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160-468: 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

320-420: A cruise missile ); and covert insertion of frogmen or special forces . Their civilian uses include: marine science ; salvage ; exploration; and facility inspection and maintenance. Submarines can be modified for specialized functions such as search-and-rescue missions and undersea cable repair. They are also used in the tourism industry and in undersea archaeology . Modern deep-diving submarines derive from

480-426: A shock wave . The presence of shock waves, along with the compressibility effects of high-flow velocity (see Reynolds number ) fluids, is the central difference between the supersonic and subsonic aerodynamics regimes. In aerodynamics, hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime

640-447: 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

800-407: A carrying capacity of 50 to 100 passengers. In a typical operation a surface vessel carries passengers to an offshore operating area and loads them into the submarine. The submarine then visits underwater points of interest such as natural or artificial reef structures. To surface safely without danger of collision the location of the submarine is marked with an air release and movement to the surface

960-482: A continuum. Continuum flow fields are characterized by properties such as flow velocity , pressure , density , and temperature , which may be functions of position and time. These properties may be directly or indirectly measured in aerodynamics experiments or calculated starting with the equations for conservation of mass, momentum , and energy in air flows. Density, flow velocity, and an additional property, viscosity , are used to classify flow fields. Flow velocity

1120-421: 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

1280-449: 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

1440-574: 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

1600-410: A flow field) enables the calculation of forces and moments acting on the object. In many aerodynamics problems, the forces of interest are the fundamental forces of flight: lift , drag , thrust , and weight . Of these, lift and drag are aerodynamic forces, i.e. forces due to air flow over a solid body. Calculation of these quantities is often founded upon the assumption that the flow field behaves as

1760-438: A fluid, the speed of sound in that fluid can be considered the fastest speed that "information" can travel in the flow. This difference most obviously manifests itself in the case of a fluid striking an object. In front of that object, the fluid builds up a stagnation pressure as impact with the object brings the moving fluid to rest. In fluid traveling at subsonic speed, this pressure disturbance can propagate upstream, changing

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1920-414: A fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as Bernoulli's principle , which provides one method for calculating aerodynamic lift. In 1757, Leonhard Euler published the more general Euler equations which could be applied to both compressible and incompressible flows. The Euler equations were extended to incorporate the effects of viscosity in

2080-468: 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

2240-465: A hand-powered acorn-shaped device designed by the American David Bushnell to accommodate a single person. It was the first verified submarine capable of independent underwater operation and movement, and the first to use screws for propulsion. In 1800, France built Nautilus , a human-powered submarine designed by American Robert Fulton . They gave up on the experiment in 1804, as did

2400-501: 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

2560-636: A noun it generally refers to a vessel that can travel underwater. The term is a contraction of submarine boat . and occurs as such in several languages, e.g. French ( sous-marin ), and Spanish ( submarino ), although others retain the original term, such as Dutch ( Onderzeeboot ), German ( Unterseeboot ), Swedish ( Undervattensbåt ), and Russian ( подводная лодка : podvodnaya lodka ), all of which mean 'submarine boat'. By naval tradition , submarines are usually referred to as boats rather than as ships , regardless of their size. Although referred to informally as boats , U.S. submarines employ

2720-502: A pivotal time in submarine development, and several important technologies appeared. A number of nations built and used submarines. Diesel electric propulsion became the dominant power system and equipment such as the periscope became standardized. Countries conducted many experiments on effective tactics and weapons for submarines, which led to their large impact in World War I . The first submarine not relying on human power for propulsion

2880-410: A range of flow velocities just below and above the local speed of sound (generally taken as Mach 0.8–1.2). It is defined as the range of speeds between the critical Mach number , when some parts of the airflow over an aircraft become supersonic , and a higher speed, typically near Mach 1.2 , when all of the airflow is supersonic. Between these speeds, some of the airflow is supersonic, while some of

3040-521: A rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow , turbulence , and boundary layers and has become increasingly computational in nature. Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, and images and stories of flight appear throughout recorded history, such as

3200-473: 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

3360-439: 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

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3520-824: A single torpedo , in 1885. A reliable means of propulsion for the submerged vessel was only made possible in the 1880s with the advent of the necessary electric battery technology. The first electrically powered boats were built by Isaac Peral y Caballero in Spain (who built Peral ), Dupuy de Lôme (who built Gymnote ) and Gustave Zédé (who built Sirène ) in France, and James Franklin Waddington (who built Porpoise ) in England. Peral's design featured torpedoes and other systems that later became standard in submarines. Commissioned in June 1900,

