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Transition Modeling
Transition modeling is the use of a model to predict the change from laminar and turbulent flows in fluids and their respective effects on the overall solution. The complexity and lack of understanding of the underlining physics of the problems makes simulating the interaction between laminar and turbulent flow to be difficult and very case specific. Transition does have the wide range of turbulence options available for most computational fluid dynamics (CFD) applications for the following reasons: * Transition involves a wide range of scales where the energy and momentum transfer are strongly influenced by inertial or non-linear effects that are unique to the simulation. * Transition also occurs by different means, such as natural and bypass, and modeling all possibilities is difficult. Most CFD programs use Reynolds-averaged Navier–Stokes equations, in which averaging eliminates linear disturbance. Common models The following is a list of commonly employed transition models i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laminar Flow
In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection. When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulent
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This increases the energy needed to pump fluid through a pipe. The onset of turbulence can be predicted by the dimensionless Reyn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid ( liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests. CFD is appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inertial Force
A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. It is related to Newton's second law of motion, which treats forces for just one object. Passengers in a vehicle accelerating in the forward direction may perceive they are acted upon by a force moving them into the direction of the backrest of their seats for example. An example in a rotating reference frame may be the impression that it is a force which seems to move objects outward toward the rim of a centrifuge or carousel. The fictitious force called a pseudo force might also be referred to as a body force. It is due to an object's inertia when the reference frame does not move inertially any more but begins to accelerate relative to the free object. In terms of the example of the passenger vehicle, a pseudo force seems to be active just before the body touches the backrest of the seat in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds-averaged Navier–Stokes Equations
The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition, whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds. The RANS equations are primarily used to describe turbulent flows. These equations can be used with approximations based on knowledge of the properties of flow turbulence to give approximate time-averaged solutions to the Navier–Stokes equations. For a stationary flow of an incompressible Newtonian fluid, these equations can be written in Einstein notation in Cartesian coordinates as: \rho\bar_j \frac = \rho \bar_i + \frac \left - \bar\delta_ + \mu \left( \frac + \frac \right) - \rho \overline \right The left hand side of this equation represents the change in mean momentum of a fluid element owing to the unsteadiness in the mean flow and the convection by the mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Theory Approach
Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems **Asymptotic stability **Linear stability **Lyapunov stability **Orbital stability **Structural stability *Stability (probability), a property of probability distributions *Stability (learning theory), a property of machine learning algorithms *Stability, a property of sorting algorithms * Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm *Stability radius, a property of continuous polynomial functions *Stable theory, concerned with the notion of stability in model theory *Stability, a property of points in geometric invariant theory *K-Stability, a stability condition for algebraic varieties. *Bridgeland stability conditions, a class of stability conditions on elements of a triangulated category. *Stability (algebraic geometry) Engineering *In atmospheric flu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermittency Transport
In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency). Pomeau and Manneville described three routes to intermittency where a nearly periodic system shows irregularly spaced bursts of chaos. These (type I, II and III) correspond to the approach to a saddle-node bifurcation, a subcritical Hopf bifurcation, or an inverse period-doubling bifurcation. In the apparently periodic phases the behaviour is only nearly periodic, slowly drifting away from an unstable periodic orbit. Eventually the system gets far enough away from the periodic orbit to be affected by chaotic dynamics in the rest of the state space, until it gets close to the orbit again and returns to the nearly periodic behaviour. Since the time spent near the periodic orbit depends sensitively on how closely the system entered its vicinity (in turn deter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laminar Fluctuation Energy Method
Laminar means "flat". Laminar may refer to: Terms in science and engineering: *Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules * Laminar armour or "banded mail", armour made from horizontal overlapping rows or bands of solid armour plates * Laminar flame speed, a property of a combustible mixture * Laminar flow, a fluid flowing in parallel layers with no disruption between the layers * Laminar organization, the way certain tissues are arranged in layers *Laminar set family, a mathematical structure. *A common leaf shape. Proper nouns: * Laminar Research, a Columbia, South Carolina, software company * Icaro Laminar, an Italian hang glider design * Pazmany Laminar, a personal light aircraft designed by Ladislao Pazmany See also * Lamina (other) Lamina may refer to: Science and technology * Planar lamina, a two-dimensional planar closed surface with mass and density, in mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Numerical Simulation
A direct numerical simulation (DNS)Here the origin of the term ''direct numerical simulation'' (see e.g. p. 385 in ) owes to the fact that, at that time, there were considered to be just two principal ways of getting ''theoretical'' results regarding turbulence, namely via turbulence theories (like the direct interaction approximation) and ''directly'' from solution of the Navier–Stokes equations. is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales ( Kolmogorov microscales), up to the integral scale L, associated with the motions containing most of the kinetic energy. The Kolmogorov scale, \eta, is given by :\eta=(\nu^/\varepsilon)^ where \nu is the kinematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
