Fluid dynamics

Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.

At small scale, all fluids are composed of molecules that collide with one another and solid objects.

The unsimplified equations do not have a general closed-form solution, so they are primarily of use in computational fluid dynamics.

Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form.

Three conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form.

The conservation laws may be applied to a region of the flow called a control volume.

The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume.

In the above integral formulation of this equation, the term on the left is the net change of momentum within the volume.

The first two terms on the right are negated since momentum entering the system is accounted as positive, and the normal is opposite the direction of the velocity u and pressure forces.

The third term on the right is the net acceleration of the mass within the volume due to any body forces (here represented by fbody).

Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, that is,

This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.

Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate.

The sub-discipline of rheology describes the stress-strain behaviours of such fluids, which include emulsions and slurries, some viscoelastic materials such as blood and some polymers, and sticky liquids such as latex, honey and lubricants.

Viscosity cannot be neglected near solid boundaries because the no-slip condition generates a thin region of large strain rate, the boundary layer, in which viscosity effects dominate and which thus generates vorticity.

Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time.

Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.

The presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well.

[10] Most flows of interest have Reynolds numbers much too high for DNS to be a viable option,[9]: 344  given the state of computational power for the next few decades.

Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 20 m/s (72 km/h; 45 mph) is well beyond the limit of DNS simulation (Re = 4 million).

Solving these real-life flow problems requires turbulence models for the foreseeable future.

Reactive flows are flows that are chemically reactive, which finds its applications in many areas, including combustion (IC engine), propulsion devices (rockets, jet engines, and so on), detonations, fire and safety hazards, and astrophysics.

In addition to conservation of mass, momentum and energy, conservation of individual species (for example, mass fraction of methane in methane combustion) need to be derived, where the production/depletion rate of any species are obtained by simultaneously solving the equations of chemical kinetics.

Magnetohydrodynamics is the multidisciplinary study of the flow of electrically conducting fluids in electromagnetic fields.

Examples of such fluids include plasmas, liquid metals, and salt water.

This branch of fluid dynamics augments the standard hydrodynamic equations with stochastic fluxes that model thermal fluctuations.

[12] As formulated by Landau and Lifshitz,[13] a white noise contribution obtained from the fluctuation-dissipation theorem of statistical mechanics is added to the viscous stress tensor and heat flux.

Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods.

These total flow conditions are a function of the fluid velocity and have different values in frames of reference with different motion.

Computer generated animation of fluid in a tube flowing past a cylinder, showing the shedding of a series of vortices in the flow behind it, called a von Kármán vortex street . The streamlines show the direction of the fluid flow, and the color gradient shows the pressure at each point, from blue to green, yellow, and red indicating increasing pressure
Typical aerodynamic teardrop shape, assuming a viscous medium passing from left to right, the diagram shows the pressure distribution as the thickness of the black line and shows the velocity in the boundary layer as the violet triangles. The green vortex generators prompt the transition to turbulent flow and prevent back-flow also called flow separation from the high-pressure region in the back. The surface in front is as smooth as possible or even employs shark-like skin , as any turbulence here increases the energy of the airflow. The truncation on the right, known as a Kammback , also prevents backflow from the high-pressure region in the back across the spoilers to the convergent part.
Flow around an airfoil
Hydrodynamics simulation of the Rayleigh–Taylor instability [ 7 ]
The transition from laminar to turbulent flow