Characteristic Numbers

Characteristic Numbers

In fluid dynamics and heat transfer, characteristic numbers are dimensionless numbers used to describe a character of the flow or to describe a character of heat transfer. Characteristic numbers can be used to compare a real situation (e.g. air flow around an airfoil and water flow in a pipe) with a small-scale model. It is necessary to keep the important characteristic numbers the same. Names of these numbers were standardized in ISO 31-12, which gives name, symbol and definition for 25 selected characteristic numbers used for the description of transport phenomena.

Reynolds Number

The Reynolds number is 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 can be interpreted that when the viscous forces are dominant (slow flow, low Re) they are sufficient enough to keep all the fluid particles in line, then the flow is laminar. Even very low Re indicates viscous creeping motion, where inertia effects are negligible. When the inertial forces dominate over the viscous forces (when the fluid is flowing faster and Re is larger) then the flow is turbulent.

reynolds number

It is a dimensionless number comprised of the physical characteristics of the flow. An increasing Reynolds number indicates an increasing turbulence of flow.

It is defined as:
Reynolds number

where:
V is the flow velocity,
D is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter etc.)
ρ fluid density (kg/m3),
μ dynamic viscosity (Pa.s),
ν kinematic viscosity (m2/s);  ν = μ / ρ.

Prandtl Number

The Prandtl number is a dimensionless number, named after its inventor, a German engineer Ludwig Prandtl, who also identified the boundary layer. The Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity. The momentum diffusivity, or as it is normally called, kinematic viscosity, tells us the material’s resistance to shear-flows (different layers of the flow travel with different velocities due to e.g. different speeds of adjacent walls) in relation to density. That is, the Prandtl number is given as:

Prandtl Number

where:

ν is momentum diffusivity (kinematic viscosity) [m2/s]

α is thermal diffusivity [m2/s]

μ is dynamic viscosity [N.s/m2]

k is thermal conductivity [W/m.K]

cp is specific heat [J/kg.K]

ρ is density [kg/m3]

Small values of the Prandtl number, Pr < < 1, means the thermal diffusivity dominates. Whereas with large values, Pr >> 1, the momentum diffusivity dominates the behavior. For example, the typical value for liquid mercury, which is about 0.025, indicates that the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. When Pr is small, it means that the heat diffuses quickly compared to the velocity.

In comparison to Reynolds number, the Prandtl number is not dependent on geometry of an object involved in the problem, but is dependent solely on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.

See also: Prandtl Number

 
References:
Heat Transfer:
  1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
  2. Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.
  3. Fundamentals of Heat and Mass Transfer. C. P. Kothandaraman. New Age International, 2006, ISBN: 9788122417722.
  4. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Introduction to Heat Transfer