Direct Numerical Simulation Of Flow Research Articles

Riblet Drag Reduction Modeling and Simulation

One of the most interesting passive drag reduction techniques is based on the use of riblets or streamwise grooved surfaces. Detailed flow features inside the grooves can be numerically detected only by Direct Numerical Simulations (DNS), still unfeasible for high Reynolds numbers and complex flows. Many papers report the DNS of flows on microgrooved surfaces providing fundamental details on the drag reduction devices, but all are limited to plate or channel flows far from engineering Reynolds numbers. The numerical simulation of riblets and other drag reduction devices at very high Reynolds numbers is difficult to perform due to the riblet dimensions (microns in aeronautical applications). To overcome these difficulties, some models for riblet simulation have been developed in recent years, due to the data provided by DNS, experiments, and theoretical analyses. In all these models, the drag reduction is modeled rather than effectively captured; however, the analysis of some nonlocal effects on practical aeronautical configurations with riblets, requires their adoption. In this paper, the capabilities of these models in predicting riblets’ performance and some interesting features of the riblets’ effect on form drag and shock waves are shown. Two models are discussed and compared showing their respective advantages and limitations and providing possible enhancements. A comparison between the two models in terms of accuracy and convergence is discussed, and two new formulae are proposed to improve one of these models. Finally, a review of the results obtained by the two models is provided showing their capabilities in the analysis of the riblet effect on complex configurations.

Deep reinforcement learning for active control of flow over a circular cylinder with rotational oscillations

An active control strategy for flow over a circular cylinder with rotational oscillations is automatically learned based on a deep reinforcement learning algorithm. Specifically, the proximal policy optimization is used to minimize the averaged drag coefficient of cylinder by properly selecting the rotational angular velocity. The data for training is sampled by direct numerical simulation of flow past a rotational circular cylinder, which is recognized by the immersed boundary method and the active control is applied to the flow in real time. The flow configurations are observed by the detecting probes located inside them and modified by the agent of deep reinforcement learning through changing the angular velocity with time. After several episodes of training, the reinforcement learning agent is shown to discover a robust and convergent control strategy, by which the cylinder is able to choose an appropriate rotational angular velocity to modify the wake based on its observation of the instantaneous flow field, resulting in a substantial drag reduction. The network architecture is tested at different Reynolds numbers, i.e. 100, 200 and 300, and drag reduction rates of 10%, 19% and 21% are obtained, respectively. Effects of initial flow field and angular velocity, position and number of detecting probes and hyper-parameters of the deep reinforcement learning architecture are also examined.

Direct Numerical Simulation of Flow over a Triangular Airfoil Under Martian Conditions

Martian conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and low sound speed require Martian rotor blades to operate in a low-Reynolds-number (1000–10,000) compressible regime, for which conventional airfoils are not designed. Here, we use PyFR to undertake high-order direct numerical simulations (DNS) of flow over a triangular airfoil at a Mach number of 0.15 and Reynolds number of 3000. Initially, spanwise periodic DNS are undertaken. Extending the domain-span-to-chord ratio from 0.3 to 0.6 leads to better agreement with wind-tunnel data at higher angles of attack, when the flow is separated. This is because smaller domain spans artificially suppress three-dimensional breakdown of coherent structures above the suction surface of the airfoil. Subsequently, full-span DNS in a virtual wind tunnel are undertaken, including all wind-tunnel walls. These capture blockage and wall boundary-layer effects, leading to better agreement with wind-tunnel data for all angles of attack compared to spanwise periodic DNS. The results are important in terms of understanding discrepancies between previous spanwise periodic DNS and wind-tunnel data. They also demonstrate the utility of high-order DNS as a tool for accurately resolving flow over triangular airfoils under Martian conditions.

