Canonical Turbulence Research Articles

Interlinking Rayleigh–Taylor/Richtmyer–Meshkov interfacial mixing with variable acceleration and canonical Kolmogorov turbulence

Canonical turbulence and Rayleigh–Taylor/Richtmyer–Meshkov mixing with variable acceleration are paradigmatic complexities in science, mathematics, and engineering, with broadly ranging applications in nature, technology, and industry. We employ scaling symmetries and invariant forms to represent these challenging processes and to assess their very different properties. We directly link—for the first time to our knowledge—the attributes of Rayleigh–Taylor/Richtmyer–Meshkov interfacial mixing with variable acceleration to those of canonical turbulence, including scaling laws, spectral shapes, and characteristic scales. We explore the role of control dimensional parameters in quantifying these processes. The theory results compare well with available observations, the chart perspectives for future experiments and simulations, and for better understanding realistic complexity.

On Machine-Learning-Aided Two-Scale Solution for Turbulent Fluid Flows

Scale-resolving solutions for computational fluid dynamics problems have usually been challenging due to their request for computing resources. A two-scale framework was proposed for more efficient solutions to couple a local fine-mesh solution with a global coarse-mesh solution. The methodology was successfully implemented and demonstrated for a canonical turbulent channel flow and for a tripped turbulent boundary layer. The solution mapping from the local fine-mesh to the global coarse-mesh region is realized by modifying the flow-governing equations in the under-resolved coarse-mesh region through adding extra forcing source terms generated from the space–time-averaged fine-mesh solutions. However, the high-gradient transitional region presents additional challenges when applying the Chebyshev spectral method for mapping the source terms; thus the high-gradient frontal region has not been fully resolved in the streamwise direction. In the present work, the propagation of the source terms is facilitated by machine learning tools (multilayer perceptron-based neural network) so as to implement the method in flowfields with high gradients or drastic changes in the mean velocity. The neural-network-based propagation model is shown to be capable of accurately estimating the source terms in the near-wall coarse-mesh region. The mean flow there thus can be nicely reproduced by the source-term propagation. The machine-learning tools thus provide potential as the more advanced source-term propagation method for the two-scale framework to be implemented in more complicated flowfields.

Two-scale solution for tripped turbulent boundary layer

Recent findings on the Reynolds-number-dependent behaviour of near-wall turbulence in terms of the ‘foot-printing’ of outer large-scale structures call for a new modelling development. A two-scale framework was proposed to couple a local fine-mesh solution with a global coarse-mesh solution by He (Intl J. Numer. Meth. Fluids, vol. 86, 2018, pp. 655–677). The methodology was implemented and demonstrated by Chen & He (J. Fluid Mech, vol. 933, 2022, p. A47) for a canonical turbulent channel flow, where the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for a conventional wall-resolved large-eddy simulation (WRLES) to $O(R{e^1})$ . The present work extends the two-scale method to turbulent boundary layers. A two-dimensional roughness element is used to trip a turbulent boundary layer. It is observed that large-scale disturbances originating at the trip have a much shorter lifetime and weaker foot-printing signatures on near-wall flow compared to those long streaky coherent structures in well-developed wall-bounded turbulent flows. Modal analyses show that the impact of trip-induced large scales can be adequately captured by a locally embedded fine-mesh block. For the tripped turbulent boundary layer, a Chebyshev block-spectral mapping is adopted to propagate source terms from the local fine-mesh blocks to the global coarse-mesh domain, driving to a target solution for the upscaled equations. The computed mean statistics and energy spectra are in good agreement with corresponding experimental data, WRLES and direct numerical simulation (DNS) results. The overall mesh count– $Re$ scaling is estimated to reduce from $O(R{e^{1.8}})$ for the full wall-resolved LES to $O(R{e^{0.9}})$ for the present two-scale solution.

A high order finite difference solver for simulations of turbidity currents with high parallel efficiency

We present a high order finite difference solver, ParaTC , for the direct numerical simulations of turbidity currents with canonical turbulent channel configuration (periodic boundary conditions in the horizontal directions and non-periodic in vertical direction). Uniform meshes are adopted in streamwise and spanwise directions, while stretched grids can be used in wall-normal direction. In order to improve the parallel efficiency, we propose a new 2D pencil-like parallel configuration with totally 6 different pencil arrangements. A parallel Thomas algorithm is also included to further reduce the communication overhead when solving tridiagonal equations. In addition, we perform an optimal search method in the initializing stage to find the fastest Poisson solver scheme among four alternatives for a specific mesh configuration. The runtime ratio between traditional pencil-like Poisson solver and present solver is about 1.5. An approximate linear strong scaling performance is achieved, and the weak scaling performance is also improved. Three benchmark simulations are preformed, and the statistics are compared with those extracted from the simulations by the spectral method, and good agreements are achieved. The source code is freely available at https://github.com/GongZheng-Justin/ParaTC .

