Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis

2018 ◽  
Vol 861 ◽  
pp. 200-222 ◽  
Author(s):  
Satoshi Nakashima ◽  
Mitul Luhar ◽  
Koji Fukagata
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
High Gain ◽  
Spectral Space ◽  
Rotation Rates ◽  
Wide Range ◽  
Effects Of Rotation ◽  
Spanwise Rotation

We study the effect of spanwise rotation in turbulent channel flow at both low and high Reynolds numbers by employing the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382). Under this formulation, the nonlinear terms in the Navier–Stokes equations are regarded as a forcing that acts upon the remaining linear dynamics to generate the turbulent velocity field in response. A gain-based decomposition of the forcing–response transfer function across spectral space yields models for highly amplified flow structures, or modes. Unlike linear stability analysis, this enables targeted analyses of the effects of rotation on high-gain modes that serve as useful low-order models for dynamically important coherent structures in wall-bounded turbulent flows. The present study examines a wide range of rotation rates. A posteriori comparisons at low Reynolds number ($\mathit{Re}_{\unicode[STIX]{x1D70F}}=180$) demonstrate that the resolvent formulation is able to quantitatively predict the effect of varying spanwise rotation rates on specific classes of flow structure (e.g. the near-wall cycle) as well as energy amplification across spectral space. For fixed inner-normalized rotation number, the effects of rotation at varying friction Reynolds numbers appear to be similar across spectral space, when scaled in outer units. We also consider the effects of rotation on modes with varying speed (i.e. modes that are localized in regions of varying mean shear), and provide suggestions for modelling the nonlinear forcing term.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Lid-Driven Square Cavity Flow: A Benchmark Solution with an 8192x8192 Grid

2021 ◽  
Author(s):  
Carlos Marchi ◽  
Cosmo D. Santiago ◽  
Carlos Alberto Rezende de Carvalho Junior
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Accurate Determination ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Discretization Error ◽  
Square Cavity ◽  
Solution Vector ◽  
Wide Range

Abstract The incompressible steady-state fluid flow inside a lid-driven square cavity was simulated using the mass conservation and Navier-Stokes equations. This system of equations is solved for Reynolds numbers of up to 10,000 to the accuracy of the computational machine round-off error. The computational model used was the second-order accurate finite volume method. A stable solution is obtained using the iterative multigrid methodology with 8192 × 8192 volumes, while degree-10 interpolation and Richardson extrapolation were used to reduce the discretization error. The solution vector comprised five entries of velocities, pressure, and location. For comparison purposes, 65 different variables of interest were chosen, such as velocity profile, its extremum values and location, extremum values and location of the stream function. The discretization error for each variable of interest was estimated using two types of estimators and their apparent order of accuracy. The variations of the 11 selected variables are shown across 38 Reynolds number values between 0.0001 and 10,000. In this study, we provide a more accurate determination of the Reynolds number value at which the upper secondary vortex appears. The results of this study were compared with those of several other studies in the literature. The current solution methodology was observed to produce the most accurate solution till date for a wide range of Reynolds numbers.

Modeling Reynolds-Number Effects in Wall-Bounded Turbulent Flows

1996 ◽  
Vol 118 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. M. C. So ◽  
H. Aksoy ◽  
S. P. Yuan ◽  
T. P. Sommer
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Strain Tensor ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Wide Range ◽  
Peak Shear Stress ◽  
Reynolds Number Effects ◽  
Near Wall

Recent experimental and direct numerical simulation data of two-dimensional, isothermal wall-bounded incompressible turbulent flows indicate that Reynolds-number effects are not only present in the outer layer but are also quite noticeable in the inner layer. The effects are most apparent when the turbulence statistics are plotted in terms of inner variables. With recent advances made in Reynolds-stress and near-wall modeling, a near-wall Reynolds-stress closure based on a recently proposed quasi-linear model for the pressure strain tensor is used to analyse wall-bounded flows over a wide range of Reynolds numbers. The Reynolds number varies from a low of 180, based on the friction velocity and pipe radius/channel half-width, to 15406, based on momentum thickness and free stream velocity. In all the flow cases examined, the model replicates the turbulence statistics, including the Reynolds-number effects observed in the inner and outer layers, quite well. Furthermore, the model reproduces the correlation proposed for the location of the peak shear stress and an appropriately defined Reynolds number, and the variations of the near-wall asymptotes with Reynolds numbers. It is conjectured that the ability of the model to replicate the asymptotic behavior of the near-wall flow is most responsible for the correct prediction of the Reynolds-number effects.

scholarly journals Finite Element Analysis of Turbulent Flows Using LES and Dynamic Subgrid-Scale Models in Complex Geometries

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Wang Wenquan ◽  
Zhang Lixiang ◽  
Yan Yan ◽  
Guo Yakun
Keyword(s):  
Finite Element ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Francis Turbine ◽  
Complex Geometries ◽  
Subgrid Scale ◽  
Element Analysis

An innovative computational model is presented for the large eddy simulation (LES) of multidimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic, and to study physical effects due to complex fluid flow. The filtered Navier-Stokes equations are used to simulate large scales; however, they are supplemented by dynamic subgrid-scale (DSGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Based on the Taylor-Galerkin schemes for the convection-diffusion problems, this model is implemented in a three-dimensional finite element code using a three-step finite element method (FEM). Turbulent channel flow and flow over a backward-facing step are considered as a benchmark for validating the methodology by comparing with the direct numerical simulation (DNS) results or experimental data. Also, qualitative and quantitative aspects of three-dimensional complex turbulent flow in a strong 3D blade passage of a Francis turbine are analyzed.