Wake transitions of six tandem circular cylinders at low Reynolds numbers

Direct numerical simulations for flow over six tandem circular cylinders at Reynolds numbers (Re) from 40 to 180 and gap ratios (G/D) from 0.5 to 18 were conducted. The main aims are to identify vortex transitions from primary to secondary vortices and from secondary to tertiary vortices and to explore the mechanisms for these transitions. In addition, the variations of the force coefficients and Strouhal numbers with the transitions are also examined. Based on the characteristics of vortex shedding frequency, flow patterns, and force coefficients on the cylinders, four flow regimes, namely, no-shedding, primary shedding, secondary shedding, and tertiary shedding regimes, were mapped out in the Re–G/D domain. The three shedding regimes always initiate from the last cylinder. With the increase of Re and/or G/D, the onset locations of the regimes shift upstream. The secondary and tertiary vortices are formed after a region of convective instability characterized by two-row parallel vortex streets or shear layers. Two physical mechanisms for the transition from primary to secondary vortices are identified. The first one is associated with shear layer instabilities developed after the decay of the primary vortices, and the second one is the merging of the primary vortices. The transition from secondary to tertiary vortices involves vortex merging only. Whereas no-shedding or primary shedding regimes occur at smaller gap ratios or lower Reynolds numbers, the three vortex shedding patterns (primary, secondary, and tertiary) can co-exist for larger gap ratios or higher Reynolds numbers, and each pattern dominates a region around the group of cylinders. The variations of the flow patterns, vortex shedding frequency, and force coefficients on the cylinders in each of the flow regimes are quantified and interpreted. When the number of cylinders is increased to more than 6 at a gap ratio of 15, no further transition is observed after the transition to tertiary wake, and the vortex shedding processes on the downstream cylinders become chaotic without a dominant frequency, suggesting that for multiple tandem cylinders, only two transitions, corresponding to the generations of the secondary and tertiary vortices, can be identified. The change in Reynolds number or gap ratio influences the onset locations of the transitions only.

A Lagrangian relaxation towards equilibrium wall model for large eddy simulation

A large eddy simulation wall model is developed based on a formal interpretation of quasi-equilibrium that governs the momentum balance integrated in the wall-normal direction. The model substitutes the law-of-the-wall velocity profile for a smooth surface into the wall-normal integrated momentum balance, leading to a Lagrangian relaxation towards equilibrium (LaRTE) transport equation for the friction–velocity vector ${\boldsymbol u}_\tau (x,z,t)$ . This partial differential equation includes a relaxation time scale governing the rate at which the wall stress can respond to imposed fluctuations due to the inertia of the fluid layer from the wall to the wall-model height. A priori tests based on channel flow direct numerical simulation (DNS) data show that the identified relaxation time scale ensures self-consistency with assumed quasi-equilibrium conditions. The new approach enables us to formally distinguish quasi-equilibrium from additional, non-equilibrium contributions to the wall stress. A particular model for non-equilibrium contributions is derived, motivated by laminar Stokes layer dynamics in the viscous sublayer when applying fast-varying pressure gradients. The new wall modelling approach is first tested in standard equilibrium channel flow in order to document various properties of the approach. The model is then applied in large eddy simulation of channel flow with a suddenly applied spanwise pressure gradient (SSPG). The resulting mean wall-stress evolution is compared with DNS with good agreement. At the onset of the SSPG, the laminar Stokes layer develops rapidly while the LaRTE portion of the stress has a delayed response due to its inherent relaxation dynamics. Results also highlight open challenges such as modelling the response of near-wall turbulence occurring above the viscous sublayer and at time scales faster than quasi-equilibrium conditions.

Investigation on spatial evolutions of two- and three-dimensional modes in a laminar separation bubble over a low-pressure turbine cascade

Separation-induced transition under a low level of freestream turbulence is investigated via direct numerical simulation of flow over a low-pressure turbine cascade. The results are comprehensively analyzed in physical and Fourier spaces to elucidate the mechanisms of flow transition in the shear layer and the recirculation region of the separation bubble. It is observed that the instability process in the upstream attached boundary layer provides considerable low-frequency waves to the separated shear layer. As a result, intense nonlinear effects occur in the shear layer leading to the growth of two-dimensional waves with low to high frequencies in sequence and, eventually, giving rise to the most-amplified wave associated with the vortex-shedding frequency. Inside the recirculation region, the corresponding two-dimensional waves are induced showing the evidence for previous research on receptivity. Different from the downstream propagation of two-dimensional waves, the collision and merging of upstream- and downstream-propagating oblique waves contribute to the initiation of three-dimensional fluctuations. The subsequent three-dimensionality of the shear layer is closely associated with the growth of three fundamental oblique waves with large spanwise wavelengths. It is illustrated that these characteristic modes correspond to λ-shaped vortices and continuously developing hairpin vortex chains.

