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Annual Review of Fluid Mechanics top

► Space-Time Correlations and Dynamic Coupling in Turbulent Flows
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 51-70, January 2017.
► Combustion and Engine-Core Noise
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 277-310, January 2017.
► Uncertainty Quantification in Aeroelasticity
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 361-386, January 2017.
► Simulation Methods for Particulate Flows and Concentrated Suspensions
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 171-193, January 2017.
► Model Reduction for Flow Analysis and Control
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 387-417, January 2017.
► Vapor Bubbles
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 221-248, January 2017.
► Saph and Schoder and the Friction Law of Blasius
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 575-582, January 2017.
► Recent Developments in the Fluid Dynamics of Tropical Cyclones
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 541-574, January 2017.
► Inflow Turbulence Generation Methods
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 23-49, January 2017.
► Blood Flow in the Microcirculation
    5 Jan, 2017
Annual Review of Fluid Mechanics, Volume 49, Issue 1, Page 443-461, January 2017.

Computers & Fluids top

► Source term based synthetic turbulence inflow generator for eddy-resolving predictions of an airfoil flow including a laminar separation bubble
  23 Mar, 2017
Publication date: 26 March 2017
Source:Computers & Fluids, Volume 146
Author(s): S. Schmidt, M. Breuer
The present paper addresses the issue of the strong dependency of eddy-resolving simulations for turbulent flows on the employed inflow conditions. Thus, the objective of this study is to analyze the influence of the inflow conditions on the external wall-bounded flow past the SD7003 airfoil and more precisely on the form and size of the laminar separation bubble. Motivated by the typically coarse resolution of the inlet region of the computational domain used for hybrid simulations, the synthetic turbulence is introduced within the flow field by a flexible source term treatment. The generated turbulent fluctuations are taken into account in the momentum equation by source terms and hence allow a shift from the inlet to a finer resolved region, where the damping of small structures due to the grid resolution is negligible. To provide a proper formulation of a synthetic turbulence inflow generator (STIG), the digital filter concept of Klein et al. (J. Comp. Phys. 186, 652–665, 2003) is merged with a large-eddy simulation (LES) as well as a hybrid LES-URANS method. The synthetically generated velocity fluctuations are distributed in an area of influence which is in accordance with the digital filter concept of the STIG. An automatic calculation of the dimension of the influence region is ensured by the employment of the integral scales which are used during the generation of the synthetic turbulence inflow generator inflow. The definition of the required input quantities for the STIG in case of the flow past a SD7003 airfoil at Rec=60,000 and an angle of attack α=4 are based on experimental data including a turbulence intensity of TI = 0.28%. Due to separation, transition and subsequent reattachment this is a demanding test case in which the shape and the size of the separation bubble strongly depends on the oncoming turbulence. The reference velocity profiles of the experimental measurements are compared with a wall-resolved LES and hybrid simulations performed on two grids with a coarser resolution. The evaluation of the results of the simulations applying the STIG and without turbulence intensity showed an improved level of agreement between the STIG based simulations and the experiment. Moreover, the turbulence intensity is varied to understand the behavior of the LSB in more detail.

► Suspension-Dr Iven Gravity Surges On Horizontal Surfaces: Effect Of The Initial Shape
  23 Mar, 2017
Publication date: Available online 18 March 2017
Source:Computers & Fluids
Author(s): N. Zgheib, T. Bonometti, S. Balachandar
We present results from highly resolved direct numerical simulations of canonical (axisymmetric and planar) and non-canonical (rectangular) configurations of horizontal suspension-driven gravity surges. We show that the dynamics along the initial minor and major axis of a rectangular release are roughly similar to that of a planar and axisymmetric current, respectively. However, contrary to expectation, we observe under certain conditions the final extent of the deposit from finite releases to surpass that from an equivalent planar current. This is attributed to a converging flow of the particle-laden mixture towards the initial minor axis, a behaviour that was previously reported for scalar-driven currents on uniform slopes (Zgheib et al. 2016). This flow is observed to be correlated with the travelling of a perturbation wave generated at the extremity of the longest side that reaches the front of the shortest side in a finite time. A semi-empirical explicit expression (based on established relations for planar and axisymmetric currents) is proposed to predict the extent of the deposit in the entire x-y plane. Finally, we observe that for the same initial volume of a suspension-driven gravity surge, a release of larger initial horizontal aspect-ratio is able to retain particles in suspension for longer periods of time.

► Numerical simulation of a vertical axis wind turbine airfoil experiencing dynamic stall at high Reynolds numbers
  23 Mar, 2017
Publication date: 13 June 2017
Source:Computers & Fluids, Volume 149
Author(s): Brian Hand, Ger Kelly, Andrew Cashman
Multi-megawatt floating vertical axis wind turbines (VAWTs) are a promising solution to exploit offshore wind energy resources in deep water sites. At this large-scale, the VAWT’s blades will operate at high Reynolds numbers and encounter dynamic stall at low tip-speed ratios. In particular, the selection of an accurate turbulence modeling approach is still a challenging undertaking in the prediction of transient blade forces during this complex unsteady event.In the present paper, the performance of Unsteady Reynolds-Averaged Navier–Stokes (U-RANS) and Detached Eddy Simulation (DES) modeling methods are compared in simulating the aerodynamics of an isolated NACA0018 airfoil experiencing Darrieus pitching motion. The U-RANS turbulence models employed were the Spalart–Allmaras (S-A) model and the kω SST model. Investigations were conducted to ensure satisfactory independency of the solution for both spatial and temporal discretisations, respectively.A quantitative assessment identified the S-A model as the most applicable for a VAWT design study as it showed the most desirable compromise between model fidelity and computational requirement. A qualitative analysis revealed that the thick VAWT airfoil creates a dynamic stall vortex topology highly concentrated at the trailing edge region.Finally, increasing the Reynolds number showed to be beneficial to the airfoil’s aerodynamic performance as a higher maximum tangential coefficient is attained, owing to the delay in flow separation to much higher angles of attack.

