Drag Coefficient – Drag Characteristics

Drag Coefficient – Drag Characteristics

As was written, the drag characteristics of a body is represented by the dimensionless drag coefficient, CD, defined as:

drag coefficient - characteristics

The reference area, A, is defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For hollow objects, the reference area may be significantly larger than the cross sectional area, but for non-hollow objects, it is exactly the same as a cross sectional area. As can be seen, the drag coefficient is primarily a function of the shape of the body and taking into account both skin friction and form drag. It may also depend on the Reynolds number and the surface roughness.

When the friction and pressure drag coefficients are available, the total drag coefficient is determined by simply adding them:

skin friction - form drag - coefficients

At low Reynolds numbers, most drag is due to friction drag. This is especially the case for highly streamlined bodies such as airfoils. On the other hand, at high Reynolds number, the pressure drop is significant, which increases form drag.

 
Drag Coefficient - Cars
The drag coefficient is a common measure in automotive design. Drag coefficient, CD, is a commonly published rating of a car’s aerodynamic resistance, related to the shape of the car. Multiplying CD by the car’s frontal area gives an index of total drag. The result is called drag area.

Since aerodynamic drag and drag force increases with the square of velocity, this property becomes critically important at higher speeds. Reducing the drag coefficient in an automobile improves the performance of the vehicle as it pertains to speed and fuel efficiency. The average modern automobile achieves a drag coefficient of between CD = 0.30 and 0.35.

Drag Force – Drag Equation

The drag force, FD,depends on the density of the fluid, the upstream velocity, and the size, shape, and orientation of the body, among other things. One way to express this is by means of the drag equation. The drag equation is a formula used to calculate the drag force experienced by an object due to movement through a fluid.

drag force - drag equation - formula

The reference area, A, is defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion. For hollow objects, the reference area may be significantly larger than the cross sectional area, but for non-hollow objects, it is exactly the same as a cross sectional area.

Calculation of the Skin Friction Coefficient

The friction factor for turbulent flow depends strongly on the relative roughness. It is determined by the Colebrook equation or can be determined using the Moody chart. The Moody chart for Re = 575 600 and ε/D = 5 x 10-4 returns following values:

Therefore the skin friction coefficient is equal to:

skin friction coefficient - example

Calculation of the Drag Force

To calculate the drag force, we have to know:

  • the skin friction coefficient, which is: CD,friction = 0.00425
  • the area of pin surface, which is: A = π.d.h = 0.1169 m2
  • the fluid density, which is: ρ = 714 kg/m3
  • the core flow velocity, which is constant and equal to Vcore = 5 m/s

From the skin friction coefficient, which is equal to the Fanning friction factor we can calculate the frictional component of the drag force. The drag force is given by:

drag force - example

Assuming that a fuel assembly can have, for example, 289 fuel pins (17×17 fuel assembly), the frictional component of the drag force is then of the order of kilonewtons. Moreover, this drag force originates purely from the skin friction on fuel bundle. But typical PWR fuel assembly contains another components, which influence the fuel assembly hydraulics:

  • Fuel rods. Fuel rods contain the fuel and burnable poisons.
  • Top nozzle. Provides the mechanical support for the fuel assembly structure.
  • Bottom nozzle. Provides the mechanical support for the fuel assembly structure.
  • Spacing grid. Ensures an exact guiding of the fuel rods.
  • Guide thimble tube. Vacant tube for control rods or in-core instrumentation.

As was written, the second component of the drag force is the form drag. Form drag known also as pressure drag arises because of the shape and size of the object. The pressure drag is proportional to the difference between the pressures acting on the front and back of the immersed body, and the frontal area.

 
References:
Reactor Physics and Thermal Hydraulics:
  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. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Drag