplied by a characteristic velocity and divided by the kinematic viscosity.

Key Facts

• Osborn Reynolds discovered that the flow regime depends mainly on the ratio of the inertia forces to viscous forces in the fluid.
• When the viscous forces are dominant (slow flow, low Re), they are sufficient to keep all the fluid particles in line, then the flow is laminar.
• When the inertial forces dominate over the viscous forces (when the fluid flows faster and Re is larger), the flow is turbulent.

• It is defined as:
  Re

in which V is the mean flow velocity, D is a characteristic linear dimension, ρ fluid density, μ dynamic viscosity, and ν kinematic viscosity.

• The Reynolds number can be used to compare a real situation (e.g.,, airflow around an airfoil and water flow in a pipe) with a small-scale model.

Hydraulic Diameter

Since the characteristic dimension of a circular pipe is an ordinary diameter D and especially reactors contain non-circular channels, the characteristic dimension must be generalized.

For these purposes, the Reynolds number is defined as:

Re

where D_h is the hydraulic diameter:

D_h

D_h for different conditions

Example: Reynolds number for primary piping and a fuel bundle

Pressurized water reactors are cooled and moderated by high-pressure liquid water (e.g.,, 16MPa). At this pressure, water boils at approximately 350°C (662°F). The inlet temperature of the water is about 290°C (? ~ 720 kg/m³). The water (coolant) is heated in the reactor core to approximately 325°C (? ~ 654 kg/m³) as the water flows through the core.

D_h

The primary circuit of typical PWRs is divided into 4 independent loops (piping diameter ~ 700mm). Each loop comprises a** steam generator** and one main coolant pump. Inside the reactor pressure vessel (RPV), the coolant first flows down outside the reactor core (through the downcomer). The flow is reversed up through the core from the bottom of the pressure vessel, where the coolant temperature increases as it passes through the fuel rods and the assemblies formed by them.

Assume:

• the primary piping flow velocity is constant and equal to 17 m/s,
• the core flow velocity is constant and equal to 5 m/s,
• the hydraulic diameter of the fuel channel, D_h, is equal to 1 cm
• the kinematic viscosity of the water at 290°C is equal to 0.12 x 10^-6 m²/s

See also: Example: Flow rate through a reactor core

Determine

• the flow regime and the Reynolds number inside the fuel channel
• the flow regime and the Reynolds number inside the primary piping

The Reynolds number inside the primary piping is equal to:

Re_D = 17 [m/s] x 0.7 [m] / 0.12×10^-6 [m²/s] = 99 000 000

This fully satisfies the turbulent conditions.

The Reynolds number inside the fuel channel is equal to:

Re_DH = 5 [m/s] x 0.01 [m] / 0.12×10^-6 [m²/s] = 416 600

This also fully satisfies the turbulent conditions.