► Direct numerical simulations of the flow around wings with spanwise waviness at a very low Reynolds number
  23 Mar, 2017
Publication date: 26 March 2017
Source:Computers & Fluids, Volume 146
Author(s): D. Serson, J.R. Meneghini, S.J. Sherwin
Inspired by the pectoral flippers of the humpback whale, the use of spanwise waviness in the leading edge has been considered in the literature as a possible way of improving the aerodynamic performance of wings. In this paper, we present an investigation based on direct numerical simulations of the flow around infinite wavy wings with a NACA0012 profile, at a Reynolds number Re=1000. The simulations were carried out using the Spectral/hp Element Method, with a coordinate system transformation employed to treat the waviness of the wing. Several combinations of wavelength and amplitude were considered, showing that for this value of Re the waviness leads to a reduction in the lift-to-drag ratio (L/D), associated with a suppression of the fluctuating lift coefficient. These changes are associated with a regime where the flow remains attached behind the peaks of the leading edge while there are distinct regions of flow separation behind the troughs, and a physical mechanism explaining this behaviour is proposed.

► Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects
  23 Mar, 2017
Publication date: 13 June 2017
Source:Computers & Fluids, Volume 149
Author(s): Fulin Tong, Changping Yu, Zhigong Tang, Xinliang Li
Direct numerical simulations (DNS) were performed to investigate the interactions of a Mach 2.9 turbulent boundary layer with shock waves of varying strengths in compression corner. The supersonic turbulent boundary layer was triggered by wall blowing-and-suction perturbations. The shock waves were produced by two-dimensional compression corners of 8, 14, 20 and 24°. Compared with previous DNS results and experimental data, the numerical calculations were validated. The effects of shock wave on the boundary layer are studied by both flow visualizations and statistical analysis, and the results show that the intensity of fluctuations is amplified greatly by the shock wave. With the increasing of turning angle, three-dimensionality of separation bubble is significantly enhanced. Based on the statistics and power spectrum of the wall pressure signals, the effect of turning angle on the unsteadiness of shock motion is also studied, and the results show that the shock motions are quite different in the small and the large turning angle cases. The motion in the 8° and 14° cases is characterized by high-frequency and small-amplitude, but the low-frequency and large-scale streamwise oscillation is the main feature in the 20° and 24° cases. The effect of turning angle on the turbulence state is analyzed by using the anisotropy of Reynolds stress tensor. The coherent vortex structures are also studied qualitatively. The results indicate that the cane-like streamwise vortexes in the near-wall region are the dominant structure for the small angle cases, while the hairpin vortexes and packets in the outer layer play the leading role in the large angle cases. According to the quantitative analysis of turbulent kinetic energy budgets in the separation region, the effect of turning angle on the transport mechanism is studied. It is found that the influence of shear layer above separation bubble on the mechanism is significant.

► Algorithm for analysis of peristaltic annular flows
  23 Mar, 2017
Publication date: 2 April 2017
Source:Computers & Fluids, Volume 147
Author(s): H.V. Moradi, S. Zandi, J.M. Floryan
A spectrally accurate algorithm suitable for the analysis of peristaltic flows in annular geometries has been developed. The bounding surfaces have cylindrical forms modified by axisymmetric waves of arbitrary form traveling in the axial direction. The problem is expressed as a superposition of the flow in a smooth annulus and modifications associated with the surface waves. The Galileo transformation has been used to convert the unsteady physical problem into a steady problem in the frame of reference moving with the wave. The Stokes stream function has been used to reduce the number of field equations to a single fourth-order partial differential equation. Numerical discretization uses Fourier expansions in the streamwise direction and Chebyshev expansions in the radial direction. Difficulties associated with the irregularities of the boundaries have been overcome using the immersed boundary conditions method (IBC). Various numerical tests have been carried out in order to verify the spectral accuracy of the proposed algorithm. Analytical solutions for the long wavelength waves as well as for the waves with small amplitudes have been used to verify the algorithm. It has been shown that the leading-order approximation for the long wavelength waves provides sufficiently accurate results for wavelengths longer than 10π. It has also been demonstrated that the changes in the mean axial pressure gradient vary proportionally to the second power of the wave amplitude S2 for waves with small enough amplitudes.

