Direct Numerical Simulation Of Flow Research Articles

Modelling and direct numerical simulation of flow and solute dispersion in the spinal subarachnoid space

The motion of the cerebrospinal fluid in the spinal subarachnoid space, a slender annular canal surrounding the spinal cord, exhibits an oscillatory velocity component driven by the pressure oscillations induced by the cardiac and respiratory cycles. A time-averaged transport equation has been recently proposed for describing solute transport along the canal, circumventing the need to compute the concentration fluctuations resulting from this fast oscillatory motion. The accuracy and limitations of this time-averaged description are tested here by means of comparisons with results of direct numerical simulations spanning hundreds of oscillation cycles, as needed to generate significant dispersion of the solute. The comparisons between the numerical results and the predictions of the analytical model include velocity fields and quantifications of transient solute-dispersion events for selected values of the flow parameters and two different idealized, canonical geometries of the spinal canal. The comparisons clearly demonstrate the accuracy of the time-averaged description of the analytical model, which is seen to provide a good fidelity at a fraction of the computational cost involved in the direct numerical simulations. The variations of canal eccentricity along the spinal canal are found to play an important role in the dynamics of the solute transport, leading to the emergence of closed recirculating Lagrangian vortices that may hinder solute dispersion along the canal, as revealed by both direct numerical simulations and time-averaged results.

Direct numerical simulation of turbulent channel flow over random rough surfaces

Abstract

Three-dimensional flip-flopping flow around a pair of dual-stepped circular cylinders in a side-by-side arrangement

Three-dimensional direct numerical simulations of flow around a pair of dual-stepped circular cylinders in a side-by-side arrangement and a proximity interference region are presented. The dual-stepped cylinders consist of two coaxial cylinders with a larger-to-smaller diameter ratio of 2. The Reynolds number and the side-by-side gap ratio, based on the larger (smaller) diameter, are 200 (100) and 1 (3), respectively. Two flip-flopping flow regimes A and B are observed behind the dual-stepped cylinders, exhibiting temporal variations of hydrodynamic drag and lift force coefficients. The flow regime B is featured by the flip-flopping, higher vortex-shedding frequencies and greater flow instability than those in the flow regime A. Half-loop and direct connections of vortices take place frequently in the narrower wake, while the vortex reconnection and multiple connection predominate the wider wake. This suggests that the dual-stepped cylinder with the narrower wake behaves similarly to a single dual-stepped cylinder. The dynamic mode decomposition analysis reveals pitchfork and Hopf bifurcation (in-phase and anti-phase synchronization) modes in the larger cylinder wake, with the interaction of these bifurcations originating from the flip-flopping flow pattern. However, the pitchfork mode is not found in the smaller cylinder wake, suggesting that its flip-flopping flow behavior is not self-originated but triggered by the flip-flopping flow mechanism of the larger cylinder.

Extreme wall shear stress events in turbulent pipe flows: spatial characteristics of coherent motions

Abstract

DNS of secondary flows over oscillating low-pressure turbine using spectral/hp element method

This paper investigates the secondary vortex flows over an oscillating low-pressure turbine blade using a direct numerical simulation (DNS) method. The unsteady flow governing equations over the oscillating blade are discretized and solved using a spectral/hp element method. Themethodemploys high-degree piecewise polynomial basis functions which results in a very high-orderfinite element approach. The results show that the blade oscillation can significantly influence the transitional flow structure and the wake profile. It was observed that the separation point over vibrating T106A blades was delayed 4.71% compared to the stationary one at Re = 51,800. Moreover, in the oscillating case, the separated shear layers roll up, break down and shed from the trailing edge. However, the blade vibration imposes additional flow disturbances on the suction surface of the blade before leaving from the trailing edge. Momentum thickness calculations revealed that after flow separation point, the momentum thickness grows rapidly which is due to the inverse flow gradients which generate vortex flows in this area. It was concluded that the additional vortex generations due to the blade vibrations cause higher momentum thickness increment compared to the conventional stationary LPT blade.

CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images

Direct numerical simulations of flow on micro-computed tomography (micro-CT) images are extensively used in many disciplines of science and engineering. Recently, we have developed a pore-scale finite volume solver (PFVS) to directly solve for flow on micro-CT images and predict permeability of digital cores. The solver assigns a local conductivity to each voxel based on geometrical and topological constraints. The local conductivity term in PFVS is conventionally calculated by an iterative local scanning algorithm, where the number of iterations depends on the size of the largest flow channel. This can increase the computation time of PFVS significantly if the largest flow channel is reasonably large. In this paper, we apply convolutional neural networks (CNN) to predict local conductivity for each voxel, thus bypassing the iterative algorithm while also preserving the mass conservation in the system by still solving for flow using conventional methods. The network is trained to convert segmented binary images of rocks into a numerical map required for flow simulation by the use of paired image-to-image translation using a ResNet-Style architecture. Comparison of the generated and original coefficient maps shows that the average error is within 1% over the 3D pore geometries used in this study. Then, we compare the absolute permeability results obtained from the original PFVS and the CNN-PFVS and the errors are within 20% with the average of 13.8%. Machine learning improves the computation time significantly especially on the images with large domain size and flow channels. On the samples tested, the speedup factor is 10 times using CNN compared to iterative calculations.

Three-dimensional wake dynamics behind a tapered cylinder with large taper ratio

We have performed direct numerical simulations of flow past a tapered circular cylinder during the early transition to three dimensions for two successive taper ratios (TR) of 20 and 12.5. Our results indicate the random occurrence of vortex splits and dislocations as the topology of the shedding signature. In particular, we observe oblique cellular shedding with multiple spanwise patterns and oppositely oriented oblique cells in the shed structure. Unlike flow imposed shear, the vortex formation length becomes sensitive to the taper ratio, which removes oblique frequency waves noticed for lower shear rate. The local Strouhal frequency (Stz) at the higher TR case exhibits a decreasing trend with remarkably smaller finite jumps at the cell boundaries and is found close to uniform cylinder flow. The wavelet analysis reveals the narrowing of the spectrum at a lower TR. A higher TR case shows a distinctly regular and evenly spaced spectrum which does not reach the maximum Stz, making it a rare event. The present results show that tapering causes the appearance of a secondary motion, which completely reverses at the downstream cylinder wake. Our numerical calculations show that pressure has an indirect role in the growth of the secondary instabilities, where isobars align along with the taper profile. The geometrically induced shear promotes greater mixing in the near wake, and we found that the maximum cross-stream velocity never exceeds 10% of the mean flow even with the steepest TR. The streamwise growth of the defect layer is slower for increasing TR and reaches an early saturation. Although the velocity deficit is higher at the steepest TR, it causes a delay in the momentum recovery along the streamwise direction. The shape factor for the lower TR case shows a delay in the laminar–turbulent transition. Finally, our global stability analysis results employing dynamic mode decomposition revealed a nonlinear dynamical system with spanwise dissipation of the dynamic modes.

On the formation of three-dimensional separated flows over wings under tip effects

We perform DNS of flow over finite-aspect-ratio NACA 0015 wings to characterize the tip effects on the wake dynamics. This study focuses on the development of three-dimensional separated flow over the wing, and discuss flow structures formed on the wing surface as well as in the far field wake. Vorticity is introduced into the flow in a predominantly two-dimensional manner. The vortex sheet from the wing tip rolls up around the free end to form the tip vortex. At its inception, the tip vortex is weak and its effect is spatially confined. As the flow around the tip separates, the tip effects extend farther in the spanwise direction, generating noticeable three dimensionality in the wake. For low-aspect-ratio wings, the wake remains stable due to the strong downwash over the entire span. Increasing the aspect ratio allows unsteady vortical flow to emerge away from the tip at sufficiently high angles of attack. These unsteady vortices shed and form closed vortical loops. For higher-aspect-ratio wings, the tip effects retard the near-tip shedding process, which desynchronizes from the two-dimensional shedding over the mid-span region, yielding vortex dislocation. At high angles of attack, the tip vortex exhibits noticeable undulations due to the strong interaction with the unsteady shedding vortices. The spanwise distribution of force coefficients is related to the three-dimensional wake dynamics and the tip effects. Vortical elements in the wake that are responsible for the generation of lift and drag forces are identified through the force element analysis. We note that at high angles of attack, a stationary vortical structure forms at the leading edge near the tip, giving rise to locally high lift and drag forces. The analysis performed here reveals how the vortical flow around the tip influences the separation physics, the global wake dynamics, and the spanwise force distributions.

