Nick Connor

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.

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:

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.

Charts: Viscosity and Density of Water (16MPa)

Laminar vs. Turbulent Flow

Laminar flow:

• Re < 2000
• ‘low’ velocity
• Fluid particles move in straight lines
• Layers of water flow over one another at different speeds with virtually no mixing between layers.
• The flow velocity profile for laminar flow in circular pipes is parabolic in shape, with a maximum flow in the center of the pipe and a minimum flow at the pipe walls.
• The average flow velocity is approximately one half of the maximum velocity.
• Simple mathematical analysis is possible.
• Rare in practice in water systems.

Turbulent Flow:

• Re > 4000
• ‘high’ velocity
• The flow is characterized by the irregular movement of particles of the fluid.
• Average motion is in the direction of the flow
• The flow velocity profile for turbulent flow is fairly flat across the center section of a pipe and drops rapidly extremely close to the walls.
• The average flow velocity is approximately equal to the velocity at the center of the pipe.
• Mathematical analysis is very difficult.
• Most common type of flow.

Reynolds Number Regimes

Laminar flow. For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. The accepted transition Reynolds number for flow in a circular pipe is Re_d,crit = 2300.

Transitional flow. At Reynolds numbers between about 2000 and 4000 the flow is unstable as a result of the onset of turbulence. These flows are sometimes referred to as transitional flows.

Turbulent flow. If the Reynolds number is greater than 3500, the flow is turbulent. Most fluid systems in nuclear facilities operate with turbulent flow.

Reynolds Number and Internal Flow

The internal flow (e.g. flow in a pipe) configuration is a convenient geometry for heating and cooling fluids used in energy conversion technologies such as nuclear power plants.

In general, this flow regime is of importance 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.

For internal flow regime an entrance region is typical. In this region a nearly inviscid upstream flow converges and enters the tube. To characterize this region the hydrodynamic entrance length is introduced and is approximately equal to:

The maximum hydrodynamic entrance length, at Re_D,crit = 2300 (laminar flow), is L_e = 138d, where D is the diameter of the pipe. This is the longest development length possible. In turbulent flow, the boundary layers grow faster, and L_e is relatively shorter. For any given problem, L_e / D has to be checked to see if L_e is negligible when compared to the pipe length. At a finite distance from the entrance, the entrance effects may be neglected, because the boundary layers merge and the inviscid core disappears. The tube flow is then fully developed.

Hydraulic Diameter

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

For these purposes the Reynolds number is defined as:

where D_h is the hydraulic diameter:

The hydraulic diameter, D_h, is a commonly used term when handling flow in non-circular tubes and channels. The hydraulic diameter transforms non-circular ducts into pipes of equivalent diameter. Using this term, one can calculate many things in the same way as for a round tube. In this equation A is the cross-sectional area, and P is the wetted perimeter of the cross-section. The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow.

Reynolds Number and External Flow

The Reynolds number describes naturally the external flow as well. In general, when a fluid flows over a stationary surface, e.g. the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought to rest by the shear stress to at the wall. The region in which flow adjusts from zero velocity at the wall to a maximum in the main stream of the flow is termed the boundary layer.

Basic characteristics of all laminar and turbulent boundary layers are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

Boundary layers may be either laminar, or turbulent depending on the value of the Reynolds number.

Also here the Reynolds number represents the ratio of inertia forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It is defined as:

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

For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. As the Reynolds number increases (with x) the flow becomes unstable and finally for higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer.

Transition from laminar to turbulent boundary layer occurs when Reynolds number at x exceeds Re_x ~ 500,000. Transition may occur earlier, but it is dependent especially on the surface roughness. The turbulent boundary layer thickens more rapidly than the laminar boundary layer as a result of increased shear stress at the body surface.

The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an “effective” shape which is usually slightly different from the physical shape. We define the thickness of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity.

To make things more confusing, the boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure.