► Advanced parallelization strategies using hybrid MPI-CUDA octree DSMC method for modeling flow through porous media
  23 Mar, 2017
Publication date: 13 June 2017
Source:Computers & Fluids, Volume 149
Author(s): Revathi Jambunathan, Deborah A. Levin
The advantages of a linear space filling Morton Z-curve to represent an unbalanced three-dimensional octree structure for the Direct Simulation Monte Carlo method are assessed. The strategies to optimize and exploit the properties of the linearized tree using simple, binary computations are presented. Hybrid MPI-CUDA communications are invoked to facilitate the use of heterogeneous architectures for large-scale computations. Strong scaling studies have shown that the parallelization strategies implemented in this work results in 85% efficiency, and weak scaling studies show nearly 100% efficiency for a problem size with 0.34 billion particles and 1.5 million immersed body surface elements. Two types of problems, supersonic external flow over fractal-like immersed body and subsonic internal flow through a porous material are solved using the multi-GPU DSMC solver. The permeability of Morgan carbon felt material is calculated by modeling the diffusion of argon gas through the material and the calculated continuum permeability values match well with published data.

► RAMS sensitivity to grid spacing and grid aspect ratio in Large-Eddy Simulations of the dry neutral Atmospheric Boundary Layer
  23 Mar, 2017
Publication date: 26 March 2017
Source:Computers & Fluids, Volume 146
Author(s): G. Ercolani, C. Gorlé, C. Corbari, M. Mancini
Large Eddy Simulation (LES) is being established as a commonplace modeling tool in many areas of research interested in reproducing Atmospheric Boundary Layer (ABL) turbulence. LES results can however be highly dependent on the combination of the numerical schemes, subgrid scale model and computational grid, and their impact on simulations should be examined. The present work focuses on assessing the impact of grid spacing on LES of an idealized neutral ABL realized with the Regional Atmospheric Modeling System (RAMS), a commonly employed mesoscale model. To this aim, nine simulations with varying grid resolutions and otherwise identical setups have been performed. The grids are obtained combining three different horizontal (64, 32, 16 m) and vertical (16, 8, 4 m) spacings, covering a domain of 4096 × 4096 × 1024 m. Results are post-processed in terms of mean profiles of momentum flux, horizontal velocity and velocity variances, as well as velocity spectra and instantaneous snapshots of velocity fields. The analysis reveals that the turbulent flow can be simulated satisfactorily by employing a computational grid with a sufficiently fine horizontal spacing and an aspect ratio that alleviates potential adverse effects of the combination of RAMS numerics and subgrid model on the solution. Based on the present results, a horizontal spacing smaller than around 30 m is suggested for the examined regime, and an aspect ratio of 4 is recommended, while both larger and smaller values should be avoided. When using different aspect ratios RAMS LESs of the neutral ABL were found to be affected by an excessive dissipation of turbulence kinetic energy.

► Accuracy preserving limiter for the high-order finite volume method on unstructured grids
  23 Mar, 2017
Publication date: 13 June 2017
Source:Computers & Fluids, Volume 149
Author(s): Yilang Liu, Weiwei Zhang
This paper proposes a distance weighted biased averaging procedure (DWBAP) and applies it to the high-order finite volume method on unstructured grids. Unlike the initial BAP limiter, we use the inverse distance weighting for biased function of the derivatives of flow variables, and meanwhile introduce the standard deviation coefficient of the reconstruction stencil to determine the value of the distance weighting. This can efficiently maintain both the property of high precision in smooth regions and control numerical oscillations in discontinuities. Through various numerical examples, it is demonstrated that the developed DWBAP limiter can capture strong shock waves and have a good property of convergence.

► A dynamic delayed detached-eddy simulation model for turbulent flows
  23 Mar, 2017
Publication date: 26 March 2017
Source:Computers & Fluids, Volume 146
Author(s): Chuangxin He, Yingzheng Liu, Savas Yavuzkurt
The current study developed a new dynamic delayed detached-eddy simulation (dynamic DDES) model based on the k-ω SST model and the well-established dynamic k-equation subgrid-scale model. Instead of using a constant model coefficient CDES in traditional DES formulations, the present model employs two coefficients Ck and Ce, which are computed dynamically by taking into account the spatial and temporal variations of the flow field at the grid and test filter levels. A modification on shielding function fd is proposed, with a spatial uniformization operator imposed on the velocity gradient to obtain a smooth and monotonous hybrid interface. A damping function φd is introduced based on the local grid resolution and flow condition to damp the Reynolds-averaged Navier–Stokes (RANS) region and achieve wall-modeled LES (WMLES) mode dynamically. The test of the model in developed channel flow shows the log-layer mismatch (LLM) problem is significantly improved with respect to the dynamic LES model and original DDES model. The use of the spatial uniformization operator and the damping function convincingly demonstrates the improvement in prediction of separated flows, with the model coefficients dynamically computed. The LES region is maximized at the limit of grid resolution and more turbulent vortical structures are resolved. The test in the ribbed channel flow shows the present model has considerably better performance in prediction of the mean and turbulence velocity in the strong shear layer and the recirculation bubble. In addition, the simulation of impinging jet shows the model exhibits rapid switching from the RANS to LES under the flow instabilities when the inflow does not include turbulence content.