Effect of limited near-wall inlet data on the direct numerical simulation of turbulent channel flow

Direct numerical simulation (DNS) of turbulent flows require a large computational domain and a long simulation time to capture and evolve the large-scale structures and attain a statistically stationary state. In contrast, experimental measurements can relatively easily capture the large-scale structures, but struggle to resolve the dissipative flow scales. This study investigates the spatial extent required for the DNS of a turbulent channel flow to recover turbulent fluctuations and energy when using experimental inlet data which is typically unable to capture fluctuations down to the viscous sub-layer. Synthetic experimental fields from streamwise periodic channel flow DNS at Reτ = 180 are used as an inlet for a channel flow DNS with inlet-outlet boundary conditions. The effect of limited near-wall data at the inlet is examined by removing the near-wall energy and fluctuations in all but the zeroth Fourier mode. The influence of limited near-wall data on the convergence of mean and streamwise fluctuating velocity profiles is less significant when the fluctuations are removed at the inlet up to y+ = 5. However, the spanwise fluctuations are slightly weakened. The spanwise energy spectra suggest that at 1/16 of the domain length (x/h ≍ π/4) the flow scales are recovered. When the fluctuations are removed up to y+ = 17 or greater, recovery of full range of flow scales requires a domain larger than x/h = 4π.

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number , non-diffusive Rayleigh numbers from to and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents and .

Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations

Computational fluid dynamics models based on Reynolds-averaged Navier–Stokes equations with turbulence closures still play important roles in engineering design and analysis. However, the development of turbulence models has been stagnant for decades. With recent advances in machine learning, data-driven turbulence models have become attractive alternatives worth further explorations. However, a major obstacle in the development of data-driven turbulence models is the lack of training data. In this work, we survey currently available public turbulent flow databases and conclude that they are inadequate for developing and validating data-driven models. Rather, we need more benchmark data from systematically and continuously varied flow conditions (e.g., Reynolds number and geometry) with maximum coverage in the parameter space for this purpose. To this end, we perform direct numerical simulations of flows over periodic hills with varying slopes, resulting in a family of flows over periodic hills which ranges from incipient to mild and massive separations. We further demonstrate the use of such a dataset by training a machine learning model that predicts Reynolds stress anisotropy based on a set of mean flow features. We expect the generated dataset, along with its design methodology and the example application presented herein, will facilitate development and comparison of future data-driven turbulence models.

On the mesh resolution of industrial LES based on the DNS of flow over the T106C turbine

A high-order Navier-Stokes solver based on the flux reconstruction (FR) or the correction procedure via reconstruction (CPR) formulation is employed to perform a direct numerical simulation (DNS) and large eddy simulations (LES) of a well-known benchmark problem – transitional flow over the low-pressure T106C turbine cascade. Hp-refinement studies are carried out to assess the resolution requirement. A 4th order (p3) simulation on the fine mesh is performed with a DNS resolution to establish a "converged" solution, including the mean pressure and skin-friction distributions, and the power spectral density in the wake. Then LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the solution. In particular, we study the error in the transition location, the mean skin-friction distribution, and the mean lift and drag coefficients. These h- and p-refinement studies provide a much-needed guideline in h- and p- resolutions to achieve a certain level of accuracy for industrial LES applications.

