Incompressible Direct Numerical Simulations Research Articles

High-subsonic boundary-layer flows of an organic vapour

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

Wall shear stress and wall heat flux in a supersonic turbulent boundary layer

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.

Validation Strategy of Reduced-Order Two-Fluid Flow Models Based on a Hierarchy of Direct Numerical Simulations

Whereas direct numerical simulation (DNS) have reached a high level of description in the field of atomization processes, they are not yet able to cope with industrial needs since they lack resolution and are too costly. Predictive simulations relying on reduced order modeling have become mandatory for applications ranging from cryotechnic to aeronautic combustion chamber liquid injection. Two-fluid models provide a good basis in order to conduct such simulations, even if recent advances allow to refine subscale modeling using geometrical variables in order to reach a unified model including separate phases and disperse phase descriptions based on high order moment methods. The simulation of such models has to rely on dedicated numerical methods and still lacks assessment of its predictive capabilities. The present paper constitutes a building block of the investigation of a hierarchy of test-cases designed to be amenable to DNS while close enough to industrial configurations, for which we propose a comparison of two-fluid compressible simulations with DNS data-bases. We focus in the present contribution on an air-assisted water atomization using a planar liquid sheet injector. Qualitative and quantitative comparisons with incompressible DNS allow us to identify and analyze strength and weaknesses of the reduced-order modeling and numerical approach in this specific configuration and set a framework for more refined models since they already provide a very interesting level of comparison on averaged quantities.

Modifications to the SIMPLE algorithm with the MDCD approach for incompressible flow simulation

PurposeThe purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the numerical robustness and optimize computational efficiency. They remarkably promote the ability of the SIMPLE algorithm for incompressible DNS (direct numerical simulation) of multiscale problems, such as transitional flows and turbulent flows, by improving the properties of dispersion and dissipation.Design/methodology/approachThe MDCD (minimized dispersion and controllable dissipation) scheme and MMIM (modified momentum interpolation method) are introduced. Six typical test cases are used to validate the modified algorithm, including the linear convective flow, lid-driven cavity flow, laminar boundary layer, Taylor vortex and DHIT (decaying homogenous isotropic turbulence). Particularly, a highly unsteady DNS of separated-flow transition in turbomachinery is precisely predicted by the modified algorithm.FindingsThe numerical examples show the distinct superiority of the modified algorithm in both internal flows and external flows. The advantages of the MDCD scheme and MMIM make the SIMPLE algorithm a promising method for DNS.Originality/valueSome effective modifications to the SIMPLE algorithm are addressed. It is the first attempt to introduce the MDCD approach into the SIMPLE-type algorithms. The new algorithm is especially suitable for the incompressible DNS of convection-dominated flows.

Measurements versus Numerical Simulations for Slotted Synthetic Jet Actuator

In many studies concerning synthetic jet flow fields the analysis is usually restricted to simple configurations, such as a single diaphragm oscillating in a cylindrical cavity, which is linked to the external environment with only one orifice/slot. Nonetheless, in many applications the requirement of small sizes and weights leads to many implementation issues, such as asymmetric actuator geometries, presence of several slots and diaphragms and irregular cavity shapes. Therefore, the design of a synthetic jet actuator for a specific flow control problem requires a dedicated study in order to characterize its behavior even in quiescent conditions. The aim of this work is to investigate the behavior of a novel synthetic jet actuator, composed of three independent diaphragms, acting on a single cavity, and linked to the external environment through four slots per diaphragm. The device has been studied in quiescent conditions, both numerically and experimentally. The experimental investigation has been carried out by means of hot-wire measurements. In particular, the distribution of the phase-averaged streamwise velocity along the slot spanwise direction has been detected near the slot exit plane. From the computational side, incompressible direct numerical simulations have been carried out using the open-source OpenFOAM code. The diaphragm motion is mimicked by a inhomogeneous inlet boundary condition, whose amplitude is chosen to match the experimental velocity at the exit plane. A fair agreement between the numerical and the experimental results is achieved for both the velocity field at the slot exit and the main non-dimensional parameters of the synthetic jet. After the validation, the numerical results are finally processed, to obtain information about the vortex motion in the external environment.

