What is Fluid Flow?

Fluid flow describes the continuous deformation and movement of liquids or gases in response to applied forces or pressure differences. Fluid flow reflects the fluid's ability to change shape or adapt to its container — unlike solids, which maintain a fixed form.

The behavior of fluids during flow is influenced by their viscosity, which measures the fluid's internal resistance to flow. Based on their viscosity characteristics, fluids are classified as either Newtonian or non-Newtonian.

Understanding fluid flow is crucial in many engineering fields, including aerospace, civil, mechanical, and biomedical engineering. It also plays a significant role in scientific disciplines such as oceanography, meteorology, and biology. To address complex fluid flow problems, engineers often employ advanced techniques like computational fluid dynamics (CFD), which combines powerful computer hardware with sophisticated numerical methods.

Fluid mechanics is the study of liquids and gases in motion based on empirical laws derived from flow measurements. Fluid flow problems typically involve determining properties such as:

• Fluid velocity — a vector quantity that describes how quickly and in which direction the fluid is moving (in meters per second)
• Fluid pressure — a vector quantity that describes the force per unit area exerted by a fluid on its surroundings or a surface it interacts with (in pascals or pounds per square inch)
• Fluid temperature — represents the average kinetic energy of molecules within a fluid, reflecting how hot or cold the fluid is (in degrees Celsius, Kelvin, or Fahrenheit) 
• Fluid viscosity — a measure of a fluid's resistance to flow and deformation, quantifying the internal friction between adjacent layers of the fluid as they move relative to one another (in pascal-seconds)

There are many subdisciplines of fluid mechanics, including aerodynamics (concerned with the study of air and gases in motion, such as calculating forces on aircraft wings) and hydrodynamics (concerned with the study of liquid in motion, such as determining the mass flow rate of petroleum through pipelines).

The Reynolds Number in Fluid Flow

Engineers frequently use dimensionless numbers to effectively reduce the number of variables and extract meaningful correlations from physical phenomena. The Reynolds number is one such number, relating the inertial forces to the viscous forces in a fluid flow.

In laminar flow, viscous forces are large compared to inertial forces. With an increasing Reynolds number, inertial forces become more dominant until the flow eventually becomes turbulent. The Reynolds number at which this happens is known as the critical Reynolds number.

The critical Reynolds number does not have a fixed value but depends on factors such as the smoothness of the boundary surfaces and the geometry of the flow. For example, for internal flows bounded by a smooth surface, its value is approximately 2,300, while for external flows it can be much higher.

Fluid flows take on many attributes, reflecting either the inherent properties of the fluid or how it is changing in space and time. Furthermore, turbulent flows present additional challenges. To date, researchers have yet to provide elegant solutions to these problems.

Laminar flow describes flows in which there is no mixing between the different fluid layers (lamina) in a flow. Laminar flows occur when viscous forces are stronger than inertial forces. Most naturally occurring flows of engineering interest will, however, transition into turbulence.

In turbulent flows, the fluid layers mix, resulting in stresses that form spinning elements (recirculation and eddies). Turbulent flow is seen when inertial forces are stronger than viscous forces.

It is worth noting that there is a third type of flow — a transitional flow — which is neither fully turbulent nor laminar.

Engineers study turbulent flows via a Reynolds decomposition, in which the flow is separated into an average component and a perturbation component. The Reynolds number is defined as the ratio of inertial forces to viscous forces within a fluid. It is a dimensionless quantity that helps determine whether a flow will be laminar or turbulent for a given configuration. It is given by:

Where ρ is the fluid density, V is the flow velocity, and L is a characteristic length (such as the diameter of a pipe).

So, for example, consider pipes that have the following characteristics:

• If R_e is less than 2,000, viscous forces dominate and the flow regime is laminar.
• If R_e is greater than 4,000, inertial forces dominate and the flow regime is turbulent.
• If R_e is between 2,000 and 4,000, the flow is transitional.

The following are the main differences between laminar and turbulent flows:

Steady vs. Unsteady Flow

A steady flow is a flow in which properties such as velocity, pressure, and density do not change with time at any given point in space. Conversely, if any of these properties do change with time, the flow is unsteady.

Turbulent flows are, by nature, unsteady. However, they can also be statistically steady, meaning that time-averaged flow conditions such as velocity remain constant with time.

Unsteady flows are commonly found in nature. However, unsteady flow models are more challenging to solve because introducing the time dimension requires considerably more computational capacity.

Uniform vs Nonuniform Flow

Uniform flow describes fluid flow in which the velocity of the fluid remains constant in direction and magnitude across the flow.

Compressible vs. Incompressible Flow

Compressibility describes the ability to bring the molecules in a fluid closer together. 

Gases are easily compressed because their molecules are far apart. Their volume and density can easily be changed by applying or easing pressure. On the other hand, liquids are difficult to compress because their molecules are much closer to each other. 

For most practical applications, liquids can be considered incompressible (except where sound propagation becomes significant, as in some unsteady flow problems).

In flow fields where velocity variations are small relative to the speed of sound in that fluid, fluid flow can be treated as incompressible (even for gases). This is significant because compressibility effects considerably heighten the complexity of the governing equations.

The Mach number is a useful dimensionless number that helps determine the significance of compressibility effects in fluid flow. For Mach numbers less than or equal to 0.3, the flow can be treated as incompressible. For higher flow speeds (high subsonic and supersonic), compressibility effects become significant, especially where shock waves are involved — for example, in jet engines, high-speed aircraft, and rockets.

