scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

Numerical Simulations of Turbulent Flow Through a 90° Elbow

2019 ◽  
Author(s):  
Ravon Venters ◽  
Brian Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Navier Stokes ◽  
Mean Square ◽  
Reynolds Stresses ◽  
Streamline Curvature ◽  
Secondary Motion ◽  
Flow Through ◽  
The Mean ◽  
Flow Transitions

Abstract Turbulent flow in an elbow has been numerically investigated. The flow was modeled using two approaches; Reynolds Averaged Navier-Stokes (RANS) and Direct Numerical Simulation (DNS) methods. The DNS allows for all the scales of turbulence to be evaluated, providing a detailed depiction of the flow. The RANS simulation, which is typically used in industry, evaluates time-averaged components of the flow. The numerical results are accompanied by experimental data, which was used to validate the two methods. Profiles of the mean and root-mean-square (RMS) fluctuating components were compared at various points along the midplane of the elbow. Upstream of the elbow, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing slightly near the walls. However, downstream of the elbow, the RANS deviated from the experiment and DNS, showing a longer region of flow re-circulation. This caused the mean and RMS velocities to significantly differ. Examining the cross-section flow field, secondary motion was clearly present. Upstream secondary motion of the first kind was observed which is caused by anisotropy of the reynolds stresses in the turbulent flow. Downstream of the bend, the flow transitions to secondary motion of the second kind which is caused by streamline curvature. Qualitatively, the RANS and DNS showed similar results upstream of the bend, however downstream, the magnitude of the secondary motion differed significantly.

Effect of a Simulated Free Surface on the Wake of a Slender Body

1986 ◽  
Vol 30 (04) ◽  
pp. 242-255
Author(s):  
P. Mitra ◽  
W. Neu ◽  
J. Schetz
Keyword(s):  
Free Surface ◽  
Turbulent Flow ◽  
Normal Component ◽  
Image Plane ◽  
Axisymmetric Body ◽  
Transverse Component ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Measurements ◽  
The Mean

Turbulent flow measurements were performed in the wake of a slender axisymmetric body in the presence of a flat plate strut and an image plane crudely representing the "rigid lid" approximation to a free surface. The tests were performed in a wind tunnel at a nominal Reynolds number of 6.0 ⨯ 105. A Yawhead probe was used for the mean flow measurements, and a Constant Temperature Anemometer System with an x-wire probe was used to obtain the turbulent flow characteristics. The presence of the image plane was found to increase the velocity defect and the static pressure as the image plane was approached. A redistribution among the various components of velocity fluctuations was noted near the image plane. The transverse component was enhanced at the expense of the normal component. The image plane also was found to influence the magnitudes and radial spread of turbulence intensities and Reynolds stresses. Some interactions between the wake of the axisymmetric body and that of the plate strut were observed. Overall, the mean velocities and the turbulence quantities indicated symmetry about the image plane throughout the wake.

A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

2016 ◽  
Vol 800 ◽  
pp. 327-357 ◽  
Author(s):  
P. Meliga ◽  
E. Boujo ◽  
F. Gallaire
Keyword(s):  
Sensitivity Analysis ◽  
Limit Cycle ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Cycle Frequency ◽  
Flow Perturbation ◽  
Self Consistent ◽  
The Mean

We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard–von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis is performed in the frame of the semi-linear self-consistent model recently introduced by Mantič et al. (Phys. Rev. Lett., vol. 113, 2014, 084501), which allows us to describe accurately the effect of the control on the mean flow, but also on the finite-amplitude fluctuation that couples back nonlinearly onto the mean flow via the formation of Reynolds stress. The sensitivity is computed with respect to arbitrary steady and synchronous time-harmonic body forces. For a small amplitude of the control, the theoretical variations of the limit-cycle frequency predict well those of the controlled flow, as obtained from either self-consistent modelling or direct numerical simulation of the Navier–Stokes equations. This is not the case if the variations are computed in the simpler mean flow approach overlooking the coupling between the mean and fluctuating components of the flow perturbation induced by the control. The variations of the limit-cycle amplitude (that falls out the scope of the mean flow approach) are also correctly predicted, meaning that the approach can serve as a relevant and systematic guideline to control strongly unstable flows exhibiting non-small, finite amplitudes of oscillation. As an illustration, we apply the method to control by means of a small secondary control cylinder and discuss the obtained results in the light of the seminal experiments of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, pp. 71–107).

scholarly journals Finite disturbance effect on the stability of a laminar incompressible wake behind a flat plate

1970 ◽  
Vol 40 (2) ◽  
pp. 315-341 ◽  
Author(s):  
D. Ru-Sue Ko ◽  
T. Kubota ◽  
L. Lees
Keyword(s):  
Flat Plate ◽  
Finite Amplitude ◽  
Single Frequency ◽  
Shape Parameters ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Parameters ◽  
Local Mean ◽  
The Mean ◽  
The Stability

An integral method is used to investigate the interaction between a two-dimensional, single frequency finite amplitude disturbance in a laminar, incompressible wake behind a flat plate at zero incidence. The mean flow is assumed to be a non-parallel flow characterized by a few shape parameters. Distribution of the fluctuation across the wake is obtained as functions of those mean flow parameters by solving the inviscid Rayleigh equation using the local mean flow. The variations of the fluctuation amplitude and of the shape parameters for the mean flow are then obtained by solving a set of ordinary differential equations derived from the momentum and energy integral equations. The interaction between the mean flow and the fluctuation through Reynolds stresses plays an important role in the present formulation, and the theoretical results show good agreement with the measurements of Sato & Kuriki (1961).

