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130-516: In engineering , airflow is a measurement of the amount of air per unit of time that flows through a particular device. It can be described as a volumetric flow rate (volume of air per unit time) or a mass flow rate (mass of air per unit time). What relates both forms of description is the air density, which is a function of pressure and temperature through the ideal gas law. The flow of air can be induced through mechanical means (such as by operating an electric or manual fan) or can take place passively, as

260-694: A broad range of more specialized fields of engineering , each with a more specific emphasis on particular areas of applied mathematics , applied science , and types of application. See glossary of engineering . The term engineering is derived from the Latin ingenium , meaning "cleverness". The American Engineers' Council for Professional Development (ECPD, the predecessor of ABET ) has defined "engineering" as: The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate

390-449: A building block for more complicated flow representations, as it provides high resolution predictions that hold across a large range of flow conditions. The modeling of two-phase flow is still under development. Different methods have been proposed, including the Volume of fluid method , the level-set method and front tracking . These methods often involve a tradeoff between maintaining

520-703: A building envelope. Because CFD models "also track the flow of solids through a system," they can be used for analysis of pollution concentrations in indoor and outdoor environments. Particulate matter generated indoors generally comes from cooking with oil and combustion activities such as burning candles or firewood. In outdoor environments, particulate matter comes from direct sources such as internal combustion engine vehicles’ (ICEVs) tailpipe emissions from burning fuel (petroleum products), windblow and soil, and indirectly from atmospheric oxidation of volatile organic compounds (VOCs), sulfur dioxide (SO2), and nitrogen oxide (NOx) emissions. One type of equipment that regulates

650-531: A building. Stack effect equates to using chimneys or similar tall spaces with openings near the top to passively draw exhaust air up and out of the space, thanks to the fact that air will rise when its temperature increases (as the volume increases and pressure decreases). Wind-driven passive ventilation relies on building configuration, orientation, and aperture distribution to take advantage of outdoor air movement. Cross-ventilation requires strategically-positioned openings aligned with local wind patterns. Airflow

780-407: A commercial scale, such as the manufacture of commodity chemicals , specialty chemicals , petroleum refining , microfabrication , fermentation , and biomolecule production . Civil engineering is the design and construction of public and private works, such as infrastructure (airports, roads, railways, water supply, and treatment etc.), bridges, tunnels, dams, and buildings. Civil engineering

910-423: A cost-effective alternative, offering a nuanced understanding of complex flow phenomena while minimizing expenses associated with traditional experimental methods. CFD can be seen as a group of computational methodologies (discussed below) used to solve equations governing fluid flow. In the application of CFD, a critical step is to decide which set of physical assumptions and related equations need to be used for

1040-533: A count of 2,000. There were fewer than 50 engineering graduates in the U.S. before 1865. In 1870 there were a dozen U.S. mechanical engineering graduates, with that number increasing to 43 per year in 1875. In 1890, there were 6,000 engineers in civil, mining , mechanical and electrical. There was no chair of applied mechanism and applied mechanics at Cambridge until 1875, and no chair of engineering at Oxford until 1907. Germany established technical universities earlier. The foundations of electrical engineering in

1170-420: A demand for machinery with metal parts, which led to the development of several machine tools . Boring cast iron cylinders with precision was not possible until John Wilkinson invented his boring machine , which is considered the first machine tool . Other machine tools included the screw cutting lathe , milling machine , turret lathe and the metal planer . Precision machining techniques were developed in

1300-450: A derivative of PMARC, named CMARC, is also commercially available. In the two-dimensional realm, a number of Panel Codes have been developed for airfoil analysis and design. The codes typically have a boundary layer analysis included, so that viscous effects can be modeled. Richard Eppler  [ de ] developed the PROFILE code, partly with NASA funding, which became available in

1430-575: A discrete lattice mesh. In this method, one works with the discrete in space and time version of the kinetic evolution equation in the Boltzmann Bhatnagar-Gross-Krook (BGK) form. The vortex method, also Lagrangian Vortex Particle Method, is a meshfree technique for the simulation of incompressible turbulent flows. In it, vorticity is discretized onto Lagrangian particles, these computational elements being called vortices, vortons, or vortex particles. Vortex methods were developed as

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1560-420: A flat velocity profile. Velocity profiles of fluid movement describe the spatial distribution of instantaneous velocity vectors across a given cross section. The size and shape of the geometric configuration that the fluid is traveling through, the fluid properties (such as viscosity), physical disruptions to the flow, and engineered components (e.g. pumps) that add energy to the flow are factors that determine what

1690-427: A function of pressure differentials present in the environment. Like any fluid, air may exhibit both laminar and turbulent flow patterns. Laminar flow occurs when air can flow smoothly, and exhibits a parabolic velocity profile ; turbulent flow occurs when there is an irregularity (such as a disruption in the surface across which the fluid is flowing), which alters the direction of movement. Turbulent flow exhibits

1820-468: A grid-free methodology that would not be limited by the fundamental smoothing effects associated with grid-based methods. To be practical, however, vortex methods require means for rapidly computing velocities from the vortex elements – in other words they require the solution to a particular form of the N-body problem (in which the motion of N objects is tied to their mutual influences). This breakthrough came in

1950-501: A non-linear and non-local pressure gradient term. These nonlinear equations must be solved numerically with the appropriate boundary and initial conditions. Reynolds-averaged Navier–Stokes (RANS) equations are the oldest approach to turbulence modeling. An ensemble version of the governing equations is solved, which introduces new apparent stresses known as Reynolds stresses . This adds a second-order tensor of unknowns for which various models can provide different levels of closure. It

2080-400: A result, many engineers continue to learn new material throughout their careers. If multiple solutions exist, engineers weigh each design choice based on their merit and choose the solution that best matches the requirements. The task of the engineer is to identify, understand, and interpret the constraints on a design in order to yield a successful result. It is generally insufficient to build

