Present Direct Numerical Simulation Research Articles

Low-Order Moments of Velocity Gradient Tensors in Two-Dimensional Isotropic Turbulence

In isotropic turbulence, symmetry of different directions can reduce the number of independent components for velocity gradient tensors. In three-dimensional isotropic turbulence, the independent components under either incompressible or compressible conditions have already been analyzed in the literature. However, for two-dimensional isotropic turbulence, they are still unclear. We derive rigorously the independent components for velocity gradient tensors of two-dimensional isotropic turbulence and give physical explanations. These theoretical results are validated using high-resolution direct numerical simulations (DNSs) of two-dimensional compressible turbulence. Results show that the present DNS setup is still not sufficient to capture the isotropy of third-order moments, suggesting that more investigations on determining the smallest scale and improving the numerical schemes for two-dimensional compressible turbulence are required.

Direct numerical simulation of a zero-pressure-gradient turbulent boundary layer with passive scalars up to Prandtl number Pr = 6

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness ${\textit {Re}}_{\theta }$ ranging up to $1080$ . Four passive scalars, characterized by the Prandtl numbers ${\textit {Pr}} = 1,2,4,6$ are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ${\sim }24\,^{\circ }{\rm C}$ , when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

High-subsonic boundary-layer flows of an organic vapour

Boundary layers of Novec649, a low-global-warming potential fluid of interest for low-grade heat recovery, are investigated numerically by means of linear stability theory, direct numerical simulation (DNS) and large-eddy simulations (LES). This organic vapour is of interest in organic Rankine cycle (ORC) turbines and realistic thermodynamic conditions are selected. Under these conditions, the vapour behaves as a dense gas and, due to its high molecular complexity, real-gas effects occur. In addition, the fluid exhibits large and highly variable heat capacities and density- as well as temperature-dependent transport properties. More specifically we report the first direct and LES of transitional and turbulent boundary layers of Novec649 at high-subsonic conditions$M=0.9$. A controlled transition is performed by using oblique modes determined by linear stability theory extended to dense gases. An oblique-type transition is obtained as in low-speed air flows, where sinuous streaks develop by the lift-up mechanism and break down into turbulence. In the turbulent state, the profiles of dynamic flow properties (velocities, turbulent intensities, turbulent kinetic energy budgets) are little affected by the gas properties and remain very close to incompressible DNS, despite the high-subsonic flow speed. The fluctuations levels for thermodynamic properties have been quantified with respect to air flows. Notwithstanding a drastic reduction, genuine compressibility effects are present. For example, the fluctuating Mach number and the acoustic mode are characteristic of high-speed flows. The influence of forcing frequency and amplitude on the established turbulent state has been investigated using LES. An analysis of integral quantities shows a slow relaxation towards a canonical equilibrium turbulent state for all cases due to the high Reynolds numbers typical of dense gas flows. Overall the present DNS constitutes a valuable reference not only for forthcoming experiments but also for future studies of free-stream transition and loss mechanisms in ORC turbines.

Modulation of Turbulence Flux Budgets by Varying Fluid Properties in Heated High Prandtl Number Flow

The accurate computational modelling of momentum and heat transfer in turbulent wall-bounded flow is still a challenging task, especially for fluids with high molecular Prandtl numbers. Due to the steep temperature gradients, the strong variation of fluid properties becomes an additional important issue. The present Direct Numerical Simulation study specially addresses this problem considering a representative working fluid in terms of a real heat transfer oil with temperature-dependent material properties. Near the heated wall, the increase in molecular viscosity significantly attenuates the turbulent convective fluxes of both momentum and heat, despite the markedly increased enthalpy fluctuations. As the thermal conductivity decreases markedly less with temperature than the viscosity, the dampened turbulent mixing significantly reduces the Nusselt number, whereas the skin friction coefficient only marginally differs from the constant fluid property case. The attenuation of the radial velocity fluctuation consistently reduces the production terms in the budgets of the turbulent momentum and heat fluxes, while the production of the enthalpy fluctuations is only shifted away from the wall without significant change in peak level. The also attenuated redistribution in the turbulent axial stress budget reduces the pressure-strain based steering of turbulence towards isotropy. Facing a consequently more anisotropic turbulent motion poses a further difficulty to standard turbulence modelling mostly developed for isotropic turbulence.

