Mean Flow Profiles Research Articles

A Numerical Approach to Analyzing Shallow Flows over Rough Surfaces

The hydraulic characteristics (such as velocity profiles, near-bed velocity profile, bed shear stress, and resistance coefficients) of shallow flows over rough surfaces were investigated using numerical simulations. A novel method is presented to simulate shallow flows over rough surfaces in a two-dimensional (2D) numerical domain, where the physical numerical domain represents bed topography. Results reveal that the model can accurately predict spatially averaged velocity profiles, turbulence characteristics, shear stresses, and uniform flow depths. The analysis identified two distinct flow regions based on mean and turbulent flow profiles. Results show that the turbulent shear stress profiles provide a more accurate estimation of the bed shear stresses. Resistance coefficients (friction factor or Manning’s roughness coefficient) vary with Froude number and submergence ratio (depth divided by roughness height).

Heat effects on supersonic jet screech: a linear stability analysis based on parabolized stability equations

In this paper, we use the parabolized stability equations (PSEs) to investigate heat effects on supersonic jet screech. The PSE is derived from the linear Euler equations, and the computations are performed on an empirical mean flow profile. Employing PSE, we can examine several important characteristics of the shear-layer instability waves, including the convection velocity, the growth rate, and the location where the instability waves attain the maximal total amplification. Equipped with these knowledge, we further explore their impacts on the jet screech. Specifically, using a newly proposed iteration scheme, we first identify a more suitable convective Mach number to predict the screech frequency in both heated and cold jets. Second, we find that the transition of the screech mode from the axisymmetric to the helical mode may be explained by the shift in the most amplified instability modes. Using this criterion, we can predict a transition Mach number for the mode staging. Third, by assuming that the effective source location is the position where the instability wave attains its maximal amplitude and using the newly obtained convective Mach number, we can predict the screech mode staging in cold and heated jets using Gao's model. The predictions agree well with the experimental data. Finally, we investigate the heat effects on screech amplitude. It is found that compared to cold jets, the difference between the frequency of the most amplified instability wave and the frequency of the jet screech is much bigger in heated jets, which may lead to a lower screech amplitude.

Direct numerical simulation of a zero-pressure-gradient turbulent boundary layer with passive scalars up to Prandtl number Pr = 6

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness ${\textit {Re}}_{\theta }$ ranging up to $1080$ . Four passive scalars, characterized by the Prandtl numbers ${\textit {Pr}} = 1,2,4,6$ are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at ${\sim }24\,^{\circ }{\rm C}$ , when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

Nonlinear dynamics and acoustic radiation of coherent structures consisting of multiple ring–helical modes in the near-nozzle region of a subsonic turbulent circular jet

This paper investigates the nonlinear evolution and acoustic radiation of coherent structures (CS) in the near-nozzle region of a subsonic turbulent circular jet. A CS is taken to be a wavepacket consisting of multiple ring/helical modes, which are considered to be inviscid instability waves supported by the mean-flow profile. As the three-dimensionality of helical modes is weak in the near-nozzle region, the ring and helical modes with the same frequency have nearly the same growth rates and critical levels. They coexist and interact with each other in their common critical layer at high Reynolds numbers. The self and mutual quadratic interactions generate a mean-flow distortion and streaks, which act back on the fundamental components through the cubic interaction. The amplitude of the CS is governed by an integro-partial-differential equation, a significant feature of which is that differentiations with respect to the azimuthal coordinate appear in the history-dependent nonlinear terms. The non-parallelism of the mean flow as well as the impact of fine-scale turbulence on CS are taken into account and found to affect the nonlinear terms. By solving the amplitude equation, the development of the constituting modes, streamwise vortices and streaks are described. For CS consisting of frequency sideband, low-frequency components are excited nonlinearly and amplify to reach a considerable level. By analysing the large-distance asymptote of the perturbation, the low-frequency acoustic waves are found to be emitted by the temporally–spatially varying mean-flow distortion and streaks generated by the nonlinear interactions of the CS, and are thereby determined on the basis of first principles. Interestingly, the energetic part of the streaky structure that contributes to the nonlinear dynamics does not radiate directly, and instead the Reynolds stresses driving the subdominant radiating components represent the true physical sources.

