Unsteady Cavity Flows: Oscillatory Flat Box Flows

1975 ◽  
Vol 42 (3) ◽  
pp. 557-563 ◽  
Author(s):  
V. O’Brien
Keyword(s):  
Reynolds Number ◽  
Incompressible Flows ◽  
Stokes Number ◽  
Analytic Solutions ◽  
Length Ratio ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Cavity Flows ◽  
Navier Stokes Equation ◽  
Reduced Frequency

The oscillatory cavity flows reported here are extensions of previously studied steady closed rectangular cavity flows (box flows). The periodic laminar incompressible flows are characterized by three numerical parameters, peak Reynolds number, a reduced frequency (or Stokes number) and the height-to-length ratio of the cavity. Depending on the height-to-length ratio, flow fields are obtained by finite-difference solutions or analytic solutions of the Navier-Stokes equation. The central portion of a flat cavity contains an oscillatory parallel flow. Experimental measurements corroborate the theory. Stokes number dependency and particularly differences from the corresponding steady flow (whose Stokes number is zero) are illustrated.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

scholarly journals Numerical analysis of high-lift configurations with oscillating flaps

2021 ◽  
Author(s):  
Johannes Ruhland ◽  
Christian Breitsamter
Keyword(s):  
Reynolds Number ◽  
Flow Separation ◽  
Separated Flow ◽  
Navier Stokes ◽  
Rotational Axis ◽  
High Lift ◽  
Hinge Point ◽  
Reduced Frequency ◽  
Flap Deflection ◽  
The Impact

AbstractThis study presents two-dimensional aerodynamic investigations of various high-lift configuration settings concerning the deflection angles of droop nose, spoiler and flap in the context of enhancing the high-lift performance by dynamic flap movement. The investigations highlight the impact of a periodically oscillating trailing edge flap on lift, drag and flow separation of the high-lift configuration by numerical simulations. The computations are conducted with regard to the variation of the parameters reduced frequency and the position of the rotational axis. The numerical flow simulations are conducted on a block-structured grid using Reynolds Averaged Navier Stokes simulations employing the shear stress transport $$k-\omega $$ k - ω turbulence model. The feature Dynamic Mesh Motion implements the motion of the oscillating flap. Regarding low-speed wind tunnel testing for a Reynolds number of $$0.5 \times 10^{6}$$ 0.5 × 10 6 the flap movement around a dropped hinge point, which is located outside the flap, offers benefits with regard to additional lift and delayed flow separation at the flap compared to a flap movement around a hinge point, which is located at 15 % of the flap chord length. Flow separation can be suppressed beyond the maximum static flap deflection angle. By means of an oscillating flap around the dropped hinge point, it is possible to reattach a separated flow at the flap and to keep it attached further on. For a Reynolds number of $$20 \times 10^6$$ 20 × 10 6 , reflecting full scale flight conditions, additional lift is generated for both rotational axis positions.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Numerical Simulation of High Reynolds Number Flow Structure in a Lid-Driven Cavity Using MRT-LES

2014 ◽  
Vol 554 ◽  
pp. 665-669
Author(s):  
Leila Jahanshaloo ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Technique ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Reynolds Number Flow ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical and fluid mechanics problems. In this paper multi-relaxation lattice Boltzmann model (MRT) coupled with a Large Eddy Simulation (LES) and the equation are applied for driven cavity flow at different Reynolds number (1000-10000) and the results are compared with the previous published papers which solve the Navier stokes equation directly. The comparisons between the simulated results show that the lattice Boltzmann method has the capacity to solve the complex flows with reasonable accuracy and reliability. Keywords: Two-dimensional flows, Lattice Boltzmann method, Turbulent flow, MRT, LES.

