Convective and absolute instabilities in counter-rotating spiral Poiseuille flow

We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent numerical investigations done by Pinter et al. [24] by measuring the absolute and convective stability boundaries of both propagating Taylor vortices (PTV) and spiral vortices (SPI). Thus our work shows that these theoretical concepts from hydrodynamic stability in open flows apply to experimental counter-rotating Taylor–Couette systems with an imposed axial through flow. PACS 47.20.-k, 05.45.-a, 47.15.fe     

Modeling plane turbulent Couette flow

Among the salient features of shear-driven plane Couette flow is the constancy of the total shear stress (viscous and turbulent) across the flow. This constancy gives rise to a quasi-homogenous core region, which makes the bulk of the flow substantially different from pressure-driven Poiseuille flow. The present second-moment closure study addresses the conflicting hypotheses relating to turbulent Couette flow. The inclusion of a new wall-proximity function in the wall-reflection part of the pressure-strain model seems mandatory, and the greement with recent experimental and direct numerical simulation (DNS) results is encouraging. Analysis of model computations in the range 750 ≤ Re ≤ 35,000 and comparisons with low-Re DNS data suggest that plane Couette flow exhibits a local-equilibrium core region, in which anisotropic, homogeneous turbulence prevails. However, the associated variation of the mean velocity in the core, as obtained by the model, conflicts with the intuitively appealing assumption of homogeneous mean shear. The constancy of the velocity gradient exhibited by the DNS therefore signals a deficiency in the modeled transport equation for the energy dissipation rate.     

Nonnormal Effects in the Taylor–Couette Problem

This work is devoted to the study of transient growth of perturbations in the Taylor–Couette problem due to linear nonnormal mechanisms. The study is carried out for a particular small gap case and is mostly focused on the linearly stable regime of counter-rotation. The exploration covers a wide range of inner and outer angular speeds as well as axial and azimuthal modes. Significant transient growth is found in the regime of stable counter-rotation. The numerical results are in agreement with former analyses based on energy methods and other independent numerical studies. The optimal energy transient growth factor appears to be consistent with experimental observations. This study might shed some light on the subcritical transition to turbulence which is found experimentally in Taylor–Couette flow when the cylinders rotate in opposite directions. Received 13 February 2001 and accepted 29 March 2002 Published online: 2 October 2002 RID="*" ID="*" This work was supported by the UK EPSRC under Grant GR/M30890. The author thanks Nick Trefethen for fruitful discussions. RID="*" ID="*" Present address: Departament de Fisica Aplicada, Univ. Politecnica de Catalunya, 08034 Barcelona, Spain (alvar@fa.upc.es) Communicated by H.J.S. Fernando     

High‐order stable interpolations for immersed boundary methods

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high‐order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier–Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two‐dimensional Taylor–Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three‐dimensional flow in an air‐conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd.     

Theoretical Investigation of an Eddy-Viscosity-Type Expression of the Reynolds Stress with Low-Reynolds-Number Effect

In low-Reynolds-number turbulent flows, the influence of the molecular viscosity is important. The turbulence models which are applied to those flows should include the low-Reynolds-number effect. In this study, turbulent flow with the molecular viscosity effect is analyzed theoretically with the aid of a two-scale direct-interaction approximation (TSDIA) and the energy spectrum and a new low-Reynolds-number-type eddy-viscosity representation are derived. An priori test for the model expression on the basis of the result of direct numerical simulation (DNS) for turbulent Couette flows is performed. Received 5 July 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by T.B. Gatski     

3D-PTV measurements in a plane Couette flow

Genuine plane Couette flow is hard to realize experimentally, and no applications of modern spatially resolving measurement techniques have been reported for this flow so far. In order to resolve this shortcoming, we designed and built a new experimental facility and present our first results here. Our setup enables us to access the flow via 3D particle tracking velocimetry and therefore to obtain truly three-dimensional flow fields for the first time experimentally in plane Couette flow. Results are analyzed in terms of basic flow properties, and a clear distinction of flow regimes (laminar for Re < 320, transitional for 320 < Re < 400, and turbulent when Re > 400) could be made. Comparison with DNS data shows good agreement in the turbulent regime and builds trust in our data. Furthermore, vortical coherent structures are studied in detail with the additional help of kalliroscope imaging, and the typical vortex spacing is determined to be roughly one gap width. As a noteworthy result, we find that the onset of the turbulent regime coincides with the range of Reynolds numbers at which a distance of 100 wall units is comparable to the gap width.     

Instability of a slip flow in a curved channel formed by two concentric cylindrical surfaces

Instability of a slip flow in a curved channel formed by two concentric cylindrical surfaces is investigated. Two cases are considered. In the first (Taylor–Couette flow) case the flow is driven by the rotation of the inner cylindrical surface; no azimuthal pressure gradient is applied. In the second case (Dean flow) both cylindrical surfaces are motionless, and the flow is driven by a constant azimuthal pressure gradient. The collocation method is used to find numerically the critical values of the Taylor and Dean numbers, which establish the instability criteria for these two cases. The dependencies of critical values of these numbers on the ratio between the radii of concave and convex walls and on the velocity slip coefficient are investigated.     