Numerical study on drag reduction and wake modification for the flows over a hydrofoil in presence of surface heterogeneity

In this article, direct numerical simulations of flow around NACA0012 hydrofoil with superhydrophobic surface (SHS) is presented. Surface heterogeneity takes into account by periodic no-slip and shear-free grates on the surface. The study is conducted for a range of [Formula: see text] degree angles of attack and at fixed Reynolds number ( Re) 1000. SHS leads to effective Navier slip on the hydrofoil surface and corresponding changes in velocity profile. Bubble separation delays for higher gas-fraction ( G.F), and minimizes the vortex shedding effects. As a result, flow remains two-dimensional (2D) for higher angles of attack as compared to flow over three-dimensional (3D) hydrofoil with no-slip boundary. Both the drag reduction and enhancement of lift force are observed. Maximum lift are observed at [Formula: see text], while the drag force continues to decrease with the gradual increase in angle of attack and patterned micro-grates fraction. Mode C with smaller wavelength is observed at [Formula: see text]. Furthermore, increase in gas-fraction leads to increase in slip length which thickens the boundary layer and mimics the vorticity implies drag reduction. Thus, replacement of the no-slip surfaces by superhydrophobic surfaces can be treated as a promising drag reduction technology.

Flow in additively manufactured super-rough channels

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$ m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness’ trough to peak sizes are 0.1 $h$ , 0.3 $h$ and 0.8 $h$ , respectively, where $h$ is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely $Re_\tau =180$ and $Re_\tau =395$ . We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate.

Direct numerical simulation of flow over a cylinder immersed in the grid-generated turbulence

In this study, we conducted three-dimensional direct numerical simulations to investigate the impact of incoming turbulence on the flow dynamics behind a single main cylinder at Reynolds number of Re = 3900. The incoming turbulence is generated by ten side-by-side cylindrical grid bars, whose center-to-center distance T is set equal to 2D, where D is the diameter of both the grid bars and the main cylinder. It is found that in the wake of the grid bars, the non-Gaussian production region and the homogeneous decay region, which are, respectively, located at X/D<4 and X/D>4, were separated by the development of turbulence intensity Ti. Compared to the uniform incoming flow, the hydrodynamic forces induced by the present incoming turbulence are markedly distinct in magnitude. Specifically, the time-averaged drag coefficient C¯d is increased by 29.4%, and more surprisingly, the root mean square value of the lift coefficient is increased by as much as 500%. Statistical analysis is then performed, in terms of the Reynolds stresses, mean field, and the turbulent wake visualization to show variations in the flow dynamics. Results indicate that the incoming turbulence could accelerate the turbulent transition of shear layers and lead to a contraction of the vortex formation region. In addition, the long streamwise streaky vortical structures leading to an increase in Reynolds stress are found in front of the cylinder surface, which illustrates that the effect of incoming turbulence has penetrated inside the front boundary layer.

A universal velocity profile for turbulent wall flows including adverse pressure gradient boundary layers

A recently developed mixing length model of the turbulent shear stress in pipe flow is used to solve the streamwise momentum equation for fully developed channel flow. The solution for the velocity profile takes the form of an integral that is uniformly valid from the wall to the channel centreline at all Reynolds numbers from zero to infinity. The universal velocity profile accurately approximates channel flow direct numerical simulation (DNS) data taken from several sources. The universal velocity profile also provides a remarkably accurate fit to simulated and experimental flat plate turbulent boundary layer data including zero and adverse pressure gradient data. The mixing length model has five free parameters that are selected through an optimization process to provide an accurate fit to data in the range $R_\tau = 550$ to $R_\tau = 17\,207$ . Because the velocity profile is directly related to the Reynolds shear stress, certain statistical properties of the flow can be studied such as turbulent kinetic energy production. The examples presented here include numerically simulated channel flow data from $R_\tau = 550$ to $R_\tau =8016$ , zero pressure gradient (ZPG) boundary layer simulations from $R_\tau =1343$ to $R_\tau = 2571$ , zero pressure gradient turbulent boundary layer experimental data between $R_\tau = 2109$ and $R_\tau = 17\,207$ , and adverse pressure gradient boundary layer data in the range $R_\tau = 912$ to $R_\tau = 3587$ . An important finding is that the model parameters that characterize the near-wall flow do not depend on the pressure gradient. It is suggested that the new velocity profile provides a useful replacement for the classical wall-wake formulation.