See also: Boundary layer thickness

See also: Tube in crossflow – external flow

Special reference: Schlichting Herrmann, Gersten Klaus. Boundary-Layer Theory, Springer-Verlag Berlin Heidelberg, 2000, ISBN: 978-3-540-66270-9

See also:

Fluid Dynamics

Boundary Layer Thickness

We define the thickness of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity. For laminar boundary layers over a flat plate, the Blasius solution of the flow governing equations gives:

where Re_x is the Reynolds number based on the length of the plate.

For a turbulent flow the boundary layer thickness is given by:

This equation was derived with several assumptions. The turbulent boundary layer thickness formula assumes that the flow is turbulent right from the start of the boundary layer.

Example: Boundary Layer Thickness

Consider a water flow (20°C) at v =  0.1 m/s past a flat plate 1 m long. Compute the boundary layer thickness in the middle of the plate. Assume that kinematic viscosity of water at 20°C is equal to 1×10^-6 m²/s.

The Reynolds number for the middle of the plate is equal to:

Re_L/2 = 0.1 [m/s] x 0.5 [m] / 1×10^-6 [m²/s] = 50 000

This satisfies the laminar conditions. The boundary layer thickness is therefore equal to:

δ ≈ 5.0 x 0.5 / (50 000)^½ = 0.011 m

See also:

Boundary Layer

Boundary Layer

In general, when a fluid flows over a stationary surface, e.g. the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought to rest by the shear stress to at the wall. The region in which flow adjusts from zero velocity at the wall to a maximum in the main stream of the flow is termed the boundary layer. The concept of boundary layers is of importance in all of viscous fluid dynamics and also in the theory of heat transfer.

Basic characteristics of all laminar and turbulent boundary layers are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

Boundary layers may be either laminar, or turbulent depending on the value of the Reynolds number.

The Reynolds number is the ratio of inertia forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It is defined as

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

For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. As the Reynolds number increases (with x) the flow becomes unstable and finally for higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer.

Transition from laminar to turbulent boundary layer occurs when Reynolds number at x exceeds Re_x ~ 500,000. Transition may occur earlier, but it is dependent especially on the surface roughness. The turbulent boundary layer thickens more rapidly than the laminar boundary layer as a result of increased shear stress at the body surface.

The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an “effective” shape which is usually slightly different from the physical shape. We define the thickness of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity.

To make things more confusing, the boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure.

Special reference: Schlichting Herrmann, Gersten Klaus. Boundary-Layer Theory, Springer-Verlag Berlin Heidelberg, 2000, ISBN: 978-3-540-66270-9

Boundary Layer Thickness

We define the thickness of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity. For laminar boundary layers over a flat plate, the Blasius solution of the flow governing equations gives:

where Re_x is the Reynolds number based on the length of the plate.

For a turbulent flow the boundary layer thickness is given by:

This equation was derived with several assumptions. The turbulent boundary layer thickness formula assumes that the flow is turbulent right from the start of the boundary layer.

Thermal Boundary Layer

Similarly as a velocity boundary layer develops when there is fluid flow over a surface, a thermal boundary layer must develop if the bulk temperature and surface temperature differ. Consider flow over an isothermal flat plate at a constant temperature of T_wall. At the leading edge the temperature profile is uniform with T_bulk. Fluid particles that come into contact with the plate achieve thermal equilibrium at the plate’s surface temperature. At this point, energy flow occurs at the surface purely by conduction. These particles exchange energy with those in the adjoining fluid layer (by conduction and diffusion), and temperature gradients develop in the fluid. The region of the fluid in which these temperature gradients exist is the thermal boundary layer. Its thickness, δ_t, is typically defined as the distance from the body at which the temperature is 99% of the temperature found from an inviscid solution. With increasing distance from the leading edge, the effects of heat transfer penetrate farther into the stream and the thermal boundary layer grows.

