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| | | Laminate hardwood flooring is very flexible flooring that provides the look of having hardwood flooring with no expensive cost. Although laminate floor does look like hardwood, it"s perhaps not made from solid wood. Because it is created from many materials bonded together under extremely ruthless It is called engineered wood. It is simple to lay and care for and when you move on it, it"s very nearly like you"re hanging. This is the reason laminate wood flooring can be called a floating floor. <br><br>You can discover ways to place laminate flooring quickly. Once you begin to see the first few panels of the floor going together, you can c-omplete the rest of the work on your own. You can install Quick Step laminate floor on nearly any space of your house. However, it is not recommended for use in bathrooms, mudrooms or another area where there may be too much moisture. The additional water may damage the flooring meaning you"d need to remove and replace one or two boards of the laminate flooring. <br><br>If you are looking at how easy it is to learn how to set laminate flooring, you"ll also learn about the benefits of Quick Step laminate flooring. As opposed to strong hardwood, laminate hardwood floor is about half the cost. It is an easy task to install and there is no finish or refinish to bother about. Adding laminate flooring doesnt need any claws, however you may elect to glue it to the subfloor. Another advantage of laminate flooring is that one may put it down on almost any kind of area, except, needless to say, carpet. It is suitable for adding on top of cement, wood or vinyl. All you"ve to do would be to ensure before you start to put the boards the ground underneath is level. <br><br>You"ll get several different instructions about how to prepare a floor beforehand, when you ask the flooring merchant about how to set laminate flooring. You need to do need to be sure the areas is free from any dirt or small items of dust that may work their way up through the laminate wood floor. Dig up supplementary info on a partner website by clicking [http://www.visto.co.za/cornice/ xps cornice]. You also have to test to make sure level and that the subfloor is sound-proof. Often individuals who have mounted the Quick Step laminate flooring report there are squeaks when they step onto it. That is not the fault of the laminate floor, but since the ground under it was not properly levelled before they started to put the planks. [http://www.visto.co.za/cornice/ Study Cornice Mouldings] contains further about the purpose of this concept. <br><br>You do need to simply take extra care when you install laminate hardwood flooring over radiant heat. If people choose to dig up further on [http://www.visto.co.za/cornice/ cornice prices], we know of many online libraries people should think about investigating. You have to learn the instructions for how-to set laminate floor and the instructions about the radiant heat before you begin. When you plan to place laminate wood floor at home, you dont have to open the packages until you are willing to start..<br><br>If you adored this article and you would like to get more info pertaining to family health insurance, [http://ceaselessprogre54.exteen.com ceaselessprogre54.exteen.com], kindly browse through our own web page. |
| The '''Vortex lattice method''', (VLM), is a numerical, [[Computational fluid dynamics]], method used mainly in the early stages of [[aerospace engineering|aircraft design]] and in [[aerodynamic]] education at university level. The VLM models the lifting surfaces, such as a [[wing]], of an aircraft as an infinitely thin sheet of discrete vortices to compute [[Lift (force)|lift]] and [[induced drag]]. The influence of the thickness, [[viscosity]] is neglected.
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| VLMs can compute the flow around a wing with rudimentary geometrical definition. For a rectangular wing it is enough to know the span and chord. On the other side of the spectrum, they can describe the flow around a fairly complex aircraft geometry (with multiple lifting surfaces with taper, kinks, twist, camber, trailing edge control surfaces and many other geometric features).
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| By simulating the flow field, one can extract the pressure distribution or as in the case of the VLM, the force distribution, around the simulated body. This knowledge is then used to compute the aerodynamic coefficients and their derivatives that are important for assessing the aircraft's handling qualities in the conceptual design phase. With an initial estimate of the pressure distribution on the wing, the structural designers can start designing the load-bearing parts of the wings, fin and [[tailplane]] and other lifting surfaces. Additionally, while the VLM cannot compute the viscous drag, the induced drag stemming from the production of lift can be estimated. Hence as the drag must be balanced with the thrust in the cruise configuration, the propulsion group can also get important data from the VLM simulation.
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| ==Historical background==
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| Bart Rademaker provides a background history of the VLM in the [[NASA]] Langley workshop documentation SP-405.<ref>NASA, ''Vortex-lattice utilization''. NASA SP-405, NASA-Langley, Washington, 1976.</ref><br />
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| The VLM is the extension of [[Prandtl]] lifting line theory,<ref>Prandtl. L, ''Applications of modern hydrodynamics to aeronautics'', NACA-TR-116, NASA, 1923.</ref> where the wing of an aircraft is modeled as an infinite number of [[Horseshoe vortex|Horseshoe vortices]]. The name was coined by V.M. Falkner in his [[Advisory Committee for Aeronautics|Aeronautical Research Council]] paper of 1946.<ref>Falkner. V.M., ''The Accuracy of Calculations Based on Vortex Lattice Theory'', Rep. No. 9621, British A.R.C., 1946.</ref> The method has since then been developed and refined further by W.P. Jones, H. Schlichting, G.N. Ward and others.