Large Eddy Simulation of the ACAT1 fan stage for broadband noise prediction

A numerical study is carried out to assess the aerodynamic and noise radiation specific features of the ACAT1 fan stage, which was tested in the framework of the European project TurbonoiseBB. This study deals with the prediction of the broadband noise radiated by the fan stage at approach conditions, and particularly focuses on the rotor–stator interaction (RSI) noise, which results from the impact of the fan wakes onto the outlet guide vanes (OGV). To this end, two wall-modeled Large Eddy Simulations (LES) with different levels of mesh refinement have been performed on the full fan-OGV stage. The finer mesh significantly improved the aerodynamic predictions in terms of mean flow profiles, but also in terms of RMS profiles and velocity spectra, for which significant disparities are highlighted for the coarser LES. Only slight disparities regarding the turbulent content of the flow remain for the finer LES. The typical flow features at approach conditions are examined and the noise sources on both the stator and the rotor are analyzed, revealing the presence of additional broadband noise sources. Noise predictions are performed by using the free-field Ffowcs Williams and Hawkings (FW-H) analogy, and Goldstein’s in-duct acoustic analogy informed with the pressure fluctuations recorded on the stator and rotor surfaces. FW-H predictions of the stator noise, though well recovering the shape of the experimental spectra, overestimate the radiated noise especially upstream of the fan. Using the finer simulation data substantially reduces the gap with the measurements. Accounting for the duct effect on the sound propagation, further improves the predictions in terms of absolute levels, leading to a good agreement between the finer simulation and the noise measurements. The breakdown of the different stator noise source contributions, in conjunction with rotor broadband noise predictions made it possible to confirm the presence of additional significant broadband noise sources, questioning the common assumption considering the RSI sources as the only dominant fan noise mechanism at approach conditions.

Spatial variation of mean flow and turbulence characteristics within channel contraction – an experimental approach

ABSTRACT The influence of three different channel contractions on the mean flow and turbulent characteristics has been measured experimentally in a recirculating flume. The velocity deficit, turbulence intensity, Reynolds stress, and turbulence scales data within the channel contractions were obtained from three-dimensional velocity fluctuations measurements using Acoustic Doppler Velocimeter. The mean flow profile shows undulation towards the free surface for all the contraction ratios, indicating the presence of the velocity-dip phenomenon due to the secondary currents. These currents changed the pattern of turbulence intensities and Reynolds shear stresses significantly within the channel contraction compared to the without contraction case. The results reveal that with the increase of channel contraction ratio, the strength of the secondary current increased considerably and resulted in a significant change in flow patterns close to the free surface compared to the bottom. The length scales of turbulent flow indicate eddy sizes in different ranges to be smaller at near-bed region within the contraction zone due to the breakdown of larger eddies.

Thermo-physical properties of liquids and gases over a heated rotating disk

The motivation of this study arises due to huge occurrence of rotating disk in field of real-world processes like rotational air cleaner, turbomachinery, centrifugal pumps, aerospace engineering and chemical engineering. A numerical investigation is undertaken to study the thermo-physical properties of Newtonian fluid flow over a strongly heated rotating disk with temperature dependent viscosity. The solar radiative heat flux is considered in the heat equation. The temperature dependent viscosity and thermo-physical properties are assumed to explore the flow behavior. Numerical solutions of the converted boundary layer equations are then achieved by using fifth order Rung-Kutta Fehlberg integration approach with a shooting method. The attained results are discussed for mean flow profiles and physical interpretations of the problem are given through graphs and tables. It is observed that temperature dependence viscosity for liquids ranges to decrease the base flow profiles, whilst the gaseous viscosity nature has the opposite impact. The mass diffusion coefficient creates enhancement in concentration field. Moreover, correlations are plotted graphically in terms of temperature, concentration, and viscosity.

Sound reflection by periodic acoustic metasurface in sheared grazing flows

The reflection performance of periodic acoustic metasurfaces (AMs) subjected to a grazing flow, consisting of a uniform region and a finite sheared layer, is studied. A convective generalized Snell’s law (CGSL) is derived to account for the effect of uniform mean flows on the reflection of AMs. Then, an AMs design method considering the mean flow profile is proposed based on the impedance transformation method. The strategy is to form a reflected phase gradient at the interface plane between the uniform and the sheared flow regions. The reflection characteristics of two acoustic porous metasurfaces (APMs), i.e., APM1 and APM2 designed for the uniform and the sheared flows, respectively, are numerically investigated. Results show that APM1 achieves efficient anomalous reflections in uniform flows, and the diffracted orders and directions of the reflected waves are well predicted by the proposed CGSL. However, the performance of APM1 deteriorates under oblique incidences if applied to a typical sheared flow. In contrast, APM2 realizes desired wavefront manipulations under the same conditions. Finally, the CGSL is extended into a three-dimensional (3D) space and is validated numerically. This study provides a means for AMs design in flow conditions, which holds good potential in aeroacoustic noise problems.

