Direct Numerical Simulation Research Articles

Vorticity skewness of finite-amplitude rapidly rotating Rayleigh–Bénard convection

Rotating Rayleigh–Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness $S$ is produced by the interaction between the $n=0,1$ and $n=1,2$ vertical eigenmodes. The $n=0$ (barotropic) mode contributes positively to $S$ mainly by stretching the vertical relative vorticity, an ageostrophic effect. The $n=2$ mode makes a minor negative contribution to $S$ by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts $S$ to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, ${Ro_g}$ . The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then the system enters the equilibrium stage. The stretching of vertical vorticity still contributes to $S$ dominantly. At ${Ro_g}\gtrsim 0.5$ , the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength, and weakens its influence on $S$ .

Sensitivity of flows over three-dimensional swept wings at low Reynolds number

High angle of attack flows over swept three-dimensional wings based on the NACA 0015 profile are studied numerically at low Reynolds numbers. Linear stability analysis is used to compute instability and receptivity of the flow via the respective three-dimensional (triglobal) direct and adjoint eigenmodes. The magnitude of the adjoint eigenvectors is used to identify regions of maximum flow receptivity to momentum forcing. It is found that such regions are located above the primary three-dimensional separation line, their spanwise position varying with wing sweep. The wavemaker region corresponding to the leading global eigenmode is computed and found to lie inside the laminar separation bubble (LSB) at the spanwise location of peak recirculation. Increasing the Reynolds number leads to the wavemaker becoming more compact in the spanwise direction, and concentrated in the top and bottom shear layers of the LSB. As sweep is introduced, the wavemaker moves towards the wing tip, following the spanwise displacement of maximum recirculation. Flow modifications resulting from application of different types of forcing are studied by direct numerical simulation initialised with insights gained from stability analysis. Periodic forcing at the regions of maximum receptivity to momentum forcing results in greater departure from the baseline case compared to same (low, linear) amplitude forcing applied elsewhere, underlining the potential of linear stability analysis to identify optimal regions for actuator positioning.

CNN for scalar-source distance estimation in grid-generated turbulence

Countermeasures against material leakage in industrial plants call for rapid leak source estimation techniques based on limited downstream information. Assuming that such scalar diffusion occurs in a turbulent environment, it is necessary to extract features from its instantaneous local concentration distribution and estimate the distance from the observation point to the source. To this end, we proposed an estimation method using a supervised deep learning of a convolutional neural network (CNN) and investigated its estimation performance in grid-generated turbulence fields. The grid turbulence fields were reproduced by direct numerical simulations at three Reynolds numbers (Re), and the CNN was trained using two-dimensional distribution images of passive scalars downstream. We confirmed that the images large enough to cover the spatial integral length scales of the scalar resulted in high estimation accuracy. For images with a coarsened brightness gradation, the small-scale feature of scalar fluctuations was lost, and the CNN attained a low estimation accuracy. By training the CNN with high-Re images, a high estimation accuracy was obtained, even for low-Re images. The opposite case (low-Re training and high-Re estimation) yielded low accuracy, where the CNN significantly underestimated the distance against the source. Based on these results, we discussed the generalizability and essential features to be learned by the CNN.

Effective models of metasurface/metainterface made of three-dimensional Helmholtz resonators

We study a reflective metasurface made of 3D subwavelength Helmholtz resonators. We provide an effective model in the time domain obtained by using a three-scale asymptotic approach. The metasurface is reduced to an homogenized boundary condition involving a resonant, frequency dependant impedance. Our effective model takes into account boundary layer effects near the neck opening, and we provide a precise method to calculate the " added length ". The study is extended to meta-interface in transmission, where the set of effective boundary conditions are replaced by effective jump conditions, and the results are discussed in frequency domain with comparison with direct numerical simulations.