Single-point structure tensors in turbulent channel flows with smooth and wavy walls

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and nonequilibrium behaviors of turbulence under arbitrary mean deformation or frame rotation. A more complete single-point characterization of the flow can be obtained using the structure dimensionality, circulicity, and inhomogeneity tensors. These tensors are one-point correlations of local stream vector gradients and carry nonlocal information regarding the structure of the flow field. We explore the potential of these tensors to improve understanding of complex turbulent flows using direct numerical simulation of flows in channels with a smooth wall and a two-dimensional sinusoidal wavy wall. To enforce no-slip and no-penetration conditions at wavy-wall boundaries, an immersed boundary method for the stream vector Poisson equation was adopted within the framework of Stylianou, Pecnik, and Kassinos, “A general framework for computing the turbulence structure tensors,” Comput. Fluids 106, 54–66 (2015). The results show that the effects of wall waviness on the inclination and aspect ratio of the two-point velocity correlation near the wall are reproduced qualitatively by their corresponding single-point tensor representations. In the outer layer, good quantitative agreement is achieved for both parameters. Additional observations on the structural changes of turbulence due to wall waviness and their relevance to turbulence modeling with surface roughness are discussed. The findings of this investigation suggest that single-point structure tensors can be appended to the modeling basis for inhomogeneous flows with geometrically complex boundaries, such as rough-wall flows, to develop improved turbulence models.

Drag forces on sparsely packed cube arrays

Flow over aligned and staggered cube arrays is a classic model problem for rough-wall turbulent boundary layers. Earlier studies of this model problem mainly looked at rough surfaces with a moderate coverage density, i.e. $\unicode[STIX]{x1D706}_{p}>O(3\,\%)$, where $\unicode[STIX]{x1D706}_{p}$ is the surface coverage density and is defined to be the ratio between the area occupied by the roughness and the total ground area. At lower surface coverage densities, i.e. $\unicode[STIX]{x1D706}_{p}<O(3\,\%)$, it is conventionally thought that cubical roughness acts like isolated roughness elements; and that the single-cube drag coefficient, i.e. $C_{d}\equiv f/(\unicode[STIX]{x1D70C}U_{h}^{2}h^{2})$, equals $C_{R}$. Here, $f$ is the drag force on one cubical roughness element, $\unicode[STIX]{x1D70C}=\text{const.}$ is the fluid density, $h$ is the height of the cube, $U_{h}$ is the spatially and temporally averaged wind speed at the cube height, and $C_{R}$ is the drag coefficient of an isolated cube. In this work, we conduct large-eddy simulations and direct numerical simulations of flow over wall-mounted cubes with very low surface coverage densities, i.e. $0.08\,\%<\unicode[STIX]{x1D706}_{p}<4.4\,\%$. The large-eddy simulations are at nominally infinite Reynolds numbers. The results challenge the conventional thinking, and we show that, at very low surface coverage densities, the single-cube drag coefficient may increase as a function of $\unicode[STIX]{x1D706}_{p}$. Our analysis suggests that this behaviour may be attributed to secondary turbulent flows. Secondary turbulent flows are often found above spanwise-heterogeneous roughness. Although the roughness considered in this work is nominally homogeneous, the secondary flows in our simulations are very similar to those observed above spanwise-heterogeneous surface roughness. These secondary vortices redistribute the fluid momentum in the outer layer, leading to high-momentum pathways above the wall-mounted cubes and low-momentum pathways at the two sides of the wall-mounted cubes. As a result, the spatially and temporally averaged wind speed at the cube height, i.e. $U_{h}$, is an underestimate of the incoming flow to the cubes, which in turn leads to a large drag coefficient $C_{d}$.