International Journal of Computational Fluid Dynamics top

► Modernization and optimization of a legacy open-source CFD code for high-performance computing architectures
  21 Mar, 2017
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► Execution of a parallel edge-based Navier–Stokes solver on commodity graphics processor units
  10 Mar, 2017
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► A dynamic framework for functional parameterisations of the eddy viscosity coefficient in two-dimensional turbulence
  16 Feb, 2017
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► The influence of magnetic field on the physical explosion of a heavy gas cloud
    8 Feb, 2017
Volume 31, Issue 1, January 2017, Page 21-35
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► A hybrid approach for nonlinear computational aeroacoustics predictions
  10 Jan, 2017
Volume 31, Issue 1, January 2017, Page 1-20
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► Comparative studies of numerical methods for evaluating aerodynamic characteristics of two-dimensional airfoil at low Reynolds numbers
    5 Jan, 2017
Volume 31, Issue 1, January 2017, Page 57-67
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► GPU accelerated simulations of three-dimensional flow of power-law fluids in a driven cube
    4 Jan, 2017
Volume 31, Issue 1, January 2017, Page 36-56
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► Erratum
  20 Dec, 2016
Volume 31, Issue 1, January 2017, Page x-x
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► Erratum
  18 Aug, 2014
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International Journal for Numerical Methods in Fluids top

► On numerical aspects of simulating flow past a circular cylinder
  23 Mar, 2017

Abstract

Three-dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set-up, which restricts the development of intrinsic wake structure, leads to an over-prediction of the onset point of the secondary wake instability (Recr). A best practice of the numerical set-up is presented for the accurate prediction of Recr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Recr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set-up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Recr, while the periodic boundary condition is recommended for simulating the wake structures above Recr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.

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This paper presents a best practice on the choices of the lateral boundary condition and cylinder span length for the prediction of the critical Reynolds number and wake transition of flow past a circular cylinder. A systematic comparison between the periodic and symmetry lateral boundary conditions is presented. The general conclusions are expected to be applicable to other bluff body configurations.

► On Stabilized Space-Time FEM for Anisotropic Meshes: II. Incompressible Navier-Stokes Equations and Applications to Blood Flow in Medical Devices
  22 Mar, 2017

Summary

In complex applications, such as the analysis of hydraulic performance of blood pumps (ventricular assist devices or VADs), the Navier-Stokes equations have to be discretized on very anisotropic meshes. If stabilized finite element formulations are applied, standard definitions of the stabilization parameter are usually not appropriate to handle elements with a high aspect ratio. If, in addition, rotating objects, moving meshes or turbulence has to be considered in the simulation, further modifications of the stabilization procedure have to be applied.

In this paper, we present stabilized space-time finite element formulations of the incompressible Navier-Stokes equations that show very good convergence properties on complex anisotropic meshes and lead to reasonable numerical accuracy in complex flows when compared to experimental data. This article is protected by copyright. All rights reserved.

► Third-order WENO scheme with a new smoothness indicator
  22 Mar, 2017

Summary

In this article, we have devised a new reference smoothness indicator for third-order weighted essentially non-oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non-oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third-order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three-point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third-order WENO schemes like WENO-JS and WENO-Z. Copyright © 2017 John Wiley & Sons, Ltd.

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In this article, we have devised a new reference smoothness indicator for third-order weighted essentially non-oscillatory (WENO) scheme to achieve desired order of convergence at critical points. This reference smoothness indicator constructed through the linear combination of first derivative information of the local and global spatial stencils. The performance enhancement of the WENO scheme (WENO-F3) through this reference smoothness indicator is verified by the standard numerical test cases. As shown in the figure, WENO-F3 scheme is efficient than WENO-JS and WENO-Z schemes.

► A new volume-preserving and continuous interface reconstruction method for 2D multi-material flow
  21 Mar, 2017

Summary

A new two-dimensional interface reconstruction method that ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first, the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a local correction phase. In each cell, the interface is made of two line segments joining two edges. This new interface reconstruction method, called Dynamic Programming Interface Reconstruction has been coupled with various advection schemes, among them the Lagrange + remap scheme. With a reasonable computational cost, it has been observed in various test cases that Dynamic Programming Interface Reconstruction is more accurate and less diffusive compared with other existing classical reconstruction methods. Copyright © 2017 John Wiley & Sons, Ltd.

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A new interface reconstruction method for two-dimensional multi-material flows, which ensures continuity of the interface and preserves volumic fractions, is presented here. It is based on the minimization of a cost functional by using dynamic programming, a fast algorithm often used in image segmentation. With a reasonable cost, it has been observed on various advection test cases that this new method, called Dynamic Programming Interface Reconstruction, is more accurate and less diffusive than other existing ones, as the Youngs method.

► Improvement of moving particle semi-implicit method for simulation of progressive water waves
  14 Mar, 2017

Summary

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi-implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2-D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.

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In this paper, an improved moving particle semi-implicit model is used to simulate the propagation of progressive waves. A combined pressure gradient model that is deduced from the Taylor series expansion is put forward as well as a new pressure detection method for free surface particles. With the modifications, the energy conservation in the wave propagation is enhanced well and the wave damping is effectively reduced.

► Issue Information
  13 Mar, 2017

No abstract is available for this article.