Numerical investigation of the saturation process in an incompressible cavity flow

A numerical study of the saturation process inside a rectangular open cavity is presented. Previous experiments and linear stability analysis of the problem completely described the flow in its onset, as well as in a saturated regime, characterized by three-dimensional centrifugal modes. The morphology of the modes found in the experiments matched the ones predicted by linear analysis, but with a shift in frequencies for the oscillating modes. A three-dimensional incompressible direct numerical simulation (DNS) is employed for a detailed investigation of the saturation process inside a cavity with dimensions similar to the one used in the experiments, to further explain the behaviour of these modes. In this work, periodic boundary conditions are first imposed to better understand the effect of the saturation process far from the walls. Then, the effects of spanwise solid wall boundary conditions are investigated with a DNS reproducing the full dynamics of the experiments. The main flow structures are identified using the dynamic mode decomposition technique and compared with previous experimental and linear stability analysis results. The main reason for the aforementioned shift in frequency is explained in this paper, as it is a function of the velocity of the main recirculating vortex.

Reynolds and Mach number effects in compressible turbulent channel flow

The effect of Reynolds and Mach number variation in compressible isothermal channel flow is investigated through a series of direct numerical simulations (DNS), at bulk Mach number Mb=1.5,3 and bulk Reynolds number up to Reb=34000, which is sufficient to sense sizeable high-Reynolds-number effects not reached before in this type of flow. Dedicated incompressible DNS are also performed at precisely matching Reynolds number, to directly gauge the performance of compressibility transformations for the mean velocity profiles and Reynolds stresses. As in previous studies, we find inaccuracy of the classical van Driest transformation to remove effects of variable density and viscosity, especially at low Reynolds number. On the other hand, almost perfect matching of incompressible mean velocity and Reynolds stress distributions is recovered throughout the wall layer by using a recently introduced transformation (Trettel and Larsson, 2014,2016), the only remaining effect of compressibility being the increase of the streamwise turbulence intensity peak with the Mach number. Temperature/velocity relations are scrutinized, with the main finding that a recent relation by Zhang et al. (2014), which explicitly accounts for finite wall heat flux, is more accurate than the classical Walz relation. The size of the typical turbulent eddies is studied through spanwise spectral densities of the velocity field, which support validity of a scaling based on the local mean shear and the local friction velocity, with the main conclusion that the actual size of the eddies does not vary with the Mach number, at a fixed outer wall distance.

Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

This paper concerns the accuracy of several high-resolution and high-order finite volume schemes in Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. The main objective is to investigate the properties of numerical schemes, originally designed for compressible flows, in low Mach compressible, near-wall turbulent flows. Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated. The performance of the schemes has been assessed against incompressible Direct Numerical Simulations. Detailed comparisons of the velocity profiles, turbulent shear stresses and higher-order turbulent statistics reveal that the low Mach correction can significantly reduce the numerical dissipation of the methods in low Mach boundary layer flows. The effects of the low Mach correction have more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes. The ninth-order Weighted Essentially Non-Oscillatory scheme is the least dissipative scheme and it is shown that the implementation of the low Mach correction in conjunction with this scheme has a significant anti-dissipative effect that adversely affects the accuracy. Finally, the computational cost required for obtaining the improved accuracy using increasingly higher order schemes is also discussed.

