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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic Dynamical System
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence Models
Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real life scenarios, including the flow of blood through the cardiovascular system, the airflow over an aircraft wing, the re-entry of space vehicles, besides others. In spite of decades of research, there is no analytical theory to predict the evolution of these turbulent flows. The equations governing turbulent flows can only be solved directly for simple cases of flow. For most real life turbulent flows, CFD simulations use turbulent models to predict the evolution of turbulence. These turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows. Closure problem The Navier–Stokes equations govern the velocity and pressure of a fluid flow. In a turbulent flow, each of these quantities may be decomposed into a mean part and a fluctuating part. Averaging the equations gives the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence
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 Rey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). 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. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Favre Averaging
Favre averaging is the density-weighted averaging method, used in variable density or compressible turbulent flows, in place of the Reynolds averaging. The method was introduced formally by the French scientist A. J. Favre in 1965, although Osborne Reynolds Osborne Reynolds (23 August 1842 – 21 February 1912) was an Irish-born innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. ... has also already introduced the density-weighted averaging in 1895. The averaging results a simplistic form for the nonlinear convective terms of the Navier-Stokes equations, at the expense of making the diffusion terms complicated. Favre averaged variables Favre averaging is carried out for all dynamical variables except the pressure. For the velocity components, u_i, the Favre averaging is defined as \widetilde= \frac where the overbar indicates the typical Reynolds averaging ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses and dissertations, preprints, abstracts, technical reports, and other scholarly literature, including court opinions and patents. Google Scholar uses a web crawler, or web robot, to identify files for inclusion in the search results. For content to be indexed in Google Scholar, it must meet certain specified criteria. An earlier statistical estimate published in PLOS One using a mark and recapture method estimated approximately 80–90% coverage of all articles published in English with an estimate of 100 million.''Trend Watch'' (2014) Nature 509(7501), 405 – discussing Madian Khabsa and C Lee Giles (2014''The Number of Scholarly Documents on the Public Web'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Espoo
Espoo (, ; sv, Esbo) is a city and municipality in the region of Uusimaa in the Republic of Finland. It is located on the northern shore of the Gulf of Finland, bordering the cities of Helsinki, Vantaa, Kirkkonummi, Vihti and Nurmijärvi while surrounding the enclaved town of Kauniainen. The city covers with a population of about 300 000 residents in 2022, making it the 2nd-most populous city in Finland. Espoo forms a major part of a substantially larger metropolitan area known as Greater Helsinki, home to over 1.5 million people in 2020. Espoo was first settled in the Prehistoric Era, with the first signs of human settlements going back as far as 8,000 years, but the population effectively disappeared in the early stages of the Iron Age. In the Early Middle Ages, the area was resettled by Tavastians and Southwestern Finns. After the Northern Crusades, Swedish settlers started migrating to the coastal areas of present-day Finland, and Espoo was established as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rauma, Finland
Rauma (; sv, Raumo) is a town and municipality of around () inhabitants on the west coast of Finland, north of Turku, and south of Pori. Its neighbouring municipalities are Eura, Eurajoki, Laitila and Pyhäranta. Granted town privileges on 17 April 1442 (then under the rule of Sweden), Rauma is known for its paper and maritime industry, high quality lace (since the 18th century) and the old wooden architecture of the city centre (Old Rauma, Vanha Rauma), which is a UNESCO World Heritage site. History In the 14th century, before it was declared a town, Rauma had a Franciscan monastery and a Catholic church. In 1550, the townsmen of Rauma were ordered to relocate to Helsinki, but this was unsuccessful and Rauma continued to grow. Practically the whole wooden part of the town of Rauma was devastated in the fires of 1640 and 1682. The city centre, which was as large as the town was until 1809, has approximately 600 wooden buildings. The neo-renaissance style of many of the house ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Texas At Austin
The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 graduate students and 3,133 teaching faculty as of Fall 2021, it is also the largest institution in the system. It is ranked among the top universities in the world by major college and university rankings, and admission to its programs is considered highly selective. UT Austin is considered one of the United States's Public Ivies. The university is a major center for academic research, with research expenditures totaling $679.8 million for fiscal year 2018. It joined the Association of American Universities in 1929. The university houses seven museums and seventeen libraries, including the LBJ Presidential Library and the Blanton Museum of Art, and operates various auxiliary research facilities, such as the J. J. Pickle Research Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Symposium On Marine Propulsion
International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * ''International'' (Kevin Michael album), 2011 * ''International'' (New Order album), 2002 * ''International'' (The Three Degrees album), 1975 *''International'', 2018 album by L'Algérino Songs * The Internationale, the left-wing anthem * "International" (Chase & Status song), 2014 * "International", by Adventures in Stereo from ''Monomania'', 2000 * "International", by Brass Construction from ''Renegades'', 1984 * "International", by Thomas Leer from ''The Scale of Ten'', 1985 * "International", by Kevin Michael from ''International'' (Kevin Michael album), 2011 * "International", by McGuinness Flint from ''McGuinness Flint'', 1970 * "International", by Orchestral Manoeuvres in the Dark from '' Dazzle Ships'', 1983 * "International (Serious)", by Estelle from '' All of Me'', 2012 Politics * Political international, any transnational organization of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence Kinetic Energy
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model. Generally, the TKE is defined to be half the sum of the variances (square of standard deviations) of the velocity components: k = \frac12 \left(\, \overline + \overline + \overline \,\right), where the turbulent velocity component is the difference between the instantaneous and the average velocity u' = u - \overline, whose mean and variance are \overline = \frac \int_0^T (u(t) - \overline) \, dt = 0 and \overline = \frac\int_0^T (u(t) - \overline)^2 \, dt \geq 0 , respectively. TKE can be produced by fluid shear, friction or buoyancy, or through external forcing at low-frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Stress
In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum. Definition The velocity field of a flow can be split into a mean part and a fluctuating part using Reynolds decomposition. We write :u_i = \overline + u_i',\, with \mathbf(\mathbf,t) being the flow velocity vector having components u_i in the x_i coordinate direction (with x_i denoting the components of the coordinate vector \mathbf). The mean velocities \overline are determined by either time averaging, spatial averaging or ensemble averaging, depending on the flow under study. Further u'_i denotes the fluctuating (turbulence) part of the velocity. We consider a homogeneous fluid, whose density ''ρ'' is taken to be a constant. For such a fluid, the components ''τ''ij'' of the Reynolds stress tensor are defined as: :\tau'_ \equiv \rho\,\overline,\, Anothe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