2210-475: A rotated difference scheme by AFWAL/Boeing that resulted in LTRAN3. CFD investigations are used to clarify the characteristics of aortic flow in details that are beyond the capabilities of experimental measurements. To analyze these conditions, CAD models of the human vascular system are extracted employing modern imaging techniques such as MRI or Computed Tomography . A 3D model is reconstructed from this data and

2340-441: A sharp interface or conserving mass . This is crucial since the evaluation of the density, viscosity and surface tension is based on the values averaged over the interface. Discretization in the space produces a system of ordinary differential equations for unsteady problems and algebraic equations for steady problems. Implicit or semi-implicit methods are generally used to integrate the ordinary differential equations, producing

2470-407: A stable solution with no numerical spreading. VC can capture the small-scale features to within as few as 2 grid cells. Within these features, a nonlinear difference equation is solved as opposed to the finite difference equation . VC is similar to shock capturing methods , where conservation laws are satisfied, so that the essential integral quantities are accurately computed. The Linear eddy model

2600-532: A system of (usually) nonlinear algebraic equations. Applying a Newton or Picard iteration produces a system of linear equations which is nonsymmetric in the presence of advection and indefinite in the presence of incompressibility. Such systems, particularly in 3D, are frequently too large for direct solvers, so iterative methods are used, either stationary methods such as successive overrelaxation or Krylov subspace methods. Krylov methods such as GMRES , typically used with preconditioning , operate by minimizing

2730-411: A technically successful product, rather, it must also meet further requirements. Constraints may include available resources, physical, imaginative or technical limitations, flexibility for future modifications and additions, and other factors, such as requirements for cost, safety , marketability, productivity, and serviceability . By understanding the constraints, engineers derive specifications for

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2860-618: A testament to the ingenuity and skill of ancient civil and military engineers. Other monuments, no longer standing, such as the Hanging Gardens of Babylon and the Pharos of Alexandria , were important engineering achievements of their time and were considered among the Seven Wonders of the Ancient World . The six classic simple machines were known in the ancient Near East . The wedge and

2990-909: A useful purpose. Examples of bioengineering research include bacteria engineered to produce chemicals, new medical imaging technology, portable and rapid disease diagnostic devices, prosthetics, biopharmaceuticals, and tissue-engineered organs. Interdisciplinary engineering draws from more than one of the principle branches of the practice. Historically, naval engineering and mining engineering were major branches. Other engineering fields are manufacturing engineering , acoustical engineering , corrosion engineering , instrumentation and control , aerospace , automotive , computer , electronic , information engineering , petroleum , environmental , systems , audio , software , architectural , agricultural , biosystems , biomedical , geological , textile , industrial , materials , and nuclear engineering . These and other branches of engineering are represented in

3120-622: A way to distinguish between those specializing in the construction of such non-military projects and those involved in the discipline of military engineering . The pyramids in ancient Egypt , ziggurats of Mesopotamia , the Acropolis and Parthenon in Greece, the Roman aqueducts , Via Appia and Colosseum, Teotihuacán , and the Brihadeeswarar Temple of Thanjavur , among many others, stand as

3250-513: Is a broad discipline that is often broken down into several sub-disciplines. Although an engineer will usually be trained in a specific discipline, he or she may become multi-disciplined through experience. Engineering is often characterized as having four main branches: chemical engineering, civil engineering, electrical engineering, and mechanical engineering. Chemical engineering is the application of physics, chemistry, biology, and engineering principles in order to carry out chemical processes on

3380-512: Is a common misconception that the RANS equations do not apply to flows with a time-varying mean flow because these equations are 'time-averaged'. In fact, statistically unsteady (or non-stationary) flows can equally be treated. This is sometimes referred to as URANS. There is nothing inherent in Reynolds averaging to preclude this, but the turbulence models used to close the equations are valid only as long as

3510-509: Is a factor of concern when designing to meet occupant thermal comfort standards (such as ASHRAE 55 ). Varying rates of air movement may positively or negatively impact individuals’ perception of warmth or coolness, and hence their comfort. Air velocity interacts with air temperature, relative humidity, radiant temperature of surrounding surfaces and occupants, and occupant skin conductivity, resulting in particular thermal sensations. Sufficient, properly-controlled and designed airflow (ventilation)

3640-435: Is a large temperature difference between the outdoor air and indoor conditioned air, the use of natural ventilation may cause unintentional heating or cooling loads on a space and increase HVAC energy consumption to maintain comfortable temperatures within ranges determined by the heating and cooling setpoint temperatures. Natural ventilation also has the flaw that its feasibility is dependent on outdoor conditions; if outdoor air

3770-405: Is a technique used to simulate the convective mixing that takes place in turbulent flow. Specifically, it provides a mathematical way to describe the interactions of a scalar variable within the vector flow field. It is primarily used in one-dimensional representations of turbulent flow, since it can be applied across a wide range of length scales and Reynolds numbers. This model is generally used as

3900-599: 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 are unique in that they can be applied in the framework of a number of different turbulence models; the main differences occur in the form of the PDF transport equation. For example, in the context of large eddy simulation , the PDF becomes the filtered PDF. PDF methods can also be used to describe chemical reactions, and are particularly useful for simulating chemically reacting flows because

4030-730: Is associated with anything constructed on or within the Earth. This discipline applies geological sciences and engineering principles to direct or support the work of other disciplines such as civil engineering , environmental engineering , and mining engineering . Geological engineers are involved with impact studies for facilities and operations that affect surface and subsurface environments, such as rock excavations (e.g. tunnels ), building foundation consolidation, slope and fill stabilization, landslide risk assessment, groundwater monitoring, groundwater remediation , mining excavations, and natural resource exploration. One who practices engineering

