Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to investigate the turbulent flows under transcritical conditions using DNS of turbulent channel flows. A fully compressible solver is used in conjunction with a Peng-Robinson real-fluid equation of state to describe the transcritical flows. A channel flow with two isothermal walls is simulated with one heated and one cooled boundary layers. The grid resolution adopted in this study is slightly finer than that required for DNS of incompressible channel flows. The simulations are conducted using both fully (FC) and quasi-conservative (QC) schemes to assess their performance for transcritical wall-bounded flows. The instantaneous flows and the statistics are analyzed and compared with the canonical theories. It is found that results from both FC and QC schemes qualitatively agree well with noticeable difference near the top heated wall, where spurious oscillations in velocity can be observed. Using the DNS data, we then examine the usefulness of Townsend attached eddy hypothesis in the context of flows at transcritical conditions. It is shown that the streamwise energy spectrum exhibits the inverse wavenumber scaling and that the streamwise velocity structure function follows a logarithmic scaling, thus providing support to the attached eddy model at transcritical conditions.
We have performed direct numerical simulations (DNS) of compressible turbulent channel flow at supercritical pressure with top and bottom isothermal walls kept respectively at a supercritical (Ttop > Tpb) and subcritical temperature (Tbot < Tpb), where Tpb is the pseudoboiling temperature. The DNS are conducted using a high-order discretization of the fully compressible Navier-Stokes equations in conservative form closed with the Peng-Robinsion (PR) state equation. Bulk density is adjusted to obtain a bulk pressure of approximately pb = 1.1pcr where pcr is the critical pressure of the working …
High-fidelity simulations of transcritical spray mixing and auto ignition in a combustion chamber are performed at high pressure and temperature conditions using a recently developed finite rate LES solver. The simulation framework is based on a diffused-interface (DI) method that solves the compressible multi-species conservation equations along with the Peng Robinson state equation and real-fluid transport properties. A finite volume approach with entropy stable scheme is employed to accurate simulate the non-linear real fluid flow. LES analysis is performed for non-reacting and reacting spr…
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Many practical combustion systems such as those in rockets, gas turbines, and internal combustion engines operate under high pressures that surpass the thermodynamic critical limit of fuel-oxidizer mixtures. These conditions require the consideration of complex fluid behaviors that pose challenges for numerical simulations, casting doubts on the validity of existing subgrid-scale (SGS) models in large-eddy simulations of these systems. While data-driven methods have shown high accuracy as closure models in simulations of turbulent flames, these models are often criticized for lack of physical …
The need for improved engine efficiencies has motivated the development of high-pressure combustion systems, in which operating conditions achieve and exceed critical conditions. Associated with these conditions are strong variations in thermo-transport properties as the fluid undergoes phase transition, and two-stage ignition with low-temperature combustion. Accurately simulating these physical phenomena at real-fluid environments remains a challenge. By addressing this issue, a high-fidelity LES-modeling framework is developed to conduct simulations of transcritical fuel spray mixing and aut…
Accurate simulations of high-pressure transcritical fuel sprays are essential for the design and optimization of next-generation gas turbines, internal combustion engines, and liquid propellant rocket engines. Most important and challenging is the accurate modelling of complex real-gas effects in high-pressure environments, especially the hybrid subcritical-to-supercritical mode of evaporation during the mixing of fuel and oxidizer. In this paper, we present a novel modeling framework for high-fidelity simulations of reacting and non-reacting transcritical fuel sprays. In this method, the high…
An extension to the classical FPV model is developed for transcritical real-fluid combustion simulations in the context of finite volume, fully compressible, explicit solvers. A double-flux model is developed for transcritical flows to eliminate the spurious pressure oscillations. A hybrid scheme with entropy-stable flux correction is formulated to robustly represent large density ratios. The thermodynamics for ideal-gas values is modeled by a linearized specific heat ratio model. Parameters needed for the cubic EoS are pre-tabulated for the evaluation of departure functions and a quadratic ex…
In this report we briefly summarize the set-up and results for direct numerical simulations (DNS) of turbulent channel flows with riblets. The DNS are carried out with OpenFOAM which allows the use of an unstructured mesh. The present results were presented at the European Drag Reduction and Flow Control Meeting in 2015.