Evidences of persisting thermal structures in Couette flows

DNS of passive thermal turbulent Couette flow at several friction Reynolds numbers (180, 250, and 500), and the Prandtl number of air are presented. The time averaged thermal flow shows the existence of long and wide thermal structures never described before in Couette flows. These thermal structures, named CTFS (Couette Thermal Flow Superstructures), are defined as coherent regions of hot and cold temperature fluctuations. They are intrinsically linked to the velocity structures present in Couette flows. Two different 2D symmetries can be recognized, which get stronger with the Reynolds number. These structures do not affect the mean flow or mean quantities as the Nusselt number. However, turbulent intensities and thermal fluxes depend on the width of the structures, mainly far from the walls. Since the width of the structures is related to the channel width, the statistics of thermal Couette flow are to some point box-dependent.     

Direct Numerical Simulation of Statistically Stationary One- and Two-Phase Turbulent Combustion: A Turbulent Injection Procedure

A new turbulent injection procedure dedicated to fully compressible direct numerical simulation (DNS) or large eddy simulation (LES) solvers is proposed. To avoid the appearance of spurious acoustic waves, this method is based on an accurate tracking of the turbulent structures crossing the boundary at the inlet of the domain. A finite difference DNS solver has been coupled with a spectral simulation in which a statistically stationary homogeneous turbulence evolves to provide fluctuating boundary conditions.A new turbulence forcing method, dedicated to spectral solvers, has been developed as well to control the major properties of the injected flow (turbulent kinetic energy, dissipation rate and integral length scale). One-dimensional Navier–Stokes characteristic boundary conditions extended to non-stationary flows are coupled with the injection procedure to evaluate is potential in four various configurations: spatially decaying turbulence, dispersion of vaporizing sprays, propagation of one- and two-phase V-shape turbulent flames.     

A modification of the artificial compressibility algorithm with improved convergence characteristics

The artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven‐cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward‐facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley & Sons, Ltd.     

Towards a Direct Numerical Simulation of a Simplified Pressurized Thermal Shock

The aim of this research work is to perform high quality direct numerical simulations (DNS) of a simplified single phase pressurized thermal shock (PTS) scenario with and without buoyancy effects. In that context, the objectives of this paper are (i) to present the road towards the DNS of a PTS design without buoyancy effects and (ii) to demonstrate that the code NEK5000 is adequate for true DNS analyses. This DNS of the PTS design will serve as a reference to validate low order CFD approaches. The higher order spectral element code NEK5000 is selected to perform the high quality DNS computations. The capabilities of this code, in order to perform the DNS for PTS like geometries, have been extensively assessed for a well-known turbulent channel flow configuration with Re_τ =?180 (turbulent Reynolds number based on the wall friction velocity). Different numerical parameters of NEK5000 have been thoroughly tested and their influence has been studied to obtain high quality turbulence statistics. This assessment of NEK5000 is further extended for the application of highly skewed hexahedral (non-orthogonal) meshes in a turbulent channel flow. The obtained results have shown that NEK5000 is capable of producing high quality DNS solution for a PTS like complex flow configuration for skewed elements (meshes) up to 60 degrees. Finally, this tested numerical framework is adopted to perform the targeted DNS computations of the simplified PTS design.     

Velocity and temperature dissimilarity in fully developed turbulent channel and plane Couette flows

The natural dissimilarity or decorrelation of stream-wise velocity and temperature fluctuations in fully developed turbulent channel and plane Couette flows was studied using direct numerical simulation (DNS). For both of the flow configurations, a Reynolds number of about 150 was used based on the friction velocity and half the distance between walls. Buoyancy effects were neglected, and only results with a molecular Prandtl number, Pr, equal to 1 are presented. The boundary conditions for the thermal field were a uniform source of energy in the domain and isothermal wall temperature for the channel and Couette flow, respectively. The importance of those events responsible for wall-normal turbulent fluxes in the generation of axial velocity and temperature dissimilarity was examined using conditional probability. It was found that the dissimilarity in the whole domain was higher in Couette than in channel flow. It was also found that for wall-normal turbulent fluxes (momentum and heat), the averaged dissimilarity in the whole domain was slightly more correlated with those events in the second or fourth quadrant, according to the quadrant analysis technique. For channel flow, the importance of both kinds of events was similar, while for Couette flow there was a predominance in the generation of dissimilarity by those events in the fourth quadrant. Also, for both flow configurations and throughout the wall-normal direction, it was found that in the buffer region there was a predominance of events in the fourth quadrant associated with dissimilarity for both wall-normal turbulent fluxes. In the frequency domain, the distribution of energy showed that there was a high-frequency shift experienced from the wall towards the centerline by the temperature spectrum with regards to the axial velocity spectrum, for which the action of the fluctuations of the wall-normal velocity was the main cause. In the central region of the flow, on the other hand, there was a global convergence of all spectra towards the pressure spectrum, with this convergence lower for Couette flow. Finally, it is shown that the dissimilarity in developed conditions is caused by the greater correlation existing for the temperature fluctuation with the instantaneous axial pressure gradient than for the velocity fluctuation with the instantaneous axial pressure gradient.     

