Use of Experimental Data for an Efficient Description of Turbulent Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S240-S245 ◽  
Author(s):  
N. Aubry
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Original System ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Wall Region ◽  
Lorenz Equations ◽  
Chaotic Solution

The proper orthogonal decomposition (POD), also called Karhunen-Loe`ve expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.

A 3-D Thin Layer Navier-Stokes Code for Supersonic Laminar and Turbulent Flows

2002 ◽  
Author(s):  
Omid Abouali ◽  
Mohammad M. Alishahi ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Mach Number ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Cross Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Laminar And Turbulent Flows ◽  
Circumferential Pressure

A 3-D Thin Layer Navier-Stokes (TLNS) code for solving viscous supersonic flows is developed. The new code uses several numerical algorithms for space and time discretization together with appropriate turbulence modeling. Roe’s method is used for discretizing the convective terms and the central differencing scheme is employed for the viscous terms. An explicit time marching technique and a finite volume space discretization are used. The developed computational model can handle both laminar and turbulent flows. The Baldwin-Lomax model and Degani-Schiff modifications are used for turbulence modeling. The computational model is applied to a hypersonic laminar flow at Mach 7.95 around a cone at different incidence angles. The circumferential pressure distribution is compared with the experimental data. The cross-sectional Mach number contours are also presented. It is shown that in addition to the outer shock, a cross-flow shock wave is also present in the flow field. The cases of supersonic turbulent flows with Mach number 3 around a tangent-ogive with incidence angles of 6° and a secant-ogive with incidence angles of 10° are also studied. The circumferential pressure distributions are compared with the experimental data and the Euler code results and good agreement is obtained. The cross-sectional Mach number contours are also presented. It is shown that in this case also in addition to the outer shock, a cross-flow shock wave is also present at the incidence angle of 10°.

scholarly journals Unstable periodic orbits in the Lorenz attractor

2011 ◽  
Vol 369 (1944) ◽  
pp. 2345-2353 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Aaron Brown ◽  
Jonas Lätt ◽  
Hui Tang ◽  
Luis M. Fazendeiro ◽  
...  
Keyword(s):  
Periodic Orbits ◽  
Stokes Equations ◽  
Traditional Approach ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Time Averaging ◽  
Unstable Periodic Orbits ◽  
Lorenz Equations ◽  
Navier Stokes Equations ◽  
Generic Orbit

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computation of unstable periodic orbits of the driven Navier–Stokes equations, which can be simulated using the lattice Boltzmann method.

Lattice Boltzmann Method Based on Large-Eddy Simulation (LES) Used to Investigate the Unsteady Turbulent Flow on Series of Cavities

2020 ◽  
Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui
Keyword(s):  
Boltzmann Equation ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Large Eddy

Abstract A numerical study is proposed to analyze the turbulent flow structures. This paper aims to determine the effect of the series of the cavities. The configuration is similar to that represented by two walls with infinite width, one of which is mobile and the other is fixed. The series of cavity are placed on the fixed wall. The objectives are to study the aero acoustic capabilities of LBM and to build and to assess the efficiency of the Lattice Boltzmann Equation (LBE) as a new computational tool to perform the Large-Eddy Simulations (LES) for turbulent flows. In the first part, the background of LBM is presented and the construction of Navier-Stokes equations from Boltzmann equation is discussed. The LBM-LES model for solving transition is developed and turbulence modeling is implemented. In the second part, the dynamics of the flows in the vicinity of cavities with symmetric or asymmetric edges are considered, to then discuss the oscillation phenomenon. The effect of the geometric of the cavity and the Reynolds numbers were studied to investigate the fluid flow dynamics. We were focusing on the dynamics of asymmetric deep cavity flows, to put forward the topology of the cavity flow and to highlight the effects of dissymmetry and aspect ratio.

About the Transition to Turbulence Through Chaotic Distortion of Vortex Shedding

2016 ◽  
pp. 4460-4480
Author(s):  
Igor V.Lebed
Keyword(s):  
Experimental Data ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Instability Development ◽  
Chaotic Solution ◽  
Direct Numerical Integration ◽  
Hydrodynamics Equations

The results of direct numerical integration of the Navier-Stokes equations are evaluated against experimental data for the problem of flow around a hard sphere at rest. The evaluation is performed for both the sequence of vortex shedding regimes, replacing stable modes after the loss of stability, and the regime of turbulence replacing vortex shedding modes as Reynolds number Re increases. The evaluation demonstrates the unsuitability of classic hydrodynamics equations to interpret the phenomenon of vortex shedding. Moreover, the attainment of critical value of Re is accompanied by loss of the direction of instability development. Wrong direction of instability development results in the attainment of multiperiodic, that is, essentially chaotic, solution. Insurmountable discrepancies between calculation results and experimental data show that the chaotic deterministic solution to the Navier-Stokes equation is not suitable for interpretation of turbulence. An analogy is revealed between the sequence of modes observed in flow around a sphere as Re increases and sequence of modes in shear layer behind a cylinder with paraboloidal nose recorded while moving downstream along the contour of streamlined body. The conclusions are as follows. The turbulence of shear flow is regular unstable vortex shedding regime distorted by chaotic fluctuations. Solutions to the classic hydrodynamics equations are incapable of interpreting both regular and chaotic turbulence component. Multimoment hydrodynamics seeks for decision of these problems along the way toward an increase in the number of principle hydrodynamic values.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

Leading Edge Film Cooling: Computations and Experiments Including Density Effects

1996 ◽  
Author(s):  
Pingfan He ◽  
Dragos Licu ◽  
Martha Salcudean ◽  
Ian S. Gartshore
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Stokes Equations ◽  
Leading Edge ◽  
Variable Density ◽  
Navier Stokes ◽  
Cooling Effectiveness ◽  
Stagnation Line ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio

The effect of varying coolant density on film cooling effectiveness for a turbine blade-model was numerically investigated and compared with experimental data. This model had a semi-circular leading edge with four rows of laterally-inclined film cooling orifices positioned symmetrically about the stagnation line. A curvilinear coordinate-based CFD code was developed and used for the numerical investigation. The code used a domain segmentation strategy in conjunction with general curvilinear grids to model the complex blade configuration. A multigrid method was used to accelerate the convergence rate. The time-averaged, variable-density, Navier-Stokes equations together with the energy or scalar equation were solved. Turbulence closure was attained by the standard k–ε model with a near-wall k model. Either air or CO2 was used as coolant in three cases of injection through single rows and alternatively staggered double raws of holes. Two different blowing rates were investigated in each case and compared with experimental data. The experimental results were obtained using a wind tunnel model, and the mass/heat analogy was used to determine the film cooling effectiveness. The higher density of the carbon dioxide coolant (approximately 1.5 times the density of air) in the isothermal mass injection experiments, was used to simulate the effects of injection of a colder air in the corresponding adiabatic heat transfer situation. Good agreement between calculated and measured film cooling effectiveness was found for low blowing ratio M ≤ 0.5 and the effect of density was not significant. At higher blowing ratio M > 1 the calculations consistently overpredict the measured values of film cooling effectiveness.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

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