Turbulence and secondary motions in square duct flow

We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence. Numerical simulations are carried out over extremely long integration times to get adequate convergence of the flow statistics, and specifically high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be in the order of 1-2% of the bulk velocity, and unaffected by Reynolds number variations. The smallness of the mean convection terms in the streamwise vorticity equation points to a simple characterization of the secondary flows, which in the asymptotic high-Re regime are found to be approximated with good accuracy by eigenfunctions of the Laplace operator. Despite their effect of redistributing the wall shear stress along the duct perimeter, we find that secondary motions do not have large influence on the mean velocity field, which can be characterized with good accuracy as that resulting from the concurrent effect of four independent flat walls, each controlling a quarter of the flow domain. As a consequence, we find that parametrizations based on the hydraulic diameter concept, and modifications thereof, are successful in predicting the duct friction coefficient

Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions

Direct numerical simulations are carried out to investigate the effect of the wall temperature on the behavior of oblique shock-wave/turbulent boundary layer interactions at freestream Mach number $2.28$ and shock angle of the wedge generator $\varphi = 8^{\circ}$. Five values of the wall-to-recovery-temperature ratio ($T_w/T_r$) are considered, corresponding to cold, adiabatic and hot wall thermal conditions. We show that the main effect of cooling is to decrease the characteristic scales of the interaction in terms of upstream influence and extent of the separation bubble. The opposite behavior is observed in the case of heating, that produces a marked dilatation of the interaction region. The distribution of the Stanton number shows that a strong amplification of the heat transfer occurs across the interaction, and the maximum values of thermal and dynamic loads are found in the case of cold wall. The analysis reveals that the fluctuating heat flux exhibits a strong intermittent behavior, characterized by scattered spots with extremely high values compared to the mean. Furthermore, the analogy between momentum and heat transfer, typical of compressible, wall-bounded, equilibrium turbulent flows does not apply for most part of the interaction domain. The pre-multiplied spectra of the wall heat flux do not show any evidence of the influence of the low-frequency shock motion, and the primary mechanism for the generation of peak heating is found to be linked with the turbulence amplification in the interaction region.Comment: submitted to PRFluid

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

We study compressible turbulent flow in a circular pipe at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Re τ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. (2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear

Direct numerical simulation of developed compressible flow in square ducts

We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers M b =0.2−3, and up to friction Reynolds number Re τ =500. The effects of flow compressibility on the secondary motions are found to be negligible, with the typical Mach number associated with the cross-stream flow always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars

On the relationship between drag and vertical velocity fluctuations in flow over riblets and liquid infused surfaces

Direct numerical simulations (DNS) of flow over triangular and rectangular riblets in a wide range of size and Reynolds number have been carried out. The flow within the grooves is directly resolved by exploiting the immersed-boundary method. It is found that the drag reduction property is primarily associated with the capability of inhibiting vertical velocity fluctuations at the plane of the crests, as in liquid-infused surfaces (LIS) devices. This is mimicked in DNS through artificial suppression of the vertical velocity component, which yields large drag decrease, proportionate to the riblets size. A parametrization of the drag reduction effect in terms of the vertical velocity variance is found to be quite successful in accounting for variation of the controlling parameters. A Moody-like friction diagram is thus introduced which incorporates the effect of slip velocity and a single, geometry-dependent parameter. Reduced drag-reduction efficiency of LIS-like riblets is found as compared to cases with artificially imposed slip velocity. Last, we find that simple wall models of riblets and LIS-like devices are unlikely to provide accurate prediction of the flow phenomenon, and direct resolution of flow within the grooves in necessary

A general framework for the evaluation of shock-capturing schemes

We introduce a standardized procedure for benchmarking shock-capturing schemes which is intended to go beyond traditional case-by-case analysis, by setting objective metrics for cross-comparison of flow solvers. The main idea is that use of shock-capturing schemes yields both distributed errors associated with propagation of wave-like disturbances in smooth flow regions, and localized errors at shocks where nonlinear numerical mechanisms are most active. Our standardized error evaluation framework relies on previous methods of analysis for the propagation error with associated cost/error mapping, and on novel analysis of the shock-capturing error based on a model scalar problem. Amplitude and phase errors are identified for a number of classical shock-capturing schemes with different order of accuracy. Whereas all schemes are found to be, as expected, first-order accurate at shocks, quantitative differences are found to be significant, and we find that certain schemes in wide use (e.g. high-order WENO schemes) may yield substantial over-amplification of incoming disturbances at shocks. Illustrative calculations are also shown for the 1D Euler equations, which support sufficient generality of the analysis, although nonlinearity suggests caution in straightforward extrapolation to other flow cases