Modeling aeroacoustic interaction of rotating propeller with porous treatments using LBM (Lattice Boltzmann method) simulations

Porous treatments are more and more employed in presence of flow as passive noise control means to mitigate the generated noise. They are generally designed according to their acoustic dissipation properties under no-flow conditions. Nevertheless, in-flow porous treatments can alter the aerodynamic properties, modify the main acoustic source itself or even generate secondary acoustic sources. While most of the modelling methods (analytical, FEM, ...) are able to model the acoustic dissipation, they do not allow to model the interaction with the main source or the possible generation of spurious acoustic sources. The Lattice Boltzmann Method (LBM) is a computational fluid dynamics method able to run Direct Numerical Simulations (DNS) as well as Large Eddy Simulations (LES). The LES method resolves the macroscopic scale of turbulence and uses a sub-grid model for the small scales of turbulence. The low numerical dissipation of the LBM enables to compute both fluid flow and acoustics quantities in a single run. In this work, the LBM implemented in ProLB software is used to model the airborne noise generated by an electric propeller installed on an aircraft wing and the effects of sound absorbing treatments. Various treatments are investigated numerically and compared to experimental data when available.

Numerical investigation on the strategy of separating burner-flame thermoacoustics

Thermoacoustic instability in combustion systems is contingent upon the thermoacoustic properties of the burner when coupled with a flame. In instances where the burner is acoustically transparent, a straightforward approach involves the separation of the burner from its corresponding flame. Acoustic velocity measurement at the upstream of the burner, in such cases, can be equated with the acoustic velocity at the downstream of the burner due to its transparency. However, when the burner possesses a complex geometry with inherent acoustic properties, this separation strategy becomes pivotal. Near-field acoustics immediately following the burner may influence the effectiveness of this separation. Additionally, burners are typically characterized in the absence of a flame (cold condition), with a common assumption that the acoustic properties of the burner remain unchanged in the presence of the flame (hot condition). This paper employs numerical simulations to scrutinize these assumptions and the separation strategy of the burner from the flame. Utilizing direct numerical simulation and an acoustic network approach, we compare the direct evaluation of the total transfer matrix of the burner with flame against the separate evaluation of the burner and flame, derived from linearized Rankine-Hugoniot relations.

Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

AbstractResults from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between $$\phi _b=0.2$$ ϕ b = 0.2 and 0.6, and the Coulomb friction coefficient is either $$\mu _c = 0$$ μ c = 0 or 0.5. The main objectives are to unravel the influence of (1) $$\phi _b$$ ϕ b and $$\mu _c$$ μ c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing $$\phi _b/\Phi _R$$ ϕ b / Φ R , where $$\Phi _R$$ Φ R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration $${\bar{\phi }}/\phi _m$$ ϕ ¯ / ϕ m , where $$\phi _m$$ ϕ m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number $$I_v$$ I v in the core region, where the macroscopic friction coefficient $$\mu $$ μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for $${\bar{\phi }}/\phi _{mp}$$ ϕ ¯ / ϕ mp as function of $$I_v$$ I v , where $$\phi _{mp}$$ ϕ mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond $$\phi _{m}$$ ϕ m at high $$\phi _b$$ ϕ b and maximum core concentrations below $$\phi _m$$ ϕ m at lower $$\phi _b$$ ϕ b .

Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in “Three-dimensional (3D) DNS of RTI triggered by acoustic excitation - Sengupta, et al. Phys. Fluids 34(5), 054108 (2022)” using more than 4 billion points with initial time steps of 7.69 ×10−8s. The set-up consists of quiescent heavy (cold) fluid atop lighter (hot) fluid initially separated by an insulated partition. Removal of this partition creates acoustic pulses in the directions normal to the interface, which provides the receptivity route of RTI to transient acoustic pulses spread over several mega-Hz frequencies, far in excess of ultrasonic frequencies. The DNS and its analysis reveal the pulses to be severely attenuated, which cannot be explained by the classical wave equation. In the present research, after demonstrating the features of the DNS results, we report in detail, the theoretical development of a wave equation incorporating losses based on the Navier-Stokes equation without Stokes' hypothesis for a quiescent ambience. Apart from the physical properties of this altered wave equation, the numerical solution of the same is obtained. The governing partial differential equation (PDE) for the propagation of disturbances in the spectral plane, provides the dispersion relation between wavenumber and circular frequency in the dissipative medium accounting for viscous losses. The presented analysis provides physical properties using the global spectral analysis (GSA). This shows the far-field perturbation to propagate either as attenuated waves or strictly in a diffusive manner depending upon the wavenumber. The PDE is solved numerically by a high-accuracy compact scheme and the four-stage, Runge-Kutta scheme for time advancement. The computed solution is shown to match not only with the developed theoretical analysis but also explains the DNS results for RTI at early times when the computed flow field truly represents the quiescent ambience.