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4160-459: Is based on wavelets, and the filter can be adapted as the flow field evolves. Farge and Schneider tested the CVS method with two flow configurations and showed that the coherent portion of the flow exhibited the − 40 39 {\displaystyle -{\frac {40}{39}}} energy spectrum exhibited by the total flow, and corresponded to coherent structures ( vortex tubes ), while

4290-425: Is called an airflow meter . Anemometers are also used to measure wind speed and indoor airflow. There are a variety of types, including straight probe anemometers, designed to measure air velocity, differential pressure, temperature, and humidity; rotating vane anemometers , used for measuring air velocity and volumetric flow; and hot-sphere anemometers. Anemometers may use ultrasound or resistive wire to measure

4420-497: Is called an engineer , and those licensed to do so may have more formal designations such as Professional Engineer , Chartered Engineer , Incorporated Engineer , Ingenieur , European Engineer , or Designated Engineering Representative . In the engineering design process, engineers apply mathematics and sciences such as physics to find novel solutions to problems or to improve existing solutions. Engineers need proficient knowledge of relevant sciences for their design projects. As

4550-630: Is important for overall Indoor Environmental Quality (IEQ) and Indoor Air Quality (IAQ), in that it provides the necessary supply of fresh air and effectively evacuates exhaust air. Engineering Engineering is the practice of using natural science , mathematics , and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and improving infrastructure , machinery , vehicles , electronics , materials , and energy systems. The discipline of engineering encompasses

4680-438: Is of concern to many fields, including meteorology , aeronautics , medicine, mechanical engineering , civil engineering , environmental engineering and building science . In building science, airflow is often addressed in terms of its desirability, for example in contrasting ventilation and infiltration . Ventilation is defined as the desired flow of fresh outdoor supply air to another, typically indoor, space, along with

4810-488: Is significantly polluted with ground-level ozone concentrations from transportation related emissions or particulate matter from wildfires for example, residential and commercial building occupants may have to keep doors and windows closed to preserve indoor environmental quality (IEQ). By contrast, air infiltration is characterized as the uncontrolled influx of air through an inadequately-sealed building envelope, usually coupled with unintentional leakage of conditioned air from

4940-485: Is simple to program. It is currently only used in few specialized codes, which handle complex geometry with high accuracy and efficiency by using embedded boundaries or overlapping grids (with the solution interpolated across each grid). where Q {\displaystyle Q} is the vector of conserved variables, and F {\displaystyle F} , G {\displaystyle G} , and H {\displaystyle H} are

5070-577: Is the Navier–Stokes equations , which define many single-phase (gas or liquid, but not both) fluid flows. These equations can be simplified by removing terms describing viscous actions to yield the Euler equations . Further simplification, by removing terms describing vorticity yields the full potential equations . Finally, for small perturbations in subsonic and supersonic flows (not transonic or hypersonic ) these equations can be linearized to yield

5200-428: Is the design and manufacture of physical or mechanical systems, such as power and energy systems, aerospace / aircraft products, weapon systems , transportation products, engines , compressors , powertrains , kinematic chains , vacuum technology, vibration isolation equipment, manufacturing , robotics, turbines, audio equipments, and mechatronics . Bioengineering is the engineering of biological systems for

5330-448: Is the equation residual at an element vertex i {\displaystyle i} , Q {\displaystyle Q} is the conservation equation expressed on an element basis, W i {\displaystyle W_{i}} is the weight factor, and V e {\displaystyle V^{e}} is the volume of the element. The finite difference method (FDM) has historical importance and

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5460-664: Is traditionally broken into a number of sub-disciplines, including structural engineering , environmental engineering , and surveying . It is traditionally considered to be separate from military engineering . Electrical engineering is the design, study, and manufacture of various electrical and electronic systems, such as broadcast engineering , electrical circuits , generators , motors , electromagnetic / electromechanical devices, electronic devices , electronic circuits , optical fibers , optoelectronic devices , computer systems, telecommunications , instrumentation , control systems , and electronics . Mechanical engineering

5590-759: 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 applied to a wide range of research and engineering problems in many fields of study and industries, including aerodynamics and aerospace analysis, hypersonics , weather simulation , natural science and environmental engineering , industrial system design and analysis, biological engineering , fluid flows and heat transfer , engine and combustion analysis, and visual effects for film and games. The fundamental basis of almost all CFD problems

5720-461: Is unique in being a structured cartesian mesh code, while most other such codes use structured body-fitted grids (with the exception of NASA's highly successful CART3D code, Lockheed's SPLITFLOW code and Georgia Tech 's NASCART-GT). Antony Jameson also developed the three-dimensional AIRPLANE code which made use of unstructured tetrahedral grids. In the two-dimensional realm, Mark Drela and Michael Giles, then graduate students at MIT, developed

5850-831: The Neo-Assyrian period (911–609) BC. The Egyptian pyramids were built using three of the six simple machines, the inclined plane, the wedge, and the lever, to create structures like the Great Pyramid of Giza . The earliest civil engineer known by name is Imhotep . As one of the officials of the Pharaoh , Djosèr , he probably designed and supervised the construction of the Pyramid of Djoser (the Step Pyramid ) at Saqqara in Egypt around 2630–2611 BC. The earliest practical water-powered machines,

5980-542: The Newcomen steam engine . Smeaton designed the third Eddystone Lighthouse (1755–59) where he pioneered the use of ' hydraulic lime ' (a form of mortar which will set under water) and developed a technique involving dovetailed blocks of granite in the building of the lighthouse. He is important in the history, rediscovery of, and development of modern cement , because he identified the compositional requirements needed to obtain "hydraulicity" in lime; work which led ultimately to

6110-451: The U.S. Army Corps of Engineers . The word "engine" itself is of even older origin, ultimately deriving from the Latin ingenium ( c.  1250 ), meaning "innate quality, especially mental power, hence a clever invention." Later, as the design of civilian structures, such as bridges and buildings, matured as a technical discipline, the term civil engineering entered the lexicon as