A high order compact scheme for hypersonic aerothermodynamics

A novel high order compact scheme for solving the compressible Navier-Stokes equations has been developed. The scheme is an extension of a method originally proposed for solving the Euler equations, and combines several techniques for the solution of compressible flowfields, such as upwinding, limiting and flux vector splitting, with the excellent properties of high order compact schemes. Extending the method to the Navier-Stokes equations is achieved via a Kinetic Flux Vector Splitting technique, which represents an unusual and attractive way to include viscous effects. This approach offers a more accurate and less computationally expensive technique than discretizations based on more conventional operator splitting. The Euler solver has been validated against several inviscid test cases, and results for several viscous test cases are also presented. The results confirm that the method is stable, accurate and has excellent shock-capturing capabilities for both viscous and inviscid flows

STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows

We present STREAmS, an in-house high-fidelity solver for direct numerical simulations (DNS) of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interaction. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated with the solution of high-speed turbulent flows and can be used across a wide range of Mach numbers, extending from the low subsonic up to the hypersonic regime. From the computational viewpoint, STREAmS is oriented to modern HPC platforms thanks to MPI parallelization and the ability to run on multi-GPU architectures. This paper discusses the main implementation strategies, with particular reference to the CUDA paradigm, the management of a single code for traditional and multi-GPU architectures, and the optimization process to take advantage of the latest generation of NVIDIA GPUs. Performance measurements show that single-GPU optimization more than halves the computing time as compared to the baseline version. At the same time, the asynchronous patterns implemented in STREAmS for MPI communications guarantee very good parallel performance especially in the weak scaling spirit, with efficiency exceeding 97% on 1024 GPUs. For overall evaluation of STREAmS with respect to other compressible solvers, comparison with a recent GPU-enabled community solver is presented. It turns out that, although STREAmS is much more limited in terms of flow configurations that can be addressed, the advantage in terms of accuracy, computing time and memory occupation is substantial, which makes it an ideal candidate for large-scale simulations of high-Reynolds number, compressible wall-bounded turbulent flows. The solver is released open source under GPLv3 license. Program summary: Program Title: STREAmS CPC Library link to program files: https://doi.org/10.17632/hdcgjpzr3y.1 Developer's repository link: https://github.com/matteobernardini/STREAmS Code Ocean capsule: https://codeocean.com/capsule/8931507/tree/v2 Licensing provisions: GPLv3 Programming language: Fortran 90, CUDA Fortran, MPI Nature of problem: Solving the three-dimensional compressible Navier–Stokes equations for low and high Mach regimes in a Cartesian domain configured for channel, boundary layer or shock-boundary layer interaction flows. Solution method: The convective terms are discretized using a hybrid energy-conservative shock-capturing scheme in locally conservative form. Shock-capturing capabilities rely on the use of Lax–Friedrichs flux vector splitting and weighted essentially non-oscillatory (WENO) reconstruction. The system is advanced in time using a three-stage, third-order RK scheme. Two-dimensional pencil distributed MPI parallelization is implemented alongside different patterns of GPU (CUDA Fortran) accelerated routines

Numerical tripping of high-speed turbulent boundary layers

The influence of turbulence inflow generation on direct numerical simulations (DNS) of high-speed turbulent boundary layers at Mach numbers of 2 and 5.84 is investigated. Two main classes of inflow conditions are considered, based on the recycling/rescaling (RR) and the digital filtering (DF) approach, along with suitably modified versions. A series of DNS using very long streamwise domains is first carried out to provide reliable data for the subsequent investigation. A set of diagnostic parameters is then selected to verify achievement of an equilibrium state, and correlation laws for those quantities are obtained based on benchmark cases. Simulations using shorter domains, with extent comparable with that used in the current literature, are then carried out and compared with the benchmark data. Significant deviations from equilibrium conditions are found, to a different extent for the various flow properties, and depending on the inflow turbulence seeding. We find that the RR method yields superior performance in the evaluation of the inner-scaled wall pressure fluctuations and the turbulent shear stress. DF methods instead yield quicker adjustment and better accuracy in the prediction of wall friction and of the streamwise Reynolds stress in supersonic cases. Unrealistically high values of the wall pressure variance are obtained by the baseline DF method, while the proposed DF alternatives recover a closer agreement with respect to the benchmark. The hypersonic test case highlights that similar distribution of wall friction and heat transfer are obtained by both RR and DF baseline methods

Towards the ultimate regime in Rayleigh-Darcy convection

Numerical simulations are used to probe Rayleigh-Darcy convection in fluid-saturated porous media towards the ultimate regime. The present three-dimensional dataset, up to Rayleigh-Darcy number, suggests that the appropriate scaling of the Nusselt number is, fitting the computed data for. Extrapolation of current predictions to the ultimate linear regime yields the asymptotic law, about less than indicated in previous studies. Upon examination of the flow structures near the boundaries, we confirm previous indications of small flow cells hierarchically nesting into supercells, and we show evidence that the supercells at the boundary are the footprints of the megaplumes that dominate the interior part of the flow. The present findings pave the way for more accurate modelling of geophysical systems, with special reference to geological sequestration