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Готові списки джерел за темами / Reynolds's equation / Книги

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Книги з теми "Reynolds's equation"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Lamarre, Francois. One-equation turbulence models for the solution of the Reynolds-averaged equations. Princeton, N. J: Princeton University, School of Engineering and Applied Science, Dept. of Mechanical and Aerospace Engineering, 1992.

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2

Hyeongsik, Kang, ed. Reynolds stress modeling of turbulent open-channel flows. Hauppauge, NY: Nova Science Publishers, 2009.

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3

Marvin, Joseph G. Turbulence modeling: Progress and future outlook. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1996.

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4

Mavriplis, Dimitri J. A three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1994.

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5

Barth, Timothy J. Numerical aspects of computing viscous high Reynolds number flows on unstructured meshes. Washington, D. C: American Institute of Aeronautics and Astronautics, 1991.

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6

Baldwin, Barrett S. A one-equation turbulence model for high Reynolds number wall-bonded flows. Moffett Field, Calif: Ames Research Center, 1990.

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7

Benocci, C. Solution of the steady state incompressible Navier-Stokes equations at high Reynolds numbers. Rhode Saint Genese, Belgium: Von Karman Institute for Fluid Dynamics, 1989.

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8

Morrison, Joseph H. A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models. Hampton, Va: Langley Research Center, 1992.

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9

Hirose, Naoki. Comparison of transonic airfoil characteristics by Navier-Stokes computation and by wind tunnel test at high Reynolds number. Tokyo: National Aerospace Laboratory, 1986.

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10

Ristorcelli, J. R. Carrying the mass flux terms exactly in the first and second moment equations of compressible turbulence. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1993.

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11

Chaussee, D. S. High-speed flow calculations past 3-D configurations based on the Reynolds averaged Navier-Stokes equations. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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12

Chaussee, D. S. High-speed flow calculations past 3-D configurations based on the Reynolds averaged Navier-Stokes equations. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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13

Benocci, C. An explicit finite difference solver for the incompresssible Reynolds averaged Navier-Stokes equations, optimized for the Alliant DSP 9000 computer. Rhode Saint Genese, Belgium: von Karman Institute for Fluid Dynamics, 1988.

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14

Mavriplis, Dimitri J. A 3D agglomeration multigrid solver for the Reynolds-averaged Navier-Stokes equations on unstructured meshes. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1995.

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15

Schmidt, Rodney C. Two-equation low-Reynolds-number turbulence modeling of transitional boundary layer flows characteristic of gas turbine blades. Cleveland, Ohio: Lewis Research Center, 1988.

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16

Lee, J. An application of a two-equation model of turbulence to three-dimensional chemically reacting flows. [Washington, DC: National Aeronautics and Space Administration, 1994.

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17

Lee, J. An application of a two-equation model of turbulence to three-dimensional chemically reacting flows. [Washington, DC: National Aeronautics and Space Administration, 1994.

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18

Hussaini, M. Moin. Investigation of low-Reynolds-number rocket nozzle design using PNS-based optimization procedure. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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19

Lee, J. An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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20

Rajeev, S. G. The Navier–Stokes Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0003.

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Анотація:

When different layers of a fluid move at different velocities, there is some friction which results in loss of energy and momentum to molecular degrees of freedom. This dissipation is measured by a property of the fluid called viscosity. The Navier–Stokes (NS) equations are the modification of Euler’s equations that include this effect. In the incompressible limit, the NS equations have a residual scale invariance. The flow depends only on a dimensionless ratio (the Reynolds number). In the limit of small Reynolds number, the NS equations become linear, equivalent to the diffusion equation. Ideal flow is the limit of infinite Reynolds number. In general, the larger the Reynolds number, the more nonlinear (complicated, turbulent) the flow.

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21

Rajeev, S. G. Viscous Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0005.

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Анотація:

Here some solutions of Navier–Stokes equations are found.The flow of a fluid along a pipe (Poisseuille flow) and that between two rotating cylinders (Couette flow) are the simplest. In the limit of large viscosity (small Reynolds number) the equations become linear: Stokes equations. Flow past a sphere is solved in detail. It is used to calculate the drag on a sphere, a classic formula of Stokes. An exact solution of the Navier–Stokes equation describing a dissipating vortex is also found. It is seen that viscosity cannot be ignored at the boundary or at the core of vortices.