3680-527: A spar as a torpedo charge. The Hunley also sank. The explosion's shock waves may have killed its crew instantly, preventing them from pumping the bilge or propelling the submarine. In 1866, Sub Marine Explorer was the first submarine to successfully dive, cruise underwater, and resurface under the crew's control. The design by German American Julius H. Kroehl (in German, Kröhl ) incorporated elements that are still used in modern submarines. In 1866, Flach

3840-407: 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

4000-447: A submarine lies in its ability to remain concealed in the depths of the ocean. Early submarines could be detected by the sound they made. Water is an excellent conductor of sound (much better than air), and submarines can detect and track comparatively noisy surface ships from long distances. Modern submarines are built with an emphasis on stealth . Advanced propeller designs, extensive sound-reducing insulation, and special machinery help

4160-422: A submarine remain as quiet as ambient ocean noise, making them difficult to detect. It takes specialized technology to find and attack modern submarines. Active sonar uses the reflection of sound emitted from the search equipment to detect submarines. It has been used since WWII by surface ships, submarines and aircraft (via dropped buoys and helicopter "dipping" arrays), but it reveals the emitter's position, and

4320-539: A successful firing solution against a three-dimensionally maneuvering target using techniques which became the basis of modern torpedo computer targeting systems. Seventy-four British submarines were lost, the majority, forty-two, in the Mediterranean. The first launch of a cruise missile ( SSM-N-8 Regulus ) from a submarine occurred in July 1953, from the deck of USS  Tunny , a World War II fleet boat modified to carry

4480-532: 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

4640-663: A test dive while at its operational limit, and USS  Scorpion due to unknown causes. During the Indo-Pakistani War of 1971 , the Pakistan Navy 's Hangor sank the Indian frigate INS  Khukri . This was the first sinking by a submarine since World War II. During the same war, Ghazi , a Tench -class submarine on loan to Pakistan from the US, was sunk by the Indian Navy . It

4800-524: A total of 74 submarines, though of mixed effectiveness. In August 1914, a flotilla of ten U-boats sailed from their base in Heligoland to attack Royal Navy warships in the North Sea in the first submarine war patrol in history. The U-boats' ability to function as practical war machines relied on new tactics, their numbers, and submarine technologies such as combination diesel–electric power system developed in

4960-560: A wide range of types and capabilities. They range from small, autonomous examples, such as one- or two-person subs that operate for a few hours, to vessels that can remain submerged for six months, such as the Russian Typhoon class , (the biggest submarines ever built). Submarines can work at depths that are greater than what is practicable (or even survivable) for human divers . The word submarine means 'underwater' or 'under-sea' (as in submarine canyon , submarine pipeline ) though as

Computational fluid dynamics - Misplaced Pages Continue

5120-537: Is a watercraft capable of independent operation underwater. (It differs from a submersible , which has more limited underwater capability.) The term “submarine” is also sometimes used historically or informally to refer to remotely operated vehicles and robots , or to medium-sized or smaller vessels (such as the midget submarine and the wet sub ). Submarines are referred to as boats rather than ships regardless of their size. Although experimental submarines had been built earlier, submarine design took off during

5280-512: 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

5440-418: Is a flow in which density is constant in both time and space. Although all real fluids are compressible, a flow is often approximated as incompressible if the effect of the density changes cause only small changes to the calculated results. This is more likely to be true when the flow speeds are significantly lower than the speed of sound. Effects of compressibility are more significant at speeds close to or above

5600-448: Is a solution in one dimension to both the momentum and energy conservation equations. The ideal gas law or another such equation of state is often used in conjunction with these equations to form a determined system that allows the solution for the unknown variables. Aerodynamic problems are classified by the flow environment or properties of the flow, including flow speed , compressibility , and viscosity . External aerodynamics

5760-416: Is a subset of the supersonic regime. Hypersonic flow is characterized by high temperature flow behind a shock wave, viscous interaction, and chemical dissociation of gas. The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence. The concept of a boundary layer is important in many problems in aerodynamics. The viscosity and fluid friction in

5920-404: 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

6080-596: 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

6240-503: Is associated with the frictional forces in a flow. In some flow fields, viscous effects are very small, and approximate solutions may safely neglect viscous effects. These approximations are called inviscid flows. Flows for which viscosity is not neglected are called viscous flows. Finally, aerodynamic problems may also be classified by the flow environment. External aerodynamics is the study of flow around solid objects of various shapes (e.g. around an airplane wing), while internal aerodynamics

6400-459: 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

6560-407: Is called laminar flow . Aerodynamics is a significant element of vehicle design , including road cars and trucks where the main goal is to reduce the vehicle drag coefficient , and racing cars , where in addition to reducing drag the goal is also to increase the overall level of downforce . Aerodynamics is also important in the prediction of forces and moments acting on sailing vessels . It