LDV Measurements of the Flow Field in the Nozzle Region of a Confined Double Annular Burner

2001 ◽  
Vol 123 (2) ◽  
pp. 228-236 ◽  
Author(s):  
Francois Schmitt ◽  
Birinchi K. Hazarika ◽  
Charles Hirsch
Keyword(s):  
Flow Field ◽  
Turbulent Flow ◽  
Turbulence Intensity ◽  
Meridional Plane ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Fine Grid ◽  
Contour Plots ◽  
The Mean ◽  
Grid Points

A database for the complex turbulent flow of a confined double annular burner in cold conditions is presented here. In the region close to the exit of the annular nozzles LDV measurements at 5515 grid points in the meridional plane were conducted. At each measurement position, validated data for 3000–16,000 particles were recorded, and the mean axial and radial velocities, axial and radial turbulence intensity and Reynolds stresses were computed. The resulting mean flow field is axisymmetric within an uncertainty of 2 percent. The contour plots of turbulent quantities on the fine grid, as well as the streamlines based on the mean flow field, are presented for the flow.

Harmonics generation and the mechanics of saturation in flow over an open cavity: a second-order self-consistent description

2017 ◽  
Vol 826 ◽  
pp. 503-521 ◽  
Author(s):  
P. Meliga
Keyword(s):  
Growth Rate ◽  
Second Harmonic ◽  
Open Cavity ◽  
Linear Growth Rate ◽  
Linear Component ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Higher Harmonics ◽  
Self Consistent ◽  
The Mean

The flow over an open cavity is an example of supercritical Hopf bifurcation leading to periodic limit-cycle oscillations. One of its distinctive features is the existence of strong higher harmonics, which results in the time-averaged mean flow being strongly linearly unstable. For this class of flows, a simplified formalism capable of unravelling how exactly the instability grows and saturates is lacking. This study builds on previous work by Mantič-Lugo et al. (Phys. Rev. Lett., vol. 113, 2014, 084501) to fill in the gap using a parametrized approximation of an instantaneous, phase-averaged mean flow, coupled in a quasi-static manner to multiple linear harmonic disturbances interacting nonlinearly with one another and feeding back on the mean flow via their Reynolds stresses. This provides a self-consistent modelling of the mean flow–fluctuation interaction, in the sense that all perturbation structures are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations. The first harmonic is sought as the superposition of two components, a linear component generated by the instability and aligned along the leading eigenmode of the mean flow, and a nonlinear orthogonal component generated by the higher harmonics, which progressively distorts the linear growth rate and eigenfrequency of the eigenmode. Saturation occurs when the growth rate of the first harmonic is zero, at which point the stabilizing effect of the second harmonic balances exactly the linear instability of the eigenmode. The model does not require any input from numerical or experimental data, and accurately predicts the transient development and the saturation of the instability, as established from comparison to time and phase averages of direct numerical simulation data.

Roles of surface tension and Reynolds stresses on the finite amplitude stability of a parallel flow with a free surface

1970 ◽  
Vol 40 (2) ◽  
pp. 307-314 ◽  
Author(s):  
S. P. Lin
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Gravity Waves ◽  
Wave Amplitude ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Inclined Plane ◽  
The Mean

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.

Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels

2003 ◽  
Vol 125 (4) ◽  
pp. 445-460 ◽  
Author(s):  
Sonu S. Varghese ◽  
Steven H. Frankel
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equation ◽  
Flow Through ◽  
The Mean ◽  
High Reynolds

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-ω turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-ε turbulence model and the standard k-ε model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.

Numerical Study of Deterministic Fluxes in Compressor Passages

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Feng Wang ◽  
Mauro Carnevale ◽  
Luca di Mare
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Navier Stokes ◽  
Design Stage ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Radial Profiles ◽  
And Performance ◽  
Stage Matching ◽  
Unsteady Effects

Computational fluid dynamics (CFD) has been widely adopted in the compressor design process, but it remains a challenge to predict the flow details, performance, and stage matching for multistage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and unsteady RANS (URANS) calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious values of flow quantities (e.g., whirl angle). The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore, the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS mixing plane solutions. The magnitudes of divergence of Reynolds stresses (RS) and deterministic stresses (DS) are compared. The effect of deterministic fluxes is demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes is also observed. The effect of deterministic fluxes is confirmed via the nonlinear harmonic (NLH) method which includes the deterministic fluxes in the mean flow, and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

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