Penetrative convection: heat transport with marginal stability assumption

This paper investigates heat transport in penetrative convection with a marginally stable temporal-horizontal-averaged field or background field. Assuming that the background field is steady and is stabilised by the nonlinear perturbation terms, we obtain an eigenvalue problem with an unknown background temperature $\tau$ by truncating the nonlinear terms. Using a piecewise profile for $\tau$ , we derived an analytical scaling law for heat transport in penetrative convection as $Ra\rightarrow \infty$ : $Nu=(1/8)(1-T_M)^{5/3}Ra^{1/3}$ ( $Nu$ is the Nusselt number; $Ra$ is the Rayleigh number and $T_M$ corresponds to the temperature at which the density is maximal). A conditional lower bound on $Nu$ , under the marginal stability assumption, is then derived from a variational problem. All the solutions to the full system should deliver a higher heat flux than the lower bound if they satisfy the marginal stability assumption. However, data from the present direct numerical simulations and previous optimal steady solutions by Ding & Wu (J. Fluid Mech., vol. 920, 2021, A48) exhibit smaller $Nu$ than the lower bound at large $Ra$ , indicating that these averaged fields are over-stabilised by the nonlinear terms. To incorporate a more physically plausible constraint to bound heat transport, an alternative approach, i.e. the quasilinear approach is invoked which delivers the highest heat transport and agrees well with Veronis's assumption, i.e. $Nu\sim Ra^{1/3}$ (Astrophys. J., vol. 137, 1963, p. 641). Interestingly, the background temperature $\tau$ yielded by the quasilinear approach can be non-unique when instability is subcritical.

DNS of heat transfer in a plane channel flow with spatial transition

In the present work Direct Numerical Simulation of heat transfer in a spatial laminar-turbulent transitional channel flow is carried out to investigate the effects of the transitional phenomenon in the temperature field. The configuration is a spatially developing channel flow with two thermal boundary conditions: Uniform Wall Temperature (UWT) and Uniform Heat Flux (UHF). The set of simulations are carried out for Re=4200 and Pr=0.1,0.2,0.5,0.71 and 1. The spatial evolution of the Nusselt number (Nu) along the transition is computed to show five distinctive qualitative zones: a laminar development, the spike zone, where the quantities evolve to reach the peak transitional zone, the post-transitional zone and finally, the fully turbulent zone. This data is employed to develop a correlation that captures the space evolution of Nu along the transition. Moreover, the analysis of flow structures shows that near the wall and downstream the onset of the transition, streaks of velocity and temperature fluctuations have strong similarity. Different turbulent statistics are calculated along the transition and compared with fully turbulent reference data. It is shown that upstream the peak transitional zone, the existence of coherent hairpin vortices yields a high-intensity region for these quantities. Additionally, it is found that the thermal boundary condition exerts influence on the profile of the second-order parameters near the wall and in the logarithmic region all along the transition.

Convective mesoscale turbulence at very low Prandtl numbers

Horizontally extended turbulent convection, termed mesoscale convection in natural systems, remains a challenge to investigate in both experiments and simulations. This is particularly so for very low molecular Prandtl numbers, such as occur in stellar convection and in the Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh–Bénard convection in square boxes of side length $L$ and height $H$ with the aspect ratio $\varGamma =L/H$ of 25, for Prandtl numbers that span almost 4 orders of magnitude, $10^{-3}\le Pr \le 7$ , and Rayleigh numbers $10^5 \le Ra \le 10^7$ , obtained by massively parallel computations on grids of up to $5.36\times 10^{11}$ points. The low end of this $Pr$ -range cannot be accessed in controlled laboratory measurements. We report the essential properties of the flow and their trends with the Rayleigh and Prandtl numbers, in particular, the global transport of momentum and heat – the latter decomposed into convective and diffusive contributions – across the convection layer, mean vertical profiles of the temperature and temperature fluctuations and the kinetic energy and thermal dissipation rates. We also explore the degree to which the turbulence in the bulk of the convection layer resembles classical homogeneous and isotropic turbulence in terms of spectra, increment moments and dissipative anomaly, and find close similarities. Finally, we show that a characteristic scale of the order of the mesoscale seems to saturate to a wavelength of $\lambda \gtrsim 3H$ for $Pr\lesssim 0.005$ . We briefly discuss possible implications of these results for the development of subgrid-scale parameterization of turbulent convection.

