Direct Numerical Simulation Data Research Articles

Anisotropy of turbulent fluctuations of velocity and third-order moments in the near wake of a circular cylinder

Turbulent structure of the near wake behind a circular cylinder in a cross flow at Re = 3900 was studied experimentally. Instantaneous velocity vector fields in the wake were measured using Smoke Image Velocimetry (SIV). The profiles of velocity components, their RMS fluctuations and Reynolds stresses were compared with direct numerical simulation and experimental data obtained by other authors. The anisotropy of turbulent fluctuations in different zones of the wake was analyzed. Third-order moments of velocity fluctuations in the near wake behind the cylinder were measured for the first time ever.

IMEX‐ODTLES: A multi‐scale and stochastic approach for highly turbulent flows

AbstractThe stochastic One‐Dimensional Turbulence (ODT) model is used in combination with a Large Eddy Simulation (LES) approach in order to illustrate the potential of the fully coupled model (ODTLES) for highly turbulent flows. In this work, we use a new C++ implementation of the ODTLES code in order to analyze the computational performance in a classical incompressible turbulent channel flow problem. The parallelization potential of the model, as well as its physical and numerical consistency are evaluated and compared to Direct Numerical Simulations (DNSs). The numerical results show that the model is capable of reproducing a representative part of the DNS data at a cheaper computational cost. This advantage can be enhanced in the future by the implementation of a straightforward parallelization approach.

Distribution of stress intensity ratio in canonical turbulent flows and converging-diverging channel

The understanding and prediction of wall-bounded turbulence are of great importance for industrial flows. The stress intensity ratio, Rb, is recognized as one key parameter, and its value was known as being around 0.3 in the wake layer of wall-bounded turbulence and the mixing layer. In this work, Rb is studied using Direct Numerical Simulation data extracted from the canonical flows (channel, pipe, flat plate boundary layer at various Reynolds numbers) and converging-diverging channel flow. It is found that in canonical flows and the converging-diverging channel flow, the stress intensity ratio exhibits a certain pattern if the stress intensity ratio varies with the eddy viscosity ratio r or turbulent Reynolds number Rek. Moreover, the r-Rb distribution shows advanced similarity against the Rek-Rb distribution, which is due to that r is consist of transport variables. The similarity is evidenced by the fact that the r-Rb distribution is insensitive to zero pressure gradient, positive pressure gradient, and geometric effects. The r-Rb distribution seems to be mainly sensitive to the friction Reynolds number. This priori study shows that the r-Rb distribution is of universality in flows of different geometric configurations, and it offers information for the construction and improvement of turbulence models.

Analysis of the vorticity tube segment in fluid turbulence

To address the geometrical properties of the turbulent velocity vector field, a new concept named streamtube segment has been developed [Wang L. On properties of fluid turbulence along streamlines. J Fluid Mech, 2010, 648: 183–203]. According to the vectorial topology, the entire velocity field can be partitioned into the so-called streamtube segments, which are organized in a non-overlapping and space-filling manner. A similar idea is implemented to study the turbulent vorticity vector field. Differently from the conventional vortex tubes, vorticity tube segments are space-filling and can be characterized by non-arbitrary parameters. Such structure enables a more quantitative, rather than illustrative, description of turbulence. In principle, these two conditions are the linkage to reproduce the entire turbulent field from decomposed geometrical units with relatively simple structures. From analyzing the direct numerical simulation data, the topological and dynamical properties of vorticity tube segments are explored, such as the scale distribution and chirality. The characteristic parameters have strong influence on the enstrophy production and vorticity stretching. Consequently the common knowledge in turbulence dynamics that vorticity is more stretched than compressed need to be rectified in the vorticity tube segment context.