► Development of the Generalized MacCormack scheme and its extension to low Mach number flows
  11 Mar, 2017

Summary

The low Mach number performance of the MacCormack scheme is examined. The inherent dissipation in the scheme is found to suffer from the degradation in accuracy observed with traditional, density-based methods for compressible flows. Two specific modifications are proposed, leading to the formation of the Generalized MacCormack Scheme within a dual-time framework (called GMC-PC). The first modification involves reformulating the flux by splitting it into particle convection and acoustic parts, with the former terms treated using the traditional MacCormack discretization and the latter terms augmented by the addition of a pressure-based artificial dissipation. The second modification involves a reformulation of the traditional non-linear fix introduced by MacCormack in 1971, which is found to be necessary to suppress pressure oscillations at low Mach numbers. The new scheme is demonstrated to have superior performance, independent of Mach number, compared to standard MacCormack implementations using several canonical test problems. This article is protected by copyright. All rights reserved.

► Damping numerical oscillations in hybrid solvers through detection of Gibbs phenomenon
  10 Mar, 2017

Summary

A Gibbs phenomenon detector that is useful in damping numerical oscillations in hybrid solvers for compressible turbulence is proposed and tested. It is designed to function in regions away from discontinuities where commonly used discontinuity sensors are ineffective. Using this Gibbs phenomenon detector in addition to a discontinuity sensor for combining central and shock capturing schemes provides an integrated way of dealing with numerical oscillations generated by shock waves and contact lines that are normal to the flow. When complete suppression of numerical oscillations is not possible, they are sufficiently localized. Canonical tests and large eddy simulations show that inclusion of the proposed detector does not cause additional damping of ‘well-resolved’ physical oscillations. Copyright © 2017 John Wiley & Sons, Ltd.

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The switching between central and dissipative flux splitting schemes in hybrid solvers based on discontinuity sensors may lead to Gibbs phenomenon characterized by two-point numerical oscillations. Such oscillations may grow and contaminate the solution severely in some cases. A way to detect such oscillations and adjust the hybridization procedure as needed is proposed to remove such oscillations. In some cases, the adjustment prevents the formation of such oscillations, while in others, they are sufficiently localized near discontinuities where they originate.

► Development of circular function-based gas-kinetic scheme (CGKS) on moving grids for unsteady flows through oscillating cascades
    8 Mar, 2017

Abstract

In this paper, the circular function-based gas-kinetic scheme (CGKS), which was originally developed for simulation of flows on stationary grids, is extended to solve moving boundary problems on moving grids. Particularly, the unsteady flows through oscillating cascades are our major interests. The main idea of the CGKS is to discretize the macroscopic equations by the finite volume method while the fluxes at the cell interface are evaluated by locally reconstructing the solution of the continuous Boltzmann Bhatnagar–Gross–Krook equation. The present solver is based on the fact that the modified Boltzmann equation, which is expressed in a moving frame of reference, can recover the corresponding macroscopic equations with Chapman–Enskog expansion analysis. Different from the original Maxwellian function-based gas-kinetic scheme, in improving the computational efficiency, a simple circular function is used to describe the equilibrium state of distribution function. Considering that the concerned cascade oscillating problems belong to cases that the motion of surface boundary is known a priori, the dynamic mesh method is suitable and is adopted in the present work. In achieving the mesh deformation with high quality and efficiency, a hybrid dynamic mesh method named radial basic functions-transfinite interpolation is presented and applied for cascade geometries. For validation, several numerical test cases involving a wide range are investigated. Numerical results show that the developed CGKS on moving grids is well applied for cascade oscillating flows. And for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved by using the present method. Copyright © 2017 John Wiley & Sons, Ltd.

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A recently developed circular function-based gas-kinetic scheme is extended into a version on moving grids for simulation of oscillation cascade problems. Because the dynamic mesh method is used to treat boundary movement, an efficient hybrid dynamic mesh method named radial basic functions-transfinite interpolation is presented and applied for cascade geometries. Numerical results prove that the developed circular function-based gas-kinetic scheme on moving grids is well applied, and for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved.

► A finite volume scheme for solving anisotropic diffusion on ALE-AMR grids
    6 Mar, 2017

Summary

In the context of High Energy Density Physics and more precisely in the field of laser plasma interaction, Lagrangian schemes are commonly used. The lack of robustness due to strong grid deformations requires the regularization of the mesh through the use of Arbitrary Lagrangian Eulerian methods. Theses methods usually add some diffusion and a loss of precision is observed. We propose to use Adaptive Mesh Refinement (AMR) techniques to reduce this loss of accuracy. This work focuses on the resolution of the anisotropic diffusion operator on Arbitrary Lagrangian Eulerian-AMR grids.

In this paper, we describe a second-order accurate cell-centered finite volume method for solving anisotropic diffusion on AMR type grids. The scheme described here is based on local flux approximation which can be derived through the use of a finite difference approximation, leading to the CCLADNS scheme. We present here the 2D and 3D extension of the CCLADNS scheme to AMR meshes. Copyright © 2017 John Wiley & Sons, Ltd.

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We are interested here in the resolution of anisotropic diffusion on non-conformal non-orthogonal 2D and 3D meshes. The numerical scheme used here is an extension of the Cell-Centered Lagrangian Diffusion CCLAD scheme, the Non-Symmetric version of this diffusion scheme the CCLADNS scheme. The figure presented here corresponds to the isotropic linear solution of a diffusion problem on a randomly perturbed 3D AMR grid. Machine precision is reached with CCLADNS scheme.