6240-589: The boundary layer . It is here that surface friction most affects flow; irregularities in surfaces may affect boundary layer thickness, and hence act to disrupt flow. Typical units to express airflow are: Airflow can also be described in terms of air changes per hour (ACH), indicating full replacement of the volume of air filling the space in question. This unit is frequently used in the field of building science, with higher ACH values corresponding to leakier envelopes which are typical of older buildings that are less tightly sealed. The instrument that measures airflow

6370-517: The inclined plane (ramp) were known since prehistoric times. The wheel , along with the wheel and axle mechanism, was invented in Mesopotamia (modern Iraq) during the 5th millennium BC. The lever mechanism first appeared around 5,000 years ago in the Near East , where it was used in a simple balance scale , and to move large objects in ancient Egyptian technology . The lever was also used in

6500-553: The shadoof water-lifting device, the first crane machine, which appeared in Mesopotamia c.  3000 BC , and then in ancient Egyptian technology c.  2000 BC . The earliest evidence of pulleys date back to Mesopotamia in the early 2nd millennium BC, and ancient Egypt during the Twelfth Dynasty (1991–1802 BC). The screw , the last of the simple machines to be invented, first appeared in Mesopotamia during

6630-624: The water wheel and watermill , first appeared in the Persian Empire , in what are now Iraq and Iran, by the early 4th century BC. Kush developed the Sakia during the 4th century BC, which relied on animal power instead of human energy. Hafirs were developed as a type of reservoir in Kush to store and contain water as well as boost irrigation. Sappers were employed to build causeways during military campaigns. Kushite ancestors built speos during

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6760-412: The 14th century when an engine'er (literally, one who builds or operates a siege engine ) referred to "a constructor of military engines". In this context, now obsolete, an "engine" referred to a military machine, i.e. , a mechanical contraption used in war (for example, a catapult ). Notable examples of the obsolete usage which have survived to the present day are military engineering corps, e.g. ,

6890-426: The 1800s included the experiments of Alessandro Volta , Michael Faraday , Georg Ohm and others and the invention of the electric telegraph in 1816 and the electric motor in 1872. The theoretical work of James Maxwell (see: Maxwell's equations ) and Heinrich Hertz in the late 19th century gave rise to the field of electronics . The later inventions of the vacuum tube and the transistor further accelerated

7020-481: The 1980s with the development of the Barnes-Hut and fast multipole method (FMM) algorithms. These paved the way to practical computation of the velocities from the vortex elements. Software based on the vortex method offer a new means for solving tough fluid dynamics problems with minimal user intervention. All that is required is specification of problem geometry and setting of boundary and initial conditions. Among

7150-593: The 36 licensed member institutions of the UK Engineering Council . New specialties sometimes combine with the traditional fields and form new branches – for example, Earth systems engineering and management involves a wide range of subject areas including engineering studies , environmental science , engineering ethics and philosophy of engineering . Aerospace engineering covers the design, development, manufacture and operational behaviour of aircraft , satellites and rockets . Marine engineering covers

7280-576: The 9th century. In 1206, Al-Jazari invented programmable automata / robots . He described four automaton musicians, including drummers operated by a programmable drum machine , where they could be made to play different rhythms and different drum patterns. Before the development of modern engineering, mathematics was used by artisans and craftsmen, such as millwrights , clockmakers , instrument makers and surveyors. Aside from these professions, universities were not believed to have had much practical significance to technology. A standard reference for

7410-531: The Antikythera mechanism, required sophisticated knowledge of differential gearing or epicyclic gearing , two key principles in machine theory that helped design the gear trains of the Industrial Revolution, and are widely used in fields such as robotics and automotive engineering . Ancient Chinese, Greek, Roman and Hunnic armies employed military machines and inventions such as artillery which

7540-478: The Bronze Age between 3700 and 3250 BC. Bloomeries and blast furnaces were also created during the 7th centuries BC in Kush. Ancient Greece developed machines in both civilian and military domains. The Antikythera mechanism , an early known mechanical analog computer , and the mechanical inventions of Archimedes , are examples of Greek mechanical engineering. Some of Archimedes' inventions, as well as

7670-471: The Courant Institute at New York University (NYU) wrote a series of two-dimensional Full Potential airfoil codes that were widely used, the most important being named Program H. A further growth of Program H was developed by Bob Melnik and his group at Grumman Aerospace as Grumfoil. Antony Jameson , originally at Grumman Aircraft and the Courant Institute of NYU, worked with David Caughey to develop

7800-516: The ISES Euler program (actually a suite of programs) for airfoil design and analysis. This code first became available in 1986 and has been further developed to design, analyze and optimize single or multi-element airfoils, as the MSES program. MSES sees wide use throughout the world. A derivative of MSES, for the design and analysis of airfoils in a cascade, is MISES, developed by Harold Youngren while he

7930-497: The RANS and the LES regions of the solutions. Direct numerical simulation (DNS) resolves the entire range of turbulent length scales. This marginalizes the effect of models, but is extremely expensive. The computational cost is proportional to R e 3 {\displaystyle Re^{3}} . DNS is intractable for flows with complex geometries or flow configurations. The coherent vortex simulation approach decomposes

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8060-634: The Transonic Small Disturbance equations. In particular, the three-dimensional WIBCO code, developed by Charlie Boppe of Grumman Aircraft in the early 1980s has seen heavy use. Developers turned to Full Potential codes, as panel methods could not calculate the non-linear flow present at transonic speeds. The first description of a means of using the Full Potential equations was published by Earll Murman and Julian Cole of Boeing in 1970. Frances Bauer, Paul Garabedian and David Korn of

