Axisymmetric boundary conditions

In axisymmetric conditions, the flow is symmetrical about the main axis at a particular radius, such that all angles and each z-slice (a horizontal plane perpendicular to the main axis) have the same value. For example, in a circular pipe where the flow and pipe axes coincide, each angle θ and each z-slice would contain the same value for a given flow variable. Vr (R, θ, Z) = Constant (r=R, θ, Z)

Boundary conditions

Boundary conditions are used to model fluid dynamics. They include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, constant pressure boundary conditions, axisymmetric boundary conditions, symmetric boundary conditions, and periodic or cyclic boundary conditions. Transient problems require initial conditions where initial values of flow variables are specified at nodes in the flow domain.

CFD

CFD stands for computational fluid dynamics

Coherent vortex simulation

The coherent vortex simulation approach decomposes the turbulent flow field into a coherent part, consisting of organized vortical motion, and the incoherent part, which is the random background flow. The structure of the wavelet filter is described in detail and applied to numerical simulations of turbulent flow.

Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to simulate the free-stream flow of fluids and the interaction of the fluid with surfaces defined by boundary conditions. High-speed supercomputers are used to perform the calculations required to simulate complex scenarios such as transonic or turbulent flows, and ongoing research yields software that improves accuracy and speed of such simulations.

Constant pressure boundary conditions

This type of boundary condition is used when the pressure at the boundary is known, but the details of the flow distribution are unknown. Typical examples include buoyancy-driven flows, internal flows with multiple outlets, free surface flows, and external flows around objects. An example is the flow outlet into the atmosphere, where pressure is atmospheric.

Detached eddy simulations

Detached eddy simulations (DES) are a modification of Reynolds-Averaged Navier–Stokes (RANS) models using the RANS model to solve turbulent flows in regions where the turbulent length scale is greater than the grid size. In regions where the turbulent length scale is less than or equal to the grid size, DES uses a subgrid-scale model developed for Large Eddy Simulation (LES). While Spalart-Allmaras model-based DES acts as LES with wall models, DES based on other models behaves as a hybrid RANS-LES model. Grid generation is more complicated due to this hybrid nature and requires more care during implementation.

Direct numerical simulation

Direct numerical simulation (DNS) resolves the entire range of turbulent length scales, which makes it the most realistic turbulence model. However, DNS is intractable for flows with complex geometries or flow configurations.

FDM

FDM stands for finite difference method.

FEM

FEM stands for finite element method.

FVM

FVM stands for finite volume method.

Finite difference method

The finite difference method (FDM) is an accurate numerical method with historical precedence. Currently, FDM is used in a few specialized codes and it has been proven that it can handle complex geometry with high accuracy and efficiency by using embedded boundaries or overlapping grids with the solution interpolated across each grid.

Finite element method

The finite element method (FEM) is a computational technique that can be used in the structural analysis of solids, but it is also applicable to fluids. To ensure conservative results, proper care must be taken in the formulation of FEM problems involving fluid dynamics. The FEM has been adapted for use with fluid dynamics governing equations, but this requires special care in ensuring that the resulting solution will be conservative. Unfortunately, FEM problems can require more memory and have slower solution times than those solved using the finite volume method (FVM).

Finite volume method

The finite volume method (FVM) is a common approach used in computational fluid dynamics (CFD), as it conserves fluxes through a particular control volume. In the FVM, the governing partial differential equations (typically the Navier-Stokes equations, the mass and energy conservation equations, and the turbulence equations) are recast in conservative form and then solved over discrete control volumes.

Flow conditioning

Flow conditions affect a flow meter's ability to accurately measure fluid flow. These conditions can include a velocity profile that is not uniform, turbulence within the flow velocity profile, and swirl (a rotational component of fluid motion). To ensure accurate inferential readings, flow conditions must be as close to those of the real-world environment as possible. Its purpose is to validate that the “real-world” environment closely resembles the “laboratory” environment for the proper performance of inferential flowmeters like orifice, turbine, and ultrasonic. Flow in pipes can be classified into four categories: fully developed flow (found in world-class flow laboratories), pseudo-fully developed flow, non-swirling (non-symmetrical flow), and moderate swirling (non-symmetrical flow).

Fluid mechanics

Fluid mechanics is the study of fluids (liquids, gases, blood, and plasmas) at rest and in motion. The field has wide-ranging applications such as mechanical and chemical engineering, astrophysics, and even biological systems.

Large eddy simulation

Large eddy simulation (LES) is a computational method that removes the smallest scales of the flow through a filtering operation and models their effect using subgrid scale models. This method is cheaper than Direct Numerical Simulation but requires more computational resources.

Lattice Boltzmann method

The lattice Boltzmann method (LBM) is a computational fluid dynamics (CFD) technique that models hydrodynamics using the discrete in space and time version of the kinetic evolution equation in the Boltzmann Bhatnagar-Gross-Krook (BGK) form. In LBM, one works with fictive particles—that is, particles that perform propagation and collision processes over a discrete lattice mesh.

Linear eddy model

The linear eddy model (LEM) is a mathematical way to describe the interactions of a scalar variable within the vector flow field. The model is primarily used in one-dimensional representations of turbulent flow and can be applied across a wide range of length scales and Reynolds numbers. It provides high-resolution predictions that hold across a large range of flow conditions.