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22

Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.

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Анотація:

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechanics. In view of Noether's theorem, the constant vector fields which act as Galilean symmetries of the Euler equation are responsible for the conservation of momentum. The chapter shows proof that all solutions to the Euler-Reynolds equations conserve momentum.

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23

Isett, Philip. Mollification along the Coarse Scale Flow. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0018.

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Анотація:

This chapter shows how to construct the appropriate mollification of the Reynolds stress along the coarse scale flow. Unlike the velocity field, which was only mollified in the spatial variables and which earned its time-regularity through the Euler-Reynolds equation, the Reynolds stress must be mollified in both space and time. Mollification along the flow is consistent with the Galilean invariance of the equations. After considering the problem of mollifying the stress in time, the chapter explains how the stress can be mollified in both space and time. It then chooses the mollification parameters, requiring that the error term generated by this mollification constitutes a small fraction of the allowable stress. It also derives estimates for the coarse scale flow as well as transport estimates for the mollified stress.

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24

Isett, Philip. The Main Iteration Lemma. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0010.

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Анотація:

This chapter properly formalizes the Main Lemma, first by discussing the frequency energy levels for the Euler-Reynolds equations. Here the bounds are all consistent with the symmetries of the Euler equations, and the scaling symmetry is reflected by dimensional analysis. The chapter proceeds by making assumptions that are consistent with the Galilean invariance of the Euler equations and the Euler-Reynolds equations. If (v, p, R) solve the Euler-Reynolds equations, then a new solution to Euler-Reynolds with the same frequency energy levels can be obtained. The chapter also states the Main Lemma, taking into account dimensional analysis, energy regularity, and Onsager's conjecture. Finally, it introduces the main theorem (Theorem 10.1), which states that there exists a nonzero solution to the Euler equations with compact support in time.

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25

Shis, Tsan-Hsing. A realizable Reynolds stress algebraic equation model. 1993.

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26

Chiang, Chu, Lumley John L. 1930-, and United States. National Aeronautics and Space Administration., eds. A new Reynolds stress algebraic equation model. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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27

Jiang, Zhu, Lumley John L. 1930-, and United States. National Aeronautics and Space Administration., eds. A new Reynolds stress algebraic equation model. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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28

M, Barton J., and United States. National Aeronautics and Space Administration., eds. Renormalization group analysis of the Reynolds stress transport equation. [Washington, DC]: National Aeronautics and Space Administration, 1992.

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29

Elliptic flow computation by low Reynolds number two-equation turbulence models. [Washington, DC]: National Aeronautics and Space Administration, 1991.

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30

Isett, Philip. Constructing the Correction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0007.

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Анотація:

This chapter explains how the correction is constructed, first by considering the transportation of the phase functions. A solution (v, p, R) to the Euler-Reynolds equations is fixed and a correction v₁ = v + V, p₁ = p + P is presented. Here v is an approximation to the “coarse scale velocity” since the solution ultimately achieved by the process will resemble v at a sufficiently coarse scale. The next step is to eliminate the Transport term. A time cutoff function is also introduced, where the time cutoff itself is differentiated in the Transport term. Finally, the chapter describes the High–High Interference term and Beltrami flows, how to construct the corrections Vsubscript I, P₀ in such a way that the Stress term can be reduced to a new stress, and the Stress equation and initial phase directions.

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31

1940-, Shih Tsan-Hsing, and United States. National Aeronautics and Space Administration., eds. Low Reynolds number two-equation modeling of turbulent flows. [Washington, D.C.]: NASA, 1991.

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32

Low Reynolds number two-equation modeling of turbulent flows. [Washington, D.C.]: NASA, 1991.

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33

Low Reynolds number two-equation modeling of turbulent flows. [Washington, D.C.]: NASA, 1991.