The ratio of these two thicknesses (velocity and thermal boundary layers) is governed by the Prandtl number, which is defined as the ratio of momentum diffusivity to thermal diffusivity. A Prandtl number of unity indicates that momentum and thermal diffusivity are comparable, and velocity and thermal boundary layers almost coincide with each other. If the Prandtl number is less than 1, which is the case for air at standard conditions, the thermal boundary layer is thicker than the velocity boundary layer. If the Prandtl number is greater than 1, the thermal boundary layer is thinner than the velocity boundary layer. Air at room temperature has a Prandtl number of 0.71 and for water at 18°C it is around 7.56, which means that the thermal diffusivity is more dominant for air than for water.

Similarly as for Prandtl Number, the Lewis number physically relates the relative thickness of the thermal layer and mass-transfer (concentration) boundary layer. The Schmidt number physically relates the relative thickness of the velocity boundary layer and mass-transfer (concentration) boundary layer.

where n = 1/3  for most applications in all three relations. These relations, in general, are applicable only for laminar flow and are not applicable to turbulent boundary layers since turbulent mixing in this case may dominate the diffusion processes.

See also:

Fluid Dynamics

External Flow

In fluid dynamics, external flow is such a flow in which boundary layers develop freely, without constraints imposed by adjacent surfaces. In comparison to internal flow, entrance flows and external flows feature highly viscous effects confined to rapidly growing “boundary layers” in the entrance region, or to 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 does not change in and their gradients may be neglected.

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

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

Fluid Flow over a Flat Plate

In general, when a fluid flows over a stationary surface, e.g. the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought to rest by the shear stress to at the wall. The region in which flow adjusts from zero velocity at the wall to a maximum in the main stream of the flow is termed the boundary layer. The concept of boundary layers is of importance in all of viscous fluid dynamics and also in the theory of heat transfer.

Basic characteristics of all laminar and turbulent boundary layers are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:

Boundary layers may be either laminar, or turbulent depending on the value of the Reynolds number.

See also: Boundary Layer

Tube in crossflow

The crossflow of tubes or cylinders shows many flow regimes, that are dependent on the Reynolds number.

• Re_D < 5. At Reynolds numbers below 1 no separation occurs.
• 5 ≤ Re_D ≤ 45. In this Reynolds number range the flow separates from the rear side of the tube and a symmetric pair of vortices is formed in the near wake.
• 40 ≤ Re_D ≤ 150. In this Reynolds number range the wake becomes unstable and vortex shedding is initiated.
• 150 < Re_D < 300.  In this Reynolds number range is the flow transitional and gradually becomes turbulent as the Reynolds number is increased.
• 300 < Re_D < 1.5·10⁵. This region is called subcritical. The laminar boundary layer separates at about 80 degrees downstream of the front stagnation point and the vortex shedding is strong and periodic.
• 2·10⁵ < Re_D < 3.5·10⁶. Three-dimensional effects disrupt the regular shedding process and the spectrum of shedding frequencies is broadened. With a further increase of Re_D, the flow enters the critical regime.
• Re_D > 3.5·10⁶. This regime is called supercritical. In this regime a regular vortex shedding is re-established with a turbulent boundary layer on the tube surface.

See also:

Flow Regime

Hydrodynamic Entrance Length

For internal flow regime an entrance region is typical. In this region a nearly inviscid upstream flow converges and enters the tube. To characterize this region the hydrodynamic entrance length is introduced and is approximately equal to:

The maximum hydrodynamic entrance length, at Re_D,crit = 2300 (laminar flow), is L_e = 138d, where D is the diameter of the pipe. This is the longest development length possible. In turbulent flow, the boundary layers grow faster, and L_e is relatively shorter. For any given problem, L_e / D has to be checked to see if L_e is negligible when compared to the pipe length. At a finite distance from the entrance, the entrance effects may be neglected, because the boundary layers merge and the inviscid core disappears. The tube flow is then fully developed.

See also:

Internal Flow

Hydraulic Diameter

The hydraulic diameter, D_h, is a commonly used term when handling flow in non-circular tubes and channels. The hydraulic diameter transforms non-circular ducts into pipes of equivalent diameter. Using this term, one can calculate many things in the same way as for a round tube. In this equation A is the cross-sectional area, and P is the wetted perimeter of the cross-section.

