Direct numerical simulation of the flow over a sphere at Re = 3700

2011 ◽  
Vol 679 ◽  
pp. 263-287 ◽  
Author(s):  
IVETTE RODRIGUEZ ◽  
RICARD BORELL ◽  
ORIOL LEHMKUHL ◽  
CARLOS D. PEREZ SEGARRA ◽  
ASSENSI OLIVA
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Shear Layer ◽  
Large Scale ◽  
Power Spectra ◽  
Numerical Data ◽  
Transition To Turbulence ◽  
Stream Velocity ◽  
Sphere Diameter ◽  
Mean Flow

The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. At this Reynolds number, flow separates laminarly near the equator of the sphere and transition to turbulence occurs in the separated shear layer. The vortices formed are shed at a large-scale frequency, St = 0.215, and at random azimuthal locations in the shear layer, giving a helical-like appearance to the wake. The main features of the flow including the power spectra of a set of selected monitoring probes at different positions in the wake of the sphere are described and discussed in detail. In addition, a large number of turbulence statistics are computed and compared with previous experimental and numerical data at comparable Reynolds numbers. Particular attention is devoted to assessing the prediction of the mean flow parameters, such as wall-pressure distribution, skin friction, drag coefficient, among others, in order to provide reliable data for testing and developing statistical turbulence models. In addition to the presented results, the capability of the methodology used on unstructured grids for accurately solving flows in complex geometries is also pointed out.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

scholarly journals Scaling of separated shear layers: an investigation of mass entrainment

2017 ◽  
Vol 826 ◽  
pp. 851-887 ◽  
Author(s):  
Francesco Stella ◽  
Nicolas Mazellier ◽  
Azeddine Kourta
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Separated Flow ◽  
Layer Growth ◽  
Upper And Lower Bounds ◽  
Stream Velocity ◽  
Physical Parameters ◽  
Separated Shear Layer ◽  
Mass Entrainment ◽  
Recirculation Length

We report an experimental investigation of the separating/reattaching flow over a descending ramp with a $25^{\circ }$ expansion angle. Emphasis is given to mass entrainment through the boundaries of the separated shear layer emanating from the upper edge of the ramp. For this purpose, the turbulent/non-turbulent interface and the separation line inferred from image-based analysis are used respectively to mark the upper and lower bounds of the separated shear layer. The main objective of this study is to identify the physical parameters that scale the development of the separated shear layer, by giving a specific emphasis to the investigation of mass entrainment. Our results emphasise the multiscale nature of mass entrainment through the separated shear layer. The recirculation length $L_{R}$, step height $h$ and free-stream velocity $U_{\infty }$ are the dominant scales that organise the separated flow (and related large-scale quantities as pressure distribution or shear layer growth rate) and set mean mass fluxes. However, local viscous mechanisms seem to be responsible for most of local mass entrainment. Furthermore, it is shown that large-scale mass entrainment is driven by incoming boundary layer properties, since $L_{R}$ scales with $Re_{\unicode[STIX]{x1D703}}$, and in particular by its turbulent state. Surprisingly, the relationships evidenced in this study suggest that these dependencies are established over a large distance upstream of separation and that they might also extend to small scales, at which viscous entrainment is dominant. If confirmed by additional studies, our findings would open new perspectives for designing effective separation control systems.

scholarly journals Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

2019 ◽  
Vol 877 ◽  
pp. 167-195 ◽  
Author(s):  
Feng-Yuan Zuo ◽  
Antonio Memmolo ◽  
Guo-ping Huang ◽  
Sergio Pirozzoli
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Shear Stresses ◽  
Mean Flow ◽  
Conical Shock

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

scholarly journals Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

2019 ◽  
Vol 880 ◽  
pp. 239-283 ◽  
Author(s):  
Christoph Wenzel ◽  
Tobias Gibis ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Self Similar

A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

scholarly journals On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
Author(s):  
A. E. PERRY ◽  
IVAN MARUSIC ◽  
M. B. JONES
Keyword(s):  
Boundary Layers ◽  
Scaling Laws ◽  
Power Spectra ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3