DNS of laboratory-scale turbulent premixed counterflow flames under elevated gravity conditions

In the present work, direct numerical simulations (DNSs) of laboratory-scale turbulent premixed counterflow flames are performed to understand the effect of elevated gravity on flame structures. In the DNS, a turbulent jet of CH4/N2/O2 mixture is injected in opposition to a stream of combustion product. Three cases were considered, i.e., one case with normal gravity and two cases with elevated gravity in different directions. The DNS results of the case under normal gravity conditions were found to be in good agreement with the experimental data. The turbulent flame speed is the highest in the case with elevated gravity aligned with the mean flame propagating direction, which is due to the increase in flame surface area and stretch factor. The gravity levels have a substantial influence on the flame extinction characteristics. It was observed that the flame front is pushed toward the direction of the gravity. When the elevated gravity antialigns with the mean flame propagating direction, the flame front travels across the stagnation plane toward the combustion product stream, leading to significant reactant dilution and flame extinction. The flame normal vector preferentially aligns with the most compressive strain rate for various gravity conditions. The tangential strain rate is the greatest (smallest) when elevated gravity antialigns (aligns) with the mean flame propagating direction. The impact of elevated gravity on the tangential strain rate at the flame fronts ultimately leads to a displacement in the flame front location relative to the stagnation plane, thereby influencing flame extinction.

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

Heat transfer enhancement in pressurized solar cavity receivers with densely packed metallic wire mesh

Pressurized solar receivers are promising candidates as heat sources for integration with high-efficiency closed-loop air and supercritical carbon-dioxide based Brayton cycles. This paper focuses on the heat transfer enhancement of such a solar receiver using inline stacked wire mesh fibers in the heat transfer fluid flow path. The study involves modelling, characterization, and performance evaluation of a cavity-receiver with densely packed wire meshes. A new experimentally validated hybrid numerical approach is presented for modelling the inline stacked wire mesh layers. Initially, a direct numerical simulation at the pore scale on a representative elementary volume (REV) of the wire mesh geometry is performed for determining the hydrodynamic and thermal characteristics of the medium. Subsequently, these hydrodynamic and thermal properties are used to define a volume-averaged macroscopic porous medium. Experiments are performed using a rectangular channel stacked with stainless steel wire meshes, heated using a plate heater, and pressurized air supplied using a reciprocating compressor. Both numerical and experimental studies are performed for a Reynolds number range of 28 to 213 resulting in a Nusselt number range of 7.2 to 213. The porous medium model predictions for pressure gradient are within 17 %, while predictions for outlet air temperature are within 5 % of the experimentally obtained values. The study predicts a maximum heat transfer enhancement of five times in a channel stacked with wire meshes compared to the case of a clear channel, but incurring a peak pressure drop of only about 1.1 kPa.

Hierarchical nested riblet surface for higher drag reduction in turbulent boundary layer

Riblets can be potentially employed to passively reduce the turbulent friction drag. However, the drag reduction performance of riblets does not currently meet expectations, which could assist in emission reduction and energy conservation in green transportation. This study proposes and validates a topological form of hierarchical nested riblets (HNR) that significantly enhances the drag reduction performance. To explore the drag reduction enhancement mechanism, direct numerical simulations are performed for flow simulation on the riblet surface under different Reynolds numbers. The results show that under the riblet dimensionless spacing of the riblet s+≈21, the drag reduction performance of the HNR surface improves by about 70% compared to that of the uniform riblet surface, which is inspired by shark skin. From the perspective of turbulence statistics, the HNR surface reduces the turbulent mixing near the wall, weakening the momentum transfer. Furthermore, the transient flow field shows that the secondary riblet in HNR prevents some turbulent flow and streamwise vortices from entering the groove, considerably weakening the dispersive stress induced by the secondary flow. Moreover, owing to the influence of the secondary riblet, small-scale turbulence develops and strengthens into large-scale turbulent motion, which is advantageous to the boundary layer flow and results in drag reduction improvement.