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| Although the computations needed can be carried out by hand, the VLM benefited from the advent of computers for the large amounts of computations that are required.
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| Instead of only one horseshoe vortex per wing, as in the lifting line theory, the VLM utilizes a lattice of horseshoe vortices, as described by Falkner in his first paper on this subject in 1943.<ref>Falkner. V.M., ''The Calculations of Aerodynamic Loading on Surfaces of any Shape'', [http://aerade.cranfield.ac.uk/ara/arc/rm/1910.pdf R&M 1910], British A.R.C., 1943.</ref> The number of vortices used vary with the required pressure distribution resolution, and with required accuracy in the computed aerodynamic coefficients. A typical number of vortices would be around 100 for an entire aircraft wing; an [[Advisory Committee for Aeronautics|Aeronautical Research Council]] report by Falkner published in 1949 mentions the use of an "84-vortex lattice before the standardisation of the 126-lattice" (p. 4).<ref>Falkner. V.M., ''A Comparison of Two Methods of Calculating Wing Loading with Allowance for Compressibility'', [http://aerade.cranfield.ac.uk/ara/arc/rm/2685.pdf R&M 2685], British A.R.C., 1949.</ref>
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| The method is comprehensibly described in all major aerodynamic textbooks, such as Katz & Plotkin,<ref>J. Katz, A. Plotkin, ''Low-Speed Aerodynamics, 2nd ed., Cambridge University Press'', Cambridge, 2001.</ref> Anderson,<ref name="McGraw-Hill Inc 1991">J.D. Anderson Jr, ''Fundamentals of aerodynamics'', 2nd ed., McGraw-Hill Inc, 1991.</ref> Bertin & Smith<ref>J.J. Bertin, M.L. Smith, ''Aerodynamics for Engineers'', 3rd ed., Prentice Hall, New Jersey, 1998.</ref> or Houghton & Carpenter<ref>E.L. Houghton, P.W. Carpenter, ''Aerodynamics for Engineering Students'', 4th ed., Edward Arnold, London, 1993.</ref>
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| ==Theory==
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| The vortex lattice methods is built on the theory of ideal flow, also known as [[Potential flow]]. Ideal flow is a simplification of the real flow experienced in nature, however for many engineering applications this simplified representation has all of the properties that are important from the engineering point of view. This method neglects all viscous effects. Turbulence, dissipation and boundary layers are not resolved at all. However, lift induced drag can be assessed and, taking special care, some stall phenomena can be modelled.
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| ===Assumptions===
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| The following assumptions are made regarding the problem in the vortex lattice method:
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| *The flow field is [[incompressible]], [[inviscid]] and [[irrotational]]. However, subsonic compressible flow can be modeled if the [[Prandtl-Glauert transformation]] is incorporated into the method.
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| *The lifting surfaces are thin. The influence of thickness on aerodynamic forces are neglected.
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| *The [[angle of attack]] and the angle of sideslip are both small, [[small angle approximation]].
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| ===Method===
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| By the above assumptions the flowfield is [[Conservative vector field]], which means that there
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| exists a velocity potential:<br />
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| <math>\bar{v} =\nabla \phi</math> | |
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| and that [[Laplace's equation]] hold.
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| Laplace’s equation is a second order linear equation, and being so it is subject
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| to the principle of superposition. Which means that if <math>y_{1}</math> and <math>y_2</math> are two solutions of | |
| the differential equation <math>L(Y)</math>, then the linear combination <math>c_1y_1 + c_2y_2</math> is also a solution for any values of the constants <math>c_1</math> and <math>c_2</math>. As Anderson<ref name="McGraw-Hill Inc 1991" /> put it "A complicated flow pattern
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| for an irrotational, incompressible flow can be synthesized by adding together a number of elementary flows, which are also irrotational and incompressible.”. Such elementary flows are the [[point source#Fluid|point source]] or sink, the doublet and the [[vortex line]], each being a solution of Laplace’s equation. These may be superposed in many ways to create the formation of line sources, vortex sheets and so on.
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| ===Aircraft Model===
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| The lifting surfaces of an aircraft is divided into several panels. A [[horseshoe vortex]] is applied on each of these panels and the velocity vector generated by the vortices at the collocation points of each panel is computed. The vortex is placed at the 1/4 chord point of each panel, and the collocation point at 3/4 chord. For a problem with <math>n</math> panels, the induced velocity of each unit strength vortex on each panel is collected in the influence matrix <math>W</math>
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| <math>\mathbf{W} = \begin{bmatrix}
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| w_{11} & w_{12} & \cdots & w_{1n}\\
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| w_{21} & \ddots & & \vdots \\
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| \vdots & & \ddots & \vdots \\
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| w_{n1} & \cdots & \cdots & w_{nn} \end{bmatrix}</math>
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| A [[Neumann boundary condition]] is applied, which prescribes that the normal velocity at the boundary is zero. It is also known as the flow tangency condition, or no cross flow condition. It means that at the boundary (e.g. the surface of a wing) the flow must be parallel to the surface. The following system of equations may be set up. The right hand side is formed by the freestream and the [[angle of attack]] so that <math>b=V_{\infty} sin(\alpha)</math>.