8190-638: The United States went to Josiah Willard Gibbs at Yale University in 1863; it was also the second PhD awarded in science in the U.S. Only a decade after the successful flights by the Wright brothers , there was extensive development of aeronautical engineering through development of military aircraft that were used in World War I . Meanwhile, research to provide fundamental background science continued by combining theoretical physics with experiments. Engineering

8320-416: The air is moving through a pipe, wide duct, open channel, or around airfoils. Reynold's number can also characterize an object (for example, a particle under the effect of gravitational settling) moving through a fluid. This number and related concepts can be applied to studying flow in systems of all scales. Transitional flow is a mixture of turbulence in the center of the velocity profile and laminar flow near

8450-427: The airflow in ducts is called a damper . The damper can be used to increase, decrease or completely stop the flow of air. A more complex device that can not only regulate the airflow but also has the ability to generate and condition airflow is an air handler . Fans also generate flows by "producing air flows with high volume and low pressure (although higher than ambient pressure)." This pressure differential induced by

8580-449: The airflow is necessary in many applications such as ventilation (to determine how much air is being replaced), pneumatic conveying (to control the air velocity and phase of transport) and engines (to control the Air–fuel ratio ). Aerodynamics is the branch of fluid dynamics (physics) that is specifically concerned with the measurement, simulation, and control of airflow. Managing airflow

8710-467: The application of flux limiters to ensure that the solution is total variation diminishing . In computational modeling of turbulent flows, one common objective is to obtain a model that can predict quantities of interest, such as fluid velocity, for use in engineering designs of the system being modeled. For turbulent flows, the range of length scales and complexity of phenomena involved in turbulence make most modeling approaches prohibitively expensive;

8840-409: The aviation pioneers around the start of the 20th century although the work of Sir George Cayley has recently been dated as being from the last decade of the 18th century. Early knowledge of aeronautical engineering was largely empirical with some concepts and skills imported from other branches of engineering. The first PhD in engineering (technically, applied science and engineering ) awarded in

8970-402: 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. The vorticity confinement (VC) method is an Eulerian technique used in the simulation of turbulent wakes. It uses a solitary-wave like approach to produce

9100-448: The control volume element. The finite element method (FEM) is used in structural analysis of solids, but is also applicable to fluids. However, the FEM formulation requires special care to ensure a conservative solution. The FEM formulation has been adapted for use with fluid dynamics governing equations. Although FEM must be carefully formulated to be conservative, it is much more stable than

9230-415: The design and use of hot-wire anemometers. Some tools are capable of calculating air flow, wet bulb temperature, dew point, and turbulence. Air flow can be simulated using Computational Fluid Dynamics (CFD) modeling, or observed experimentally through the operation of a wind tunnel . This may be used to predict airflow patterns around automobiles, aircraft, and marine craft, as well as air penetration of

9360-571: The design, development, manufacture and operational behaviour of watercraft and stationary structures like oil platforms and ports . Computer engineering (CE) is a branch of engineering that integrates several fields of computer science and electronic engineering required to develop computer hardware and software . Computer engineers usually have training in electronic engineering (or electrical engineering ), software design , and hardware-software integration instead of only software engineering or electronic engineering. Geological engineering

9490-407: The development and large scale manufacturing of chemicals in new industrial plants. The role of the chemical engineer was the design of these chemical plants and processes. Aeronautical engineering deals with aircraft design process design while aerospace engineering is a more modern term that expands the reach of the discipline by including spacecraft design. Its origins can be traced back to

9620-418: The development of electronics to such an extent that electrical and electronics engineers currently outnumber their colleagues of any other engineering specialty. Chemical engineering developed in the late nineteenth century. Industrial scale manufacturing demanded new materials and new processes and by 1880 the need for large scale production of chemicals was such that a new industry was created, dedicated to

9750-516: The discretisation handles discontinuous solutions gracefully. The Euler equations and Navier–Stokes equations both admit shocks and contact surfaces. Some of the discretization methods being used are: The finite volume method (FVM) is a common approach used in CFD codes, as it has an advantage in memory usage and solution speed, especially for large problems, high Reynolds number turbulent flows, and source term dominated flows (like combustion). In

9880-462: The early 1980s. This was soon followed by Mark Drela 's XFOIL code. Both PROFILE and XFOIL incorporate two-dimensional panel codes, with coupled boundary layer codes for airfoil analysis work. PROFILE uses a conformal transformation method for inverse airfoil design, while XFOIL has both a conformal transformation and an inverse panel method for airfoil design. An intermediate step between Panel Codes and Full Potential codes were codes that used

10010-407: The edges. Each of these three flows have distinct mechanisms of frictional energy losses that give rise to different behavior. As a result, different equations are used to predict and quantify the behavior of each type of flow. The speed at which a fluid flows past an object varies with distance from the object's surface. The region surrounding an object where the air speed approaches zero is known as

10140-483: The energy transfer between the measurement device and the passing particles. A hot-wire anemometer, for example, registers decreases in wire temperature, which can be translated into airflow velocity by analyzing the rate of change. Convective cooling is a function of airflow rate, and the electrical resistance of most metals is dependent upon the temperature of the metal, which is affected by the convective cooling. Engineers have taken advantage of these physical phenomena in

10270-449: The fan is what causes air to flow. The direction of airflow is determined by the direction of the pressure gradient. Total or static pressure rise, and therefore by extension airflow rate, is determined primarily by the fan speed measured in revolutions per minute (RPM). In control of HVAC systems to modulate the airflow rate, one typically changes the fan speed, which often come in 3-category settings such as low, medium, and high. Measuring

10400-431: The finer the resolution of the simulation, and therefore the higher the computational cost). If a majority or all of the turbulent scales are not modeled, the computational cost is very low, but the tradeoff comes in the form of decreased accuracy. In addition to the wide range of length and time scales and the associated computational cost, the governing equations of fluid dynamics contain a non-linear convection term and