Journal of Computational Physics top

► Second-order discretization in space and time for radiation-hydrodynamics
  23 Mar, 2017
Publication date: 1 June 2017
Source:Journal of Computational Physics, Volume 338
Author(s): Simon Bolding, Joshua Hansel, Jarrod D. Edwards, Jim E. Morel, Robert B. Lowrie
Second-order accurate discretizations for radiation-hydrodynamics are currently an area of interest in the high energy density laboratory physics and astrophysics communities. Second-order methods used to solve the hydrodynamics equations and second-order methods used to solve the radiation transport equation often differ fundamentally, making it difficult to combine them in a second-order manner. Here, we present an implicit–explicit (IMEX) method for solving the 1D equations of radiation-hydrodynamics that is second-order accurate in space and time. Our radiation-hydrodynamics model consists of the 1D Euler equations coupled with a gray radiation S2 approximation. Our RH method combines the MUSCL-Hancock method for solving the Euler equations with the TR/BDF2 time integration scheme and the linear-discontinuous Galerkin finite-element spatial discretization scheme for the S2 radiation equations. The MUSCL-Hancock method is commonly used for hydrodynamic calculations and the linear-discontinuous Galerkin scheme is the standard for the Sn equations of radiative transfer. While somewhat similar, these schemes vary fundamentally with respect to the treatment of spatial slopes. We address the challenges inherent to coupling these different numerical methods and demonstrate how these challenges can be overcome. Using the method of manufactured solutions, we show that the method is second-order accurate in space and time for both the equilibrium diffusion and streaming limit, and we show that the method is capable of computing radiative shock solutions accurately by comparing our results with semi-analytic solutions.

► Extrapolation-based implicit–explicit Peer methods with optimised stability regions
  23 Mar, 2017
Publication date: 15 May 2017
Source:Journal of Computational Physics, Volume 337
Author(s): Jens Lang, Willem Hundsdorfer
In this paper we investigate a new class of implicit–explicit (IMEX) two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach based on already computed stage values is applied to construct IMEX methods with favourable stability properties. Optimised IMEX-Peer methods of order p=2,3,4, are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other implicit–explicit methods are included.

► The boundary-constraint method for constructing vortex-surface fields
  23 Mar, 2017
Publication date: 15 June 2017
Source:Journal of Computational Physics, Volume 339
Author(s): Shiying Xiong, Yue Yang
We develop a boundary-constraint method for constructing the vortex-surface field (VSF) in a three-dimensional fluid velocity–vorticity field. The isosurface of the VSF is a vortex surface consisting of vortex lines, which can be used to characterize the evolution of vortical structures in a Lagrangian sense. The evolution equation with pseudo-time is solved under the VSF boundary constraint to obtain a numerical solution of the VSF. Compared with the existing two-time method, the boundary-constraint method constructs the VSF from a single velocity dataset at a given time instead of a time series of velocity fields starting from a simple condition. This improvement significantly increases the applicability of the VSF method and reduces the demanding computational cost and required velocity data size. Using the boundary-constraint method, we construct the VSFs in Taylor–Green flow and transitional channel flow. In addition, the uniqueness of the VSF solution is discussed and the convergence of the error in the calculation of VSFs is analyzed.

► Adaptive fast interface tracking methods
  23 Mar, 2017
Publication date: 15 May 2017
Source:Journal of Computational Physics, Volume 337
Author(s): Jelena Popovic, Olof Runborg
In this paper, we present a fast time adaptive numerical method for interface tracking. The method uses an explicit multiresolution description of the interface, which is represented by wavelet vectors that correspond to the details of the interface on different scale levels. The complexity of standard numerical methods for interface tracking, where the interface is described by N marker points, is O(N/Δt), when a time step Δt is used. The methods that we propose in this paper have O(tol1/plogN+NlogN) computational cost, at least for uniformly smooth problems, where tol is some given tolerance and p is the order of the time stepping method that is used for time advection of the interface. The adaptive method is robust in the sense that it can handle problems with both smooth and piecewise smooth interfaces (e.g. interfaces with corners) while keeping a low computational cost. We show numerical examples that verify these properties.

► A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
  23 Mar, 2017
Publication date: 15 June 2017
Source:Journal of Computational Physics, Volume 339
Author(s): Daniel P. Garrick, Mark Owkes, Jonathan D. Regele
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

► A fast iterative scheme for the linearized Boltzmann equation
  23 Mar, 2017
Publication date: 1 June 2017
Source:Journal of Computational Physics, Volume 338
Author(s): Lei Wu, Jun Zhang, Haihu Liu, Yonghao Zhang, Jason M. Reese
Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L=(L+Nδh)Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier–Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne–Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard–Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

► Lagrangian transported MDF methods for compressible high speed flows
  23 Mar, 2017
Publication date: 15 June 2017
Source:Journal of Computational Physics, Volume 339
Author(s): Peter Gerlinger
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier–Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).

► Gradient recovery for elliptic interface problem: II. Immersed finite element methods
  23 Mar, 2017
Publication date: 1 June 2017
Source:Journal of Computational Physics, Volume 338
Author(s): Hailong Guo, Xu Yang
This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work Guo and Yang (2016) [17], we developed a novel gradient recovery technique for finite element method based on the body-fitted mesh. In this paper, we propose new gradient recovery methods for two immersed interface finite element methods: symmetric and consistent immersed finite method (Ji et al. (2014) [23]) and Petrov–Galerkin immersed finite element method (Hou et al. (2004) [22], and Hou and Liu (2005) [20]). Compared to the body-fitted mesh based gradient recovery method, the new methods provide a uniform way of recovering gradient on regular meshes. Numerical examples are presented to confirm the superconvergence of both gradient recovery methods. Moreover, they provide asymptotically exact a posteriori error estimators for both immersed finite element methods.

