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Register a new userDirect numerical simulations of turbulent channel flow under transcritical conditions
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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.
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A simple theory, based on observations of snowflake distribution in a turbulent flow, is proposed to model the growth of inertial particles as a result of dynamic clustering at scales larger than the Kolmogorov length scale. Particles able to stick or coalesce are expected to grow in size in flow regions where preferential concentration is predicted by a critical Stokes number $St=tau_p/tau_f simeq 1 $. We postulate that, during growth, $St$ remains critical, with the particle response time $tau_p$ evolving according to the specific flow time scale $tau_f$ defined by the vortices around which progressively larger particles end up orbiting. This mechanism leads to the prediction of the limiting size of aggregating particles in a turbulent flow. Such limit is determined by the extent of the turbulent inertial range, which can be formulated as a function of accessible integral-scale quantities. The proposed dynamically critical Stokes growth provides a framework to interpret particle aggregation, size growth and particle cluster growth in various geophysical multi-phase flows.
A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re_tau = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.
We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarises. These different behaviors are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centerline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.
Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the large-scale behavior are derived. One of the most popular reduced models is the Reynolds averaged Navier-Stokes (RANS) equations. The goal is to solve the RANS equations for the mean velocity and pressure field. However, the RANS equations contain a term called the Reynolds stress tensor, which is not known in terms of the mean velocity field. Many RANS turbulence models have been proposed to model the Reynolds stress tensor in terms of the mean velocity field, but are usually not suitably general for all flow fields of interest. Data-driven turbulence models have recently garnered considerable attention and have been rapidly developed. In a seminal work, Ling et al (2016) developed the tensor basis neural network (TBNN), which was used to learn a general Galilean invariant model for the Reynolds stress tensor. The TBNN was applied to a variety of flow fields with encouraging results. In the present study, the TBNN is applied to the turbulent channel flow. Its performance is compared with classical turbulence models as well as a neural network model that does not preserve Galilean invariance. A sensitivity study on the TBNN reveals that the network attempts to adjust to the dataset, but is limited by the mathematical form that guarantees Galilean invariance.
This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method to direct numerical simulation (DNS) of a turbulent channel flow at Re$_tau$=180 using two different forcing strategies that are designed to separately assess the anisotropy and nonlocality of momentum mixing. In the first strategy, the leading term of the Kramers-Moyal expansion of the eddy viscosity operator is quantified where the macroscopic forcing is employed to reveal all 81 tensorial coefficients that essentially represent the local-limit eddy viscosity. The results indicate: (1) eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both mean strain rate and mean rotation rate tensors, and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity operator is considered as an integration kernel representing the nonlocal influence of mean gradients on the Reynolds stresses. Considering the average of this kernel in the homogeneous directions, the macroscopic forcing is designed to reveal the nonlocal effects in the wall-normal direction for all 9 components of the Reynolds stresses. Our results indicate that while the shear component of the Reynolds stress is reasonably controlled by the local mean gradients, other components of the Reynolds stress are highly nonlocal. These two analyses provide accurate verification data for quantitative testing of anisotropy and nonlocality effects in turbulence closure models.
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