Multiscale analysis of Reynolds stresses and its dissipation rates for premixed flame–wall interaction

Direct numerical simulation (DNS) data of flame–wall interaction (FWI) has been utilized to analyze the multiscale nature of turbulent Reynolds stresses and dissipation rate tensor anisotropies within turbulent reacting flow boundary layers across a broad range of scales. The DNS data of head-on quenching of premixed flames propagating through turbulent boundary layers, representative of friction Reynolds numbers Reτ of 110 and 180, has been explicitly filtered using both two- and three-dimensional Gaussian filter kernels for the purpose of multiscale analysis. The low-pass filter results demonstrate the transition from a 2-component limit to a 1-component limit near the wall with increasing filter width, accompanied by a decrease in isotropy, suggesting a significant alteration in dominant flow patterns and a diminishing tendency toward isotropy. The high-pass filter results indicate a progressive increase in anisotropy with the progress of FWI at the channel center, emphasizing the anisotropy of the large scales with the progress of FWI. Furthermore, behaviors of the second and third invariants of the Reynolds stress tensor remain qualitatively similar to that of the dissipation rate tensor at all stages of FWI, suggesting a link between viscous dissipation and Reynolds stress distributions; notably, there is a stronger isotropic tendency in the dissipation rate tensor when the flame is away from the wall, intensifying with an increase in Reynolds numbers. However, as FWI progresses, the shift in the trend toward the 1-component limit indicates an increase in anisotropy within the turbulent reacting flow for the region near the center of the channel.

Development of the gas–liquid drag model for flows on sieve plates in distillation columns via direct numerical simulation

Development of the gas–liquid drag model for flows on sieve plates in distillation columns via direct numerical simulation

Direct numerical simulation of droplet impact onto dry stationary and moving walls at low to high Weber numbers

The accurate prediction of the drop-wall impact dynamics and regime are of interest in many engineering applications. Considerable progress has been made in different elements of Direct Numerical Simulation (DNS) approaches. However, identifying the optimal combination of improved submodels that perform well under a wide range of operating conditions, covering low to high Weber numbers with varying surface wettabilities and wall motions, still requires further investigation. Here, we conduct a comparative study on the performance of key DNS elements, including the Interface Tracking (IT) algorithm for the widely-used volume-of-fluid approach, Contact Angle (CA), Contact-Line Velocity (CLV), Instability Actuation (IA), and numerical discretization. The study spans a broad range of Weber numbers, encompassing various impact phenomena such as drop oscillation, partial rebound, fingering, and splash. It is concluded that the Kistler CA model provides the most accurate predictions among the models considered here. In terms of IT, the Multidimensional Universal Limiter with Explicit Solution (MULES) algorithm is the most efficient one, especially for moderate to high Weber numbers. For high Weber numbers, involving the fingering instability and splash events, while applying the IA mechanism slightly improves the results, using a high-quality fine-enough grid and appropriate numerical discretization scheme to control the dispersion and dissipation errors are more important ingredients. It is shown that the recommended model combination is also able to predict the important features of drop impact on moving walls with reasonable accuracy.

Interfacial characterization of spinning water film along a concave wall

Abstract Thin liquid film flowing down the inner concave surface of a vertical cylindrical vessel is examined. At the top of the vessel, the water is injected horizontally at high speed circumferentially along the vessel wall and flows downwards due to the action of gravity. This turbulent film flow is modeled using the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) approaches combined with the volume-of-fluid method. The results of both methods are validated with direct numerical simulation. The Favre-filtered two-phase LES, which is implemented and studied in this paper, can reasonably predict the film thickness similarly to that of the RANS approach using the elliptic blending Reynolds stress model, although it requires fine resolution in the wall region. The effect of volume flow rate on the film structure and thickness is investigated. The film thickness is shown to be nearly constant when the wall is partially wetted and changes as the cubic root of the volume flow rate when the spinning film encloses the entire circumference of the vessel.