► Prediction of discretization error using the error transport equation
  23 Mar, 2017
Publication date: 15 June 2017
Source:Journal of Computational Physics, Volume 339
Author(s): Ismail B. Celik, Don Roscoe Parsons
This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier–Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the ‘true error’. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

► Multiscale modeling of nonlinear electric conductivity in graphene-reinforced nanocomposites taking into account tunnelling effect
  23 Mar, 2017
Publication date: 15 May 2017
Source:Journal of Computational Physics, Volume 337
Author(s): Xiaoxin Lu, Julien Yvonnet, Fabrice Detrez, Jinbo Bai
Tunnelling effect is a possible mechanism to explain the apparent large electric conductivity and nonlinear electric behavior of graphene-reinforced nanocomposites with polymer matrix. In this work, a numerical modeling framework is proposed to evaluate the effective electric conductivity in polymer composites reinforced with graphene sheets, taking into account the electrical tunnelling effect, which allows conduction between graphene sheets at nanometric distances. We introduce a nonlinear Finite Element formulation and a numerical methodology to model the nonlocal and nonlinear effects introduced by the tunnelling effect conduction model within the polymer matrix between close graphene sheets. In addition, to avoid meshing the thickness of the graphene sheets and in view of their very high aspect ratio, a highly conducting surface model is employed. The computed effective conductivity is evaluated over representative volume elements containing arbitrary distributed graphene sheets. The results exhibit tendencies and percolation thresholds which are in qualitative agreement with the available experimental results.

Journal of Turbulence top

► Turbulent structures in an optimal Taylor–Couette flow between concentric counter-rotating cylinders
  22 Mar, 2017
Volume 18, Issue 5, May 2017, Page 480-496
.
► Turbulence structures in high-speed air flow along a thin cylinder
    8 Mar, 2017
.
► Streak instability in near-wall turbulence revisited
    2 Mar, 2017
Volume 18, Issue 5, May 2017, Page 443-464
.
► Analogue of the Cole-Hopf transform for the incompressible Navier–Stokes equations and its application
    2 Mar, 2017
Volume 18, Issue 5, May 2017, Page 465-479
.
► Prandtl number effects in decaying homogeneous isotropic turbulence with a mean scalar gradient
    1 Mar, 2017
Volume 18, Issue 5, May 2017, Page 418-442
.
► Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model
  23 Feb, 2017
Volume 18, Issue 5, May 2017, Page 391-417
.

Physics of Fluids top

► Fluid-structure interaction of a rolling restrained body of revolution at high angles of attack
  22 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Publisher’s Note: “Mechanism of gas saturated oil viscosity anomaly near to phase transition point” [Phys. Fluids 29, 012106 (2017)]
  22 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Manipulation of three-dimensional Richtmyer-Meshkov instability by initial interfacial principal curvatures
  20 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Smoothed particle hydrodynamics method from a large eddy simulation perspective
  20 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Developing a fast and tunable micro-mixer using induced vortices around a conductive flexible link
  17 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Energy transfer and motion synchronization between mechanical oscillators through microhydrodynamic coupling
  17 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Dynamic interference of two anti-phase flapping foils in side-by-side arrangement in an incompressible flow
  17 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Effect of interfacial slip on the deformation of a viscoelastic drop in uniaxial extensional flow field
  16 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Rarefied gas flow in converging microchannel in slip and early transition regimes
  16 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.
► Theoretical analysis and simulation of obstructed breakup of micro-droplet in T-junction under an asymmetric pressure difference
  16 Mar, 2017
Physics of Fluids, Volume 29, Issue 3, March 2017.

Theoretical and Computational Fluid Dynamics top

► Numerical investigation of mixed convection heat transfer from two isothermal circular cylinders in tandem arrangement: buoyancy, spacing ratio, and confinement effects
    1 Apr, 2017

Abstract

This paper presents a two-dimensional numerical study for mixed convection in a laminar cross-flow with a pair of stationary equal-sized isothermal cylinders in tandem arrangement confined in a channel. The governing equations are solved using the control volume method on a nonuniform orthogonal Cartesian grid, and the immersed boundary method is employed to identify the cylinders placed in the flow field. The numerical scheme is first validated against standard cases of symmetrically confined isothermal circular cylinders in plane channels, and grid convergence tests were also examined. The objective of the present study was to investigate the influence of buoyancy and the blockage ratio constraint on the flow and heat transfer characteristics of the immersed cylinder array. Using a fixed Reynolds number based on cylinder diameter of \(Re_{D} = 200\) , a fixed value of the Prandtl number of \(Pr = 7\) , and a blockage ratio of \(D/H = 0.2\) , all possible flow regimes are considered by setting the longitudinal spacing ratio ( \(\sigma = L/D\) ) between the cylinder axes to 2, 3, and 5 for values of the buoyancy parameter (Richardson number) in the range \(-1\le Ri\le 4\) . The interference effects and complex flow features are presented in the form of mean and instantaneous velocity, vorticity, and temperature distributions. The results demonstrate how the buoyancy, spacing ratio, and wall confinement affect the wake structure and vortex dynamics. In addition, local and average heat transfer characteristics of both cylinders are comprehensively presented for a wide range in the parametric space.

