Glossary of Terms
algebraic yPlus turbulence model
Low-Reynolds number, algebraic turbulence model that solves for the wall distance, y+ (in viscous units).
anisotropy
Directional dependence. Is often obtained from homogenization of regular structures, for example, monolithic structures in tubular reactors.
Boussinesq approximation
An approximate method to include buoyancy effects, for which the density variation is only taken into account in the buoyancy term.
Brinkman equations
A set of equations extending Darcy’s law in order to include transport of momentum through shear in porous media flow.
boundary layer
Region in a fluid close to a solid surface. This region is characterized by large gradients in velocity and other properties. In turbulent flow it is often treated with approximate methods because of the difficulty to resolve the large gradients.
bubbly flow
Flow with gas bubbles dispersed in a liquid.
conjugate heat transfer
heat transfer that takes place in both a solid and a fluid.
creeping flow
Models the Navier–Stokes equations without the contribution of the inertial term. This is often referred to as Stokes flow and is applicable when viscous flow dominates, such as in very small channels or microfluidic devices.
crosswind diffusion
A numerical technique for stabilization of convection-dominated PDEs by artificially adding diffusion perpendicular to the direction of the streamlines. It reduces oscillations near sharp gradients.
Darcy’s law
Equation that gives the velocity vector as proportional to the pressure gradient. Often used to describe flow in porous media.
Euler flow
Flow of an inviscid fluid. Often used to approximate high speed compressible flows.
Euler–Euler model
A two-phase flow model that treats both phases as interpenetrating continua.
Fick’s laws
The first law states that the diffusive flux of a solute infinitely diluted in a solvent is proportional to its concentration gradient. The second law introduces the first law into a differential material balance for the temporal evolution of the solute.
fluid-structure interaction (FSI)
When a fluid flow affects the deformation of a solid object and vice versa.
fully developed laminar flow
Laminar flow along a channel or pipe that only has velocity components in the streamwise direction. The velocity profile does not change downstream.
Hagen-Poiseuille equation
See Poiseuille’s law.
heterogeneous reaction
Reaction that takes place at the interface between two phases.
homogeneous reaction
Reaction that takes place in the bulk of a solution.
intrinsic volume averages
The physical properties of the fluid, such as density, viscosity, and pressure.
k-ε turbulence model
A two-equation RANS model that solves for the turbulent kinetic energy, k, and the dissipation of turbulence kinetic energy, ε. Utilizes wall functions to describe the flow close to solid walls.
k-ω turbulence model
A two-equation RANS model that solves for the turbulent kinetic energy, k, and the specific dissipation rate, ω. Utilizes wall functions to describe the flow close to solid walls.
L-VEL turbulence model
Low-Reynolds number, algebraic turbulence model that solves for the tangential velocity near walls, u+ (in viscous units).
law of the wall
See wall function.
low-Reynolds k-ε turbulence model
Two-equation RANS model that solves for the turbulence kinetic energy, k, and the dissipation of turbulence kinetic energy, ε. Includes damping functions to be able to describe regions with low Reynolds numbers, for example close to solid walls.
low Reynolds number
The region close to the wall where viscous effects dominate.
Mach number
Dimensionless number equal to the flow velocity over the speed of sound. Compressible effects because of the flow speed can be neglected for Mach number less than 0.3.
multiphase flow
Flow with more than one phase.
Navier–Stokes equations
The momentum balance equation for a Newtonian fluid coupled to the equation of continuity. The meaning of the term originally only referred to the momentum balance but it is here used in the more general context.
Newtonian fluid
A fluid for which the stress is proportional to the rate of strain. Many common fluids such as water and air are Newtonian.
non-Newtonian fluid
A fluid for which the stress is not proportional to the rate of strain. Blood and suspensions of polymers are examples of non-Newtonian fluids.
Poiseuille’s law
Equation stating that the mass rate of flow in a tube is proportional to the pressure difference per unit length and to the fourth power of the tube radius. The law is valid for fully developed laminar flow.
pressure work
Describes the reversible conversion of work, performed by the pressure in a fluid, into heat.
RANS
Reynolds-averaged Navier–Stokes; implying that a time-averaging operation has been performed on the equations of motion. The Reynolds’ stresses (correlations between fluctuating velocity components) obtained from this averaging operation have to be obtained from an additional set of equations — a closure. Turbulence models like the k-ε and Spalart–Allmaras models constitute closures to the RANS equations.
Reynolds number
A dimensionless number that describes the relative importance between inertia and viscous effects. Flow at high Reynolds number have a tendency to undergo transition to turbulence.
Soret effect
Mass diffusion due to temperature gradients in multicomponent mixtures.
Spalart–Allmaras turbulence model
A one-equation turbulence model that solves for the undamped turbulent kinematic viscosity, .
SST turbulence model
The Shear Stress Transport model is a two-equation turbulence model combining the k-ω model in the near-wall region with the k-ε model in the free stream. The SST model is a low-Reynolds number model requiring high resolution near walls. The dependent variables are the turbulent kinetic energy, k, and the turbulent dissipation rate, ω.
Stokes flow
See creeping flow.
streamline diffusion
A numerical technique for stabilization of convection-dominated PDEs by artificially adding upwinding in the streamline direction.
superficial volume averages
The flow velocities, which correspond to a unit volume of the medium including both pores and matrix. They are sometimes called Darcy velocities, defined as volume flow rates per unit cross section of the medium.
thin-film flow
Flow in very thin regions where the it can be assumed to always have a fully developed profile.
viscous heating
The heat irreversibly generated from work by viscous friction in a fluid.
wall function
Semi-empirical expression for the boundary-layer flow used in turbulence models. Often based on the assumption of negligible variations in the pressure gradient tangential to the surface.