Computational fluid dynamics - Misplaced Pages Continue

6720-409: Is called potential flow and allows the differential equations that describe the flow to be a simplified version of the equations of fluid dynamics , thus making available to the aerodynamicist a range of quick and easy solutions. In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effects of compressibility. Compressibility is a description of

6880-533: Is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight , which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed

7040-484: 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

7200-518: Is susceptible to counter-measures. A concealed military submarine is a real threat, and because of its stealth, can force an enemy navy to waste resources searching large areas of ocean and protecting ships against attack. This advantage was vividly demonstrated in the 1982 Falklands War when the British nuclear-powered submarine HMS  Conqueror sank the Argentine cruiser General Belgrano . After

7360-577: 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

7520-447: 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

7680-497: Is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe. Aerodynamic problems can also be classified according to whether

7840-415: Is the study of flow through passages inside solid objects (e.g. through a jet engine). Unlike liquids and solids, gases are composed of discrete molecules which occupy only a small fraction of the volume filled by the gas. On a molecular level, flow fields are made up of the collisions of many individual of gas molecules between themselves and with solid surfaces. However, in most aerodynamics applications,

8000-427: Is the study of the motion of air , particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics , and is an important domain of study in aeronautics . The term aerodynamics is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and

8160-457: 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

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8320-426: Is used because gas flows with a Mach number below that value demonstrate changes in density of less than 5%. Furthermore, that maximum 5% density change occurs at the stagnation point (the point on the object where flow speed is zero), while the density changes around the rest of the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible flows. The term Transonic refers to

8480-418: Is used in the design of mechanical components such as hard drive heads. Structural engineers resort to aerodynamics, and particularly aeroelasticity , when calculating wind loads in the design of large buildings, bridges , and wind turbines . The aerodynamics of internal passages is important in heating/ventilation , gas piping , and in automotive engines where detailed flow patterns strongly affect

8640-468: Is used to classify flows according to speed regime. Subsonic flows are flow fields in which the air speed field is always below the local speed of sound. Transonic flows include both regions of subsonic flow and regions in which the local flow speed is greater than the local speed of sound. Supersonic flows are defined to be flows in which the flow speed is greater than the speed of sound everywhere. A fourth classification, hypersonic flow, refers to flows where

8800-471: The Gato , Balao , and Tench classes were commissioned during the war. During the war, 52 US submarines were lost to all causes, with 48 directly due to hostilities. US submarines sank 1,560 enemy vessels, a total tonnage of 5.3 million tons (55% of the total sunk). The Royal Navy Submarine Service was used primarily in the classic Axis blockade . Its major operating areas were around Norway, in

8960-483: The Ancient Greek legend of Icarus and Daedalus . Fundamental concepts of continuum , drag , and pressure gradients appear in the work of Aristotle and Archimedes . In 1726, Sir Isaac Newton became the first person to develop a theory of air resistance, making him one of the first aerodynamicists. Dutch - Swiss mathematician Daniel Bernoulli followed in 1738 with Hydrodynamica in which he described

9120-507: The Holland Torpedo Boat Company from 1901 to 1903. Construction of the boats took longer than anticipated, with the first only ready for a diving trial at sea on 6 April 1902. Although the design had been purchased entirely from the US company, the actual design used was an untested improvement to the original Holland design using a new 180 horsepower (130 kW) petrol engine. These types of submarines were first used during

9280-634: The Mediterranean (against the Axis supply routes to North Africa), and in the Far East. In that war, British submarines sank 2 million tons of enemy shipping and 57 major warships, the latter including 35 submarines. Among these is the only documented instance of a submarine sinking another submarine while both were submerged. This occurred when HMS  Venturer engaged U-864 ; the Venturer crew manually computed

9440-525: The Russo-Japanese War of 1904–05. Due to the blockade at Port Arthur , the Russians sent their submarines to Vladivostok , where by 1 January 1905 there were seven boats, enough to create the world's first "operational submarine fleet". The new submarine fleet began patrols on 14 February, usually lasting for about 24 hours each. The first confrontation with Japanese warships occurred on 29 April 1905 when

9600-511: The bathyscaphe , which evolved from the diving bell . Most large submarines consist of a cylindrical body with hemispherical (or conical) ends and a vertical structure, usually located amidships, which houses communications and sensing devices as well as periscopes . In modern submarines, this structure is called the " sail " in American usage and "fin" in European usage. A feature of earlier designs

9760-416: The flow speed is below, near or above the speed of sound . A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when