► Ground effects on separated laminar flows past an inclined flat plate
    1 Apr, 2017

Abstract

The appearance of a ground surface can play an important role in the flow structures for the flows past a flat plate. We conduct two-dimensional numerical simulations on viscous flows past a flat plate inclined at an angle of attack of \(20^\circ \) with ground effects using a finite-volume method. Results show that the effects on the separated flow from the ground are highly dependent on the gap (G) between the plate and the ground. As the gap decreases, the strength of vortices generated from the trailing edge is restrained, which is consistent with experimental observations. Further decrease in the gap even eliminates the vortex shedding and yields a steady flow. It is also found that the flow between the gap can either be accelerated at large gap ratios ( \({G/L >1}\) , G is the gap, L is the plate length), or be decelerated at small gap ratios ( \({G/L <1}\) ). Furthermore, the numerical results show that the wake flow behind the plate can significantly change the distribution of surface shear stress on the ground. Specifically, the mean shear stress on the ground in the downstream region at a gap ratio \(G/L = 2.0\) is one order of magnitude larger than that at a small gap ratio \(G/L = 0.3\) , and the length of the downstream region where the shear stress can be effectively changed is much larger than the plate length, which provides a guideline to manipulate the ground wall surface shear stress using an inclined plate in the vicinity of the wall.

► Rigorous theory for transient capillary imbibition in channels of arbitrary cross section
    1 Apr, 2017

Abstract

This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon.

► Effective slip for flow through a channel bounded by lubricant-impregnated grooved surfaces
    1 Apr, 2017

Abstract

This study aims to investigate effective slip arising from pressure-driven flow through a slit channel bounded by lubricant-impregnated grooved surfaces. The problem for flow over longitudinal grooves is solved analytically using the methods of domain decomposition and eigenfunction expansion, while that for flow over transverse grooves is solved numerically using the front tracking method. It is found that the effective slip length and the lubricant flow rate can depend strongly on the geometry of the microstructure, the direction of flow, and the lubricant viscosity. In particular, the effective slip can be effectively enhanced by increasing the thickness of a lubricating film atop the ribs. Under the same conditions, a flow that is parallel to the lubricant-impregnated grooves will have a larger effective slip, but also a larger lubricant flow rate, when compared with the case of flow normal to the grooves. It is also shown that, in the case of transverse grooves, because of the downward displacement of the interface between the working/lubricating fluids, the effective slip length and lubricant flow rate may vary non-monotonically with the groove depth.

► Influence of molecular diffusion on alignment of vector fields: Eulerian analysis
    1 Apr, 2017

Abstract

The effect of diffusive processes on the structure of passive vector and scalar gradient fields is investigated by analyzing the corresponding terms in the orientation and norm equations. Numerical simulation is used to solve the transport equations for both vectors in a two-dimensional, parameterized model flow. The study highlights the role of molecular diffusion in the vector orientation process and shows its subsequent action on the geometric features of vector fields.

► On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere
    1 Apr, 2017

Abstract

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier–Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

► Saddle point of attachment in jet–crossflow interaction
  15 Mar, 2017

Abstract

Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.

► Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers
    7 Mar, 2017

Abstract

Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases shows that they enable convergence toward solutions that are unstable to stationary and oscillatory disturbances, with either a single or multiple frequency content. Finally, comparisons with SFD are also performed, showing significant reduction in computer cost for complex flows by using the implicit multi-step MGM schemes.

► Formation and behavior of counter-rotating vortex rings
    2 Mar, 2017

Abstract

Concentric, counter-rotating vortex ring formation by transient jet ejection between concentric cylinders was studied numerically to determine the effects of cylinder gap ratio, \(\frac{\Delta R}{R}\) , and jet stroke length-to-gap ratio, \(\frac{L}{\Delta R}\) , on the evolution of the vorticity and the trajectories of the resulting axisymmetric vortex pair. The flow was simulated at a jet Reynolds number of 1000 (based on \(\Delta R\) and the jet velocity), \(\frac{L}{\Delta R} \) in the range 1–20, and \(\frac{\Delta R}{R}\) in the range 0.05–0.25. Five characteristic flow evolution patterns were observed and classified based on \(\frac{L}{\Delta R} \) and \(\frac{\Delta R}{R}\) . The results showed that the relative position, relative strength, and radii of the vortex rings during and soon after formation played a prominent role in the evolution of the trajectories of their vorticity centroids at the later time. The conditions on relative strength of the vortices necessary for them to travel together as a pair following formation were studied, and factors affecting differences in vortex circulation following formation were investigated. In addition to the characteristics of the primary vortices, the stopping vortices had a strong influence on the initial vortex configuration and effected the long-time flow evolution at low \(\frac{L}{\Delta R}\) and small \(\frac{\Delta R}{R}\) . For long \(\frac{L}{\Delta R} \) and small \(\frac{\Delta R}{R}\) , shedding of vorticity was sometimes observed and this shedding was related to the Kelvin–Benjamin variational principle of maximal energy for steadily translating vortex rings.

► Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe
    1 Mar, 2017

Abstract

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.


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