10530-450: The finite volume approach. FEM also provides more accurate solutions for smooth problems comparing to FVM. Another advantage of FEM is that it can handle complex geometries and boundary conditions. However, FEM can require more memory and has slower solution times than the FVM. In this method, a weighted residual equation is formed: where R i {\displaystyle R_{i}}

10660-476: The finite volume method, the governing partial differential equations (typically the Navier-Stokes equations, the mass and energy conservation equations, and the turbulence equations) are recast in a conservative form, and then solved over discrete control volumes. This discretization guarantees the conservation of fluxes through a particular control volume. The finite volume equation yields governing equations in

10790-421: The first commercial piston steam engine in 1712, was not known to have any scientific training. The application of steam-powered cast iron blowing cylinders for providing pressurized air for blast furnaces lead to a large increase in iron production in the late 18th century. The higher furnace temperatures made possible with steam-powered blast allowed for the use of more lime in blast furnaces , which enabled

10920-409: The first half of the 19th century. These included the use of gigs to guide the machining tool over the work and fixtures to hold the work in the proper position. Machine tools and machining techniques capable of producing interchangeable parts lead to large scale factory production by the late 19th century. The United States Census of 1850 listed the occupation of "engineer" for the first time with

11050-692: The first work using computers to model fluid flow, as governed by the Navier–Stokes equations, was performed at Los Alamos National Lab , in the T3 group. This group was led by Francis H. Harlow , who is widely considered one of the pioneers of CFD. From 1957 to late 1960s, this group developed a variety of numerical methods to simulate transient two-dimensional fluid flows, such as particle-in-cell method, fluid-in-cell method, vorticity stream function method, and marker-and-cell method . Fromm's vorticity-stream-function method for 2D, transient, incompressible flow

11180-659: The fluid are traveling in parallel lines which gives rise to parallel streamlines. In a turbulent flow, particles are traveling in random and chaotic directions which gives rise to curved, spiraling, and often intersecting streamlines. The Reynolds number , a ratio indicating the relationship between viscous and inertial forces in a fluid, can be used to predict the transition from laminar to turbulent flow. Laminar flows occur at low Reynold's numbers where viscous forces dominate, and turbulent flows occur at high Reynold's numbers where inertial forces dominate. The range of Reynold's number that defines each type of flow depends on whether

11310-467: The fluxes in the x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} directions respectively. Spectral element method is a finite element type method. It requires the mathematical problem (the partial differential equation) to be cast in a weak formulation. This is typically done by multiplying the differential equation by an arbitrary test function and integrating over

11440-404: The form, where Q {\displaystyle Q} is the vector of conserved variables, F {\displaystyle F} is the vector of fluxes (see Euler equations or Navier–Stokes equations ), V {\displaystyle V} is the volume of the control volume element, and A {\displaystyle \mathbf {A} } is the surface area of

11570-598: The important three-dimensional Full Potential code FLO22 in 1975. Many Full Potential codes emerged after this, culminating in Boeing's Tranair (A633) code, which still sees heavy use. The next step was the Euler equations, which promised to provide more accurate solutions of transonic flows. The methodology used by Jameson in his three-dimensional FLO57 code (1981) was used by others to produce such programs as Lockheed's TEAM program and IAI/Analytical Methods' MGAERO program. MGAERO

11700-632: The incoherent parts of the flow composed homogeneous background noise, which exhibited no organized structures. Goldstein and Vasilyev applied the FDV model to large eddy simulation, but did not assume that the wavelet filter eliminated all coherent motions from the subfilter scales. By employing both LES and CVS filtering, they showed that the SFS dissipation was dominated by the SFS flow field's coherent portion. Probability density function (PDF) methods for turbulence, first introduced by Lundgren , are based on tracking

11830-419: 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

11960-620: The interior of a building to the exterior. Buildings may be ventilated using mechanical systems, passive systems or strategies, or a combination of the two. Mechanical ventilation uses fans to induce flow of air into and through a building. Duct configuration and assembly affect air flow rates through the system. Dampers, valves, joints and other geometrical or material changes within a duct can lead to flow pressure (energy) losses. Passive ventilation strategies take advantage of inherent characteristics of air, specifically thermal buoyancy and pressure differentials, to evacuate exhaust air from within

12090-514: The invention of Portland cement . Applied science led to the development of the steam engine. The sequence of events began with the invention of the barometer and the measurement of atmospheric pressure by Evangelista Torricelli in 1643, demonstration of the force of atmospheric pressure by Otto von Guericke using the Magdeburg hemispheres in 1656, laboratory experiments by Denis Papin , who built experimental model steam engines and demonstrated

12220-468: The length scale which is explicitly or implicitly involved in the RANS model. So while Spalart–Allmaras model based DES acts as LES with a wall model, DES based on other models (like two equation models) behave as a hybrid RANS-LES model. Grid generation is more complicated than for a simple RANS or LES case due to the RANS-LES switch. DES is a non-zonal approach and provides a single smooth velocity field across

12350-410: The limits within which a viable object or system may be produced and operated. 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

12480-457: The linearized potential equations. Historically, methods were first developed to solve the linearized potential equations. Two-dimensional (2D) methods, using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s. One of the earliest type of calculations resembling modern CFD are those by Lewis Fry Richardson , in the sense that these calculations used finite differences and divided

12610-535: The lower order codes was that they ran much faster on the computers of the time. Today, VSAERO has grown to be a multi-order code and is the most widely used program of this class. It has been used in the development of many submarines , surface ships , automobiles , helicopters , aircraft , and more recently wind turbines . Its sister code, USAERO is an unsteady panel method that has also been used for modeling such things as high speed trains and racing yachts . The NASA PMARC code from an early version of VSAERO and

12740-428: The most typical choice is the bilinear test or interpolating function of the form v ( x , y ) = a x + b y + c x y + d {\displaystyle v(x,y)=ax+by+cxy+d} . In a spectral element method however, the interpolating and test functions are chosen to be polynomials of a very high order (typically e.g. of the 10th order in CFD applications). This guarantees

