Triangular instability of a strained Lamb–Oseen vortex

This study uses computational methods to analyze fluid flow characteristics NACA 4415 in ultra-low, low, and moderate Reynolds number categories. The turbulence model chosen is the standard k-ε. The ultra-low Reynolds number used is 5×10^3, while the Reynolds number for the low category is 4.17×10^4. For the moderate category, the Reynolds number is 3×10^6. The variation of the grid being tested is the grid with the number of elements 5×10^4, 10^5 and 2×10^5. The grid with the number of elements 2×10^5 gives the best results. At the ultra-low Reynolds number, there is no stall condition. The stall condition at the low Reynolds number is AoA=12°. At the moderate Reynolds number, the stall occurs at AoA=18°. The largest Cl is in the moderate Reynolds number. Meanwhile, the smallest Cd is at the ultra-low Reynolds number. Based on the analysis of pressure contours, velocity contours and velocity streamlines, the fluid flow patterns seen are not much different. However, there is a significant difference in their values.

A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

We study the scaling properties of heat transfer $Nu$ in turbulent thermal convection at large Prandtl number $Pr$ using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number $Re$. At low Reynolds number, $Nu Pr^{-1/2}$ and $Re$ are a function of $Ra Pr^{-3/2}$. At large Reynolds number $Nu Pr^{1/3}$ and $Re Pr$ are function only of $Ra Pr^{2/3}$ (within logarithmic corrections). In practice, since $Nu$ is always close to $Ra^{1/3}$, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF6 (large $Re$) and in alcohol/water (lower $Re$). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve $Nu(Ra,Pr)$ which may be used to describe all measurements at $Pr\ge 0.7$.

Systematic flow measurements of profile and mixing losses were made across the blade pitches of a linear turbine cascade at low and moderate Reynolds numbers. The effect of Reynolds number on mixing behavior and development of the wake downstream of the trailing edge were investigated by means of traverse results at different planes downstream of the cascade. The experimental loss data were compared with predictions of theoretical boundary layer flow methods and of computational fluid dynamics (CFD) analyses. Several turbulence models available in commercial CFD tools and in the open CFD code OpenFOAM were considered for the present case study. It was found that substantial deviations between the numerical predictions and the experimental data occurred. These deviations may be attributed to the fact that at low Reynolds numbers, laminar and transitional boundary layer flows and flow separation phenomena became relevant. Based on the experimental two-dimensional loss data, the validity of simple Reynolds number scaling rules was assessed.

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.

Turbulent heat transfer in channel flows is an important area of research due to its simple geometry and diverse industrial applications. Reynolds-Averaged Navier–Stokes (RANS) models are the most-affordable simulation methodology and are often the only viable choice for investigating industrial flows. However, accurate modelling of wall-bounded flows is challenging in RANS, and the assessment of the performance of RANS models for heated turbulent channel flow has not been sufficiently investigated for a wide range of Reynolds and Prandtl numbers. In this study, five RANS models are assessed for their ability to predict heat transfer in channel flows across a wide range of Reynolds and Prandtl numbers (Pr) by comparing the RANS results with respect to the corresponding Direct Numerical Simulation data. The models include three Eddy Viscosity Models (EVMs): standard k−ϵ, low Reynolds number k−ϵLS, and k−ωSST, as well as two Reynolds Stress Models (RSMs): Launder–Reece–Rodi and Speziale–Sarkar–Gatski models. The study analyses the Reynolds number effects on turbulent heat transfer in a channel flow at a Pr of 0.71 for friction Reynolds number values of 180,395,640, and 1020. The results show that all models accurately predict velocity across all Reynolds numbers, but the accuracy of mean temperature prediction drops with increasing Reynolds number for all models, except for the k−ωSST model. The study also analyses the Pr effects on turbulent heat transfer in a channel flow with Pr values between 0.025 and 10.0. An error analysis is performed on the results obtained from different turbulence models, and it is shown that the k−ωSST model has the smallest error for the predictions of the mean temperature and Nusselt number for high-Prandtl-number flows, while the low Reynolds number k−ϵLS model shows the smallest errors for low-Prandtl-number flows at different Reynolds numbers. An analytical solution is utilised to identify Pr effects on forced convection in a channel flow into three different regimes: analytical region, transitional region, and turbulent diffusion-dominated region. These regimes are helpful to discuss the validity of the models in relation to the Pr. The findings of this paper provide insights into the performance of different RANS models for heat transfer predictions in a channel flow.