Transverse vortex-induced vibration of a sphere with the application of Lorentz force at low Reynolds number

In this study, the transverse vortex-induced vibration (VIV) of an elastically mounted sphere with the application of a streamwise Lorentz force is investigated through direct numerical simulation. The research parameter range is 300 ≤ Re ≤ 1100 and −0.8 ≤ N ≤ 1, where Re is the Reynolds number and N is the interaction parameter of the Lorentz force. The dependence of sphere responses, forces, and wake structures on Re and N is illustrated in detail. Within this range, two oscillation patterns are identified: VIV and desynchronization. Three wake patterns are identified: two-sided hairpin vortex emerges in the VIV region, while one-sided hairpin vortex and double-threaded wake structures are observed in the desynchronization region. The evolution of these wake patterns is related to the motion of the rear stagnation point (RSP) and separation line (SL) on the sphere surface. A large positive or negative Lorentz force suppresses the motion of RSP and SL, leading to the one-sided hairpin vortex or double-threaded wake structures replacing the two-sided hairpin vortex. Finally, the oscillation patterns are summarized on a map of amplitude response contours in the Re-N space.

Two-dimensional boundary layer receptivity to finite periodic disturbances

Receptivity is the focus and frontier of the research on boundary layer transition and flow drag reduction, but the temporal and spatial evolution of Tollmien–Schlichting waves (T-S waves) is not yet fully investigated, limiting the development of highly efficient laminar flow control techniques. In the present study, the local receptivity problem of the laminar boundary layer on a zero-pressure-gradient flat plate is investigated by using the direct numerical simulation, considering both the temporal and spatial evolution characteristics of the T-S waves. External disturbances at fixed frequencies are introduced in the form of velocity pulsations with different periods to excite T-S waves. The temporal and spatial evolution characteristics of the T-S waves excited by different forms and periods of disturbances are studied. It is found that the amplitude, frequency, and wave velocity of the T-S wave induced by the external multi-period disturbances are different from those induced by the constant disturbances. These conclusions are the same as those of T-S wave induced by wall inhalation. After a further investigation on this particular phenomenon, the influence mechanism of external disturbances on the receptivity process is revealed. This new research finding enriches the instability theory and provides a reference for more efficient applications on active laminar flow control technologies.

Double-reflection symmetry of thermal convection for Rayleigh number up to 1010

The Rayleigh–Bénard convection system exhibits certain known symmetries at low Rayleigh numbers that are broken as the Rayleigh number increases. In this study, we investigate the statistical symmetry of Rayleigh–Bénard convection at moderately high Rayleigh numbers through direct numerical simulations. The simulations are conducted for a fluid confined within two-dimensional walls, with an aspect ratio of unity and a fixed Prandtl number. Although elliptical large-scale circulations break both left-right and top-down reflection symmetries, we observe the emergence of a restored double-reflection symmetry. This symmetry is evident in the velocity and temperature fields, as well as in the variations of mean velocity and temperature profiles along the streamwise direction and the characteristics of the kinetic and thermal boundary layers. For Rayleigh numbers ranging between 107 and 1010, our results demonstrate a remarkable data collapse under this double-reflection transformation.

Stabilization Mechanisms of Traveling Crossflow Mode in Hypersonic Swept Wing Flows

Momentum potential theory (MPT) is employed to establish a physics-based interpretation of the traveling crossflow mode and analyze the underlying stabilization mechanisms of associated control methods, such as wall cooling, wall suction, and grooves. The traveling crossflow mode over a swept wing with a Mach number of 6 is first solved using direct numerical simulations. The MPT decomposition illustrates the vortical nature of the traveling crossflow mode, with the vortical component having a higher magnitude than the acoustic and thermal components. The vortical source makes the greatest contribution to the mode instability, whereas the response of the source terms depends on the control method used. Wall cooling primarily impacts the thermal component, thus decreasing the thermal source and subsequently changing the vortical source. Wall suction influences the vortical component directly, and only the vortical source undergoes a small reduction. The acoustic and vortical components are sensitive to grooves. The compression waves induced by grooves are identified as the source of the stabilization effect.