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9920-480: 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

10080-538: The 19th century, and submarines were adopted by several navies. They were first used widely during World War I (1914–1918), and are now used in many navies , large and small. Their military uses include: attacking enemy surface ships (merchant and military) or other submarines; aircraft carrier protection; blockade running ; nuclear deterrence ; stealth operations in denied areas when gathering intelligence and doing reconnaissance ; denying or influencing enemy movements; conventional land attacks (for example, launching

10240-635: The British, when they reconsidered Fulton's submarine design. In 1850, Wilhelm Bauer 's Brandtaucher was built in Germany. It remains the oldest known surviving submarine in the world. In 1864, late in the American Civil War , the Confederate navy 's H. L. Hunley became the first military submarine to sink an enemy vessel, the Union sloop-of-war USS  Housatonic , using a gun-powder-filled keg on

10400-469: 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

10560-501: The English clergyman and inventor George Garrett and the Swedish industrialist Thorsten Nordenfelt led to the first practical steam-powered submarines, armed with torpedoes and ready for military use. The first was Nordenfelt I , a 56-tonne, 19.5-metre (64 ft) vessel similar to Garrett's ill-fated Resurgam (1879), with a range of 240 kilometres (130 nmi; 150 mi), armed with

10720-599: The French steam and electric Narval employed the now typical double-hull design, with a pressure hull inside the outer shell. These 200-ton ships had a range of over 160 km (100 mi) underwater. The French submarine Aigrette in 1904 further improved the concept by using a diesel rather than a gasoline engine for surface power. Large numbers of these submarines were built, with seventy-six completed before 1914. The Royal Navy commissioned five Holland-class submarines from Vickers , Barrow-in-Furness , under licence from

10880-736: The German developments in submarine technology with the creation of the K-class submarines . However, these submarines were notoriously dangerous to operate due to their various design flaws and poor maneuverability. During World War II , Germany used submarines to devastating effect in the Battle of the Atlantic , where it attempted to cut Britain's supply routes by sinking more merchant ships than Britain could replace. These merchant ships were vital to supply Britain's population with food, industry with raw material, and armed forces with fuel and armaments. Although

11040-513: 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

11200-762: The Pacific War destroyed more Japanese shipping than all other weapons combined. This feat was considerably aided by the Imperial Japanese Navy's failure to provide adequate escort forces for the nation's merchant fleet. During World War II, 314 submarines served in the US Navy, of which nearly 260 were deployed to the Pacific. When the Japanese attacked Hawaii in December 1941, 111 boats were in commission; 203 submarines from

11360-462: The Pacific in World War II. Mine -laying submarines were developed in the early part of the 20th century. The facility was used in both World Wars. Submarines were also used for inserting and removing covert agents and military forces in special operations , for intelligence gathering, and to rescue aircrew during air attacks on islands, where the airmen would be told of safe places to crash-land so

11520-496: 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

11680-567: The Russian submarine Som was fired upon by Japanese torpedo boats, but then withdrew. Military submarines first made a significant impact in World War I . Forces such as the U-boats of Germany saw action in the First Battle of the Atlantic , and were responsible for sinking RMS  Lusitania , which was sunk as a result of unrestricted submarine warfare and is often cited among the reasons for

11840-632: 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

12000-608: The U-boats had been updated in the interwar years, the major innovation was improved communications, encrypted using the Enigma cipher machine . This allowed for mass-attack naval tactics ( Rudeltaktik , commonly known as " wolfpack "), which ultimately ceased to be effective when the U-boat's Enigma was cracked . By the end of the war, almost 3,000 Allied ships (175 warships, 2,825 merchantmen) had been sunk by U-boats. Although successful early in

12160-780: The US, the Soviet Union (now Russia), the UK, and France have been powered by a nuclear reactor . In 1959–1960, the first ballistic missile submarines were put into service by both the United States ( George Washington class ) and the Soviet Union ( Golf class ) as part of the Cold War nuclear deterrent strategy. During the Cold War, the US and the Soviet Union maintained large submarine fleets that engaged in cat-and-mouse games. The Soviet Union lost at least four submarines during this period: K-129

12320-412: The air is approximated as being significant only in this thin layer. This assumption makes the description of such aerodynamics much more tractable mathematically. In aerodynamics, turbulence is characterized by chaotic property changes in the flow. These include low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time. Flow that is not turbulent

12480-563: The airflow is not supersonic. Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde during cruise can be an example of a supersonic aerodynamic problem. Supersonic flow behaves very differently from subsonic flow. Fluids react to differences in pressure; pressure changes are how a fluid is "told" to respond to its environment. Therefore, since sound is, in fact, an infinitesimal pressure difference propagating through