Laminar–turbulent intermittency in pipe flow for an Herschel–Bulkley fluid: Radial receptivity to finite-amplitude perturbations

We investigate the laminar-to-turbulent transition for non-Newtonian Herschel–Bulkley fluids that exhibit either a shear-thinning or shear-thickening behavior. The reduced-order model developed in this study also includes the effect of yield-stress for the fluid. Within our model framework, we investigate how the Newtonian dynamics change when significant non-Newtonian effects are considered either via the flow index n or the yield-stress τ0 or both. We find that an increase in τ0 as well as a decrease in n lead to a delayed transition if a perturbation of the given turbulent intensity is injected at various radial locations. As the radial position of the injection for the perturbation is varied in this study, our reduced-order model allows for the investigation of the flow receptivity to the finite-amplitude perturbations and to their radial position of inception. We observe that, for a given mean flow profile, the same perturbation becomes more prone to induce turbulence the closer it approaches the wall because of its initial amplitude being relatively higher with respect to the local mean flow. An opposite trend is found when the perturbation amplitude is rescaled on the local mean flow.

A new class of approximate analytical solutions of the Pridmore-Brown equation

There is only a limited amount of known analytical solutions to the Pridmore-Brown equation, mostly employing asymptotic behavior for a certain frequency limit and specifically chosen flow profiles. In this paper, we show the possibility of transformation of the Pridmore-Brown equation into the Schrödinger-like equation for the case of two-dimensional homentropic mean flow without critical layers. The corresponding potential that depends on the mean flow profile can then be approximated by a quartic polynomial, leading to a triconfluent Heun equation whose solution based on the triconfluent Heun functions is generally known. The quality of this approximation procedure is presented for the case of symmetric polynomial flow profiles for various values of polynomial order and the Mach number. A more detailed example is then shown for a quadratic mean flow profile, where the solution is accurate up to the third order of the Mach number.

Influence of sidewalls on three-dimensional turbulent wall jet: An experimental and numerical approach

In this study, with the help of with and without sidewall configurations, experimental and numerical approaches are utilised to investigate the sidewall influence on a three-dimensional turbulent wall jet. The mean flow profile of the three-dimensional turbulent wall jet is measured through experimental method and compared with the numerical results. In addition, the numerical method is used to characterise the turbulence characteristics of the wall jet for both the configurations. A 200 mm square nozzle (height h=20 ± 0.5 mm) is used to generate the developing jet exit profile for the experimental results. The Reynolds number based on the jet exit velocity and nozzle height is 25,000. The numerical results are obtained by solving the Reynolds Average Navier stokes (RANS) equations with low Reynolds number k−ε turbulence models proposed by Yang and Shih and Launder and Sharma. The experimental results are obtained by a single probe hotwire anemometer and a K-type thermocouple. It is observed that the sidewall affects the temperature distribution just after the potential core region x/h=5 whereas the velocity distribution is affected in the fully developed region after the downstream location x/h=22.5. Sidewalls drastically influenced the thermal and velocity decay in wall-normal and lateral directions. It is found from the numerical simulation that the decay of maximum streamwise velocity is increased by 9%, whereas centerline temperature decay is decreased by 25% in sidewall configuration as compared to without sidewall configuration. The contour plots of temperature and velocity also exhibit the sidewall effect on the whole domain. The Reynolds shear stress <u′v′> dominates in the vertical jet centerline plane atz=0, whereas <u′w′> dominates in the lateral direction at ymax plane in both the configurations. On the vertical jet centerline plane at z=0, Reynolds shear stress <u′v′> is nearly increased by 10% in the presence of sidewall compared to without sidewall configuration. The entrainment of the ambient fluid initially decreases, but after the downstream location x/h=22.4, it increases for the case of the sidewall compared to the corresponding case without the sidewall. This happens owing to an increase in maximum turbulent kinetic energy generation inside the flow domain by 10%. The turbulent heat flux <T′V′> dominates in lateral and wall-normal shear layers in both the configurations. The correlations of decay of temperature and velocity are also suggested through numerical techniques.