Characteristics of boundary-layer transition driven by diverse streamwise vortices

The present direct numerical simulations investigate the dynamics of diverse streamwise vortices in a zero-pressure gradient incompressible laminar boundary layer and the onset of turbulence. Due to the critical role of streamwise vortices in bypass transitions, we compare the transition mechanisms induced by a single vortex and vortex pairs. We initially examine the evolution of a single vortex by employing streamwise vortex profiles at two wall-normal locations. The single streamwise vortex will prompt a more rapid eruption from the bottom part of the boundary layer if moved nearer to the wall, as observed in the experimental study by Manu et al. [“Evolution of isolated streamwise vortices in the late stages of boundary-layer transition,” Exp. Fluids 48, 431–440 (2010)]. In the late stages of boundary-layer transition, the vortex–wall interaction emerges to be particularly pronounced. The second set of simulations triggers flow transition by imposing counter-rotating vortex pairs at the inlet of the computational domain. Streamwise vortex pairs with net upward flows cause intense, sporadic ejections of near-wall fluids into the boundary-layer edge, providing the first signs of inflectional instability in all considered cases. Instead of vortex–wall interactions, flow structures created by vortex pairs penetrate deeply into the inviscid region, resulting in substantial unsteady viscous-inviscid interactions. When counter-rotating vortices accompany to form a net downward flow, the initial formation of each vortex is analogous to that of a single vortex. The instability frequency and wavelength of the transitional flow produced by a vortex introduced in the middle of the boundary layer are lower than those imposed near the wall. The transitional flow generated by the vortex pair exhibits longer-wavelength instability than the single vortex cases.

On the wavenumber–frequency spectrum of the wall pressure fluctuations in turbulent channel flow

Direct numerical simulations (DNS) of turbulent channel flows up to${Re}_{\tau} \approx 1000$are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

Simulating Relic Gravitational Waves from Inflationary Magnetogenesis

Abstract We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.03% and 0.5% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs develop a spectrum that extends to higher frequencies in the millihertz (nanohertz) range for models with reheating temperatures of around 100 GeV (150 MeV) at the beginning of the radiation-dominated era. However, even though the turbulent cascade is fully developed, the GW spectrum shows a sharp drop for frequencies above the peak value. This suggests that the turbulence is less efficient in driving GWs than previously thought. The peaks of the resulting GW spectra may well be in the range accessible to space interferometers, pulsar timing arrays, and other facilities.

Laminar to turbulent transition in a finite length square duct subjected to inlet disturbance

Laminar to turbulent flow transition in a finite length square duct has been carried out by imposing novel spatiotemporal finite amplitude inlet disturbance on the laminar flow. The present direct numerical simulation study demonstrates the effect of inlet disturbance on laminar to turbulent transition. A laminar flow in a finite length square duct is considered at bulk Reynolds number Re = 2260 and Re = 1540, to which a novel spatiotemporal disturbance is introduced through a narrow banded region at the inlet of the square duct. The puff (transition) and slug (turbulent) flow dynamics indicate the laminar to turbulent transition in a square duct. Disturbance introduced at Re = 2260 laminar flow propagates downstream, giving puff and slug flow phenomena similar to pipe flows. However, at Re = 1540, inlet disturbance shows only a puff-like structure. The four vortex mean secondary flow is observed in a puff region, while the conventional eight vortex is observed in the slug region. The coherent structures of the transition (puff) flow show the presence of dual-type hairpin structures. The turbulent kinetic energy spectrum indicates conventional −5/3 spectra for slug flow and −2 energy spectra for puff flow. Thus, in this paper, it is shown that the puff and slug characteristics of laminar to turbulent transition in a square duct are similar to that of a circular duct. It is also shown that the novel inlet disturbance through a narrow banded region captures the dynamics of laminar to turbulent transition in a square duct.