Outlet boundary conditions

Outlet boundary conditions require the specification of the distribution of all flow variables, mainly flow velocity. This type of boundary condition is commonly used when outlet velocity is known. The flow attains a fully developed state where no change occurs in the flow direction when the outlet is located far away from geometrical disturbances. In such regions, outlets can be outlined and gradients equated to zero in the flow direction except for pressure.

Periodic or cyclic boundary condition

A periodic boundary condition occurs when a problem has a repeated pattern in flow distribution more than twice, thus violating the mirror image requirements required for symmetric boundary conditions. The most common example is a swept vane pump, where the marked area is repeated four times in r-theta coordinates. In each Z-slice, the cyclic-symmetric areas should have the same flow variables and distribution.

Probability density function methods

Probability density function methods for turbulence, first introduced by Lundgren, are based on tracking the one-point PDF of the velocity. This approach is analogous to the kinetic theory of gases, in which the macroscopic properties of a gas are described by a large number of particles. PDF methods can be used to describe chemical reactions, and are particularly useful for simulating chemically reacting flows because the chemical source term is closed and does not require a model. The PDF is commonly tracked by using Lagrangian particle methods; when combined with large eddy simulation, this leads to a Langevin equation for subfilter particle evolution.

Reynolds stress

The Reynolds stress is a component of the total stress tensor in fluid dynamics. It is obtained by averaging over the equations of motion to account for turbulent fluctuations in fluid momentum.

Reynolds-averaged Navier–Stokes

Reynolds-averaged Navier–Stokes equations, which are the oldest approach to turbulence modeling, introduce new apparent stresses known as Reynolds stresses into the governing equations. An ensemble version of the governing equations is solved, which introduces new apparent stresses known as Reynolds stresses into the second order tensor of unknowns for which various models can provide different levels of closure. This method is sometimes referred to as URANS (Unsteady Reynolds-Averaged Navier–Stokes). A common misconception is that these equations do not apply to flows with a time-varying mean flow because they are "time-averaged." Statistically unsteady (or non-stationary) flows can equally be treated by this method.

Spectral element method

The spectral element method is a finite element type method, which requires the partial differential equation to be cast in a weak formulation. One method for solving a differential equation is to multiply it by an arbitrary function and integrate it over the whole domain. The test functions are completely arbitrary, belonging to an infinite-dimensional function space. When the solution domain is infinite-dimensional, it is not practical to represent the solution space by a discrete spectral element mesh.

Symmetric boundary condition

A boundary condition where conditions on the two sides of a boundary are assumed to be the same. All variables have the same value and gradients at the same distance from the boundary. The condition acts like a mirror that reflects all flow distribution to the other side. The no-flow and no-flux boundary conditions are examples of symmetric boundary conditions.

Turbulent flows

Computational modeling of turbulent flows is used in engineering applications to predict fluid velocity and other properties, particularly when non-turbulent components of the flow are small compared to turbulent fluctuations. Numerical models can be classified into three categories based on computational expense: (1) if all turbulence scales are modeled and resolved, the model corresponds to an expensive solution; (2) if only a few large-scale turbulence structures are modeled while unresolved small-scale structures are resolved by a grid-based model or resolved by another method such as DNS, the model is medium cost; (3) if none of the scales are modeled but only resolved by a grid-based model or resolved by another method such as DNS, the model has a low computational expense. Most engineering applications require medium or high computational expense models due to limitations on the accuracy, which stems from unresolved scales.

Two-phase flow

Two-phase flow is still being studied; many methods have been proposed for modeling it, including the Volume of fluid method, level-set method, and front tracking. These methods involve a tradeoff between maintaining a sharp interface and conserving mass. Evaluating density, viscosity, and surface tension involve averaging over the interface, which is often blurred in practice.

Vortex method

Vortex methods represent a mesh-free technique for simulating incompressible turbulent flows. In it, vorticity is discretized onto Lagrangian particles called vortons or vortex particles. The most recent development of this method is the Barnes-Hut and fast multipole algorithm, which allows for the simulation of turbulent flows of any dimensionality.

Vorticity confinement method

The vorticity confinement (VC) method produces a solitary-wave-like solution in the simulation of turbulent wakes. It uses an Eulerian technique to satisfy conservation laws and accurately compute essential integral quantities. VC can capture small-scale features within as few as 2 grid cells.

Wall boundary conditions

Wall boundary conditions are used to bound fluid and solid regions. In viscous flows, the no-slip boundary condition is enforced at walls by default, but you can specify a tangential velocity component in terms of the translational or rotational motion of the wall boundary.

Wind tunnel

Wind tunnels are large, air-filled tubes through which a controlled stream of air is directed at an object. Researchers use these tunnels to study the way objects move through the air by replicating flying conditions. The object is placed inside the wind tunnel, and sensors measure its motion as the air flows around it. Some wind tunnels are large enough to accommodate full-size versions of vehicles; others are small enough to fit only a helmet or golf club. The most common use for this type of tunnel is testing aircraft design or studying how wind affects athletes when they play sports.