12870-496: The new time-stepping schemes arise in the scientific world. The lattice Boltzmann method (LBM) with its simplified kinetic picture on a lattice provides a computationally efficient description of hydrodynamics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over

13000-417: The next discussion highlights the hierarchy of flow equations solved with CFD. Note that some of the following equations could be derived in more than one way. In all of these approaches the same basic procedure is followed. The stability of the selected discretisation is generally established numerically rather than analytically as with simple linear problems. Special care must also be taken to ensure that

13130-535: The one-point PDF of the velocity, f V ( v ; x , t ) d v {\displaystyle f_{V}({\boldsymbol {v}};{\boldsymbol {x}},t)d{\boldsymbol {v}}} , which gives the probability of the velocity at point x {\displaystyle {\boldsymbol {x}}} being between v {\displaystyle {\boldsymbol {v}}} and v + d v {\displaystyle {\boldsymbol {v}}+d{\boldsymbol {v}}} . This approach

13260-478: The physical space in cells. Although they failed dramatically, these calculations, together with Richardson's book Weather Prediction by Numerical Process , set the basis for modern CFD and numerical meteorology. In fact, early CFD calculations during the 1940s using ENIAC used methods close to those in Richardson's 1922 book. The computer power available paced development of three-dimensional methods. Probably

13390-474: The power to weight ratio of steam engines made practical steamboats and locomotives possible. New steel making processes, such as the Bessemer process and the open hearth furnace, ushered in an area of heavy engineering in the late 19th century. One of the most famous engineers of the mid-19th century was Isambard Kingdom Brunel , who built railroads, dockyards and steamships. The Industrial Revolution created

13520-464: The problem at hand. To illustrate this step, the following summarizes the physical assumptions/simplifications taken in equations of a flow that is single-phase (see multiphase flow and two-phase flow ), single-species (i.e., it consists of one chemical species), non-reacting, and (unless said otherwise) compressible. Thermal radiation is neglected, and body forces due to gravity are considered (unless said otherwise). In addition, for this type of flow,

13650-474: The rapid convergence of the method. Furthermore, very efficient integration procedures must be used, since the number of integrations to be performed in numerical codes is big. Thus, high order Gauss integration quadratures are employed, since they achieve the highest accuracy with the smallest number of computations to be carried out. At the time there are some academic CFD codes based on the spectral element method and some more are currently under development, since

13780-550: The residual by similar factors, leading to a mesh-independent number of iterations. For indefinite systems, preconditioners such as incomplete LU factorization , additive Schwarz , and multigrid perform poorly or fail entirely, so the problem structure must be used for effective preconditioning. Methods commonly used in CFD are the SIMPLE and Uzawa algorithms which exhibit mesh-dependent convergence rates, but recent advances based on block LU factorization combined with multigrid for

13910-421: The residual over successive subspaces generated by the preconditioned operator. Multigrid has the advantage of asymptotically optimal performance on many problems. Traditional solvers and preconditioners are effective at reducing high-frequency components of the residual, but low-frequency components typically require many iterations to reduce. By operating on multiple scales, multigrid reduces all components of

14040-486: The resolution required to resolve all scales involved in turbulence is beyond what is computationally possible. The primary approach in such cases is to create numerical models to approximate unresolved phenomena. This section lists some commonly used computational models for turbulent flows. Turbulence models can be classified based on computational expense, which corresponds to the range of scales that are modeled versus resolved (the more turbulent scales that are resolved,

14170-421: The resulting definite systems have led to preconditioners that deliver mesh-independent convergence rates. CFD made a major break through in late 70s with the introduction of LTRAN2, a 2-D code to model oscillating airfoils based on transonic small perturbation theory by Ballhaus and associates. It uses a Murman-Cole switch algorithm for modeling the moving shock-waves. Later it was extended to 3-D with use of

14300-434: The rise of engineering as a profession in the 18th century, the term became more narrowly applied to fields in which mathematics and science were applied to these ends. Similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. Canal building was an important engineering work during the early phases of the Industrial Revolution. John Smeaton

14430-426: The same with full cognizance of their design; or to forecast their behavior under specific operating conditions; all as respects an intended function, economics of operation and safety to life and property. Engineering has existed since ancient times, when humans devised inventions such as the wedge, lever, wheel and pulley, etc. The term engineering is derived from the word engineer , which itself dates back to

14560-406: The significant advantages of this modern technology; In the boundary element method, the boundary occupied by the fluid is divided into a surface mesh. High-resolution schemes are used where shocks or discontinuities are present. Capturing sharp changes in the solution requires the use of second or higher-order numerical schemes that do not introduce spurious oscillations. This usually necessitates

14690-526: The simultaneous expulsion of exhaust air from indoors to the outdoors. This may be achieved through mechanical means (i.e. the use of a louver or damper for air intake and a fan to induce flow through ductwork) or through passive strategies (also known as natural ventilation ). While natural ventilation has economic benefits over mechanical ventilation because it typically requires far less operational energy consumption, it can only be utilized during certain times of day and under certain outdoor conditions. If there

14820-464: The state of mechanical arts during the Renaissance is given in the mining engineering treatise De re metallica (1556), which also contains sections on geology, mining, and chemistry. De re metallica was the standard chemistry reference for the next 180 years. The science of classical mechanics , sometimes called Newtonian mechanics, formed the scientific basis of much of modern engineering. With

14950-419: The surface. The level of friction is quantified by a parameter called the "roughness length." Streamlines connect velocities and are tangential to the instantaneous direction of multiple velocity vectors. They can be curved and do not always follow the shape of the container. Additionally, they only exist in steady flows, i.e. flows whose velocity vectors do not change over time. In a laminar flow, all particles of

