Numerical Simulation of Flows Driven by a Torsionally Oscillating Lid in a Square Cavity

1992 ◽  
Vol 114 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Thin Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Numerical Data ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Phase Lag ◽  
Two Dimensional ◽  
Force Coefficient

Numerical studies were made of the flow of a viscous fluid in a two-dimensional square container. The flows are driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions were acquired by solving the time-dependent, two-dimensional incompressible Navier-Stokes equations. Results are presented for wide ranges of two principal physical parameters, i.e., Re, the Reynolds number and ω′, the nondimensional frequency of the lid oscillation. Comprehensive details of the flow-structure are presented. When ω′ is small, the flow bears qualitative similarity to the well-documented steady driven-cavity flow. The flow in the bulk of cavity region is affected by the motion of the sliding upper lid. On the contrary, when ω′ is large, the fluid motion tends to be confined within a thin layer near the oscillating lid. In this case, the flow displays the characteristic features of a thin-layer flow. When ω′ is intermediate, ω′ ~ O(1), the effect of the side walls is pronounced; the flow pattern reveals significant changes between the low-Re and high-Re limits. Streamline plots are constructed for different parameter spaces. Physically informative interpretations are proposed which help gain physical insight into the dynamics. The behavior of the force coefficient Cf has been examined. The magnitude and phase lag of Cf are determined by elaborate post-processings of the numerical data. By utilizing the wealth of the computational results, characterizations of Cf as functions of Re and ω′ are attempted. These are in qualitative consistency with the theoretical predictions for the limiting parameter values.

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

The structure of two-dimensional separation

1990 ◽  
Vol 220 ◽  
pp. 397-411 ◽  
Author(s):  
Laura L. Pauley ◽  
Parviz Moin ◽  
William C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Shedding Frequency

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

Applying Ensemble Kalman Filter to Transonic Flows Through a Two-Dimensional Turbine Cascade

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Sasuga Ito ◽  
Masato Furukawa ◽  
Kazutoyo Yamada ◽  
Kaito Manabe
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Optimization Approach ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Eddy Simulation

Abstract Turbulence is one of the most important phenomena in fluid dynamics. Large eddy simulation (LES) generally allows us to analyze smaller eddies than when using simulations based on unsteady Reynolds-averaged Navier–Stokes equations (URANS). In addition, the numerical solutions of LES show good agreements with experiments and numerical solutions based on direct numerical simulation. URANS simulations are, however, frequently used in academia and industry because LES computations are much more expensive compared with URANS simulations. In this investigation, an optimization of unsolved coefficients of the k–ω two equations model is performed on the transonic flow around T106A low-pressure turbine cascade to improve the accuracy of turbulence prediction with URANS. For the optimization approach, two-dimensional URANS is combined with ensemble Kalman filter which is one of the data assimilation techniques. In the assimilation process, a time- and spanwise-averaged LES result is used as pseudo-experimental data. Three-dimensional URANS simulations are performed for the evaluation of the optimization effect. URANS simulations are also applied to a different turbine cascade flow for the evaluation of the robustness of the optimized coefficients. These URANS results confirmed that the optimized coefficients improve the accuracy of turbulence prediction.

scholarly journals Structure and stability of non-symmetric Burgers vortices

1998 ◽  
Vol 363 ◽  
pp. 199-228 ◽  
Author(s):  
AURELIUS PROCHAZKA ◽  
D. I. PULLIN
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Structure And Stability ◽  
Two Dimensional Flow ◽  
Steady Solutions ◽  
Pseudo Spectral Method ◽  
Burgers Vortices

We investigate, numerically and analytically, the structure and stability of steady and quasi-steady solutions of the Navier–Stokes equations corresponding to stretched vortices embedded in a uniform non-symmetric straining field, (αx, βy, γz), α+β+γ=0, one principal axis of extensional strain of which is aligned with the vorticity. These are known as non-symmetric Burgers vortices (Robinson & Saffman 1984). We consider vortex Reynolds numbers R=Γ/(2πv) where Γ is the vortex circulation and v the kinematic viscosity, in the range R=1−104, and a broad range of strain ratios λ=(β−α)/(β+α) including λ>1, and in some cases λ[Gt ]1. A pseudo-spectral method is used to obtain numerical solutions corresponding to steady and quasi-steady vortex states over our whole (R, λ) parameter space including λ where arguments proposed by Moffatt, Kida & Ohkitani (1994) demonstrate the non-existence of strictly steady solutions. When λ[Gt ]1, R[Gt ]1 and ε≡λ/R[Lt ]1, we find an accurate asymptotic form for the vorticity in a region 1<r/(2v/γ)1/2[les ]ε1/2, giving very good agreement with our numerical solutions. This suggests the existence of an extended region where the exponentially small vorticity is confined to a nearly cat's-eye-shaped region of the almost two-dimensional flow, and takes a constant value nearly equal to Γγ/(4πv)exp[−1/(2eε)] on bounding streamlines. This allows an estimate of the leakage rate of circulation to infinity as ∂Γ/∂t =(0.48475/4π)γε−1Γ exp (−1/2eε) with corresponding exponentially slow decay of the vortex when λ>1. An iterative technique based on the power method is used to estimate the largest eigenvalues for the non-symmetric case λ>0. Stability is found for 0[les ]λ[les ]1, and a neutrally convective mode of instability is found and analysed for λ>1. Our general conclusion is that the generalized non-symmetric Burgers vortex is unconditionally stable to two-dimensional disturbances for all R, 0[les ]λ[les ]1, and that when λ>1, the vortex will decay only through exponentially slow leakage of vorticity, indicating extreme robustness in this case.