VISCOSITY IN SEAKEEPING

The paper addresses the issue of actuality in ship hydrodynamics: the estimation of ship’s linear and angular oscillations with respect to the state of equilibrium. The prediction of seakeeping properties raises a question about a relative importance of viscous and free-surface effects (Quérard et al. 2009), yet this question remains of more general importance in fluid mechanics, since it is related to the dynamic characteristics of objects/bodies immersed in a liquid. From a theoretical standpoint, the problem refers to flows with moving boundaries. It can also be considered in terms of fluid-structure interaction (FSI), however, not necessarily linked with the computation of the body deformation and stresses due to the flow. As the Author correctly notices, the computational solution to this problem in its full setup reveals to be extremely costly due to the 3D and unsteady nature of the fluid motion under turbulent flow conditions at nominally high Reynolds numbers (Re~109, as stated by the Author in Tab. 1) in presence of the free surface. For this reason, the full solution, or direct numerical simulation (DNS), of the governing Navier-Stokes (N-S) equations at these Re will remain unfeasible in the foreseeable future; see, e.g., Pozorski (2017) for an estimation of the DNS capability in simple wall-bounded turbulent flows. The situation gets even worse in ship hydrodynamics when a DNS of fluid flow would need to be coupled to the dynamics of the rigid body (of complex geometry, usually).

Approach to the 4/3 law for turbulent pipe and channel flows examined through a reformulated scale-by-scale energy budget

In this study, we propose a scale-by-scale (SBS) energy budget equation for flows with homogeneity in at least one direction. This SBS budget represents a modified form of the equation first proposed by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109) for the channel centreline – the primary difference is that, here, we consider the role of pressure along with the errors associated with the isotropic approximations of the interscale divergence and Laplacian of the squared velocity increment. The term encompassing the effects of mean shear is also characterised such that the present analysis can be extended straightforwardly to locations away from the centreline. We show, based on a detailed analysis of previously published channel flow direct numerical simulations and pipe flow experiments near the centreline, how several terms in the present SBS budget equation (including the third-order velocity structure function) behave with increasing Reynolds number. The behaviour of these terms is shown to imply a rate of emergence and subsequent growth of the 4/3 law scale subrange at the channel centreline and pipe axis. The analysis also suggests that the peak magnitude of the third-order velocity structure function occurs at a scale that is fixed in proportion to the Taylor microscale at sufficiently high Reynolds number.

Three-dimensional direct numerical simulation of flow induced by an oscillating sphere close to a plane boundary

The dynamic interaction of submerged spherical structures with ocean waves alters the local flow field and is responsible for the movement of sediments over the seabed, which would have detrimental effects on the ecosystems. The present research aims to gain insight into the effect of a plane boundary on the vorticity dynamics and shear modifications on the plane boundary induced by the flow due to an oscillating sphere. The flow field around an oscillating sphere close to a plane boundary is investigated numerically by three-dimensional direct numerical simulation of the Navier–Stokes equations. The sphere oscillates perpendicular to the plane boundary modeling the seabed. The flow structure, resulting mean and fluctuating shear stress distribution on the plane boundary, and the Lagrangian particle transport are investigated as a function of the sphere oscillation amplitude, Reynolds number, and the distance of the sphere from the plane boundary. The systematic correlations for the variation of maximum shear stress on the plane boundary are estimated from scaling parameters. The time-mean results are then linked to the Lagrangian particle transport where it is observed that the Lagrangian path lines track the mean streamlines closely. Further, the particles at the stagnation zone cease drifting and oscillate about a constant mean position. The practical significance of this result is that a ring of zero mean shear on the seabed is found toward where particles congregate. This provides a guide for the optimum location for the mooring anchors, minimizing the risk of anchor scour or undermining.

Direct Numerical Simulation of Flow and Heat Transfer in Complex Ducts

Direct Numerical Simulation of Flow and Heat Transfer in Complex Ducts

High-order accurate direct numerical simulation of flow over a MTU-T161 low pressure turbine blade

Reynolds Averaged Navier-Stokes (RANS) simulations and wind tunnel testing have become the go-to tools for industrial design of Low-Pressure Turbine (LPT) blades. However, there is also an emerging interest in use of scale-resolving simulations, including Direct Numerical Simulations (DNS). These could generate insight and data to underpin development of improved RANS models for LPT design. Additionally, they could underpin a virtual LPT wind tunnel capability, that is cheaper, quicker, and more data-rich than experiments. The current study applies PyFR, a Python based Computational Fluid Dynamics (CFD) solver, to fifth-order accurate petascale DNS of compressible flow over a three-dimensional MTU-T161 LPT blade with diverging end walls at a Reynolds number of 200,000 on an unstructured mesh with over 11 billion degrees-of-freedom per equation. Various flow metrics, including isentropic Mach number distribution at mid-span, surface shear, and wake pressure losses are compared with available experimental data and found to be in agreement. Subsequently, a more detailed analysis of various flow features is presented. These include the separation/transition processes on both the suction and pressure sides of the blade, end-wall vortices, and wake evolution at various span-wise locations. The results, which constitute one of the largest and highest-fidelity CFD simulations ever conducted, demonstrate the potential of high-order accurate GPU-accelerated CFD as a tool for delivering industrial DNS of LPT blades.