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34

United States. National Aeronautics and Space Administration., ed. Fast methods to numerically integrate the Reynolds equation for gas fluid films. [Washington, DC]: National Aeronautics and Space Administration, 1992.

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35

Center, Langley Research, ed. Dynamical system analysis of Reynolds stress closure equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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36

Isett, Philip. A Main Lemma for Continuous Solutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0005.

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Анотація:

This chapter introduces the Main Lemma that implies the existence of continuous solutions. According to this lemma, there exist constants K and C such that the following holds: Let ϵ‎ > 0, and suppose that (v, p, R) are uniformly continuous solutions to the Euler-Reynolds equations on ℝ x ³, with v uniformly bounded⁷ and suppR ⊆ I x ³ for some time interval. The Main Lemma implies the following theorem: There exist continuous solutions (v, p) to the Euler equations that are nontrivial and have compact support in time. To establish this theorem, one repeatedly applies the Main Lemma to produce a sequence of solutions to the Euler-Reynolds equations. To make sure the solutions constructed in this way are nontrivial and compactly supported, the lemma is applied with e(t) chosen to be any sequence of non-negative functions whose supports are all contained in some finite time interval.

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37

Isett, Philip. The Euler-Reynolds System. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0001.

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Анотація:

This chapter provides a background on the Euler-Reynolds system, starting with some of the underlying philosophy behind the argument. It describes low frequency parts and ensemble averages of Euler flows and shows that the average of any family of solutions to Euler will be a solution of the Euler-Reynolds equations. It explains how the most relevant type of averaging to convex integration arises during the operation of taking weak limits, which can be regarded as an averaging process. The chapter proceeds by focusing on weak limits of Euler flows and the hierarchy of frequencies, concluding with a discussion of the method of convex integration and the h-principle for weak limits. The method inherently proves that weak solutions to Euler may fail to be solutions.

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38

Center, Langley Research, ed. A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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39

Center, Langley Research, ed. A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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40

United States. National Aeronautics and Space Administration., ed. An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows. Washington, DC: National Aeronautics and Space Administration, 1991.

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41

J, Barth Timothy, and Ames Research Center, eds. A one-equation turbulence transport model for high Reynolds number wall-bounded flows. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1990.

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42

A one-equation turbulence transport model for high Reynolds number wall-bounded flows. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1990.

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43

A one-equation turbulence transport model for high Reynolds number wall-bounded flows. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1990.

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44

V, Venkatakrishnan, and Institute for Computer Applications in Science and Engineering., eds. Agglomeration multigrid for viscous turbulent flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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45

Carrying the mass flux terms exactly in the first and second moment equations of compressible turbulence. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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46

Escudier, Marcel. Turbulent flow. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0018.

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Анотація:

In this chapter the principal characteristics of a turbulent flow are outlined and the way that Reynolds’ time-averaging procedure, applied to the Navier-Stokes equations, leads to a set of equations (RANS) similar to those governing laminar flow but including additional terms which arise from correlations between fluctuating velocity components and velocity-pressure correlations. The complex nature of turbulent motion has led to an empirical methodology based upon the RANS and turbulence-transport equations in which the correlations are modelled. An important aspect of turbulent flows is the wide range of scales involved. It is also shown that treating near-wall turbulent shear flow as a Couette flow leads to the Law of the Wall and the log law. The effect of surface roughness on both the velocity distribution and surface shear stress is discussed. It is shown that the distribution of mean velocity within a turbulent boundary layer can be represented by a linear combination of the near-wall log law and an outer-layer Law of the Wake.

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47

V, Wilson Robert, and Langley Research Center, eds. Streamwise vorticity generation in laminar and turbulent jets. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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48

Center, Langley Research, ed. Numerical study of turbulence model predictions for the MD 30P/30N and NHLP-2D three-element highlift configurations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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49

High-speed flow calculations past 3-D configurations based on the Reynolds averaged Navier-Stokes equations. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1988.

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50

Solution of the Euler equations with viscous-inviscid interaction for high Reynolds number transonic flow past wing/body configurations. [Washington, DC?: National Aeronautics and Space Administration, 1987.

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