We show a method, for direct numerical simulations, to trigger and maintain turbulent bands directly at low Reynolds numbers in channel flow. The key is to impose a moving localised force which induces a local flow with sufficiently strong inflectional instability. With the method, we can trigger and maintain turbulent bands at Reynolds numbers down to $Re \simeq 500$. More importantly, we can generate any band patterns with desired relative position and orientation. The usual perturbation approach resorts to turbulent fields simulated at higher Reynolds numbers, random noise, or localised vor…
The first direct measurements of effective magnetic diffusivity in turbulent flow of electro-conductive fluids (the so-called beta-effect) under magnetic Reynolds number Rm >> 1 are reported. The measurements are performed in a nonstationary turbulent flow of liquid sodium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re \approx 3 10^6, which corresponds to the magnetic Reynolds number Rm \approx 30. The magnetic diffusivity of the liquid metal was determined by measuring the phase shift between the induced and the applied magnetic fields. The maximal d…
A direct Biot-Savart integration is used to decompose the strain rate into its local and nonlocal constituents, allowing the vorticity alignment with the local and nonlocal strain rate eigenvectors to be investigated. These strain rate tensor constituents are evaluated in a turbulent flow using data from highly-resolved direct numerical simulations. While the vorticity aligns preferentially with the intermediate eigenvector of the \textit{combined} strain rate, as has been observed previously, the present results for the first time clearly show that the vorticity aligns with the most extension…
A bird-feather-inspired herringbone riblet texture was investigated for turbulent drag reduction. The texture consists of blade riblets in a converging/diverging or herringbone pattern with spanwise wavelength $Λ_f$. The aim is to quantify the drag change for this texture as compared to a smooth wall and to study the underlying mechanisms. To that purpose, Direct Numerical Simulations of turbulent flow in a channel with height $L_z$ were performed. The FIK-identity for drag decomposition was extended to textured walls and was used to study the drag change mechanisms. For $Λ_f/L_z \gtrsim O(10)…
One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced when predicted with existing literature model. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate …
The work reported below is a first of its kind study of the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/non-turbulent interface, with emphasis on the small scale aspects. The main tools used are a three-dimensional particle tracking system (3D-PTV) allowing to measure and follow in a Lagrangian manner the field of velocity derivatives and direct numerical simulations (DNS). The comparison of flow properties in the turbulent (A), intermediate (B) and non-turbulent (C) regions in the proximity of the interface allows for direct observ…
This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0020
Direct numerical simulations of turbulent open channel flow with friction Reynolds numbers of $Re_τ=200,400,600$ are performed. Their results are compared with closed channel data in order to investigate the influence of the free surface on turbulent channel flows. The free surface affects fully developed turbulence statistics in so far that velocities and vorticities become highly anisotropic as they approach it. While the vorticity anisotropy layer scales in wall units, the velocity one is found to scale ith outer flow units and exhibits much larger extension. Furthermore the influence of th…
In this note we introduce speed and direction variables to describe the motion of incompressible viscous flows. Fluid velocity ${\bf u}$ is decomposed into ${\bf u}=u{\bf r}$, with $u=|{\bf u}|$ and ${\bf r}={\bf u}/|{\bf u}|$. We consider a directional split of the Navier-Stokes equations into a coupled system of equations for $u$ and for ${\bf r}$. Equation for $u$ is particularly simple but solely maintains the energy balance of the system. Under the assumption of a weak correlation between fluctuations in speed and direction in a developed turbulent flow, we further illustrate the applicat…
Machine learning is used to develop closure terms for coarse grained model of two-dimensional turbulent flow directly from the coarse grained data by adding a source term to the Navier-Stokes equations to ensure that the coarse-grained flow evolves in the correct way. The source term is related to the average flow using a Neural Network with a relatively simple structure and smoothed slightly to prevent instabilities in a posteriori test. The time dependent coarse grained flow field is generated by filtering fully resolved results and the predicted coarse field evolution agrees well with the f…
Over the last decades the knowledge on the small scales of turbulent wall flows has experienced a significant advance, especially in the near-wall region where the highest production of turbulent energy and the maximum turbulence intensity occur. The development of computers has played an important role in this progress, making direct numerical simulations affordable (Kim, Moin & Moser, 1987), and offering wider observational possibilities than most laboratory experiments. The large scales have received less attention, and it has not been until recently that their significance and their real s…
We present convincing evidence of a direct connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum. We use this finding to explain Nikuradse's experimental results of pressure drop for turbulent flows in rough pipes, in terms of a modified Kolmogorov length scale that varies with the surface roughness. Furthermore, we use Laufer's measurements of turbulent energy spectra in pipe flow to calculate -- to a good approximation -- the turbulent component of the pressure drop directly from an averaged turbulent energy spectrum. We also show that the incompressibi…