On exactly self-similar turbulent boundary layers and single-layer scaling

Turbulent boundary layers are traditionally thought to obey two layer scaling. However, it was shown by Dixit and Ramesh [J. Fluid Mech. 615, 445–475 (2008)] that the so-called sink flow turbulent boundary layer obeys a Blasius-like scaling all through the boundary layer. We make this single layer scaling as an operational definition for perfectly equilibrium flow and derive equations for a general class of equilibrium flows with permeable walls allowing suction and blowing of fluid. Using the above definition, constraints required to be satisfied by such equilibrium turbulent boundary layers are derived and discussed in detail. Using direct numerical simulations (DNS), we demonstrate the existence of such turbulent boundary layers, and various properties of these boundary layers are studied in detail. In particular, it is shown that the mean velocity profiles and other turbulent statistics display excellent similarity, and various boundary layer parameters in such boundary layers vary systematically with the magnitude of blowing/suction parameter. By extension, it is also demonstrated by DNS that higher order moments (up to third order moments) also display streamwise self-similarity. We believe that this is an important result where self-similarity is demonstrated for the first time for higher moments of fluctuating velocity. The non-universality of the log-law coefficients in favorable pressure gradient flows is already known [S. A. Dixit and O. N. Ramesh, J. Fluid Mech. 615, 445–475 (2008) and Chauhan et al., in Proceedings of 11th EUROMECH European Turbulence Conference on Turbulence, Porto, Portugal (Springer Proceedings in Physics, 2007), pp. 239–241]. We demonstrate their non-universal nature in equilibrium boundary layers with suction and blowing using the present direct numerical simulations. Remarkably, the ratio of Reynolds shear stress (u′v′¯) to streamwise (u′2¯) and spanwise turbulent intensity (w′2¯) in these boundary layers is constant over the log-region in the mean velocity profile even though u′2¯, w′2¯, and u′v′¯ by themselves show variation with y+ in the log region, indicative of the absence of inactive motion in these flows. It is shown that the dominance of active motion and more importantly the absence of inactive motion leads to a universality of scaling that manifests as a single layer Blasius scaling with self-similarity in such flows. Equivalently, it could also be seen as a single layer scaling with all variables all through the boundary layer. This would mean that the friction velocity scales the entire boundary layer, which could be taken to suggest equivalence of attached eddies with the active component of motion.

Simulation of a turbulent flow subjected to favorable and adverse pressure gradients

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted “speed bump” geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proved to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest fidelity simulation techniques. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation and development of internal layers, where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump.

Direct numerical simulation of an evaporating turbulent diluted jet-spray at moderate reynolds number

The evaporation of liquid droplets dispersed in jet-sprays is involved in many industrial applications and natural phenomena. Despite the relevance of the problem, a satisfactory comprehension of the mechanisms that regulate the process has still not been achieved. Indeed, a wide range of turbulent scales and an enormous number of droplets are typically involved, causing the numerical and theoretical tackling of the problem to be challenging. In this context, we address the Direct Numerical Simulation (DNS) of a turbulent jet-spray at a bulk Reynolds number Re=10,000. We focus on the effect of the jet Reynolds number on the evaporation process and the preferential segregation of droplets. The analysis is conducted by comparing the outcomes of the present DNS with that from a lower Reynolds number one in corresponding conditions, Re=6,000. The problem is addressed by employing the point-droplet approximation in the hybrid Eulerian-Lagrangian framework. We present detailed statistical analyses of both the gas and the dispersed phases. We found that the mean droplet vaporization length grows as the bulk Reynolds number is increased from Re=6,000 to Re=10,000, while keeping all the remaining conditions fixed. We attribute this result to the complex interaction between the inertia of the droplets and the dynamics of the turbulent gaseous phase. In particular, at the higher Reynolds number, the effect of the faster turbulent fluctuations of the jet mixing layer, which tend to fasten the process, is compensated by the slower mass transfer from the liquid droplets to the surrounding environment. We also observe intensive preferential segregation of the dispersed phase that originates from the entrainment of dry environmental air into the mixing layer and is intensified by small-scale clustering in the far-field region. We show how the preferential segregation is responsible for a strongly heterogeneous Lagrangian evolution of the dispersed droplets. All these aspects contribute to the Reynolds-number dependence of the overall droplet evaporation rate. Finally, we discuss the accuracy of the d-square law, often used in spray modelling, for present cases. We found that using this law based on environmental conditions leads to a relevant overestimation of the droplet evaporation rate.

