Smooth Turbulent Flow Research Articles

Direct numerical simulation of coflowing rough and smooth turbulent channel flows

Turbulent channel flow with underlying rough and smooth surfaces present abreast is investigated using direct numerical simulations. Secondary roll cells, exhibiting a strong updraft in the smooth half of the channel, are observed. The roll cells have significantly attenuated the bulk flow and turbulence in the smooth half of the channel.

Friction factor from velocity profiles in smooth turbulent channel flows

Fluid dynamics plays an important role in many Renewable energies studies, i.e. wind and tidal turbines, wave energy geothermal and solar power, …). Friction factor f is an important parameter for the determination of pressure drop in different processes and systems. In this study, we use DNS data of turbulent smooth channels to evaluate different methods. First, a recalibration of Dean’s correlation (Dean, 1978) is proposed. The aim of the study is to obtain accurate wall friction factors from velocity profiles. On the one hand, we obtained two implicit analytical relations based on the law-of-the-wall: a logarithmic friction relation similar to that of pipes and a linear-logarithmic friction relation. On the other hand, we obtained f from the computation of the average velocity. It is first calculated from the law-of-the-wall and allows a good prediction of f for Reτ > 395 but presents a gap for low Reτ which is related to inaccurate velocities. Low-Reynolds number effect in channel flows has been previously observed in different experimental and computational studies. In order to provide suitable friction factor values, it is important to predict velocities accurately on the overall channel height. We used therefore a more appropriate method which consists to use for y+ < 20 the momentum equation with an eddy viscosity formulation (Absi, 2019) and the log-wake law for high y+ values. This method provides accurate friction factor values and allows good agreement with DNS data.

Turbulent kinetic energy estimate in the near wall region of smooth turbulent channel flows

Turbulent kinetic energy estimate in the near wall region of smooth turbulent channel flows

Open Channel Flow Friction Factor: Logarithmic Law

ABSTRACT Lim, H.S., 2018. Open channel flow friction factor: Logarithmic law. The friction factor in open channel flow is considered to increase proportionally with wall roughness compared to that of pipe flow because of undulation at the free surface. The undulation is considered to be driven from the bottom and side walls. The increment factor associated with free surface undulation, shape distortion, and meandering is related to the Manning coefficient, and the incremented friction factor is substituted into the friction factor of circular pipe smooth (stretching) turbulent flow so as to yield the friction factor for open channel flow. The new equation for friction factor or mean velocity provides similar results to the Manning equation and the Ganguillet-Kutter (GK) equation for small streams. However, it is found that the Manning equation results in larger values of mean velocity in wide rivers compared with the GK equation and the new logarithmic equation based on the concept termed as “smooth turbu...

An experimental study on near-orthogonal wave–current interaction over smooth and uniform fixed roughness beds

An experimental study of periodic waves interacting with near-orthogonal turbulent currents is presented in this paper. Mean velocity profiles for current-alone, wave-alone and combined wave–current flows are measured with Acoustic Doppler Velocimeters to resolve the changes in mean flow kinematics due to wave–current interaction. In this study, the near-bottom wave orbital velocity is approximately 1.5 times greater than the depth-averaged current velocity, and the log-profile method is used to determine the bottom roughness from the measured velocity profiles. The primary focus is on 90° wave–current interaction, while selected findings for 60° and 120° wave–current orientations are also presented. In the smooth bed experiment, the interaction is shown to be linear due to the relatively low Reynolds-number flows generated in the facility — a relatively common scenario in small-scale laboratory setups that has not received much attention in previous studies. The smooth turbulent flow equation, with modification of the input shear velocity, is found to accurately predict the mean flow roughness for linear interaction. The bottom roughness is subsequently increased with the introduction of a layer of uniform 12.5mm marbles to achieve a more realistic rough turbulent flow regime. The results agree qualitatively with previous experimental findings that showed a reduction in the near-bottom mean velocity due to a wave-enhanced (apparent) roughness. However, the Grant–Madsen (GM) model is found to over-estimate the apparent roughness when the angle of wave–current interaction is large, implying a lack of directional sensitivity of this model under “strong-wave, weak-current” conditions. A tentative explanation of this shortcoming is given in the paper. However, it is not possible to extend the GM model analysis to the present near-orthogonal wave–current flows, as results suggest that both 60° and 120° wave–current cases are sufficiently contaminated by the wave-induced mass transport component in the current direction to invalidate the use of the log-profile method to resolve the bottom roughness. In addition to the modification of current profiles by waves, the present study also shows a drastic transformation of wave-induced mass transport profiles by the external turbulent currents. The veering of mean flow over depth is consistent with the superposition of a wave-induced return flow on the external current, while additional veering in the near-bottom region may be attributed to turbulence asymmetry induced by the current component in the direction of the near-bottom wave orbital velocity which is shown to vary locally by ±10° due to parasitic waves emanating from the current inlet and outlet.