A sub-grid scale cavitation inception model

Unresolved pressure fluctuations at the sub-grid scale (SGS) level of large eddy simulation (LES) or Reynolds-averaged Navier–Stokes computations affect cavitation inception predictions, as SGS low pressures are simply ignored. We present a framework to take the unresolved SGS flow into account. Representing the SGS flow as canonical turbulence, in this paper, homogeneous isotropic turbulence (HIT), the pressure fluctuations, and transport and cavitating behavior of nuclei in such turbulence can be evaluated from direct numerical simulations (DNS) and used to create a model of cavitation inception that accounts for SGS fluctuations. To accomplish this, nuclei of different sizes were transported in DNS of HIT using their pressure history to drive the Rayleigh–Plesset equation that simulates bubble dynamics. In this way, expected average cavitation frequencies were tabulated for a range of SGS Taylor scale Reynolds numbers (Reλ), nucleus size, turbulent kinetic energy dissipation rate, and mean pressure. The model uses this table to estimate the cavitation event rate in each cell of a computational fluid dynamics solution. Inception can then be predicted by comparing the total cavitation rate with the detection criterion. The model is first assessed on two cases of HIT (at Reλ = 240 and 324) by comparing the pressure statistics, which it predicts in LES runs using the SGS cavitation model against the statistics of DNS. Then, a high Reλ (1660–1880) HIT flow is simulated using LES, and cavitation events are compared against experimental data. The inception model successfully predicts the inception pressure and the cavitation rates in the flow.

Macroscopic turbulent kinetic energy budget in flow through a wall-bounded compact bank of cylinders

The flow in devices, such as heat exchangers, can be idealized as turbulent flow past an array of regularly spaced obstacles. Engineering calculations in such devices are easily handled if the flow can be represented by its volume-average quantities. This paper reports an investigation into the volume-averaged flowfield in a regular array of cylinders of finite height in crossflow at two Reynolds numbers (ReD). The investigation is based on scale-resolving computations and is thus the first to analyze the true form of the macroscopic turbulent kinetic energy (TKE) conservation law in the presence of macroscopic shear. Volume-averaging is performed parallel to the end walls in order to obtain profiles of macroscopic flow quantities. In inner coordinates, the macroscopic velocity profiles are similar to the canonical turbulent channel flow profiles, but with different values of the von Kármán constant and log-law y-intercept. The volume-averaged TKE is defined so as to include contributions from both the macroscopic and microscopic components of the flow. While the macroscopic TKE profile is very different to that of channel flow, the macroscopic TKE budget terms are remarkably similar. One notable exception is that the production rate stays large throughout the domain rather than attenuating rapidly after a near-wall peak. An extension to a widely used macroscopic turbulence model is proposed, which enables it to match the volume-averaged TKE production rate predicted by the large eddy simulations.

Contribution of Reynolds shear stress to near-wall turbulence in Rayleigh–Bénard convection

Direct numerical simulations of Rayleigh–Bénard convection flows are performed for Pr=0.7 with Ra=5×108 and 2×1010, and for Pr=0.021 with Ra=107 and 5×108, where Pr and Ra are the Prandtl number and the Rayleigh number, respectively. The velocity-gradient production based on the short-time averaging shows the near-wall intensive positive peak and negative region. The correlations between the Reynolds shear stresses and the wall-normal and transverse gradients of the horizontal mean velocities locally and temporally result in the positive and negative velocity-gradient production near the wall. The eigenvalues of the anisotropic Reynolds stress tensors on the barycentric map show that the short-lived anisotropy related to the one-directional stretching occurs along the wall-normal distance; this behavior is similar to that of a canonical turbulent channel flow. The results indicate that the local and temporal Reynolds shear stresses near the wall with the shear of the horizontal mean velocities play an important role in the near-wall velocity-gradient production, which leads to the turbulent regime in the Rayleigh–Bénard convection flow with an increase in Rayleigh number.

Kolmogorovian Active Turbulence of a Sparse Assembly of Interacting Marangoni Surfers

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors among which the so-called active turbulence where spatially and time disordered flow patterns spontaneously arise in a variety of {active systems}. De facto, the active turbulence naming suggests a connection with a second seminal class of out-of-equilibrium systems, fluid turbulence, and yet of very different nature with energy injected at global system scale rather than at the elementary scale of single constituents. Indeed the existence of a possible strong-tie between active and canonical turbulence remains an open question and a field of profuse research. Using an assembly of self-propelled interfacial particles, we show experimentally that this active system shares remarkable quantitative similarities with canonical fluid turbulence, as described by the celebrated 1941 phenomenology of Kolmogorov. Making active matter entering into the universality class of fluid turbulence not only benefits to its future development but may also provide new insights for the longstanding description of turbulent flows, arguably one of the biggest remaining mysteries in classical physics.