A modal Discontinuous Galerkin (DG) method is assessed for the Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of freely decaying turbulence. We consider as benchmark test case the TaylorGreen vortex flow. Inviscid computations show the conservation and dissipation properties of the DG scheme in the context of 3D non-linear flow problems. DG DNS computations carried at low and moderate Reynolds numbers (Re = 400 and Re = 1600, respectively) show good agreement with a reference solution generated using a Fourier pseudo-spectral code. LES computations are carried out at larger Reynolds number (Re = 3000), and compared to a reference filtered DNS. The Variational Multiscale Simulation framework, which can be straightforwardly implemented in a modal DG code is compared to the classical Smagorinsky approach for LES.

Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non‐zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006;96:134503; Subramanian and Koch, Phys Fluids. 2006;18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow‐gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier‐Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233–240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow‐gradient plane. However, the wake near the flow‐gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. © 2010 American Institute of Chemical Engineers AIChE J, 2011

A smoke visualization experiment has beenperformed in the first 3,m ofneutral and unstable atmospheric boundary layersat very large Reynolds number(ReΘ > 106). Under neutral atmosphericconditions mean wind profiles agreewell with those in the canonical flatplate zero-pressure-gradient turbulentboundary layer. The experiment was designedto minimize the temperaturedifference between the passive marker (smoke)and the air to ensure that anyobserved structures were due to vortical, ratherthan buoyant, motions. Imagesacquired in the streamwise–wall-normal planeusing a planar laser light-sheetare strikingly similar to those observed inlaboratory experiments at low to moderate Reynolds numbers. They reveal large-scaleramp-like structures withdownstream inclination of 3°–35°.This inclination isinterpreted as the hairpin packet growthangle following the hairpin vortexpacket model ofAdrian, Meinhart, and Tomkins.The distribution of this characteristicangle agrees with the results of experiments at far lower Reynolds numbers,suggesting a similarity in structures among low, moderate, and high Reynoldsnumber boundary layers at vastly different scales. These results indicate thatthe hairpin vortex packet model extends over a large range of scales. Theeffect of vertical heat transport in an unstable atmosphere on wall structuresis investigated in terms of the hairpin vortex packet model.

A field observation array for the atmospheric surface layer (ASL) was built on a dry flat bed of Qingtu Lake in Minqin (China) as the Qingtu Lake Observation Array (QLOA) site, which is similar to the Surface Layer Turbulence and Environmental Science Test (SLTEST) site in the Utah (USA) Western desert. The present observation array can synchronously perform multi-point measurements of wind velocity and temperature at different vertical and streamwise positions. In other words, three-dimensional turbulent ASL flows can be measured at the QLOA station and Reynolds numbers as high as $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{6})$ can be achieved with steady wind conditions. By careful selection and pretreatment for measured data of more than 1200 h, the QLOA data have been validated to be reliable for high Reynolds number turbulent boundary layer research. Results from correlation and spectral analysis confirm that very large scale motions (VLSMs) exist in the ASL at a Reynolds number up to $Re_{\unicode[STIX]{x1D70F}}\approx 4\times 10^{6}$. Through premultiplied spectral analysis, it is revealed that the spectral energy in the high-wavenumber region decreases with height, similar to turbulent boundary layers at low or moderate Reynolds numbers, while it increases with height in the low-wavenumber region resulting in a log–linear increase of VLSMs energy with height, which is different from turbulent boundary layers at low or moderate Reynolds numbers. The present analyses support the view that the evolution of the VLSMs cannot be fully attributed to a ‘bottom-up’ mechanism alone, and probably other mechanisms, including a ‘top-down’ mechanism, also play a role.