2007 ◽  
Vol 594 ◽  
pp. 59-69 ◽  
Author(s):  
MATTHEW J. RINGUETTE ◽  
MINWEI WU ◽  
M. PINO MARTÍN
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Coherent Structures ◽  
Mass Flux ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Turbulence Structure ◽  
Taylor’S Hypothesis ◽  
Mach 3

We demonstrate that data from direct numerical simulation of turbulent boundary layers at Mach 3 exhibit the same large-scale coherent structures that are found in supersonic and subsonic experiments, namely elongated, low-speed features in the logarithmic region and hairpin vortex packets. Contour plots of the streamwise mass flux show very long low-momentum structures in the logarithmic layer. These low-momentum features carry about one-third of the turbulent kinetic energy. Using Taylor's hypothesis, we find that these structures prevail and meander for very long streamwise distances. Structure lengths on the order of 100 boundary layer thicknesses are observed. Length scales obtained from correlations of the streamwise mass flux severely underpredict the extent of these structures, most likely because of their significant meandering in the spanwise direction. A hairpin-packet-finding algorithm is employed to determine the average packet properties, and we find that the Mach 3 packets are similar to those observed at subsonic conditions. A connection between the wall shear stress and hairpin packets is observed. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long low-momentum structures. This finding is consistent with the very large-scale motion model of Kim & Adrian (1999).

scholarly journals Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingtuan Yang ◽  
Nan Gui ◽  
Gongnan Xie ◽  
Jie Yan ◽  
Jiyuan Tu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Turbulent Energy ◽  
Swirling Flows ◽  
Small Scale

This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows.

Identification of Bypass Transition Onset Markers Using Direct Numerical Simulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Shanti Bhushan ◽  
D. Keith Walters ◽  
S. Muthu ◽  
Crystal L. Pasiliao
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
General Purpose ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Flow Parameters ◽  
Rans Models ◽  
Large Scale Flow

Efficacy of several large-scale flow parameters as transition onset markers are evaluated using direct numerical simulation (DNS) of boundary layer bypass transition. Preliminary results identify parameters (k2D/ν) and u′/U∞ to be a potentially reliable transition onset marker, and their critical values show less than 15% variation in the range of Re and turbulence intensity (TI). These parameters can be implemented into general-purpose physics-based Reynolds-averaged Navier–Stokes (RANS) models for engineering applications.

scholarly journals Channel flow over large cube roughness: a direct numerical simulation study

2010 ◽  
Vol 651 ◽  
pp. 519-539 ◽  
Author(s):  
STEFANO LEONARDI ◽  
IAN P. CASTRO
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Channel Flow ◽  
Outer Part ◽  
Area Coverage ◽  
Immersed Boundary ◽  
Mean Flow ◽  
Surface Drag ◽  
Effective Roughness ◽  
Plane Displacement

Computations of channel flow with rough walls comprising staggered arrays of cubes having various plan area densities are presented and discussed. The cube height h is 12.5% of the channel half-depth and Reynolds numbers (uτh/ν) are typically around 700 – well into the fully rough regime. A direct numerical simulation technique, using an immersed boundary method for the obstacles, was employed with typically 35 million cells. It is shown that the surface drag is predominantly form drag, which is greatest at an area coverage around 15%. The height variation of the axial pressure force across the obstacles weakens significantly as the area coverage decreases, but is always largest near the top of the obstacles. Mean flow velocity and pressure data allow precise determination of the zero-plane displacement (defined as the height at which the axial surface drag force acts) and this leads to noticeably better fits to the log-law region than can be obtained by using the zero-plane displacement merely as a fitting parameter. There are consequent implications for the value of von Kármán's constant. As the effective roughness of the surface increases, it is also shown that there are significant changes to the structure of the turbulence field around the bottom boundary of the inertial sublayer. In distinct contrast to two-dimensional roughness (longitudinal or transverse bars), increasing the area density of this three-dimensional roughness leads to a monotonic decrease in normalized vertical stress around the top of the roughness elements. Normalized turbulence stresses in the outer part of the flows are nonetheless very similar to those in smooth-wall flows.

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