For many people, “mechanics” conjures up images of engines and solid materials. When we talk about fluid mechanics, you’d like to know why we talk about mechanics for materials that aren’t solid at all? In this article, we take you into this world, which includes hydrodynamics, aerodynamics and meteorology. Discover the main applications of fluid mechanics for engineering studies!

### What is a fluid?

Fluids differ from solids in their ability to deform to fit the shape of a container. A distinction is made between :
• Gaseous fluids, whose molecules or atoms move freely and which have the property of occupying all available space.
• Liquid fluids, which deform while retaining their own volume and may have a free surface.
Fluid mechanics is based on the approximation that it is possible to study fluids on a macroscopic scale. Interactions at the molecular level are generally ignored, and are considered as continuous media.

### What effects can fluid mechanics help us understand?

By formalizing the properties of a fluid as those of a continuous medium, it is possible to represent :
• Immobile fluids: this discipline is called hydrostatics or fluid statics.
• Fluids in motion: this is what we call fluid dynamics.

#### Fluids at rest: hydrostatics

Fluid statics involves the balance between the forces of pressure (the resultant of which is Archimedes’ buoyancy) and gravity. In particular, it can be used to determine :
• the pressure exerted on an object immersed in a liquid, such as a submarine;
• the draught of a ship or the submerged height of an iceberg;
• atmospheric pressure as a function of altitude.

#### Fluids in motion: fluid dynamics

Fluid dynamics is the branch of fluid mechanics dedicated to the study of fluid motion. Why take an interest in fluid motion? Because many natural and technological mechanisms are based on fluid dynamics:
• winds, temperatures, cloud movement and precipitation in meteorology ;
• in hydraulics, the flow of liquids in channels, head losses in pipes and the design of pumps and turbines;
• in aerodynamics, the overall calculation of the lift and drag of an aircraft wing, but also the calculation of the pressures exerted on each load-bearing surface;
• in engines and nuclear power plants, and heat transfer.
It’s knowledge of these mechanisms that has enabled us to fly airplanes, run heat engines and power plants. The design of fuel-efficient industrial plants and vehicles also involves taking into account the contributions of fluid mechanics. Experimental studies in wind tunnels and hydrodynamic tunnels have left their mark on the history of fluid mechanics. Working with reduced-scale models, flows are similar to full-scale flows. To do this, it is necessary to respect similarity rules applied to dimensionless numbers such as :
• the Froude number Fr, to characterize the effect of gravity;
• Reynolds number Re, to characterize the effect of viscosity;
• Mach number M, to represent compressibility.
Wind tunnel studies have identified a large number of phenomena related to fluid viscosity and compressibility:
• We studied laminar and turbulent flows, introducing dyes to highlight current lines.
• Knowledge of compressible fluid flow and shock waves has been expanded. These occur particularly on aircraft when speeds approach the speed of sound.
• We have acquired in-depth knowledge of the behavior of a fluid in the presence of an obstacle, with boundary layer and detachment phenomena.
• We explored the wakes of planes and ships.

### The importance of modeling and digital simulation

Experimental studies in fluid dynamics reached their peak in the mid-twentieth century and into the 1980s. Advances in computer technology and digital simulation now make it possible to calculate complex configurations and situations:
• flow around a complete aircraft or helicopter;
• motors, propellers and rotors ;
• permanent or unsteady flows ;
• turbulent flows ;
• multiphase flows ;
• coupling with vibratory, chemical, thermodynamic or electromagnetic phenomena…
The best-known example is weather forecasting. Increasingly powerful simulation models provide forecasts on an ever more precise scale. Numerical simulation thus provides access to flow characteristics that would be impossible to measure in complex situations. It also makes it possible to vary the design or flow conditions in order to compare the corresponding performance at lower cost. The ability to couple fluid dynamics simulations with other models (structural calculations, combustion, heat exchange, etc.) obviously opens up considerable possibilities. Simulation software for engineering is now powerful and user-friendly. So it’s hardly surprising that manufacturers have fully embraced them in their development cycles.

### The main types of fluid mechanics modeling

Without going into the details of mathematical models, it is nevertheless useful to briefly explain what these models are based on. General conservation equations such as conservation of mass or momentum are used. They are expressed as systems of partial differential equations, often non-linear, which cannot be solved exactly. Resolution is only possible in an approximate way, thanks to the use of assumptions about the state of the system.

#### Newtonian fluids

These are fluids for which the relationship between shear stress and velocity gradient is linear. The coefficient linking these values is called viscosity. It is a function of fluid temperature but not of shear. Newtonian fluids obey the Navier-Stokes equations. They apply to gases and most liquids, including water. Many of today’s numerical models are based on these equations.

#### Non-Newtonian fluids

Some liquids have a viscosity that varies with stress. Yogurt, honey and blood, for example, have a viscosity that varies when shear is applied. The study of the behavior of these fluids falls within a discipline called rheology.

#### Modeling turbulent flows

Representing turbulence in fluid dynamics remains a major challenge. Turbulent flows include vortex scales that interact with each other, right down to the finest scales that dissipate through viscosity. The direct simulation of these vortex structures (DNS: Direct Numerical Simulation) is in fact limited by the size of the mesh used: numerically solving all the spatial and temporal scales of a flow would in most cases cost months or even years of computation. More commonly, a statistical approach is used to model the average stresses associated with turbulence in an “average flow”. This is the RANS (Reynolds Averaged Navier Stokes Equations) approach. Today’s numerical resources make it possible to resolve some of the largest turbulent scales. One example is the LES (Large Eddy Simulation) approach.

#### Modeling two-phase flows

The most widely used method for representing two-phase flows is the VOF (Volume Of Fluid) method. It involves studying the evolution of the interface between immiscible fluids. Each fluid is usually assumed to be incompressible and to have its own density.

#### Some cases of model simplification

• For some aerodynamic calculations, viscosity and conduction effects are neglected. We then use Euler’s equations, corresponding to the assumption of a perfect fluid. This means that the Reynolds number tends towards infinity.
• In hydrodynamics and for low-velocity gas flows (up to Mach 0.3), it is generally assumed that the fluid is incompressible. Its density does not vary with pressure, but it can vary with temperature, resulting in convection.
So now you understand why our simulation engineers are true experts in fluid mechanics? Contact us to find out more.