scholarly journals Numerical Investigation of Liquid–Liquid Mixing in Modified T Mixer with 3D Obstacles

2021 ◽  
pp. 25-32
Author(s):  
Md. Readul Mahmud
Keyword(s):  
Numerical Investigation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Channel Length ◽  
Navier Stokes ◽  
Mixing Efficiency ◽  
Mixing Performance ◽  
Wide Range

The fluids inside passive micromixers are laminar in nature and mixing depends primarily on diffusion. Hence mixing efficiency is generally low, and requires a long channel length and longtime compare to active mixers. Various designs of complex channel structures with/without obstacles and three-dimensional geometries have been investigated in the past to obtain an efficient mixing in passive mixers. This work presents a design of a modified T mixer. To enhance the mixing performance, circular and hexagonal obstacles are introduced inside the modified T mixer. Numerical investigation on mixing and flow characteristics in microchannels is carried out using the computational fluid dynamics (CFD) software ANSYS 15. Mixing in the channels has been analyzed by using Navier–Stokes equations with water-water for a wide range of the Reynolds numbers from 1 to 500. The results show that the modified T mixer with circular obstacles has far better mixing performance than the modified T mixer without obstacles. The reason is that fluids' path length becomes longer due to the presence of obstacles which gives fluids more time to diffuse. For all cases, the modified T mixer with circular obstacle yields the best mixing efficiency (more than 60%) at all examined Reynolds numbers. It is also clear that efficiency increase with axial length. Efficiency can be simply improved by adding extra mixing units to provide adequate mixing. The value of the pressure drop is the lowest for the modified T mixer because there is no obstacle inside the channel. Modified T mixer and modified T mixer with circular obstacle have the lowest and highest mixing cost, respectively. Therefore, the current design of modified T with circular obstacles can act as an effective and simple passive mixing device for various micromixing applications.

scholarly journals Stochastic Modelling of Turbulent Flows for Numerical Simulations

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 108 ◽  
Author(s):  
Carlo Cintolesi ◽  
Etienne Mémin
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Stochastic Modelling ◽  
Turbulent Channel Flow ◽  
Alternative Formulation ◽  
Stochastic Representation ◽  
Practical Applications ◽  
Local Variance

Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier–Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy–viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at R e τ = 590 . The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model.

scholarly journals Turbulence Modeling of Torsional Couette Flows

2008 ◽  
Vol 2008 ◽  
pp. 1-27 ◽  
Author(s):  
Sofia Haddadi ◽  
Sébastien Poncet
Keyword(s):  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Rate Coefficients ◽  
Aspect Ratios ◽  
Numerical Predictions ◽  
Wide Range ◽  
Rsm Model ◽  
First Time

The present study considers the numerical modeling of the turbulent flow inside a rotor-stator cavity subjected or not to a superimposed throughflow. Extensive numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are performed mainly in the case of turbulent flows with merged boundary layers known as turbulent torsional Couette flows and belonging to regime III of Daily and Nece (1960). The RSM model has already shown its capability of predicting accurately the mean and turbulent fields in various rotating disk configurations (Poncet, 2005; Poncet et al., 2005, 2007, 2008). For the first time, a detailed mapping of the hydrodynamic flow over a wide range of rotational Reynolds numbers (180 000≤Re≤10 000 000), aspect ratios of the cavity (0.02≤G≤0.05), and flow rate coefficients (−10000≤Cw≤10000) is here provided in the turbulent torsional Couette flow regime.

scholarly journals Coherent large-scale structures from the linearized Navier–Stokes equations

2019 ◽  
Vol 873 ◽  
pp. 89-109 ◽  
Author(s):  
Anagha Madhusudanan ◽  
Simon. J. Illingworth ◽  
Ivan Marusic
Keyword(s):  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Scale Structures ◽  
Viscosity Profile ◽  
Wide Range ◽  
Scale Structures

The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=2000$ is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.

A Theoretical and Experimental Study of Confined Vortex Flow

1969 ◽  
Vol 36 (4) ◽  
pp. 687-692 ◽  
Author(s):  
G. J. Farris ◽  
G. J. Kidd ◽  
D. W. Lick ◽  
R. E. Textor
Keyword(s):  
Flow Field ◽  
Radial Flow ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Wide Range

The interaction of a vortex with a stationary surface was studied both theoretically and experimentally. The flow field examined was that produced by radially inward flow through a pair of concentric rotating porous cylinders that were perpendicular to, and in contact with, a stationary flat plane. The complete Navier-Stokes equations were solved over a range of tangential Reynolds numbers from 0–300 and a range of radial Reynolds numbers from 0 to −13, the minus sign indicating radially inward flow. In order to facilitate the solution, the original equations were recast in terms of a dimensionless stream function, vorticity, and third variable related to the tangential velocity. The general validity of the numerical technique was demonstrated by the agreement between the theoretical and experimental results. Examination of the numerical results over a wide range of parameters showed that the entire flow field is very sensitive to the amount of radial flow, especially at the transition from zero radial flow to some finite value.

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