Viscous vs. Nonviscous Flow

Viscosity is a measure of the friction in a fluid. As layers within a fluid rub against each other, there is friction. High viscosity (e.g., honey) indicates a high amount of friction and vice versa. For a liquid, viscosity decreases with rising temperature. This is because molecules move more freely in a warmer liquid and can more easily slide over each other. For a gas, however, viscosity increases with temperature.

Single vs. Multidimensional Flow

Flow dimensionality points to the number of spatial dimensions that significantly affect the characteristics of a flow — note that time is often referred to as a dimension.

In one-dimensional flows, quantities such as velocity, pressure, and density vary significantly in one dimension only. One-dimensional flow models are useful in flow conditions in which changes in the other two dimensions are negligible (for example, in a pipe with constant diameter in which variations occur along the length of the pipe only).

In two-dimensional flow models, variations in the third dimension are either uniform or negligible. This occurs in high aspect ratio flows, in which one dimension is considerably larger than another. For example, in boundary layer development along a flat plate, variations in flow properties across the width of the plate are negligible compared to variations along the length and height. Also, many weather system models are two-dimensional because the Earth’s atmosphere is very thin relative to the surface of the Earth.

Three-dimensional flow models are the most ubiquitous in engineering applications, capturing the full complexity of these flows in three dimensions. In these cases, complex geometries create intricate fluid motions that are also influenced by three-dimensional variations in quantities such as pressure, velocity, or density.

While simplified one- and two-dimensional models provide for reduced analytical effort, they are not always a valid option. The choice of model depends on the problem under consideration. Engineers often rely on simplified models at initial design stages, opting for advanced 3D modeling at final verification stages.

External vs. Internal Flow

The main differences between external and internal flows result from the nature of the boundaries surrounding these flows.

External flows occur where at least one side is unbounded, resulting in boundary layer and wake effects. On the other hand, internal flows occur within confined (solid) boundaries, in which pressure drops and flow distributions are often of interest.

Examples of external flows include air flowing over an aircraft’s fuselage (in which aerodynamic forces such as lift and drag are often of interest), water flowing across a ship’s hull, or wind blowing over a building. The shape and orientation of objects influence the behaviors of external flows, forming boundary layers (viscous regions at object-flow interfaces) and flow separations.

Examples of internal flows include air or water flowing through pipes or ducts. They are confined by the boundary walls, and momentum lost to the walls results in a drop in pressure along the flow direction.

Multiphase Flow

A multiphase flow describes a flow incorporating the simultaneous occurrence of two or more distinct thermodynamic phases. These phases may take the form of gases, liquids, or solids and be of the same or different components, such as water/water vapor flow, oil/water flow, or liquid-solid suspensions.

Multiphase flows are typically categorized into two-phase and three-phase flows, although more complex systems can include additional phases.

Common two-phase flows include:

• Gas-liquid flows — found in evaporators and condensers
• Gas-solid flows — found in bioreactors
• Liquid-solid flows — found in slurry transport and sedimentation systems

Three-phase flows include gas-liquid-solid flows (such as in chemical reactors and fluidized beds) and gas-liquid-liquid flows (found in oil recovery systems).

Modeling multiphase flow is complex due to the interaction between different phases. It is central to a variety of engineering problems, including chemical processing and pharmaceuticals (e.g., mixing, filtration, and separation), power generation (steam turbine and combustion modeling), and oil and gas (reduction of flaring and venting). Engineers use approaches such as the Euler-Lagrange, Euler-Euler, or volume of fluid (VOF) methods to solve these problems.

Direct numerical simulation (DNS) of turbulent flows based on the Navier–Stokes equations (excluding turbulence modeling) is possible at moderate Reynolds numbers. However, due to the excessive computational resources required, most engineering flows exhibit Reynolds numbers too high for direct numerical simulation. For instance, any flight vehicle large enough to carry a human being is beyond the reach of DNS (Re = 4 million).

Therefore, engineers combine Reynolds-averaged Navier–Stokes (RANS) equations with turbulence modeling to provide effective characterization of turbulent flows. RANS models account for the additional momentum and heat transfer caused by turbulence through Reynolds stresses. RANS models are widely used in engineering applications because they are computationally less intensive than DNS while providing reasonable accuracy for many types of turbulent flows.

Large eddy simulation (LES) and its variants are other modeling approaches that provide a middle ground between DNS and RANS. LES resolves the larger scales of turbulence directly and models the smaller scales, making it more accurate than RANS. It is crucial when trying to model flows in which transience is important, such as external aerodynamics of cars and combustion within gas turbine engines. 

The ability to understand fluid flow provides the first step in developing effective computational models. Laminar flow solutions are relatively straightforward, and engineers can use deterministic mathematical models. However, the range of applicability of these models is limited. 

Most practical problems involve turbulent flows, which are the most difficult to model because of their unsteady and nondeterministic nature. Accurately modeling turbulent flows remains a challenge that engineers are actively working to address.

Nonetheless, Ansys Fluent software is the industry-leading fluid simulation tool known for its advanced physics modeling capabilities and accuracy.

Fluent software is a powerful tool for engineers, offering efficient and accurate solutions to complex fluid simulation problems. It provides a wide range of physical models and techniques, including:

• A vast range of turbulence models 
• Reduced order modeling
• A vast range of multiphase flow models
• Numerous combustion models
• Fluid-structure interactions
• Highly scalable parallel capabilities for meshing and solving

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