Mean dynamics and transition to turbulence in oscillatory channel flow

The mean dynamics in oscillatory channel flow is examined to investigate the dynamical mechanisms underlying the transition to turbulence in oscillatory wall-bounded flow. The analyses employ direct numerical simulation data acquired at three Stokes Reynolds numbers: $Re_{s}=648$, 801 and 1009, where the lower $Re_{s}$ flow is transitional over the entire cycle and the two higher $Re_{s}$ flows exhibit flow characteristics similar to steady turbulent wall-bounded flow during part of the cycle. The flow evolution over a half-period of oscillation for all three $Re_{s}$ is as follows: near-wall streamwise velocity streaks develop during the early accelerating portion of the cycle; then at some later point in the cycle that depends on $Re_{s}$, the near-wall streaks breakdown (demarking the onset of the nonlinear development stage), and the near-wall Reynolds stress grows explosively; the Reynolds stress remains elevated for part of the cycle before diminishing (yet remaining finite) during the late decelerating portion of the cycle. This process is then repeated indefinitely. The present findings demonstrate that transition to turbulence occurs when the nonlinear development stage begins during the accelerating portion of the cycle. This crucially leads to the diminishing importance of the centreline momentum source, the emergence of a locally accelerating/decelerating internal layer centred about the edge of the Stokes layer and the wall-normal rearrangement of the mean forces prior to the start of the decelerating portion of the cycle. The rearrangement of mean forces culminates in a four layer structure in the mean balance of forces. This is significant on a number of accounts since empirical and theoretical evidence suggests that the formation of a four layer structure is an important characteristic of a self-similar hierarchal structure that underlies logarithmic dependence of the mean velocity profile in steady turbulent wall-bounded flows (Klewicki et al., J. Fluid Mech., vol. 638, 2009, pp. 73–93). When the nonlinear development stage begins during the decelerating portion of the cycle (i.e. at $Re_{s}=648$), a four layer structure is not observed in the mean balance of forces and the flow remains weakly transitional over the entire cycle.

Assessment of performance of subgrid stress models for a LES technique for predicting suppression of turbulence and heat transfer in channel flows under the influence of body forces

The main purpose of this work was to assess the performance of subgrid stress models for large eddy simulation (LES) of the flow and heat transfer of a conductive liquid simulating a molten salt (Pr = 4.1) in a square duct under the influence of a transverse magnetic field and an upward flow of air in a vertical heated pipe under a strong influence of buoyancy. An analysis of these problems is important when choosing the most appropriate subgrid-scale LES model for calculating the flows of an electrically conductive liquid under the combined influence of a magnetic field and buoyancy forces. Four subgrid-scale (SGS) models were verified: the Smagorinsky model with damping function (SMP), a coherent structure model (CSM), a WALE model and a hybrid model based on the equation for turbulent kinetic energy (KDES). For magnetohydrodynamic (MHD) flow in the duct, computations were performed in a domain with periodic inlet-exit boundaries and in a domain corresponding to the entrance region of a duct with a transverse magnetic field. Mixed convection of the air in the vertical heated pipe was simulated only in the domain with periodic boundaries. The results are compared with available data of direct numerical simulations (DNS).For MHD flow in the duct, the best predictions of DNS data for the average and fluctuating velocity components at Ha=21.2 and Re=5602 were obtained with the CSM and WALE models. The skin-friction and heat transfer coefficients are well known to have a minimum as Ha increases due to turbulence suppression by the magnetic field. The SMP and KDES models predict a minimum at Hadip≈22, whereas the CSM and WALE models predict a minimum at Hadip≈30 for Re=5602. The DNS data marked these values as the lower and upper boundaries of the complete turbulence suppression region for the same Reynolds number.For mixed convection of the air upward flows in a circular heated pipe at Re=5300, the CSM and WALE models showed weaker suppression of turbulence due to buoyancy forces when compared to the DNS results. The results of calculations of skin-friction and heat transfer coefficients performed with the help of the SMP and KDES models are much more coincident with the DNS data.

Reynolds Stress Model for Viscoelastic Drag-Reducing Flow Induced by Polymer Solution.

Viscoelasticity drag-reducing flow by polymer solution can reduce pumping energy of pipe flow significantly. One of the simulation manners is direct numerical simulation (DNS). However, the computational time is too long to accept in engineering. Turbulent model is a powerful tool to solve engineering problems because of its fast computational ability. However, its precision is usually low. To solve this problem, we introduce DNS to provide accurate data to construct a high-precision turbulent model. A Reynolds stress model for viscoelastic polymer drag-reducing flow is established. The rheological behavior of the drag-reducing flow is described by the Giesekus constitutive Equation. Compared with the DNS data, mean velocity, mean conformation tensor, drag reduction, and stresses are predicted accurately in low Reynolds numbers and Weissenberg numbers but worsen as the two numbers increase. The computational time of the Reynolds stress model (RSM) is only 1/120,960 of DNS, showing the advantage of computational speed.

Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

An artificial neural network (ANN) is used to establish the relation between the resolved-scale flow field and the subgrid-scale (SGS) stress tensor, to develop a new SGS model for large-eddy simulation (LES) of isotropic turbulent flows. The data required for training and testing of the ANN are provided by performing filtering operations on the flow fields from direct numerical simulations (DNSs) of isotropic turbulent flows. We use the velocity gradient tensor together with filter width as input features and the SGS stress tensor as the output labels for training the ANN. In the a priori test of the trained ANN model, the SGS stress tensors obtained from the ANN model and the DNS data are compared by computing the correlation coefficient and the relative error of the energy transfer rate. The correlation coefficients are mostly larger than 0.9, and the ANN model can accurately predict the energy transfer rate at different Reynolds numbers and filter widths, showing significant improvement over the conventional models, for example the gradient model, the Smagorinsky model and its dynamic version. A real LES using the trained ANN model is performed as the a posteriori validation. The energy spectrum computed by the improved ANN model is compared with several SGS models. The Lagrangian statistics of fluid particle pairs obtained from the improved ANN model almost approach those from the filtered DNS, better than the results from the Smagorinsky model and dynamic Smagorinsky model.

Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzelet al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter$\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption,$\unicode[STIX]{x1D6EC}_{c}$values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form$\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$with the kinematic (incompressible) displacement thickness$\unicode[STIX]{x1D6FF}_{K}^{\ast }$is shown to be a valid parameter of the form$\unicode[STIX]{x1D6EC}_{c}$and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale,$\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the$\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$stress and thus also the wall shear stress$\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of$\text{d}L_{0}/\text{d}x$leads to palpable improvements.

Physical Insights on MILD Combustion From DNS

MILD combustion is gaining interest in recent times because it is attractive for “green” combustion technology. However, its fundamental aspects are not well understood. Recent progresses made on this topic using direct numerical simulation data are presented and discussed in a broader perspective. It is shown that a revised theory involving at least two chemical timescales is required to describe the inception of this combustion not only showing both autoignition and flame characteristics but also a strong interaction between these two phenomena. The reaction zones have complex morphological and topological features and the most probable shape is pancake-like structure implying micro-volume combustion under MILD conditions unlike the sheet-combustion in conventional cases. Relevance of the MILD (micro-volume) combustion to supersonic combustion is explored theoretically and qualitative support is shown and discussed using experimental and numerical Schlieren images.

Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.

Three-dimensional visualization of destruction events of turbulent momentum transfer in a plane jet

Destruction events of momentum transfer as represented by the Reynolds (shear) stress via the pressure–rate-of-strain interaction in a plane jet are investigated using direct numerical simulation data. To obtain three-dimensional pictures of the turbulent structures, pseudo-three-dimensional data are constructed on the basis of Taylor’s frozen hypothesis from time series of the relevant quantities. The coherent motion in the plane jet is extracted by means of conditional sampling analogous to variable-interval time averaging. We obtain a large-scale coherent structure consisting of horseshoelike vortices and a Kármán-vortex-like very large spanwise vortex street. Furthermore, we find that the active Reynolds stress destruction is localized around the large-scale coherent vortex structure. However, the coherent structure itself does not contribute to the Reynolds stress destruction, but the remaining incoherent motions do. For the significant pressure–rate-of-strain events in the incoherent motion, we display invariant maps of the velocity gradient tensor and the principal axes of strain to facilitate a discussion of the consistency of the numerical results with an illustration by Hinze [Turbulence, 2nd ed. (McGraw-Hill, 1975), pp. 325–328] and with our own experimental results [Takahashi et al., “Experimental investigation on destruction of Reynolds stress in a plane jet,” Exp. Fluids 60, 46 (2019)]. Consequently, the present results suggest that the illustration of the Reynolds stress destruction by Hinze is not completely applicable to a plane jet.

Impact of Prandtl numbers on turbulence modeling

A low-Reynolds number (LRN) turbulence model is devised that includes the near-wall turbulence modeling and turbulent Prandtl numbers σ(k,ε,t). A secondary source term added in the -equation accounts substantially for the anisotropic production in near-wall regions. Hence, improved predictions of adverse pressure-gradient flows, involving separation and reattachment are obtained with a considerable reduction in the turbulent kinetic energy and length scale magnitudes. The eddy-viscosity formulation responds to both rotational and irrotational strains to better predict nonequilibrium flows. The current model employs no wall function/distance parameter to bridge the near-wall integration as required by conventional k-ε models. Model predictions are compared with direct numerical simulation (DNS) and experimental data; a good correlation is achieved.

Statistical analysis of temperature distribution on vortex surfaces in hypersonic turbulent boundary layer

The nonuniform temperature distribution (NUTD) on the coherent vortex surfaces of hypersonic turbulent boundary layer (TBL) is studied using the conditional sampling technique. The direct numerical simulation data of Mach 8 flat-plate TBL flows with different wall temperatures, Tw/T∞ = 10.03 and 1.9, are used for this research, and the coherent vortex surface is identified by the Ω-criterion. Two characteristic sides of the vortex are defined, which are represented by the positive and negative streamwise velocity fluctuations (±u′) of the vortex surfaces. The conditional sampling results between the mean temperature of the two sides show that there is a significant difference of up to 20% at the same wall-normal location. Furthermore, the velocity-temperature fluctuation correlations (Ru′T′ and Rv′T′) at the characteristic sides of vortex surfaces are studied. It is found that the temperature fluctuations are redistributed by the vortex rotational motion that has taken effect through Ru′T′ and Rv′T′ and then lead to the NUTD. The NUTD features are changed quantitatively by wall cooling but share the similar mechanism as that of the higher-temperature case.