Transfert de chaleur en écoulement puisé au point d'arrêt d'un cylindre chaud

Non-Newtonian Behavior of an Insoluble Monolayer: Effects of Inertia

The practical implication of nanofluids is essentially dependent on their accurate modelling, particularly in comparison with the high cost of experimental investigations, yet the accuracy of different computational approaches to simulate nanofluids remains controversial to this day. Therefore, the present study is aimed at analysing the homogenous, multiphase Eulerian–Eulerian (volume of fluid, mixture, Eulerian) and Lagrangian–Eulerian approximation of nanofluids containing nonspherical nanoparticles. The heat transfer and pressure drop characteristics of the multiwalled carbon nanotubes (MWCNT)-based and multiwalled carbon nanotubes/graphene nanoplatelets (MWCNT/GNP)-based nanofluids are computed by incorporating the influence of several physical mechanisms, including interfacial nanolayering. The accuracy of tested computational approaches is evaluated by considering particle concentration and Reynolds number ranges of 0.075–0.25 wt% and 200–470, respectively. The results demonstrate that for all nanofluid combinations and operational conditions, the Lagrangian–Eulerian approximation provides the most accurate convective heat transfer coefficient values with a maximum deviation of 5.34% for 0.25 wt% of MWCNT–water nanofluid at the largest Reynolds number, while single-phase and Eulerian–Eulerian multiphase models accurately estimate the thermal fields of the diluted nanofluids at low Reynolds numbers, but overestimate the results for denser nanofluids at high Reynolds numbers.

The interaction of a vortex and a pipe flow, modelled as the Lamb–Oseen vortex and the Poiseuille flow, respectively, is investigated by means of stability analyses and direct numerical simulations (DNS). From the distribution of the most unstable mode, it is observed that the instability is induced by the combination of the radial gradients of the base azimuthal and axial velocity components, e.g. an axial (or azimuthal) vorticity perturbation acts on the axial (or azimuthal) base velocity via a lift-up effect to generate axial (or azimuthal) velocity streaks, which are further stretched by the base azimuthal (or axial) velocity to create azimuthal (or axial) vorticity. This lift-up-stretch mechanism is confirmed in DNS of the model base flow initially perturbed by the most unstable mode. After nonlinear saturation, the perturbations decay since the flow no longer supports instability after sufficient radial mixing induced by the lift-up of the azimuthal and axial velocity components. These observations suggest that the vorticity outside the vortex core can be suppressed by instabilities if a streamwise boundary layer flow exists outside the core.

A simple but very efficient numerical method based on the finite difference technique has been developed for solving time-dependent non-linear flow problems. The governing equations of motion are discretized by a backward-time central-space scheme, whereby only the variables in the non-linear terms other than the main variable of the transport equation are replaced with the corresponding values calculated previously. The resulting algebraic equations for each main variable are solved by directly applying the Gaussian algorithm altered by considering the sparse structure of the diagonal-banded coefficient matrix adequately. The method is applied here to study the unsteady axisymmetric isotherm flow of an incompressible viscous fluid in a spherical shell with a stationary inner sphere and a rotating outer sphere. The description given in literature of the flow under consideration concentrates analytically on the asymptotic behaviour for very large Reynolds number Re starting from the almost rigid rotation. The case of small or moderate Reynolds numbers could be studied numerically only for Re 1000. Therefore, no data are available for the large intermediate region at high Reynolds numbers. In contrast to literature, consistent solutions for a large range of Reynolds number from 10 to 20000 are obtained with the method described here. A comparison of the results with those in literature shows a good agreenment up to Re=1000. At high Re the flow field confirms certain features such as the Stewartson shear layers as predicted by the asymptotic theory. With the results presented, a contribution is made for filling the gap between the asymptotic theory and numerical results in literature.