Validation of a Large-Eddy Simulation Approach for Prediction of the Ground Roughness Influence on Wind Turbine Wakes

The ability of high-fidelity computational fluid mechanics simulation to quantitatively predict the influence of ground roughness on the evolution of the wake of a three-bladed horizontal axis wind turbine model is tested by comparison with wind tunnel measurements. The approach consists of the implicit approximate deconvolution large-eddy simulation formulation of Hickel et al., (2006), that is, for the first time, combined with a wall-stress model for flow over rough surfaces and with the actuator line approach (ALM) for modeling of the rotor. A recycling technique is used for the generation of turbulent inflow that matches shear exponents α=0.16 (medium roughness) and α=0.32 (high roughness) and turbulence level of the reference experiments at hub height. Satisfactory agreement of the spectral content in simulation and experiment is achieved for a grid resolution of 27 cells per rotor radius. Except for minor differences due to neglecting nacelle and tower in the simulation the LES reproduces the shapes of mean flow and Reynolds stress profiles in the wake. The deviations between measurement and simulation are more prominent in a vertical cut plane through the rotor center than in a horizontal cut plane. Simulation and experiment deviate with respect to the roughness influence on the development of the wake width; however, the relative change of the maximum wake deficit and of the vertical wake center position due to changes in ground roughness is reproduced very well.

Improved weighted compact nonlinear scheme for implicit large-eddy simulations

Weighted compact nonlinear scheme (WCNS) is improved by replacing the nonlinear explicit interpolation with a nonlinear compact interpolation. The non-oscillatory behaviour of the weighting technique and the spectral resolution of the compact interpolation are maintained simultaneously. In order to investigate the performance of implicit large-eddy simulations (ILES) using WCNS with the new interpolation, several fundamental turbulent flows with relatively complex configurations are validated. Encouraging results are obtained in predicting mean flow profiles, unsteady vortex shedding and the frequency spectra, indicating that the improved WCNS is a promising algorithm for simulations of turbulent compressible flows.

Significance of binary chemical reaction, enthalpy and variable thermophysical properties over a radioactive heated rotated disk

In present work, we assume the thermo-physical characteristics of viscous fluid on a heated rotating disk. We used the modified Newtonian fluid model for temperature dependent viscosity and calculated the mean flow profiles under the viscosity effect near the heated rotating disk. We determine the behavior with modified activation enthalpy and radiation effects by utilizing the heat phenomena while the mass transfer process is investigated by using thermophoretic, chemical reaction and activation energy. The rudimentary flow can be solved numerically via von Kàrmàn similarity solution that has been cracked by using a shooting method. We regulate the base flow profiles and provide a physical clarification of the problem through graphs and tables. Correlations in term of velocity, viscosity, temperature and concentration are plotted graphically.

The coupled dynamics of internal waves and hairpin vortices in stratified plane Poiseuille flow

A simulation of stably stratified plane Poiseuille flow at a moderate Reynolds number ( $\textit {Re}_\tau = 550$ ) and Richardson number ( $\textit {Ri}_\tau = 480$ ) is presented. For the first time, the dynamics in the channel core are shown to be described as a series of internal waves that approximately obey a linear wave dispersion relationship. For a given streamwise wavenumber $k_x$ there are two internal wave solutions, a dominant low frequency mode and a weaker-amplitude high-frequency mode, respectively corresponding to ‘backward’ and ‘forward’ propagating internal waves relative to the mean flow. Analysis of linearised equations shows that the dominant low-frequency mode appears to arise due to a particularly sensitive response of the mean flow profiles to incoherent forcing. Instantaneous visualisations reveal that hairpin vortices dominate the outer region of the channel flow, neighbouring the buoyancy dominated channel core. These hairpins are fundamentally different from those observed in canonical unstratified boundary layer flows, as they arise via quasi-linear local processes far from the wall, governed by background shear. Outer region ejection events are common and can be induced by high amplitude waves. Ejected hairpins are transported into the channel core, in turn ‘ringing’ the prevailing strong buoyancy gradient and thus generating high-amplitude internal waves, high dissipation and wave breaking, induced by spanwise vortex stretching and baroclinic vorticity generation. Such spontaneous and sustained generation of quasi-linear internal waves by wall-bounded sheared turbulence may provide novel idealised solutions for, and insight into, large-scale turbulent mixing in a wide range of environmental and industrial flows.

Assessment of the validity of a log-law for wall-bounded turbulent bubbly flows

There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded, turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von Kármán constant, and this is used in various modelling studies. We provide a critique of this idea, and present several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the log-law for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence and the bubble-induced turbulence must play a role.