Example: Reynolds number for a primary piping and a fuel bundle

It is an illustrative example, following data do not correspond to any reactor design.

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). 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.

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). From the bottom of the pressure vessel, the flow is reversed up through the core, 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.

See also:

Internal Flow

Internal Flow

In fluid dynamics, internal flow is a flow for which the fluid is confined by a surface. Detailed knowledge of behaviour of internal flow regimes is of importance 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.

For internal flow regime an entrance region is typical. In this region a nearly inviscid upstream flow converges and enters the tube. To characterize this region the hydrodynamic entrance length is introduced and is approximately equal to:

The maximum hydrodynamic entrance length, at Re_D,crit = 2300 (laminar flow), is L_e = 138d, where D is the diameter of the pipe. This is the longest development length possible. In turbulent flow, the boundary layers grow faster, and L_e is relatively shorter. For any given problem, L_e / D has to be checked to see if L_e is negligible when compared to the pipe length. At a finite distance from the entrance, the entrance effects may be neglected, because the boundary layers merge and the inviscid core disappears. The tube flow is then fully developed.

Hydraulic Diameter

To further simplify calculations and enlarge the range of applications, the hydraulic diameter is introduced:

The hydraulic diameter, D_h, is a commonly used term when handling flow in non-circular tubes and channels. The hydraulic diameter transforms non-circular ducts into pipes of equivalent diameter. Using this term, one can calculate many things in the same way as for a round tube. In this equation A is the cross-sectional area, and P is the wetted perimeter of the cross-section.

Most industrial flows, especially those in nuclear engineering are turbulent. For single straight pipe analysis, assuming unidirectional flow, geometric and kinematic pipe-design problems rely on the Moody chart and can be grouped as follows:

• Evaluate the necessary pump characteristics (Q-H characteristics) based on the computed pressure drop Δp in order to convey a given maximum flow rate.
• Calculate a specified pressure drop for the pipe of diameter D, of given pipe length and flow rate. This problem requires an iterative procedure because the Reynolds number, and hence the friction factor f, is not known.
• Calculate the flow rate Q for a given pipe geometry (D, L, ε/D) and pressure drop, where ε/D is the relative surface roughness. This problem requires an iterative procedure because the Reynolds number, and hence the friction factor f, is not known.

Example: Reynolds number for a primary piping and a fuel bundle

It is an illustrative example, following data do not correspond to any reactor design.

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). 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.

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). From the bottom of the pressure vessel, the flow is reversed up through the core, 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 2 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 0.02 [m] / 0.12×10^-6 [m²/s] = 833 000

This also fully satisfies the turbulent conditions.

See also:

Flow Regime

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 behaviour of internal flow regimes is of importance 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 such 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, or to 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 does not change in 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 on the following picture. Far from the body the flow is nearly inviscid, it can be defined as the flow of a fluid around a body that is completely submerged in it.

See also:

Flow Regime

Laminar vs Turbulent Flow

Laminar Flow

In fluid dynamics, laminar flow is characterized by smooth or in regular paths of particles of the fluid, in contrast to turbulent flow, that 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 flowing over one another at different speeds with virtually no mixing between layers, fluid particles move in definite 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 irregular movement of particles (one can say chaotic) of the fluid. 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 behaviour of turbulent flow regime is of importance 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 said to be the “last unsolved problem in classical mathemetical 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.

See also:

Flow Regimes

Single-phase vs Multi-phase Fluid Flow

Single-phase Fluid Flow

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

When at certain important locations in fluid flow systems the simultaneous flow of liquid and gas occurs, the problem must be solved as 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, multiphase 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 multiphase flow can be 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), which is an accident of importance in reactor safety and in all thermal-hydraulic analyses (DNBR analyses).

Characteristics of Multiphase Fluid Flow

All multiphase flow problems have features which 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 multiphase flows is of much greater importance than in the case of single-phase flows.
• The sound speed changes dramatically for materials undergoing 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 multiphase flows, while it is a parameter of no consequence in single-phase flows.
• The change of phase 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 multiphase flow.

See also:

Flow Regimes