# Flow Regime

From a practical engineering point of view, the flow regime can be categorized according to several criteria.

All fluid flow is classified into one of two broad categories or regimes. These two flow regimes are:

• Single-phase Fluid Flow
• Multi-phase Fluid Flow (or Two-phase Fluid Flow)

This is a basic classification. All of the fluid flow equations (e.g.,, Bernoulli’s Equation) and relationships discussed in this section (Fluid Dynamics) were derived for the flow of a single phase of fluid, whether liquid or vapor. Solution of multi-phase fluid flow is very complex and difficult, and therefore it is usually in advanced courses of fluid dynamics.

Another usually more common classification of flow regimes is according to the shape and type of streamlines. All fluid flow is classified into one of two broad categories. The fluid flow can be either laminar or turbulent, and therefore these two categories are:

• Laminar Flow
• Turbulent Flow

Laminar flow is characterized by smooth or regular paths of particles of the fluid. Therefore the laminar flow is also referred to as streamline or viscous flow. In contrast to laminar flow, turbulent flow is characterized by the irregular movement of particles of the fluid. The turbulent fluid does not flow in parallel layers, the lateral mixing is very high, and there is a disruption between the layers. Most industrial flows, especially those in nuclear engineering, are turbulent.

The flow regime can also be classified according to the geometry of a conduit or flow area. From this point of view, we distinguish:

• Internal Flow
• External Flow

Internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of the behavior of internal flow regimes is important in engineering because circular pipes can withstand high pressures and hence are used to convey liquids. On the other hand, external flow is such a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces. Detailed knowledge of the behavior of external flow regimes is of importance, especially in aeronautics and aerodynamics.

Single-phase vs. Multi-phase Fluid Flow

## Single-phase Fluid Flow

A classic study of fluid dynamics concentrates on the flow of a single homogeneous phase, e.g.,, water, air, steam. The fluid flow equations and relationships normally discussed in this section are for the flow of a single phase of fluid, whether liquid or vapor.

When the simultaneous flow of liquid and gas occurs at certain important locations in fluid flow systems, the problem must be solved as a two-phase flow. The relatively simple relationships used for analyzing single-phase flow are insufficient for analyzing two-phase flow.

## Two-phase Fluid Flow

By definition, multi-phase flow is the interactive flow of two or more distinct phases with common interfaces in, say, a conduit. Each phase, representing a volume fraction (or mass fraction) of solid, liquid, or gaseous matter, has its own properties, velocity, and temperature.

A multi-phase flow can be a simultaneous flow of:

• Materials with different states or phases (e.g.,, water-steam mixture).
• Materials with different chemical properties but in the same state or phase (e.g.,, oil droplets in water).

There are many combinations in industrial processes, but the most common being the simultaneous flow of steam and liquid water (as encountered in steam generators and condensers). In reactor engineering, a great deal of study has been performed on the nature of two-phase flow in case of a loss-of-coolant accident (LOCA), an accident of importance in reactor safety, and all thermal-hydraulic analyses (DNBR analyses).

## Characteristics of Multiphase Fluid Flow

All multi-phase flow problems have features that are characteristically different from those found in single-phase problems.

• In the case of steam and liquid water, the density of the two phases differs by a factor of about 1000. Therefore the influence of gravitational body force on multi-phase flows is of much greater importance than in the case of single-phase flows.
• The sound speed changes dramatically for materials undergoing a phase change and can be orders of magnitude different. This significantly influences a flow through an orifice.
• The relative concentration of different phases is usually a dependent parameter of great importance in multi-phase flows, while it is a parameter of no consequence in single-phase flows.
• The phase change means flow-induced pressure drops can cause further phase change (e.g.,, water can evaporate through an orifice), increasing the relative volume of the gaseous, compressible medium and increasing efflux velocities, unlike single-phase incompressible flow where decreasing of an orifice would decrease efflux velocities.
• The spatial distribution of the various phases in the flow channel strongly affects the flow behavior.
• There are many types of instabilities in multi-phase flow.
Laminar vs. Turbulent Flow

## Laminar Flow

In fluid dynamics, laminar flow is characterized by smooth or regular paths of fluid particles, in contrast to turbulent flow, which is characterized by the irregular movement of particles of the fluid. The fluid flows in parallel layers (with minimal lateral mixing), with no disruption between the layers. Therefore the laminar flow is also referred to as streamline or viscous flow.

The term streamline flow is descriptive of the flow because, in laminar flow, layers of water flow over one another at different speeds with virtually no mixing between layers. Fluid particles move indefinite and observable paths or streamlines.

When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow (laminar flow or turbulent flow) may occur depending on the velocity, viscosity of the fluid, and the size of the pipe (or on the Reynolds number). Laminar flow tends to occur at lower velocities and high viscosity.

## Turbulent Flow

In fluid dynamics, turbulent flow is characterized by the fluid’s irregular movement of particles (one can say chaotic). In contrast to laminar flow, the fluid does not flow in parallel layers, the lateral mixing is very high, and there is a disruption between the layers. Turbulence is also characterized by recirculation, eddies, and apparent randomness. In turbulent flow, the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction.

Detailed knowledge of the behavior of turbulent flow regimes is important in engineering because most industrial flows, especially those in nuclear engineering, are turbulent. Unfortunately, the highly intermittent and irregular character of turbulence complicates all analyses. In fact, turbulence is often the “last unsolved problem in classical mathematical physics.”

The main tool available for their analysis is CFD analysis. CFD is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve turbulent fluid flows. It is widely accepted that the Navier–Stokes equations (or simplified Reynolds-averaged Navier–Stokes equations) are capable of exhibiting turbulent solutions, and these equations are the basis for essentially all CFD codes.

Internal vs. External Flow

## Internal Flow

In fluid dynamics, internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of the behavior of internal flow regimes is important in engineering because circular pipes can withstand high pressures and hence are used to convey liquids. Non-circular ducts are used to transport low-pressure gases, such as air in cooling and heating systems. The internal flow configuration is a convenient geometry for heating and cooling fluids used in energy conversion technologies such as nuclear power plants.

## External Flow

In fluid dynamics, external flow is a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces. In comparison to internal flow, external flows feature highly viscous effects confined to rapidly growing “boundary layers” in the entrance region of thin shear layers along the solid surface. Accordingly, there will always exist a region of the flow outside the boundary layer. In this region, velocity, temperature, and/or concentration do not change, and their gradients may be neglected.

This effect causes the boundary layer to be expanding, and the boundary-layer thickness relates to the fluid’s kinematic viscosity.

This is demonstrated in the following picture. Far from the body, the flow is nearly inviscid, and it can be defined as the flow of a fluid around a body that is completely submerged in it.

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

Fluid Dynamics