12640-576: The amount of change of density in the flow. When the effects of compressibility on the solution are small, the assumption that density is constant may be made. The problem is then an incompressible low-speed aerodynamics problem. When the density is allowed to vary, the flow is called compressible. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3 (about 335 feet (102 m) per second or 228 miles (366 km) per hour at 60 °F (16 °C)). Above Mach 0.3,

12800-466: 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;

12960-654: The belief that the vessel was evacuating anti-Israeli militias. The ship was hit by two torpedoes, managed to run aground but eventually sank. There were 25 dead, including her captain. The Israeli Navy disclosed the incident in November 2018. Before and during World War II , the primary role of the submarine was anti-surface ship warfare. Submarines would attack either on the surface using deck guns, or submerged using torpedoes . They were particularly effective in sinking Allied transatlantic shipping in both World Wars, and in disrupting Japanese supply routes and naval operations in

13120-402: 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

13280-635: The choice between statistical mechanics and the continuous formulation of aerodynamics. The assumption of a fluid continuum allows problems in aerodynamics to be solved using fluid dynamics conservation laws . Three conservation principles are used: Together, these equations are known as the Navier–Stokes equations , although some authors define the term to only include the momentum equation(s). The Navier–Stokes equations have no known analytical solution and are solved in modern aerodynamics using computational techniques . Because computational methods using high speed computers were not historically available and

13440-457: The continuum assumption is reasonable. The continuum assumption is less valid for extremely low-density flows, such as those encountered by vehicles at very high altitudes (e.g. 300,000 ft/90 km) or satellites in Low Earth orbit . In those cases, statistical mechanics is a more accurate method of solving the problem than is continuum aerodynamics. The Knudsen number can be used to guide

13600-446: 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

13760-458: The craft. A mechanism was used to twist the water out of the bags and cause the boat to resurface. In 1749, the Gentlemen's Magazine reported that a similar design had initially been proposed by Giovanni Borelli in 1680. Further design improvement stagnated for over a century, until application of new technologies for propulsion and stability. The first military submersible was Turtle (1775),

13920-556: The designation USS ( United States Ship ) at the beginning of their names, such as USS  Alabama . In the Royal Navy, the designation HMS can refer to "His Majesty's Ship" or "His Majesty's Submarine", though the latter is sometimes rendered "HMS/m" and submarines are generally referred to as boats rather than ships . According to a report in Opusculum Taisnieri published in 1562: Two Greeks submerged and surfaced in

14080-463: The desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continues to motivate new research in aerodynamics, while work continues to be done on important problems in basic aerodynamic theory related to flow turbulence and the existence and uniqueness of analytical solutions to the Navier–Stokes equations. Understanding the motion of air around an object (often called

14240-441: The development of the homing torpedo, better sonar systems, and nuclear propulsion , submarines also became able to hunt each other effectively. The development of submarine-launched ballistic missile and submarine-launched cruise missiles gave submarines a substantial and long-ranged ability to attack both land and sea targets with a variety of weapons ranging from cluster bombs to nuclear weapons . The primary defense of

14400-437: The discrete molecular nature of gases is ignored, and the flow field is assumed to behave as a continuum . This assumption allows fluid properties such as density and flow velocity to be defined everywhere within the flow. The validity of the continuum assumption is dependent on the density of the gas and the application in question. For the continuum assumption to be valid, the mean free path length must be much smaller than

14560-515: 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

14720-460: 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

14880-673: The enemyes by the Grace of God and worke of expert Craftsmen I hope to perform." It is unclear whether he carried out his idea. Jerónimo de Ayanz y Beaumont (1553–1613) created detailed designs for two types of air-renovated submersible vehicles. They were equipped with oars, autonomous floating snorkels worked by inner pumps, portholes and gloves used for the crew to manipulate underwater objects. Ayanaz planned to use them for warfare, using them to approach enemy ships undetected and set up timed gunpowder charges on their hulls. The first submersible of whose construction there exists reliable information

15040-402: The entry of the United States into the war. At the outbreak of the war, Germany had only twenty submarines available for combat, although these included vessels of the diesel-engined U-19 class, which had a sufficient range of 5,000 miles (8,000 km) and speed of 8 knots (15 km/h) to allow them to operate effectively around the entire British coast., By contrast, the Royal Navy had

15200-431: 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

15360-447: 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}}

15520-476: 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

15680-599: The first flights, Frederick W. Lanchester , Martin Kutta , and Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with boundary layers . As aircraft speed increased designers began to encounter challenges associated with air compressibility at speeds near