Analysis of the Interconnections between Classic Vortex Models of Coherent Structures Based on DNS Data

Low- and high-speed streaks (ejection, Q2, and sweep, Q4, events in quadrant analysis) are significant features of coherent structures in turbulent flow. Streak formation is closely related to turbulent structures in several vortex models, such as attached eddy models, streamwise vortex analysis models, and hairpin vortex models, which are all standard models. Vortex models are complex, whereby the relationships among the different vortex models are unclear; thus, further studies are still needed to complete our understanding of vortices. In this study, 30 sets of direct numerical simulation (DNS) data were obtained to analyze the mechanics of the formation of coherent structures. Image processing techniques and statistical analysis were used to identify and quantify streak characteristics. We used a method of vortex recognition to extract spanwise vortices in the x–z plane. Analysis of the interactions among coherent structures showed that the three standard vortex models all gave reasonably close results. The attached eddy vortex model provides a good explanation of the linear dimensions of streaky structures with respect to the water depth and Q2 and Q4 events, whereby it can be augmented to form the quasi-streamwise vortex model. The legs of a hairpin vortex envelop low-speed streaky structures and so move in the streamwise direction; lower-velocity vortex legs also gradually accumulate into a streamwise vortex. Statistical analysis allowed us to combine our present results with some previous research results to propose a mechanism for the formation of streaky structures. This study provides a deeper understanding of the interrelationships among different vortex models.

A critical comparison of two-fluid model, discrete particle method and direct numerical simulation for modeling dense gas-solid flow of rough spheres

Interphase drag coefficient is a critical input in two-fluid model (TFM) and discrete particle method (DPM). In this study, extensive TFM and DPM simulations were carried out to study of the hydrodynamics of gas-solid flows of monodisperse, rough particles in a dense fluidized bed using fourteen drag coefficient correlations available in literature, the simulation results were then compared to the direct numerical simulation (DNS) and experimental data of Tang et al. (2016). It was shown that (i) all TFM and DPM simulations result in a lower bed expansion rate than those of DNS and experiment, which indicates that the true interphase drag force is underestimated by all fourteen drag coefficient correlations; (ii) all DPM simulations can correctly capture, at least in a qualitative sense, the main hydrodynamic features obtained from DNS, but some TFM simulations with the exactly same drag coefficients show anomalous phenomena. This is not an indicator of the failure of the used drag coefficients but might be a sign of the deficiency of the used particle phase stress model in this specific situation; (iii) the time-averaged differential pressure drops of DPM and TFM simulations agree well with DNS results, but the characteristic frequency of pressure fluctuation found in DNS is overestimated by a factor of 2–3 by all DPM and TFM simulations; and (iv) the magnitude of local and global granular temperatures of TFM, DPM and DNS are all in a fair agreement, but the degree of the anisotropy of both local and global granular temperature found in DNS is systematically underestimated by DPM and TFM, especially, the local granular temperature in TFM simulations is inherently isotropic due to the fundamental assumption of the used kinetic theory. This study highlights the need of a better interphase drag coefficient and a better particle phase stress model for modeling dense gas-solid flow.

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.

Rare transitions to thin-layer turbulent condensates

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time $\unicode[STIX]{x1D70F}_{d}$ of the 2-D condensate to 3-D flow state and the build-up time $\unicode[STIX]{x1D70F}_{b}$ of the 2-D condensate. We show that both of these times $\unicode[STIX]{x1D70F}_{d},\unicode[STIX]{x1D70F}_{b}$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modelled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations are examined several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the “quarter scale” data from four algorithms presented in the θ-group study of Thornber et al. [“Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [“Analysis of turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow using direct numerical simulation data,” Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Terms arising from the compressibility of the flow are examined, in particular the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

Statistical properties of thermally expandable particles in soft-turbulence Rayleigh-B\xe9nard convection

.The dynamics of inertial particles in Rayleigh-Bénard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS) in the soft-turbulence regime. We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes’ force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, tau_{T}, and the thermal expansion coefficient of particles relative to that of the fluid, K = alpha_{p}/alpha_{f}. In particular, the residence time is constant for small thermal response times, tau_{T} lesssim 1, and increasing with tau_{T} for larger thermal response times, tau_{T} gtrsim 1. Also, the thermal BL residence time is increasing with decreasing K. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with tau_{T} for larger response times, thus explaining the trends in the DNS data well.Graphical abstract