An attempt to improve accuracy of higher‐order statistics and spectra in direct numerical simulation of incompressible wall turbulence by using the compact schemes for viscous terms

We attempt to improve accuracy in the high‐wavenumber region in DNS of incompressible wall turbulence such as found in fully developed turbulent channel flow. In particular, it is shown that the improvement of accuracy of viscous terms in the Navier–Stokes equations leads to the improvement of accuracy of higher‐order statistics and various spectra. It is emphasized that increase in required computational cost will not be crucial when incompressible flow is simulated, because the introduction of a higher‐order scheme into the viscous terms does not increase computational cost for solving the Poisson equation. We introduced fourth‐order and eighth‐order central compact schemes for discretizing the viscous terms in DNS of a fully developed turbulent channel flow. The results are compared with those using second‐order and fourth‐order central‐difference schemes applied to the viscous terms and those obtained by the spectral method. The results show that accuracy improvement of the viscous terms improve accuracy of higher‐order statistics (i.e., skewness and flatness factors of streamwise velocity fluctuation) and various spectra of velocity and pressure fluctuations in the high‐wavenumber region. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear Stability of Taylor Vortices in Infinite Cylinders

We consider the Taylor‐Couette problem in an infinitely extended cylindrical domain in the case when Couette flow is weakly unstable and a family of spatially periodic equilibria, called the Taylor vortices, has bifurcated from this trivial ground state. We show that those Taylor vortices which are not linearly unstable in the sense of Eckhaus are in fact nonlinearly stable with respect to small spatially localized perturbations. The main difficulty in showing this result stems from the fact that on unbounded cylindrical domains the Taylor vortices are only linearly marginally stable with continuous spectrum up to the imaginary axis. Bloch‐wave representations of the solutions and renormalization theory allow us to show that the nonlinear problem behaves asymptotically like the linearized one which is under a diffusive regime. (Accepted September 8, 1997)     

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k– model are not consistent with most of the new turbulent scaling laws.     

Direct numerical simulation of turbulent pipe flow

Fully developed turbulent pipe flow at low Re-number is studied by means of direct numerical simulation (DNS). In contrast to many previous DNS's of turbulent flows in rectangular geometries, the present DNS code, developed for a cylindrical geometry, is based on the finite volume technique rather than being based on a spectral method. The statistical results are compared with experimental data obtained with two different experimental techniques. The agreement between numerical and experimental results is found to be good which indicates that the present DNS code is suited for this kind of numerical simulations.     

DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow

The Lie group, or symmetry approach, developed by Oberlack (see e.g. Oberlack [26] and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient turbulent boundary layer flow. The approach unifies and extends the work done by Oberlack for the mean velocity of stationary parallel turbulent shear flows. From the two-point correlation (TPC) equations the knowledge of the symmetries allows us to derive a variety of invariant solutions (scaling laws) for turbulent flows, one of which is the new exponential mean velocity profile that is found in the mid-wake region of flat-plate boundary layers. Further, a third scaling group was found in the TPC equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier–Stokes and Euler equations, which have one and two scaling groups, respectively. The present focus is on the exponential law in the outer region of turbulent boundary layer corresponding new scaling laws for one- and two-point correlation functions. A direct numerical simulation (DNS) of a flat plate turbulent boundary layer with zero pressure gradient was performed at two different Reynolds numbers Re=750,2240. The Navier–Stokes equations were numerically solved using a spectral method with up to 140 million grid points. The results of the numerical simulations are compared with the new scaling laws. TPC functions are presented. The numerical simulation shows good agreement with the theoretical results, however only for a limited range of applicability. PACS 02.20.-a, 47.11.+j, 47.27.Nz, 47.27.Eq     

A Reynolds stress model for turbulent flow of homogeneous polymer solutions

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.     

On predicting particle-laden turbulent flows

The paper provides an overview of the challenges and progress associated with the task of numerically predicting particle-laden turbulent flows. The review covers the mathematical methods based on turbulence closure models as well as direct numerical simulation (DNS). In addition, the statistical (pdf) approach in deriving the dispersed-phase transport equations is discussed. The review is restricted to incompressible, isothermal flows without phase change or particle-particle collision. Suggestions are made for improving closure modelling of some important correlations.Lecture presented at a workshop on turbulence in particulate multiphase flow, Fluid Dynamics Laboratory, Battelle Pacific Northwest Laboratory, Richland, WA, March 22–23, 1993.     

Critical Reynolds number in plasma flows on a stabilized plasmatron section

A technique for determining the criterion of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The technique uses experimental data and the methods of numerical simulation of plasma flows. A criterial generalization of the experimental data which for the first time makes it possible to establish the boundary of transition from the laminar to the turbulent flow regime on a stabilized plasmatron channel section is proposed. The experimental results are in good agreement with the theoretical dependences derived in the study. A curve (analog of the neutral curve) separating the domains of existence of laminar and turbulent plasma flows in a cylindrical channel is constructed in the space of the plasmatron working parameters.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 49–61. Original Russian Text Copyright © 2004 by Sinkevich and Chikunov.