Direct numerical simulations of premixed and stratified flame propagation in turbulent channel flow

Direct numerical simulations are performed to investigate the transient upstream flame propagation (flashback) through homogeneous and fuel-stratified hydrogen-air mixtures transported in fully-developed turbulent channel flows. Results indicate that, for both cases, the flame maintains steady propagation against the bulk flow direction and the global flame shape and the local flame characteristics are both affected by the occurrence of fuel stratification. Globally, the mean flame shape undergoes an abrupt change when the approaching reactants transition from an homogeneous to a stratified mixing configuration. A V-shaped flame surface, whose leading-edge is located in the near-wall region, characterizes the non-stratified, homogeneous mixture case while a U-shaped flame surface, whose leading-edge propagates upstream at the channel centreline, distinguishes the case with fuel stratification (fuel-lean in the near-wall region and fuel-rich away from the wall). The characteristic thickness, wrinkling and displacement speed of the turbulent flame brush are subject to considerable changes across the channel due to the dependence of the turbulence and mixture properties on the distance from the channel walls. More specifically, the flame transitions from a moderately wrinkled, thin-flamelet combustion regime in the homogeneous mixture case to a strongly wrinkled flame brush more representative of a thickened-flame combustion regime in the near-wall region of the fuel-stratified case. The combustion regime may be related to Karlovitz number and it is shown that a nominal channel-flow Karlovitz number, Kachin, based on the wallnormal variation of canonical turbulence (tη = (ν/e) 1/2) and chemistry (tl = δl/Sl) time scales in fully-developed channel flow, compares well with an effective Karlovitz number, Kachfl, extracted from the present DNS datasets using conditionally sampled values of tη and tl in the immediate vicinity of the flame (0.1 < C < 0.3).

Vitiated High Karlovitz n-decane/air Turbulent Flames: Scaling Laws and Micro-mixing Modeling Analysis

Turbulent flames with high Karlovitz numbers have deserved further attention in the most recent literature. For a fixed value of the Damkohler number (ratio between an integral mechanical time and a chemical time), the increase of the Karlovitz number (ratio between a chemical time and a micro-mixing time) by an order of magnitude implies the increase of the turbulent Reynolds number by two orders of magnitude (Bray, Symp. (Int.) Combust. 26, 1–26 1996). In the practice of real burners featuring a limited range of variation of their turbulent Reynolds number, high Karlovitz combustion actually goes with a drastic reduction of the Damkohler number. Within this context, the relation between the dilution by burnt gases and the apparition of high Karlovitz flames is discussed. Basic scaling laws are reported which suggest that the overall decrease of the burning rate due to very fast mixing can indeed be compensated by the energy brought to the reaction zone by burnt gases. To estimate the validity of these scaling laws, in particular the response of the quenching Karlovitz versus the dilution level with a vitiated stream, the micro-mixing rate is varied in a multiple-inlet canonical turbulent and reactive micro-mixing problem. A reduced n-decane/air chemical kinetics is used, which has been derived from a more detailed scheme using a combination of a directed relation graphs analysis with a Genetic Algorithm. The multiple-inlet canonical micro-mixing problem includes liquid fuel injection and dilution by burnt gases, both calibrated from conditions representative of an aeronautical combustion chamber. The results confirm the possibility of reaching, with the help of a vitiated mixture, very high Karlovitz combustion before quenching occurs.

Efficient simulation of multidimensional continuum and non-continuum flows by a parallelised unified gas kinetic scheme solver

ABSTRACTWe develop an efficient, parallel, gas-kinetic solver for computing both continuum and non-continuum flows over non-Cartesian geometries by utilising the unified gas kinetic scheme (UGKS). UGKS, however, requires the computationally expensive update of a six-dimensional phase space at each time step restricting its application to canonical, laminar problems and simple geometries. In this paper, we demonstrate that the applications of UGKS can be increased by parallelising it and combining it with a recently developed, Cartesian grid method (UGKS-CGM). We demonstrate that our Cartesian grid methodology as well as UGKS parallelization perform and scale well on a range of numerical test cases even for a very large number of cores. Finally, we demonstrate that the solver accurately computes canonical turbulence at low Knudsen numbers. These results demonstrate that the parallelised UGKS code can be utilised to effectively study the non-equilibrium effects of rarefaction on laminar and turbulent non-continuum flows.