Cavity flows driven by buoyancy and shear

1972 ◽  
Vol 51 (2) ◽  
pp. 221-231 ◽  
Author(s):  
K. Torrance ◽  
R. Davis ◽  
K. Eike ◽  
P. Gill ◽  
D. Gutman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Navier Stokes Equations ◽  
Moving Wall ◽  
Aspect Ratios ◽  
Range Of Values

Fluid motion driven by the combined effects of a moving wall and natura convection is examined for rectangular cavities with heightlwidth ratios of ½, 1 and 2. The Reynolds number and Prandtl number are held fixed at Re = 100 and Pr = 1; the Grashof number is varied over the range of values Gr = 0, ±104, ±106. Flow and temperature fields obtained from numerical solutions of the Navier-Stokes equations reveal a marked influence of buoyancy for the larger aspect ratios when Gr = ±106 and the dominance of buoyancy for all aspect ratios when Gr = ± 106. Results are compared with earlier work where possible and some observations are offered on the convergence of the numerical solutions.

Fluid motion inside a spinning nutating cylinder

1985 ◽  
Vol 150 ◽  
pp. 121-138 ◽  
Author(s):  
Harold R. Vaughn ◽  
William L. Oberkampf ◽  
Walter P. Wolfe
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Internal Fluid

The incompressible three-dimensional Navier–Stokes equations are solved numerically for a fluid-filled cylindrical cannister that is spinning and nutating. The motion of the cannister is characteristic of that experienced by spin-stabilized artillery projectiles. Equations for the internal fluid motion are derived in a non-inertial aeroballistic coordinate system. Steady-state numerical solutions are obtained by an iterative finite-difference procedure. Flow fields and liquid induced moments have been calculated for viscosities in the range of 0.9 × 104−1 × 109 cSt. The nature of the three-dimensional fluid motion inside the cylinder is discussed, and the moments generated by the fluid are explained. The calculated moments generally agree with experimental measurements.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

Numerical Solutions of the Navier-Stokes Equations in Inlet Regions

1972 ◽  
Vol 39 (4) ◽  
pp. 873-878 ◽  
Author(s):  
J. W. McDonald ◽  
V. E. Denny ◽  
A. F. Mills
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Improved Method ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Vorticity Equations

Numerical solutions of the Navier-Stokes equations are obtained for steady two-dimensional flow in the inlet region of both a tube and a channel. The entering flow is considered to be either uniform (u = constant, v = 0) or irrotational (u = constant, ω = 0). Values of Reynolds number Re = u0a/ν range from 0.75 to 2 × 106. An improved method for solving the stream function-vorticity equations of hydrodynamics has been developed. The method is stable at all Reynolds numbers and appears to be computationally superior to previous methods.

scholarly journals Calculation of the pressure on the valves of a sluice

1997 ◽  
Vol 19 (3) ◽  
pp. 25-34
Author(s):  
Tran Gia Lich ◽  
Le Kim Luat ◽  
Han Quoc Trinh
Keyword(s):  
Numerical Method ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Sweep Method ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Interior Points

This paper is devoted to a numerical method for calculating the pressure on the vertical two-dimensional valve basing on Navier-Stokes equations. Numerical solutions at interior points are established by splitting Navie-Stokes unsteady two-dimensional equations into two unsteady one-dimensional equations. An implicit scheme is obtained and the solution for these equations is established by the double sweep method. The values at the boundary points are calculated by the method of characteristics.

scholarly journals Multi-block technique applied to Navier-Stokes equations in two dimensions

2018 ◽  
Vol 39 (2) ◽  
pp. 115
Author(s):  
Jeferson Osmar de Almeida ◽  
Diomar Cesar Lobão ◽  
Cleyton Senior Stampa ◽  
Gustavo Benitez Alvarez
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Numerical Data ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Numerical Solver

In this work, numerical solutions of the two-dimensional Navier-Stokes and Euler equations using explicit MacCormack method on multi-block structured mesh are presented for steady state and unsteady state compressible fluid flows. The multi-block technique and generalized coordinate system are used to develop a numerical solver which can be applied for a large range of compressible flow problems on complex geometries without modifying the governing equations and numerical method. Besides that the numerical method is based on a finite difference approach and the generalized coordinates introduced allow the application of the boundary conditions easily. The subsonic flow over a backward facing step and supersonic flow over a curved ramp are presented, and the results are compared with the experimental and numerical data.

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