Feasibility investigation of compressible direct numerical simulation with a preconditioning method at extremely low Mach numbers

Compressible direct numerical simulation (DNS) with a preconditioning method is conducted for the turbulent channel flow of at an extremely low Mach number of 0.005. The turbulence statistics are in excellent agreement with incompressible DNS results, which indicates that the preconditioning method is able to accurately simulate the turbulence at an extremely low Mach number under the condition of sufficient resolution without any subgrid scale model or special treatment of numerical dissipation. In addition, the effects of the computational time step are investigated. It is shown that when the time step is shorter than 0.32 wall units, accurate results can be obtained and the total computational time is independent of the length of the time step. This study thus validates the feasibility of the compressible DNS with a preconditioning method for an extremely low Mach number and provides useful guidelines for simulating turbulence.

NON-LOCALITY OF HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC TURBULENCE

We compare non-locality of interactions between different scales in hydrodynamic (HD) turbulence and magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium. We use three-dimensional incompressible direct numerical simulations to evaluate non-locality of interactions. Our results show that non-locality in MHD turbulence is much more pronounced than that in HD turbulence. Roughly speaking, non-local interactions count for more than 10% of total interactions in our MHD simulation on a grid of 5123 points. However, there is no evidence that non-local interactions are important in our HD simulation with the same numerical resolution. We briefly discuss how non-locality affects the energy spectrum.

Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

AbstractThe purpose of the present paper is to evaluate very‐high‐order upwind schemes for the direct numerical simulation (DNS) of compressible wall‐turbulence. We study upwind‐biased (UW) and weighted essentially nonoscillatory (WENO) schemes of increasingly higher order‐of‐accuracy (J. Comp. Phys. 2000; 160:405–452), extended up to WENO17 (AIAA Paper 2009‐1612, 2009). Analysis of the advection–diffusion equation, both as Δx→0 (consistency), and for fixed finite cell‐Reynolds‐number ReΔx (grid‐resolution), indicates that the very‐high‐order upwind schemes have satisfactory resolution in terms of points‐per‐wavelength (PPW). Computational results for compressible channel flow (Re∈[180, 230]; M̄CL∈[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid‐resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O(Δt2) time‐integration and O(Δx2) discretization of the viscous terms, comparative studies of various orders‐of‐accuracy for the convective terms demonstrate that very‐high‐order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd.

Large-Eddy Simulation of Separated Flow in a Channel with Streamwise-Periodic Constrictions

Large-eddy simulations using the approximate-deconvolution subgrid-scale model of compressible flow in a channel with streamwise-periodic constrictions are performed at two Reynolds numbers of 2800 and 10,595. The goal of the study is the evaluation of this subgrid-scale model for massively separated flows. The Mach number was chosen as 0.2 to facilitate comparison with incompressible flow data. A relatively coarse structured grid and a finite-volume discretization employing a skew-symmetric fourth-order central scheme are used with a four-stage Runge-Kutta method for time integration. The results are compared to data from the literature obtained with incompressible direct numerical simulations, as well as highly resolved large-eddy simulations. Despite the chosen coarse resolution, good agreement of the statistical quantities and important flow features, such as separation and reattachment locations, is achieved. In contrast to previous works we also consider the flow properties at the straight upper wall. We introduce a new measure quantifying the time fraction of reverse flow along the wall. Furthermore, we analyze the energy density spectra of the velocity fluctuations and study the turbulence structure with Lumley's flatness parameter and realizability map. We also illustrate the vortex systems associated with the shedding and other instantaneous flow structures.

Growth of kidney and antikidney vortices over a square jet in crossflow

The present paper reports on triple-decked evolution of the kidney vortices and the growth of unsteady antikidney-type vortices over a square jet in crossflow. Incompressible direct numerical simulations are performed with Reynolds number 2000 and jet to crossflow velocity ratio 2.5, to extract such flow details. Out of the three different decks, the lower deck kidney vortices maintain their steady appearance over the jet hole; however, vortices in the middle and the upper decks were unsteady in nature. Frequent shedding of the frontal hovering vortices and their convex wrapping over the front part of the jet hole are found to be responsible for the multidecked growth of the kidney vortices. On the other hand, unsteady antikidney-type vortices are noted to grow over the central part of the hole, and their growth is verified to be attributed due to concave windward folding of the frontal jet shear layer. Notably, the present findings remained consistent with existing experimentally observed features of such flows.