Energy transport characteristics of converging Richtmyer–Meshkov instability

In this paper, the Richtmyer–Meshkov (RM) instability in spherical and cylindrical converging geometries with a Mach number of about 1.5 is investigated by using the direct numerical simulation method. The heavy fluid is sulfur hexafluoride, and the light fluid is nitrogen. The shock wave converges from the heavy fluid into the light fluid. The main focus is on the energy transport characteristics in the mixing layer during the entire development process from early instability to late-time turbulent mixing. First, the turbulence kinetic energy transport equation is analyzed, and it is found that the production and dissipation mechanisms of the turbulence induced by the spherical and cylindrical converging RM instabilities in the mixing layer are the same. The turbulent diffusion terms are crucial in the whole development processes of the mixing layers. Before the reflected shock waves transit the interfaces, the dissipation terms can be ignored relative to other terms, and after that, the dissipation terms are close to the production terms and play an important role. The compressibility terms are approximate to the production terms and promote the production of turbulence kinetic energy in the later stage. The viscous diffusion terms can be ignored throughout the process. Then, the enstrophy transport equation is researched, and it is found that, in the mixing layers, the baroclinicity terms play a leading role in the early stage, while the vortex stretching terms play a leading role in the later stage, and the vortex stretching term of the spherical converging geometry develops faster than that of the cylindrical converging geometry. The compressibility terms are positive in the early stage, which promote the production of enstrophy. After the reflected shock waves transit the interfaces, the compressibility terms become negative, which inhibit the production of enstrophy. In addition, the results of the present direct numerical simulation also show that the density fluctuation spectra in the centers of the mixing layers of the spherical and cylindrical converging RM instabilities present the obvious −5/3 scaling law.

Inertia–Gravity Waves Breaking in the Middle Atmosphere at High Latitudes: Energy Transfer and Dissipation Tensor Anisotropy

Abstract We present direct numerical simulations of inertia–gravity waves breaking in the middle–upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave’s least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.

Thermogravitational and hybrid convection in an obstructed compact cavity

The flow over a topography or a step is a fundamental problem in fluid dynamics with relevance to many fields and circumstances. In the present analysis direct numerical simulation (DNS) is used to examine the properties of the thermofluid-dynamic field in a square cavity with a heated obstruction located on the bottom. The involved dynamics include forced flow driven by injection of cold fluid through an orifice and the buoyancy convection of thermal origin, which naturally emerges in the considered cavity as a result of the prevailing temperature gradients. The relative importance of these mechanisms is assessed by considering different values of the Rayleigh number (spanning several orders of magnitude) and using a peculiar analysis hierarchy where selected effects are intentionally switched on or off depending on the targeted regime. In particular, first, attention is paid to pure thermogravitational convection driven by the presence of vertical and horizontal heated surfaces (the hot sides of the obstruction); then, the hybrid regime is examined where buoyancy convection is modulated by currents of forced flow for values of the Richardson number ≅ 1. We also explore the resulting patterning behavior for different thermal and kinematic boundary conditions (distinct thermal behaviors of the top wall and alternate positions of the inflow and outflow sections). For each case, the Nusselt number relating to the vertical and horizontal sides of the obstruction is evaluated and put in relation with the flow topology. The study is also supported by analysis of the frequency spectrum for the situations in which relatively chaotic states emerge.

Geometric Effects of Shallow Dimples in Turbulent Channel Flows at $$Re_{\tau }\approx 180$$: A Vorticity Transport Perspective

Shallow dimples have shown a great potential to reduce turbulent drag in several experiments. However, the mechanism underlying their effects on turbulence dynamics remains a subject of deliberation. In this numerical study, a vorticity transport perspective is adopted to elucidate the geometric effects of shallow dimples on the turbulence dynamics in a fully-developed turbulent channel flow. The geometric modifications considered in the present direct numerical simulation at a bulk Reynolds number of 2800 include changing the planform design and modulating the streamwise wall slope. The planform design had a significant impact on the mean flow topology and the drag property. Out of the five planform designs, diamond (shape) dimples produced the highest amount of total drag reduction of $$\approx 7\%$$, whereas symmetric circular dimples caused the greatest increase in total drag by $$\approx 6\%$$. Results revealed that geometric modifications of shallow dimples mainly affect the vorticity redistribution process that predominates in the inner region of a turbulent boundary layer, and in turn the generation of Reynolds stress. The drag property of a dimpled surface was found to scale with the velocity–vorticity correlation term representing the physical process of vorticity stretching and reorientation. The occurrence of flow separation near the leading edge of the dimple altered the vorticity dispersion process in the outer region, thereby modifying the generation of Reynolds stress in the bulk flow. On the other hand, the vortex dispersion process in the inner layer can be altered by modulating the streamwise wall slope. Accordingly, the vorticity redistribution process was modified but the near-wall generation of Reynolds stress was unaffected. Thus, only the form drag varied with the streamwise wall slope, while the viscous drag remained largely the same.

Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation

A direct numerical simulation (DNS) initialized with an implicit large eddy simulation (ILES) is performed for temporally evolving planar jets and turbulent boundary layers. In the ILES, an initial laminar flow develops into a fully developed state of the planar jet or the boundary layer. Subsequently, the DNS is started from the flow field obtained by the ILES. This hybrid ILES/DNS methodology is tested for the planar jet and boundary layer by comparing the results with full DNS started from the initial laminar flow. The ILES results used as the initial conditions of the DNS do not possess small-scale fluctuations. However, the small-scale fluctuations in the DNS grow with time and develop well within an interval of the integral time scale, where the influences of initial conditions taken from the ILES disappear for an energy spectrum of velocity fluctuations. The DNS initialized with the ILES well reproduces small-scale characteristics of turbulence, such as Reynolds number dependence of skewness and flatness of velocity derivative and energy spectrum of velocity fluctuations in the inertial subrange and viscous range. The DNS initialized with the ILES predicts well statistics dominated by large scales, such as 1st- and 2nd-order statistics and longitudinal auto-correlation function, in agreement with previous experimental and numerical studies. Reynolds number dependence of the mean velocity, root-mean-squared velocity fluctuations, Reynolds stress, shape factor, and skin friction in the turbulent boundary layers in the present DNS are consistent with previous experimental studies. These investigations confirm advantages of applying the ILES at the transitional flow region in the DNS of turbulent shear flows at high Reynolds numbers.

Modulation of sound waves for flow past a rotary oscillating cylinder in a non-synchronous region

Modulation of sound waves for the laminar flow past a rotary oscillating circular cylinder has been studied for a free-stream Reynolds number Re = 150 and Mach number M = 0.2. Modulation of sound waves has been observed if the combination of applied rotary oscillation frequency and amplitude belongs to the nonsynchronous region where the hydrodynamic and acoustic quantities vary with the vortex shedding frequency as well as the applied forcing frequency. Two-dimensional direct numerical simulations (DNS) are carried out on a highly refined grid using high resolution physical dispersion relation preserving schemes for a nondimensional forcing frequency-ratio range 0.1 ≤ fr ≤ 2.0 at a nondimensional surface speed A1 = 0.1. Both the synchronous and the nonsynchronous zones are identified based on the time-varying fluctuations in the lift and the drag coefficients. In the nonsynchronous zone, modulation phenomena of the lift and the drag coefficients are explained by plotting the stream-function contours over multiple vortex shedding cycles. The modulation periods associated with the fluctuating lift and the drag coefficients are different for some cases. This particular observation is in contrast with the observation expressed in the previous studies investigating similar problems. Disturbance pressure fields obtained from the present DNS data are used to analyze the characteristics of radiated sound fields, especially in the nonsynchronous zone. Information related to aerodynamic sound sources has been obtained using approximated Lighthill’s stress tensor, and it is shown that the aerodynamic sound sources also display the modulation phenomenon similar to that observed in the vortex shedding process. Sound fields related to the nonsynchronous zone also exhibit the modulation phenomenon and are governed by the shedding frequency, the forcing frequency, and their linear combinations. Radiated sound field characteristics are further related to the time-varying fluctuations of the lift and the drag coefficients using Curle’s acoustic analogy. Modulated sound waves observed along the upstream and the transverse directions have similar time variation as that of the drag and the lift coefficients, respectively. The phenomenon of beat formation has been observed for the ranges 0.9 ≤ fr ≤ 0.99 and 1.2 ≤ fr ≤ 1.4. Although the observed modulation of sound waves varies significantly with the forcing frequency-ratio, the net radiated sound power has almost remained constant in the nonbeating, nonsynchronous zone. Furthermore, it is confirmed that the dominant sound modes obtained during the proper orthogonal decomposition of disturbance pressure fields in the nonsynchronous zone are related to the shedding frequency-ratio, the forcing frequency-ratio, and their linear combinations.