The turbulent boundary layer over a flat plate is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations as a test bed for a synthetic turbulence generator (STG) inflow boundary condition. The inlet momentum thickness Reynolds number is approximately 1,000. The study provides validation of the ability of the STG to develop accurate turbulence in 5 to 7 boundary layer thicknesses downstream of the boundary condition. Also tested was the effect of changes in the stabilization scheme on the development of the boundary layer. Moreover, the grid resolution requi…
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the tradi…
A study of large-scale motions from a new direct numerical simulation database of the turbulent boundary layer up to Reθ ~ 2500 is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape or angle are investigated. The features of the detected structures are compared to their mean counterpart…
In a plane Couette cell a thin fluid layer consisting of water is sheared between a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cells flow channel is large compared to the film separation. To extract the flow velocity in the experiments a correlation image velocimetry (CIV) method is used on pictures recorded with a high speed camera. The flow is recorded at a resolution that allows to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent pattern tha…
The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasi-adiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully-developed turbulent conditions using a five-species, chemically-reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inle…
We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 minutes, comparable with the time of rain formation.
We present the results of a Direct Numerical Simulation of a particle-laden spatially developing turbulent boundary layer up to Reθ = 2500. Two main features differentiate the behavior of inertial particles in a zero- pressure-gradient turbulent boundary layer from the more commonly studied case of a parallel channel flow. The first is the variation along the streamwise direction of the local dimensionless parameters defining the fluid-particle in- teractions. The second is the coexistence of an irrotational free-stream and a near-wall rotational turbulent flow. As concerns the first issue, an…
Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and appropriateness of mixture-averaged diffusion has not been verified for three-dimensional, turbulent, premixed flames. In this study we evaluated the role of multicomponent mass diffusion in premixed, three-dimensional high Karlovitz-number hydrogen, n-heptane, and toluene flames, representing a range of fuel Lewis numbers. We also studied a premixed, unsta…
Direct numerical simulations of free round jets at a Reynolds number ($Re_{D}$) of $5000$, based on jet diameter ($D$) and jet-exit bulk velocity ($U_{e}$), are performed to study jet turbulence characteristics at supercritical pressures. The jet consists of $\mathrm{N_{2}}$ that is injected into $\mathrm{N_{2}}$ at same temperature. To understand turbulent mixing, a passive scalar is transported with the flow at unity Schmidt number. Two sets of inflow conditions that model jets issuing from either a smooth contraction nozzle (laminar inflow) or a long pipe nozzle (turbulent inflow) are consi…
We present an efficient solver for massively-parallel direct numerical simulations of incompressible turbulent flows. The method uses a second-order, finite-volume pressure-correction scheme, where the pressure Poisson equation is solved with the method of eigenfunction expansions. This approach allows for very efficient FFT-based solvers in problems with different combinations of homogeneous pressure boundary conditions. Our algorithm explores all combinations of pressure boundary conditions valid for such a solver, in a single, general framework. The method is implemented in a 2D pencil-like…
We report numerical evidences of the influence of the blades' shape and of their direction of rotation on turbulent flows generated by counter-rotating bladed-disks enclosed in a cylinder, known as the von Kármán swirling flow. We show that, although the mean flows generated by stirrers with straight or curved blades can be topologically similar, turbulence production occurs in different zones. The structure and intensity of the turbulent fluctuating field also varies with the geometry, and retains significant anisotropy. From the direct numerical simulations fields, we analyse the dynamics of…
We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both local and non-local case. Comparison with a high Reynolds number turbulent von Karman flow is provided and discussed.
We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power "-1/2", in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Re…
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for Reynolds numbers descending from 2300 to 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps near Re=1900, to a patt…
Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow -- the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotempor…
This article describes the fluid dynamics video: "Turbulent Bubbly Channel Flow: Role of Bubble Deformability." The effect of bubble deformability on the flow rate of bubbly upflow in a turbulent vertical channel is examined using direct numerical simulations. A series of simulations with bubbles of decreasing deformability shows a transition from flow where deformable bubbles remain in the middle of the channel to a situation where nearly spherical bubbles slide along the walls.