Study of trajectories of jets in crossflow using direct numerical simulations

This paper studies the trajectories and near field of round jets in crossflow. Incompressible direct numerical simulations are performed at velocity ratios of 1.5 and 5.7 and the effects of jet velocity profile and boundary layer thickness on the jet trajectory are examined. The ‘rd’ scaling used at present (Margason 1993) does not contain any information on these parameters, and trajectories scaled by rd do not collapse. The trajectory is strongly influenced by the near field which depends on both the jet velocity profile and the crossflow boundary layer. A length scale is proposed to describe the near field of the jet. An analytical expression is proposed for this length scale which is a measure of the relative inertia of the jet and the crossflow. Incorporating this length scale significantly improves the scaling of the trajectories.

Numerical investigation of fully developed channel flow using shock-capturing schemes

The ability to simulate wall-bounded channel flows with second- and third-order shock-capturing schemes is tested on both subsonic and supersonic flow regimes, respectively at Mach 0.5 and 1.5. Direct numerical simulations (DNSs) and large-eddy simulations (LESs) are performed at Reynolds number 3000. In both flow regimes, results are compared with well-documented DNS, LES or experimental data. At Ma 0=0.5, a simple second-order centred scheme provides results in excellent agreement with incompressible DNS databases, while the addition of artificial or subgrid-scale (SGS) dissipation decreases the resolution accuracy giving just satisfactory results. At Ma 0=1.5, the second-order space accuracy is just sufficient to well resolve small turbulence scales on the chosen grid: without any dissipation models, such accuracy provides results in good agreement with reference data, while the addition of dissipation models considerably reduces the turbulence level and the flow appears almost laminar. Moreover, the use of explicit dissipative SGS models reduces the results accuracy. In both flow regimes, the numerical dissipation due to the discretization of the convective terms is also interpreted in terms of SGS dissipation in an LES context, yielding a generalised dynamic coefficient, equivalent to the dynamic coefficient of the Germano et al. [Phys. Fluids A 3(7) (1991) 1760] SGS model. This new generalised coefficient is thus developed to compare the order of magnitude of the intrinsic numerical dissipation of a shock-capturing scheme with respect to the SGS dissipation.

Subgrid-Scale Models for Large-Eddy Simulations of Compressible Wall Bounded Flows

A comparative assessment of six subgrid-scale models is presented in the case of a compressible plane channel flow over isothermal walls, four of which are based on the recent mixed-scale model. A supersonic and a subsonic case in temporal development at Mach 1.5 and 0.5, respectively, are considered for a Reynolds number equal to 3000, with comparison to the direct numerical simulations (DNS) of Coleman et al. in the first case, and the incompressible DNS of Kim et al. in the second case. For each Mach number, two grids are considered, with about 20 and 5 times less grid points as in the reference DNS, and the results are globally satisfactory, although not excellent. In particular, the wall friction is globally underestimated by about 10%, both in the subsonic and the supersonic cases. Among the models tested are several original combinations, which vanish at the wall without requiring any damping function

Small‐Scale Interaction of Turbulence with Thermonuclear Flames in Type Ia Supernovae

Microscopic turbulence-flame interactions of thermonuclear fusion flames occurring in Type Ia supernovae were studied by means of incompressible direct numerical simulations with a highly simplified flame description. The flame is treated as a single diffusive scalar field with a nonlinear source term. It is characterized by its Prandtl number, Pr 1, and laminar flame speed, Slam. We find that if Slam ≥ u', where u' is the rms amplitude of turbulent velocity fluctuations, the local flame propagation speed does not significantly deviate from Slam even in the presence of velocity fluctuations on scales below the laminar flame thickness. This result is interpreted in the context of subgrid-scale modeling of supernova explosions and the mechanism for deflagration-detonation transitions.