A critical comparison of smooth and sharp interface methods for phase transition

In this study, the Local Front Reconstruction Method (LFRM) is extended to allow for the direct numerical simulation of flows with phase transition. The LFRM is a hybrid front tracking method without connectivity, which can easily handle complex topological changes. The expansion due to phase change is incorporated as a non-zero divergence condition at the interface. The energy equation is treated with two different approaches: smooth interface approach and sharp interface approach. The smooth interface approach uses a one fluid formulation to solve the energy equation with an interfacial source term accounting for phase change. This interfacial source term enforces the saturation temperature at the interface. However, in the sharp interface approach, the thermal properties are not volume-averaged near the interface and the saturation temperature is imposed as a boundary condition at the interface. A detailed mathematical formulation and numerical implementation pertaining to both approaches is presented. Both implementations are verified using 1D and 3D test cases and produce a good match with analytical solutions. A comparison of results highlights certain advantages of the sharp interface approach over the smooth interface approach such as better accuracy and convergence rate, reduced fluctuations in the velocity field and a physically bounded temperature field near the interface. Finally, both approaches are validated with a 3D simulation of the rise and growth of a vapor bubble in a superheated liquid under gravity, where a good agreement with experimental data is observed for the bubble growth rate.

Microscale, scanning defocusing volumetric particle-tracking velocimetry

We present a novel defocusing particle tracking velocimetry (PTV) method for micro-fluidic systems. This method delivers 3-dimensional 3-component (3D3C) flow measurements, and does not require an additional calibration procedure to obtain the relationship between particle out-of-plane position and its diameter/intensity. A micro-fluidic device is mounted on a nano-positioning piezo stage that sweeps periodically in the out-of-plane direction. A high-speed camera is synchronized with the stage to capture oversampled two-dimensional microscopy images at different out-of-plane positions. 3D intensity volume is formed by stacking those 2D images. Flow tracers are identified from the intensity volume by a 3D Hessian filter, and segmented by erosion–dilation dynamic thresholding. Fitting of each identified-particle to a defocusing intensity model gives the parameters used in the hybrid algorithm of particle image velocimetry and a generalized multi-parametric PTV. Artificial image data, generated from direct numerical simulations of flow through porous media, are used for error analysis. When compared with classic nearest neighbor tracking our method shows improvements on tracking reliability by 2.5–12%, with seeding density as high as 1.6e−3 particles per voxel. Both mean and rms errors are improved by 80–95% and 49–74%, respectively. An application to micro-fluidic devices is presented by measuring the steady-state flow through a refractive-index-matched randomly-packed glass bead channel. The presented method will serve as a powerful tool for probing flow physics in micro-fluidics with complex geometries.

Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at

A weakly compressible flow direct numerical simulation of a controlled-diffusion aerofoil at $8^{\circ }$ geometrical angle of attack, a chord-based Reynolds number of $Re_{c}=150\,000$ and a Mach number of $M=0.25$ based on the free-stream velocity relevant to many industrial applications was conducted to improve the understanding of the impact of the pressure gradient on the development of turbulent structures. The evolution equations for the two invariants $Q$ and $R$ of the velocity-gradient tensor have been studied at various locations along the aerofoil chord on its suction side. The shape of the mean evolution of the velocity-gradient tensor invariants were found to vary strongly when the flow encounters favourable, zero and adverse pressure gradients and as well for different wall-normal locations. The coupling between the pressure-Hessian tensor and the velocity-gradient tensor was found to be the major factor that causes these changes and is greatly influenced by the mean pressure-gradient condition and the wall-normal distance. Striking differences exist from the mean trajectories of this coupling at least in the log layer and outer layer subject to different mean pressure gradients. The nonlinearity and viscous diffusion effects keep their respective invariant characters regardless of the pressure-gradient effects and wall-normal locations. The wall and the mean adverse pressure gradient were both found to suppress the vortical stretching features of the flow. These features are of great importance for the development of future turbulence models on wall-bounded flows, especially on surfaces with significant curvature such as cambered aerofoils and blades for which significant mean pressure gradients exist.

Direct numerical simulation of flow over a slotted cylinder at low Reynolds number

Direct numerical simulation was conducted to investigate the flow past a slotted cylinder at low Reynolds number (Re) of 100. The slotting of cylinder affects the boundary layer separation, vortex formation position, recirculation region length and wake width, which are determined by the type of slit. The streamwise slit (SS1), T-shaped slit (SS3) and Y-shaped slit (SS4) act as passive jets, while the transverse slit (SS2) achieves an alternate self-organized boundary layer suction and blowing. The flow rate in slits fluctuates over time due to the alternate vortex shedding and fluctuating pressure distribution around the cylinder surface. One fluctuation cycle of flow rate is caused by a pair of vortices shedding for SS2, SS3 and SS4, while it is created by each vortex shedding for SS1. The wall shear stress and flow impact on the slit wall partly contribute to the hydrodynamic forces acting on the slotted cylinder. Taking into account the internal wall of slit, the transverse slit plays the best role in suppressing the fluid forces with drag reduction of 1.7% and lift reduction of 17%.