15840-453: The first half of the 1800s, resulting in the Navier–Stokes equations . The Navier–Stokes equations are the most general governing equations of fluid flow but are difficult to solve for the flow around all but the simplest of shapes. In 1799, Sir George Cayley became the first person to identify the four aerodynamic forces of flight ( weight , lift , drag , and thrust ), as well as the relationships between them, and in doing so outlined

16000-535: The first practical self-propelled or "locomotive" torpedo. The spar torpedo that had been developed earlier by the Confederate States Navy was considered to be impracticable, as it was believed to have sunk both its intended target, and H. L. Hunley , the submarine that deployed it. The Irish inventor John Philip Holland built a model submarine in 1876 and in 1878 demonstrated the Holland I prototype. This

16160-630: 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

16320-477: The flow pattern ahead of the object and giving the impression that the fluid "knows" the object is there by seemingly adjusting its movement and is flowing around it. In a supersonic flow, however, the pressure disturbance cannot propagate upstream. Thus, when the fluid finally reaches the object it strikes it and the fluid is forced to change its properties – temperature , density , pressure , and Mach number —in an extremely violent and irreversible fashion called

16480-458: The flow speed is much greater than the speed of sound. Aerodynamicists disagree on the precise definition of hypersonic flow. Compressible flow accounts for varying density within the flow. Subsonic flows are often idealized as incompressible, i.e. the density is assumed to be constant. Transonic and supersonic flows are compressible, and calculations that neglect the changes of density in these flow fields will yield inaccurate results. Viscosity

16640-570: The flow speed is much greater than the speed of sound. Aerodynamicists disagree over the precise definition of hypersonic flow; a rough definition considers flows with Mach numbers above 5 to be hypersonic. The influence of viscosity on the flow dictates a third classification. Some problems may encounter only very small viscous effects, in which case viscosity can be considered to be negligible. The approximations to these problems are called inviscid flows . Flows for which viscosity cannot be neglected are called viscous flows. An incompressible flow

16800-416: The fluid flow can be computed. Blood properties such as density and viscosity, and realistic boundary conditions (e.g. systemic pressure) have to be taken into consideration. Therefore, making it possible to analyze and optimize the flow in the cardiovascular system for different applications. Aerodynamics Aerodynamics ( Ancient Greek : ἀήρ aero (air) + Ancient Greek : δυναμική (dynamics))

16960-467: 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

17120-404: 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

17280-465: The high computational cost of solving these complex equations now that they are available, simplifications of the Navier–Stokes equations have been and continue to be employed. The Euler equations are a set of similar conservation equations which neglect viscosity and may be used in cases where the effect of viscosity is expected to be small. Further simplifications lead to Laplace's equation and potential flow theory. Additionally, Bernoulli's equation

17440-521: The highest submerged speeds during World War II ( I-201 -class submarines) and submarines that could carry multiple aircraft ( I-400 -class submarines). They were also equipped with one of the most advanced torpedoes of the conflict, the oxygen-propelled Type 95 . Nevertheless, despite their technical prowess, Japan chose to use its submarines for fleet warfare, and consequently were relatively unsuccessful, as warships were fast, maneuverable and well-defended compared to merchant ships. The submarine force

17600-593: 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

17760-630: 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

17920-433: The length scale of the application in question. For example, many aerodynamics applications deal with aircraft flying in atmospheric conditions, where the mean free path length is on the order of micrometers and where the body is orders of magnitude larger. In these cases, the length scale of the aircraft ranges from a few meters to a few tens of meters, which is much larger than the mean free path length. For such applications,

18080-468: 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

18240-455: 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

18400-535: 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

18560-435: The missile with a nuclear warhead . Tunny and its sister boat, Barbero , were the United States' first nuclear deterrent patrol submarines. In the 1950s, nuclear power partially replaced diesel–electric propulsion. Equipment was also developed to extract oxygen from sea water. These two innovations gave submarines the ability to remain submerged for weeks or months. Most of the naval submarines built since that time in

18720-428: 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

18880-496: 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

19040-417: 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

19200-535: 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

19360-403: The path toward achieving heavier-than-air flight for the next century. In 1871, Francis Herbert Wenham constructed the first wind tunnel , allowing precise measurements of aerodynamic forces. Drag theories were developed by Jean le Rond d'Alembert , Gustav Kirchhoff , and Lord Rayleigh . In 1889, Charles Renard , a French aeronautical engineer, became the first person to reasonably predict