15080-437: The time over which these changes in the mean occur is large compared to the time scales of the turbulent motion containing most of the energy. RANS models can be divided into two broad approaches: Large eddy simulation (LES) is a technique in which the smallest scales of the flow are removed through a filtering operation, and their effect modeled using subgrid scale models. This allows the largest and most important scales of

15210-414: The transition from charcoal to coke . These innovations lowered the cost of iron, making horse railways and iron bridges practical. The puddling process , patented by Henry Cort in 1784 produced large scale quantities of wrought iron. Hot blast , patented by James Beaumont Neilson in 1828, greatly lowered the amount of fuel needed to smelt iron. With the development of the high pressure steam engine,

15340-424: The turbulence to be resolved, while greatly reducing the computational cost incurred by the smallest scales. This method requires greater computational resources than RANS methods, but is far cheaper than DNS. Detached eddy simulations (DES) is a modification of a RANS model in which the model switches to a subgrid scale formulation in regions fine enough for LES calculations. Regions near solid boundaries and where

15470-415: The turbulent flow field into a coherent part, consisting of organized vortical motion, and the incoherent part, which is the random background flow. This decomposition is done using wavelet filtering. The approach has much in common with LES, since it uses decomposition and resolves only the filtered portion, but different in that it does not use a linear, low-pass filter. Instead, the filtering operation

15600-594: The turbulent length scale is less than the maximum grid dimension are assigned the RANS mode of solution. As the turbulent length scale exceeds the grid dimension, the regions are solved using the LES mode. Therefore, the grid resolution for DES is not as demanding as pure LES, thereby considerably cutting down the cost of the computation. Though DES was initially formulated for the Spalart-Allmaras model (Philippe R. Spalart et al., 1997), it can be implemented with other RANS models (Strelets, 2001), by appropriately modifying

15730-576: The use of a piston, which he published in 1707. Edward Somerset, 2nd Marquess of Worcester published a book of 100 inventions containing a method for raising waters similar to a coffee percolator . Samuel Morland , a mathematician and inventor who worked on pumps, left notes at the Vauxhall Ordinance Office on a steam pump design that Thomas Savery read. In 1698 Savery built a steam pump called "The Miner's Friend". It employed both vacuum and pressure. Iron merchant Thomas Newcomen , who built

15860-424: The velocity profile looks like. Generally, in encased flows, instantaneous velocity vectors are larger in magnitude in the middle of the profile due to the effect of friction from the material of the pipe, duct, or channel walls on nearby layers of fluid. In tropospheric atmospheric flows, velocity increases with elevation from ground level due to friction from obstructions like trees and hills slowing down airflow near

15990-445: The whole domain. Purely mathematically, the test functions are completely arbitrary - they belong to an infinite-dimensional function space. Clearly an infinite-dimensional function space cannot be represented on a discrete spectral element mesh; this is where the spectral element discretization begins. The most crucial thing is the choice of interpolating and testing functions. In a standard, low order FEM in 2D, for quadrilateral elements

16120-623: Was a steam jack driven by a steam turbine , described in 1551 by Taqi al-Din Muhammad ibn Ma'ruf in Ottoman Egypt . The cotton gin was invented in India by the 6th century AD, and the spinning wheel was invented in the Islamic world by the early 11th century, both of which were fundamental to the growth of the cotton industry . The spinning wheel was also a precursor to the spinning jenny , which

16250-507: Was a graduate student at MIT. The Navier–Stokes equations were the ultimate target of development. Two-dimensional codes, such as NASA Ames' ARC2D code first emerged. A number of three-dimensional codes were developed (ARC3D, OVERFLOW , CFL3D are three successful NASA contributions), leading to numerous commercial packages. Recently CFD methods have gained traction for modeling the flow behavior of granular materials within various chemical processes in engineering. This approach has emerged as

16380-513: Was a key development during the early Industrial Revolution in the 18th century. The earliest programmable machines were developed in the Muslim world. A music sequencer , a programmable musical instrument , was the earliest type of programmable machine. The first music sequencer was an automated flute player invented by the Banu Musa brothers, described in their Book of Ingenious Devices , in

16510-642: Was developed by the Greeks around the 4th century BC, the trireme , the ballista and the catapult . In the Middle Ages, the trebuchet was developed. The earliest practical wind-powered machines, the windmill and wind pump , first appeared in the Muslim world during the Islamic Golden Age , in what are now Iran, Afghanistan, and Pakistan, by the 9th century AD. The earliest practical steam-powered machine

16640-665: Was mainly applied to ship hulls and aircraft fuselages. The first lifting Panel Code (A230) was described in a paper written by Paul Rubbert and Gary Saaris of Boeing Aircraft in 1968. In time, more advanced three-dimensional Panel Codes were developed at Boeing (PANAIR, A502), Lockheed (Quadpan), Douglas (HESS), McDonnell Aircraft (MACAERO), NASA (PMARC) and Analytical Methods (WBAERO, USAERO and VSAERO ). Some (PANAIR, HESS and MACAERO) were higher order codes, using higher order distributions of surface singularities, while others (Quadpan, PMARC, USAERO and VSAERO) used single singularities on each surface panel. The advantage of

16770-505: Was the first self-proclaimed civil engineer and is often regarded as the "father" of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbors, and lighthouses. He was also a capable mechanical engineer and an eminent physicist . Using a model water wheel, Smeaton conducted experiments for seven years, determining ways to increase efficiency. Smeaton introduced iron axles and gears to water wheels. Smeaton also made mechanical improvements to

16900-425: Was the first treatment of strongly contorting incompressible flows in the world. The first paper with three-dimensional model was published by John Hess and A.M.O. Smith of Douglas Aircraft in 1967. This method discretized the surface of the geometry with panels, giving rise to this class of programs being called Panel Methods. Their method itself was simplified, in that it did not include lifting flows and hence

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