The direct numerical simulation of compressible fully developed turbulent Couette flow between two parallel plates with equal temperatures moving in opposite directions with some velocity was performed. The algorithm was tested on well known numerical solution for incompressible Poiseuille channel flow and found to provide its well description. The slip effects in studied flow are found to be negligibly small at the values of accommodation coefficients for velocity and temperature of the order of unity. The considerable increase of mean temperature with decreasing the accommodation coefficient…
This letter confirms the existence of heat transfer enhancement (HTE) and reduction (HTR) in turbulent natural convection with polymer additives. HTE and HTR were numerically predicted by Benzi et al.(PRL, 104, 024502, 2010) in homogenous turbulent convection, but experiments by Ahlers & Nikolaenko(PRL, 104, 034503, 2010) in turbulent natural convection observed HTR only. Using direct numerical simulation of natural convection, the present study reconciles earlier numerical and experimental work on the basis of the dominant role of polymer length in the polymer dynamics in extensional flows.
Direct numerical simulation of a thermal turbulent boundary layer: an analogy to simulate bushfires and a testbed for artificial intelligence remote sensing of bushfire propagation
We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. In spite of the strong anisotropy of the forcing, we find that turbulence recovers almost complete isotropy at small scales. Nonetheless, the signature of the forcing remains in the mean flow (averaged over time and over the homogeneous direction) and this allows to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further find that the flow is characterized by large temporal fluc…
The turbulent flow in an infinitely extended plane channel is analysed by solving the Navier-Stokes equations with a DNS approach. Solutions are obtained in a numerical solution domain of finite size in the streamwise as well as in the lateral direction setting periodic boundary conditions in both directions. Their impact on large scale structures in the turbulent flow field is analysed carefully in order to avoid their suppression. When this is done appropriately well known stripe patterns in these flows can be observed and analysed especially with respect to their relative motion compared to…
Here we show the hairpin vortices point the upstream direction of flow instead of downstream, and this characteristic is found intrinsic behavior for turbulent buoyancy-driven boundary layer. We uncover the coherent vortices straddle high-speed streak instead of low-speed streak; moreover, the quadrant of the tangential Reynolds shear stresses dominates the first and third quadrant instead of the second and fourth one. These findings may help to improve our understanding of buoyancy-driven flow and buoyancy effects in turbulent models.
The interaction between small- and large-scale structures, and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$. A DNS database at $Re_τ=101$ is built to replicate the highest $Re$ considered in a recent experimental work by Kawata and Alfredsson (Phys. Rev. Lett., vol.120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\langle δu_i δu_j \rangle$, i.e. the Anisotropic Generalized Kolmogo…
This paper reviews some of the principal uses, over almost seven decades, of correlations, in both Eulerian and Lagrangian frames of reference, of properties of turbulent flows at variable spatial locations and variable time instants. Commonly called space--time correlations, they have been fundamental to theories and models of turbulence as well as for the analyses of experimental and direct numerical simulation turbulence data.
Starting with an integral formulation of mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking Damk{ö}hler's hypotheses. Major approximations and interim results are validated using a large Karlovitz number, unity Lewis number, Direct Numerical Simulation (DNS) dataset of n-heptane/air mixture, computed with reduced chemistry. A new length scale quantifying the fluctuation distance of the isotherms within the premixed flame structure is introduced.
In melt-blowing processes mico- and nanofibers are produced by the extrusion of polymeric jets into a directed, turbulent high-speed airflow. Up to now the physical mechanism for the drastic jet thinning is not fully understood, since in the existing literature the numerically computed/predicted fiber thickness differs several orders of magnitude from those experimentally measured. Recent works suggest that this discrepancy might arise from the neglect of the turbulent aerodynamic fluctuations in the simulations. In this paper we confirm this suggestion numerically. Due to the complexity of th…
The turbulent flow of a fluid carrying trace amounts of a condensable species through a differentially cooled vertical channel geometry is simulated using single-phase direct numerical simulations. The release of latent heat during condensation is modeled by interdependent temperature and vapor concentration source terms governing the relation between the removal of excess vapor from the system and the associated local increase in fluid temperature. A coupling between condensation and turbulence is implemented via solutal and thermal buoyancy. When compared to simulations of an identical syste…