Experimental Investigation of Mean Flow Profile Effects on Impedance Eduction

The results of experimental and computational studies of the three-dimensional mean flow velocity profile influence on the impedance eduction are presented. In order to measure the three-dimensional velocity profile, the TsAGIâ€(tm)s “Interferometer with flow†facility was upgraded so that additional holes were made in one cross section of the rectangular duct. As a result, it became possible to measure the longitudinal flow velocity in this cross section along 6 lines using a Pitot tube or a hot wire anemometer. The full three-dimensional velocity profile is determined by interpolating the values measured.Experimental results of the velocity profile for various experiment conditions are presented. Based on the numerical solution of the three-dimensional Pridmore-Brown equation by means of Finite Element Method and the gradient descent method, the problem of impedance eduction are investigated. The influence of the flow velocity profile and the form of functional on the obtained impedance values are discussed. The impedance values educted by means of this approach are compared with the impedance values obtained using two-dimensional impedance eduction methods, which didnâ€(tm)t taking into account the three-dimensional non homogeneity of the flow velocity field.

Impact of off-bottom seaweed cultivation on turbulent variation in the hydrodynamic environment: A flume experiment study with mimic and natural Saccharina latissima thalli

The seaweed industry is growing worldwide to meet future resource needs in terms of food and fuel. In the meantime, the impact of expanding off-bottom seaweed cultivation on its environment is unclear. For example, it remains poorly understood how off-bottom seaweeds affect the local hydrodynamic environment, especially concerning turbulence that is more important for nutrient transport and availability than the mean flow velocity. Here, we carried out well-controlled flume experiments with mimic seaweed thalli, which are available, controllable, and stable, to investigate the impact of off-bottom seaweed canopies on whole-depth flow velocities in terms of both mean flow and turbulence velocity profiles. A careful comparison of behavior in the flow between natural and mimic seaweed thalli was made before these experiments. The results show that the floating seaweed thalli generate a surface boundary layer and have a profound impact on the velocity structure in the bottom boundary layer. More importantly, the generation, growth and dissipation of turbulence in the seaweed thalli area deeply affect the downstream distribution of near-bed turbulent strength and associated bed shear stress. Ignoring this turbulent variation would cause inaccurate predictions of morphological changes of the seabed. Our findings suggest that expanding the seaweed cultivation area may cause high risks of bed degradation and low diffusion in the downstream cultivation area. These findings provide novel insights into the environmental influence of off-bottom seaweed cultivation, with important implications for optimizing management strategies to promote seaweed productivity while minimizing seabed destabilization.

Interactions between Tandem Cylinders in an Open Channel: Impact on Mean and Turbulent Flow Characteristics

The flow hydrodynamics around a single cylinder differ significantly from the flow fields around two cylinders in a tandem or side-by-side arrangement. In this study, the experimental results on the mean and turbulence characteristics of flow generated by a pair of cylinders placed in tandem in an open-channel flume are presented. An acoustic Doppler velocimeter (ADV) was used to measure the instantaneous three-dimensional velocity components. This study investigated the effect of cylinder spacing at 3D, 6D, and 9D (center to center) distances on the mean and turbulent flow profiles and the distribution of near-bed shear stress behind the tandem cylinders in the plane of symmetry, where D is the cylinder diameter. The results revealed that the downstream cylinder influenced the flow development between cylinders (i.e., midstream) with 3D, 6D, and 9D spacing. However, the downstream cylinder controlled the flow recirculation length midstream for the 3D distance and showed zero interruption in the 6D and 9D distances. The peak of the turbulent metrics generally occurred near the end of the recirculation zone in all scenarios.

Wind in a Natural and Artificial Wildland Fire Fuel Bed

Fuel beds represent the layer of fuel that typically supports continuous combustion and wildland fire spread. We examine how wind propagates through and above loose and packed pine needle beds and artificial 3D-printed fuel beds in a wind tunnel. Vertical profiles of horizontal velocities are measured for three artificial fuel beds with prescribed porosities and two types of fuel beds made with long-leaf pine needles. The dependence of the mean velocity within the fuel bed with respect to the ambient velocity is linked to the porosity. Experimental results show significant structure to the vertical profile of mean flow within the bed, and suggest that small-scale sweeps and ejections play a role in this system redistributing momentum similar to larger-scale canopy flows.