OPEN SOURCE COMPUTATIONS OF PLANING HULL RESISTANCE

2015 ◽  
Vol 157 (B2) ◽  
Author(s):  
M Ferrando ◽  
S Gaggero ◽  
D Villa
Keyword(s):  
Open Source ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equation ◽  
Free Surfaces ◽  
Hydrodynamic Parameters ◽  
Physical Problems ◽  
Engineering Problems ◽  
Simulation Strategy ◽  
Computational Fluid Dynamics Cfd

In recent years, the application of Computational Fluid Dynamics (CFD) methods experienced an exponential growth: the increase of the computational performances and the generalization of the Navier-Stokes equation to more complex physical problems made possible the solution of complex problems like free surfaces flows. The physical complexity of planing hulls flows poses some issues in the ability to numerically predict the global hydrodynamic parameters (hull resistance, dynamic attitude) of these configurations and on the expected confidence on the numerical results. In the last decade, commercial RANS software have been successfully applied for the prediction of the planing hull characteristics with reasonable correlation to the available experimental measurements. Recently, moreover, the interest in Open Source approaches, also for the solution of engineering problems, has rapidly grow. In this work, a set of calculations on a systematic series standard hull shape has been carried out, adopting from pre- to post- processing only Open Source tools. The comparison and the validation, through the available experimental measurements, of the computed results will define an optimal simulation strategy to include this kind of tools in the usual design loop.

Mechanics of a Free-Surface Liquid Film Flow

1987 ◽  
Vol 54 (4) ◽  
pp. 951-954 ◽  
Author(s):  
Cyrus K. Aidun
Keyword(s):  
Differential Equation ◽  
Free Surface ◽  
Film Flow ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equation ◽  
Higher Order Terms ◽  
Liquid Film Flow ◽  
Surface Liquid ◽  
Similar Equation

The mechanics of a free surface viscous liquid curtain flowing steadily between two vertical guide wires under the influence of gravity is investigated. The Navier-Stokes equation is integrated over the film thickness and an integro-differential equation is derived for the average film velocity. An approximate nonlinear differential equation, attributed to G. I. Taylor, is obtained by neglecting the higher order terms. An analytical solution is obtained for a similar equation which neglects the surface tension effects and the results are compared with the experimental measurements of Brown (1961).

Flowfield around a Body with Elastic Walls

2008 ◽  
Vol 33-37 ◽  
pp. 1083-1088
Author(s):  
Norio Arai ◽  
Kota Fujimura ◽  
Yoko Takakura
Keyword(s):  
Stokes Equation ◽  
Bluff Body ◽  
Incompressible Flows ◽  
Small Deformation ◽  
Uniform Flow ◽  
The Body ◽  
Body Motion ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Elastic Walls

When a bluff body is located in a uniform flow, the flow is separated and vortices are formed. Consequently, the vortices cause “flow-induced vibrations”. Especially, if the Strouhal number and the frequency of the body oscillation coincide with the natural frequency, the lock-in regime will occur and we could find the large damages on it. Therefore, it is profitable, in engineering problems, to clarify this phenomenon and to suppress the vibration, in which the effect of elastic walls on the suppression is focused. Then, the aims of this article are to clarify the oscillatory characteristics of the elastic body and the flowfield around the body by numerical simulations, in which a square pillar with elastic walls is set in a uniform flow. Two dimensional incompressible flows are solved by the continuity equation, Navier-Stokes equation and the Poisson equation which are derived by taking divergence of Navier-Stokes equation. Results show that a small deformation of elastic walls has a large influence on the body motion. In particular, the effect is very distinct at the back.

A Sharp Surface Tension Modeling Method for Capillarity-Dominant Two-Phase Incompressible Flows

2007 ◽  
Author(s):  
Zhaoyuan Wang ◽  
Albert Y. Tong
Keyword(s):  
Surface Tension ◽  
Incompressible Flows ◽  
Jump Condition ◽  
Navier Stokes ◽  
Pressure Jump ◽  
Interfacial Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Numerical Instabilities ◽  
Spurious Currents

A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.

scholarly journals Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

2013 ◽  
Vol 729 ◽  
pp. 285-308 ◽  
Author(s):  
Maciej J. Balajewicz ◽  
Earl H. Dowell ◽  
Bernd R. Noack
Keyword(s):  
Reynolds Number ◽  
Galerkin Method ◽  
Stokes Equation ◽  
High Reynolds Number ◽  
Transient Flow ◽  
Navier Stokes ◽  
Power Balance ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
High Reynolds

AbstractWe generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

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