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| <math>\begin{bmatrix}
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| w_{11} & w_{12} & \cdots & w_{1n}\\
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| w_{21} & \ddots & & \vdots \\
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| \vdots & & \ddots & \vdots \\
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| w_{n1} & \cdots & \cdots & w_{nn} \end{bmatrix}
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| \begin{bmatrix}
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| \Gamma_{1} \\
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| \Gamma_{2} \\
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| \vdots \\
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| \Gamma_{n} \end{bmatrix}=
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| \begin{bmatrix}
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| b_{1} \\
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| b_{2} \\
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| \vdots \\
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| b_{n} \end{bmatrix}
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| </math>
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| From this system of equations the strength <math>\Gamma</math> of the vortices can be solved for, and the forces acting on the panels be computed with
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| <math>F=\rho_{air} \Gamma (V_{\infty}+V_{induced}) l
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| </math>
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| ==References==
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| {{Reflist}}
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| == External links==
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| * http://web.mit.edu/drela/Public/web/avl/
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| ==Sources==
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| *NASA, ''Vortex-lattice utilization''. NASA SP-405, NASA-Langley, Washington, 1976.
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| *Prandtl. L, ''Applications of modern hydrodynamics to aeronautics'', NACA-TR-116, NASA, 1923.
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| *Falkner. V.M., ''The Accuracy of Calculations Based on Vortex Lattice Theory'', Rep. No. 9621, British A.R.C., 1946.
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| *J. Katz, A. Plotkin, ''Low-Speed Aerodynamics, 2nd ed., Cambridge University Press'', Cambridge, 2001.
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| *J.D. Anderson Jr, ''Fundamentals of aerodynamics'', 2nd ed., McGraw-Hill Inc, 1991.
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| *J.J. Bertin, M.L. Smith, ''Aerodynamics for Engineers'', 3rd ed., Prentice Hall, New Jersey, 1998.
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| *E.L. Houghton, P.W. Carpenter, ''Aerodynamics for Engineering Students'', 4th ed., Edward Arnold, London, 1993.
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| *Lamar, J. E., Herbert, H. E., ''Production version of the extended NASA-Langley vortex lattice FORTRAN computer program. Volume 1: User's guide'', NASA-TM-83303, NASA, 1982
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| *Lamar, J. E., Herbert, H. E., ''Production version of the extended NASA-Langley vortex lattice FORTRAN computer program. Volume 2: Source code'', NASA-TM-83304, NASA, 1982
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| *Melin, Thomas, ''A Vortex Lattice MATLAB Implementation for Linear Aerodynamic Wing Applications'', Royal Institute of Technology (KTH), Sweden, December, 2000
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| [[Category:Fluid dynamics]]
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| [[Category:Aerodynamics]]
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Laminate hardwood flooring is very flexible flooring that provides the look of having hardwood flooring with no expensive cost. Although laminate floor does look like hardwood, it"s perhaps not made from solid wood. Because it is created from many materials bonded together under extremely ruthless It is called engineered wood. It is simple to lay and care for and when you move on it, it"s very nearly like you"re hanging. This is the reason laminate wood flooring can be called a floating floor.
You can discover ways to place laminate flooring quickly. Once you begin to see the first few panels of the floor going together, you can c-omplete the rest of the work on your own. You can install Quick Step laminate floor on nearly any space of your house. However, it is not recommended for use in bathrooms, mudrooms or another area where there may be too much moisture. The additional water may damage the flooring meaning you"d need to remove and replace one or two boards of the laminate flooring.
If you are looking at how easy it is to learn how to set laminate flooring, you"ll also learn about the benefits of Quick Step laminate flooring. As opposed to strong hardwood, laminate hardwood floor is about half the cost. It is an easy task to install and there is no finish or refinish to bother about. Adding laminate flooring doesnt need any claws, however you may elect to glue it to the subfloor. Another advantage of laminate flooring is that one may put it down on almost any kind of area, except, needless to say, carpet. It is suitable for adding on top of cement, wood or vinyl. All you"ve to do would be to ensure before you start to put the boards the ground underneath is level.
You"ll get several different instructions about how to prepare a floor beforehand, when you ask the flooring merchant about how to set laminate flooring. You need to do need to be sure the areas is free from any dirt or small items of dust that may work their way up through the laminate wood floor. Dig up supplementary info on a partner website by clicking xps cornice. You also have to test to make sure level and that the subfloor is sound-proof. Often individuals who have mounted the Quick Step laminate flooring report there are squeaks when they step onto it. That is not the fault of the laminate floor, but since the ground under it was not properly levelled before they started to put the planks. Study Cornice Mouldings contains further about the purpose of this concept.
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