Validating under-resolved turbulence intensities for PIV experiments in canonical wall-bounded turbulence

The discrepancy between measured turbulence intensity obtained from experiments in wall-bounded turbulence and the fully resolved reference results (usually from DNS datasets) are often attributed to spatial resolution issues, especially in PIV measurements due to the presence of spatial averaging within the interrogation region/volume. In many cases, in particular at high Reynolds numbers (where there is a lack of DNS data), there is no attempt to verify that this is the case. There is a risk that attributing unexpected PIV statistics to spatial resolution, without careful checks, could mask wider problems with the experimental setup or test facility. Here, we propose a robust technique to validate the under-resolved PIV obtained turbulence intensity profiles for canonical wall-bounded turbulence. This validation scheme is independent of Reynolds number and does not rely on empirical functions. It is based on arguments that (1) the viscous-scaled small-scale turbulence energy is invariant with Reynolds number and that (2) the spatially under-resolved measurement is sufficient to capture the large-scale energy. This then suggests that we can estimate the missing energy from volume-filtered DNS data at much lower Reynolds numbers. Good agreement is found between the experimental results and estimation profiles for all three velocity components, demonstrating that the estimation tool successfully computes the missing energy for given spatial resolutions over a wide range of Reynolds numbers. A database for a canonical turbulent boundary layer and associated MATLAB function are provided that enable this missing energy to be calculated across a range of interrogation volume sizes, so that users do not require access to raw DNS data. This methodology and tool will provide PIV practitioners, investigating canonical wall-bounded turbulent flow with a convenient check of the effects of spatial resolution on a given experiment.

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence

AbstractTurbulent mixing in a Richtmyer–Meshkov unstable light–heavy–light (air–${\mathrm{SF} }_{6} $–air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.14) is investigated using ensemble statistics obtained from simultaneous velocity–density measurements. The mixing is driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller-scale vortices. After reshock the flow appears to transition to a turbulent (likely three-dimensional) state, at which time our planar measurements are used to probe the developing flow field. The density self-correlation $b= - \langle \rho v\rangle $ (where $\rho $ and $v$ are the fluctuating density and specific volume, respectively) and terms in its evolution equation are directly measured experimentally for the first time. Amongst other things, it is found that production terms in the $b$ equation are balanced by the dissipation terms, suggesting a form of equilibrium in $b$. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. A length-scale analysis suggests that an inertial range is beginning to form, consistent with the onset of a mixing transition. The developing turbulence is observed to reduce non-Boussinesq effects in the flow, which are found to be small over much of the layer after reshock. Second-order two-point structure functions of the density field exhibit a power-law behaviour with a steeper exponent than the standard $2/ 3$ power found in canonical turbulence. The absence of a significant $2/ 3$ region is observed to be consistent with the state of the flow, and the emergence of the steeper power-law region is discussed.

Boundary layer dynamics over London, UK, as observed using Doppler lidar during REPARTEE-II

Abstract. Urban boundary layers (UBLs) can be highly complex due to the heterogeneous roughness and heating of the surface, particularly at night. Due to a general lack of observations, it is not clear whether canonical models of boundary layer mixing are appropriate in modelling air quality in urban areas. This paper reports Doppler lidar observations of turbulence profiles in the centre of London, UK, as part of the second REPARTEE campaign in autumn 2007. Lidar-measured standard deviation of vertical velocity averaged over 30 min intervals generally compared well with in situ sonic anemometer measurements at 190 m on the BT telecommunications Tower. During calm, nocturnal periods, the lidar underestimated turbulent mixing due mainly to limited sampling rate. Mixing height derived from the turbulence, and aerosol layer height from the backscatter profiles, showed similar diurnal cycles ranging from c. 300 to 800 m, increasing to c. 200 to 850 m under clear skies. The aerosol layer height was sometimes significantly different to the mixing height, particularly at night under clear skies. For convective and neutral cases, the scaled turbulence profiles resembled canonical results; this was less clear for the stable case. Lidar observations clearly showed enhanced mixing beneath stratocumulus clouds reaching down on occasion to approximately half daytime boundary layer depth. On one occasion the nocturnal turbulent structure was consistent with a nocturnal jet, suggesting a stable layer. Given the general agreement between observations and canonical turbulence profiles, mixing timescales were calculated for passive scalars released at street level to reach the BT Tower using existing models of turbulent mixing. It was estimated to take c. 10 min to diffuse up to 190 m, rising to between 20 and 50 min at night, depending on stability. Determination of mixing timescales is important when comparing to physico-chemical processes acting on pollutant species measured simultaneously at both the ground and at the BT Tower during the campaign. From the 3 week autumnal data-set there is evidence for occasional stable layers in central London, effectively decoupling surface emissions from air aloft.