19520-579: The performance of the engine. Urban aerodynamics are studied by town planners and designers seeking to improve amenity in outdoor spaces, or in creating urban microclimates to reduce the effects of urban pollution. The field of environmental aerodynamics describes ways in which atmospheric circulation and flight mechanics affect ecosystems. Aerodynamic equations are used in numerical weather prediction . Sports in which aerodynamics are of crucial importance include soccer , table tennis , cricket , baseball , and golf , in which most players can control

19680-476: 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

19840-485: The point where entire aircraft can be designed using computer software, with wind-tunnel tests followed by flight tests to confirm the computer predictions. Understanding of supersonic and hypersonic aerodynamics has matured since the 1960s, and the goals of aerodynamicists have shifted from the behaviour of fluid flow to the engineering of a vehicle such that it interacts predictably with the fluid flow. Designing aircraft for supersonic and hypersonic conditions, as well as

20000-455: The power needed for sustained flight. Otto Lilienthal , the first person to become highly successful with glider flights, was also the first to propose thin, curved airfoils that would produce high lift and low drag. Building on these developments as well as research carried out in their own wind tunnel, the Wright brothers flew the first powered airplane on December 17, 1903. During the time of

20160-405: The preceding years. More submersibles than true submarines, U-boats operated primarily on the surface using regular engines, submerging occasionally to attack under battery power. They were roughly triangular in cross-section, with a distinct keel to control rolling while surfaced, and a distinct bow. During World War I more than 5,000 Allied ships were sunk by U-boats. The British responded to

20320-463: 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,

20480-421: The problem flow should be described using compressible aerodynamics. According to the theory of aerodynamics, a flow is considered to be compressible if the density changes along a streamline . This means that – unlike incompressible flow – changes in density are considered. In general, this is the case where the Mach number in part or all of the flow exceeds 0.3. The Mach 0.3 value is rather arbitrary, but it

20640-474: 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

20800-548: 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

20960-420: 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

21120-486: 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,

21280-418: 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

21440-685: The river Tagus near the City of Toledo several times in the presence of The Holy Roman Emperor Charles V , without getting wet and with the flame they carried in their hands still alight. In 1578, the English mathematician William Bourne recorded in his book Inventions or Devises one of the first plans for an underwater navigation vehicle. A few years later the Scottish mathematician and theologian John Napier wrote in his Secret Inventions (1596) that "These inventions besides devises of sayling under water with divers, other devises and strategems for harming of

21600-406: 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

21760-624: The sinking the Argentine Navy recognized that they had no effective defense against submarine attack, and the Argentine surface fleet withdrew to port for the remainder of the war. An Argentine submarine remained at sea, however. Although the majority of the world's submarines are military, there are some civilian submarines, which are used for tourism, exploration, oil and gas platform inspections, and pipeline surveys. Some are also used in illegal activities. The Submarine Voyage ride opened at Disneyland in 1959, but although it ran under water it

21920-450: The speed of sound. The Mach number is used to evaluate whether the incompressibility can be assumed, otherwise the effects of compressibility must be included. Subsonic (or low-speed) aerodynamics describes fluid motion in flows which are much lower than the speed of sound everywhere in the flow. There are several branches of subsonic flow but one special case arises when the flow is inviscid , incompressible and irrotational . This case

22080-459: The speed of sound. The differences in airflow under such conditions lead to problems in aircraft control, increased drag due to shock waves , and the threat of structural failure due to aeroelastic flutter . The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach who was one of the first to investigate the properties of the supersonic flow. Macquorn Rankine and Pierre Henri Hugoniot independently developed

22240-473: The submarines could rescue them. Submarines could carry cargo through hostile waters or act as supply vessels for other submarines. Submarines could usually locate and attack other submarines only on the surface, although HMS  Venturer managed to sink U-864 with a four torpedo spread while both were submerged. The British developed a specialized anti-submarine submarine in WWI, the R class . After WWII, with

22400-446: The theory for flow properties before and after a shock wave , while Jakob Ackeret led the initial work of calculating the lift and drag of supersonic airfoils. Theodore von Kármán and Hugh Latimer Dryden introduced the term transonic to describe flow speeds between the critical Mach number and Mach 1 where drag increases rapidly. This rapid increase in drag led aerodynamicists and aviators to disagree on whether supersonic flight

22560-437: 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

22720-458: The trajectory of the ball using the " Magnus effect ". General aerodynamics Subsonic aerodynamics Transonic aerodynamics Supersonic aerodynamics Hypersonic aerodynamics History of aerodynamics Aerodynamics related to engineering Ground vehicles Fixed-wing aircraft Helicopters Missiles Model aircraft Related branches of aerodynamics Aerothermodynamics Submarine A submarine (or sub )