Direct numerical simulation of flow and heat transfer in a simplified pressurized thermal shock scenario

Direct numerical simulation (DNS) is carried out using a high order spectral element method in order to analyse the flow and thermal fields in a Pressurized Thermal Shock (PTS) scenario. The adopted configuration is representative of a simplified reactor pressure vessel. It consists of a square duct that intersects perpendicularly with a rectangular vessel (downcomer). Cold water is injected from the square duct. It impinges against the wall of the downcomer that contains water at higher temperature, and a mixing between the cold and hot water occurs in the downcomer. The fluid properties are assumed to be constant; hence the temperature is treated as a passive scalar. A secondary flow inlet in the upper part of the downcomer is used to mimic the effect of density driven flow. The friction Reynolds number in the duct equals to 180, and a unitary Prandtl number of the fluid is used. The thermal field is solved with two types of boundary conditions, i.e., iso-thermal and adiabatic conditions, which encompass the two extreme scenarios of a conjugate heat transfer problem. A careful meshing strategy is adopted and the mesh resolution is verified a posteriori in order to meet DNS quality. The mean flow and turbulent statistics are analysed first, and a particular attention is devoted to the analysis of the vortical structures at the edges of the duct flow. The instantaneous flow field is then analysed in order to study the turbulent structure and the vorticity field within the impingement region. The mean temperature and the turbulent statistics of the thermal fields are subsequently analysed for both thermal boundary conditions. The case with iso-thermal boundary condition corresponds to the initial phase of the thermal mixing during a PTS scenario. It is characterized by the presence of cold fluid near the impinging wall and pockets of fluid at higher temperature near the exit of the duct. Regions with large temperature fluctuations are observed near the edges of the duct and at the interface between the deflected impinging fluid and the descending fluid in the downcomer. The case with adiabatic boundary condition corresponds to the later stage of the thermal mixing during a PTS scenario in which a thermal equilibrium is reached. For this case, a region with lower temperature is observed in the downcomer within the impinging jet region and in the region below, whereas the fluid at higher temperature remains confined in the remaining part of the downcomer.

An immersed boundary method for flows with dense particle suspensions

The immersed boundary method (IBM) is a well-suited tool for the direct numerical simulation of flows with dense particle suspensions, which feature strong and complex flow-particle and particle–particle interactions. With the aim to model such flows, this paper proposes to extend the Regularised Discrete Momentum Forcing (RDMF-) IBM of Abdol Azis et al. (2018) to immersed boundaries (IBs) whose motion is coupled to the flow. A modification to the direct-forcing formulation, resulting in an offset of the imposed no-slip boundary from a moving immersed boundary, is proposed. This offset is exploited in an iterative strong flow-particle coupling scheme, where the boundary forces are applied at the location of the IB known from the previous time level, while correctly enforcing the no-slip condition at the new location of the IB. This avoids having to reconstruct the interpolation and spreading stencils for every linear iteration of the flow-particle coupling, therefore reducing the computational load of the method. A technique to ensure the stable modelling of flows involving light particles is also presented and is shown to stably cope with a wide range of particle–fluid density ratios. The framework is validated by comparing the results of the simulation of a single sedimenting sphere with published experimental results. Simulations of the fluidisation of heavy rigid particles, as well as of the ascent of closely packed light particles, are also presented. Use of the radius retraction procedure, to compensate for the diffuse representation of the smooth-interface IBM, is demonstrated to consistently yield significant improvements for moving IB cases with low to intermediate Reynolds numbers. The present framework shows good stability properties for a wide range of flow regimes with concentrated particle suspensions.