Random generation of irregular natural flow or pore networks

Over the past years, tomographic scanning techniques like micro-CT have become popular for the acquisition of high-fidelity void-space geometries of natural porous media (e.g., Bultreys et al., 2016; Raeini et al., 2017). Limitations both in computing time and memory prohibit, however, direct numerical simulations of flow and transport in large resp. detailed sample geometries. Flow or pore networks derived from scans alleviate this limitation, but still necessitate a methodology to extrapolate to larger samples. In this work, we present a network generation algorithm that is particularly suited for heterogeneous irregular networks. While emulating from an existing base network new networks of equal or larger sizes, the outlined algorithm scales approximately linearly with the network node or pore count and maintains (1) node connectivity resp. pore coordination-number statistics, (2) geometrical pore/throat properties, as well as (3) the potentially inhomogeneous spatial clustering of pores. While existing methods address the first two properties, the third point is crucial especially in heterogeneous media to match flow/transport properties like the permeability that have a strong dependence on the spatial distance between connected pores. Moreover, the cubical networks generated by our algorithm are periodic in all spatial directions, thus eliminating topological boundary effects, which are not present in natural media. Bounded networks of arbitrary sizes can then be recovered by cutting the generated networks and thus flow/transport processes at larger scales can be studied while incorporating physically-based descriptions of pore-scale processes.

Turbulent secondary flows in channels with no-slip and shear-free boundaries

Abstract

Direct numerical simulation of flow and heat transfer in bidisperse gas-solid systems

The flow and heat transfer in bidisperse gas-solid systems with particle diameter ratio ranging from 1:2 to 1:4 have been numerically investigated via an immersed boundary-lattice Boltzmann method. The modeling for the overall Nusselt number (Nu) is pursued. The results show that the overall Nu obtained from the simulation results can be predicted well using the monodisperse correlations by defining an appropriate equivalent diameter. An accurate model to predict Nu for each species is formulated through a correction to the monodisperse heat transfer correlations. Since the relative solid volume fraction ratio of large-to-small spheres has marginal influence on Nu for each species, the correction term is only closed as a function of the total solid volume fraction and scaled particle diameter. The predictability of the model is evaluated. The results demonstrate that the model can give more accurate estimations for Nu of each species.

The Terminal Velocity of Axisymmetric Cloud Drops and Raindrops Evaluated by the Immersed Boundary Method

AbstractThe terminal velocity of cloud drops and raindrops used in numerical model calculations can significantly affect weather predictions. Current formulations rely on laboratory experiments made in the 1940s and 1960s. Because these experiments were performed only at typical environmental conditions of 20°C and 1013 hPa, parameterizations have been introduced to deduce the terminal velocity aloft without rigorous evaluation. In this study, an incompressible two-phase flow direct numerical simulation model is used to calculate the free-falling motion of axisymmetric drops with diameters between 0.025 and 0.5 mm to study the terminal fall velocity. Simulated terminal fall velocities of free-falling drops at 20°C and 1013 hPa agree within 3.2% with the previous empirical parameterization (Beard formula), and 4.5% with existing laboratory data in the diameter range between 0.3 and 0.5 mm. The velocities converge to the analytic Hadamard–Rybczynski solution within 2% for small Reynolds numbers, demonstrating the robustness of our simulations. Simulations under various atmospheric conditions show that existing empirical parameterizations that account for the air density dependence of the terminal velocity have errors up to 11.8% under the conditions examined in this study. We propose a new empirical formula that describes the air density dependence of the terminal velocity. It is also shown that the falling speed of a small drop is not sensitive to shape oscillation, and the terminal velocity decreases by only less than 1.3% when the axis ratio increases by 12% with reduced surface tension. Internal circulation within falling drops is also presented and compared with previous studies.

Channel flow with large longitudinal ribs

Abstract