22880-424: 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

23040-414: 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

23200-594: 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

23360-466: The war, Germany's U-boat fleet suffered heavy casualties, losing 793 U-boats and about 28,000 submariners out of 41,000, a casualty rate of about 70%. The Imperial Japanese Navy operated the most varied fleet of submarines of any navy, including Kaiten crewed torpedoes, midget submarines ( Type A Ko-hyoteki and Kairyu classes ), medium-range submarines, purpose-built supply submarines and long-range fleet submarines . They also had submarines with

23520-445: 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

23680-507: 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

23840-485: Was achievable until the sound barrier was broken in 1947 using the Bell X-1 aircraft. By the time the sound barrier was broken, aerodynamicists' understanding of the subsonic and low supersonic flow had matured. The Cold War prompted the design of an ever-evolving line of high-performance aircraft. Computational fluid dynamics began as an effort to solve for flow properties around complex objects and has rapidly grown to

24000-613: Was built at the Chilean government's request by Karl Flach , a German engineer and immigrant. It was the fifth submarine built in the world and, along with a second submarine, was intended to defend the port of Valparaiso against attack by the Spanish Navy during the Chincha Islands War . Submarines could not be put into widespread or routine service use by navies until suitable engines were developed. The era from 1863 to 1904 marked

24160-440: Was designed and built in 1620 by Cornelis Drebbel , a Dutchman in the service of James I of England . It was propelled by means of oars. By the mid-18th century, over a dozen patents for submarines/submersible boats had been granted in England. In 1747, Nathaniel Symons patented and built the first known working example of the use of a ballast tank for submersion. His design used leather bags that could fill with water to submerge

24320-696: Was followed by a number of unsuccessful designs. In 1896, he designed the Holland Type VI submarine, which used internal combustion engine power on the surface and electric battery power underwater. Launched on 17 May 1897 at Navy Lt. Lewis Nixon 's Crescent Shipyard in Elizabeth, New Jersey , Holland VI was purchased by the United States Navy on 11 April 1900, becoming the Navy's first commissioned submarine, christened USS  Holland . Discussions between

24480-718: Was lost in 1968 (a part of which the CIA retrieved from the ocean floor with the Howard Hughes -designed ship Glomar Explorer ), K-8 in 1970, K-219 in 1986, and Komsomolets in 1989 (which held a depth record among military submarines—1,000 m (3,300 ft)). Many other Soviet subs, such as K-19 (the first Soviet nuclear submarine, and the first Soviet sub to reach the North Pole) were badly damaged by fire or radiation leaks. The US lost two nuclear submarines during this time: USS  Thresher due to equipment failure during

24640-655: 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

24800-443: Was not a true submarine, as it ran on tracks and was open to the atmosphere. The first tourist submarine was Auguste Piccard , which went into service in 1964 at Expo64 . By 1997, there were 45 tourist submarines operating around the world. Submarines with a crush depth in the range of 400–500 feet (120–150 m) are operated in several areas worldwide, typically with bottom depths around 100 to 120 feet (30 to 37 m), with

24960-488: Was the " conning tower ": a separate pressure hull above the main body of the boat that enabled the use of shorter periscopes. There is a propeller (or pump jet) at the rear, and various hydrodynamic control fins. Smaller, deep-diving, and specialty submarines may deviate significantly from this traditional design. Submarines dive and resurface by using diving planes and by changing the amount of water and air in ballast tanks to affect their buoyancy . Submarines encompass

25120-597: Was the French Plongeur ( Diver ), launched in 1863, which used compressed air at 1,200  kPa (180  psi ). Narcís Monturiol designed the first air-independent and combustion -powered submarine, Ictíneo II , which was launched in Barcelona , Spain in 1864. The submarine became feasible as potential weapon with the development of the Whitehead torpedo , designed in 1866 by British engineer Robert Whitehead ,

25280-608: Was the first submarine combat loss since World War II. In 1982 during the Falklands War , the Argentine cruiser General Belgrano was sunk by the British submarine HMS  Conqueror , the first sinking by a nuclear-powered submarine in war. Some weeks later, on 16 June, during the Lebanon War , an unnamed Israeli submarine torpedoed and sank the Lebanese coaster Transit , which was carrying 56 Palestinian refugees to Cyprus , in

25440-424: 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

25600-469: Was the most effective anti-ship weapon in the American arsenal. Submarines, though only about 2 percent of the U.S. Navy, destroyed over 30 percent of the Japanese Navy, including 8 aircraft carriers, 1 battleship and 11 cruisers. US submarines also destroyed over 60 percent of the Japanese merchant fleet, crippling Japan's ability to supply its military forces and industrial war effort. Allied submarines in

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