Modeling bedform development under turbulent flows using Large-Eddy-Simulation and Immersed-Boundary-Method

A numerical model was built to study the mechanism of sedimentary bedform development in hydraulically smooth turbulent flows. The model consisted of a module for flows, a module for sediment transport, and a module for bed surface evolution. The flow was unsteady, three-dimensional and modeled by a Large-Eddy-Simulation (LES) method coupled with an Immersed-Boundary-Method (IBM). Governing equations were discretized on a fixed Cartesian grid by Finite Difference Method. Sediment (bedload) transport was estimated by Van Rijn formula corresponding to bed shear stress distribution obtained from the flow solution. The bed surface evolution was adapted to the sediment flux and described by the Exner–Polya equation. Updated bed surface was then used as the boundary for solving the flow field in the next time step. Time-advancement was discretized by the Adams–Bashforth method. The model was first validated by two test cases of bed shear stress and turbulence statistics over fixed sinusoidal bed surfaces. It was then employed to study initiation and development of bedforms from an initially flat bed to fully developed forms. Formation of newly and successively formed bedforms, growing and downstream propagating process of existing bedforms were very close to experimental observations. Instantaneous bed shear stress and corresponding sediment flux around evolving bedforms, which were difficult to observe in experiments, were also well produced by this model.

A rational approach to seepage flow effects on bottom friction beneath random waves

The bottom friction beneath random waves is predicted taking into account the effect of seepage flow. This is achieved by using wave friction factors for rough turbulent, smooth turbulent and laminar flow valid for regular waves together with a modified Shields parameter which includes the effect of seepage flow. Examples using data typical to field conditions are included to illustrate the approach. The analytical results can be used to make assessment of seepage effects on the bottom friction based on available wave statistics. Generally, it is recommended that a stochastic approach should be used rather than using the rms values in an otherwise deterministic approach.

Experimental validation of a 2D overland flow model using high resolution water depth and velocity data

• A 2D overland flow model is validated using high resolution depth and velocity data. • Manning and Keulegan formulations produce similar and satisfactory results. • More complex formulations do not improve model performance. • The friction coefficient can be related to the micro and macro-rugosity of the bed. • The model might be used as the hydraulic base of a distributed soil erosion model. This paper presents a validation of a two-dimensional overland flow model using empirical laboratory data. Unlike previous publications in which model performance is evaluated as the ability to predict an outlet hydrograph, we use high resolution 2D water depth and velocity data to analyze to what degree the model is able to reproduce the spatial distribution of these variables. Several overland flow conditions over two impervious surfaces of the order of one square meter with different micro and macro-roughness characteristics are studied. The first surface is a simplified representation of a sinusoidal terrain with three crests and furrows, while the second one is a mould of a real agricultural seedbed terrain. We analyze four different bed friction parameterizations and we show that the performance of formulations which consider the transition between laminar, smooth turbulent and rough turbulent flow do not improve the results obtained with Manning or Keulegan formulas for rough turbulent flow. The simulations performed show that using Keulegan formula with a physically-based definition of the bed roughness coefficient, a two-dimensional shallow water model is able to reproduce satisfactorily the flow hydrodynamics. It is shown that, even if the resolution of the topography data and numerical mesh are high enough to include all the small scale features of the bed surface, the roughness coefficient must account for the macro-roughness characteristics of the terrain in order to correctly reproduce the flow hydrodynamics.

Wind loads on a residential solar water heater

This experimental study aims to address the effects of freestream turbulence intensity (TI) on wind loads on a residential solar water heater with and without a guide plate. Highly turbulent flow was produced by a turbulence generation grid at the inlet of the working section. Results show that the distributions of mean longitudinal and spanwise pressures are associated with tilt angle, guide plate, and freestream TI. Interactions between separation and corner vortices on the upper surface and impingement of shear layer from the tip of a guide plate on the lower surface would induce higher levels of fluctuating pressure, particularly in turbulent flow. A similarity parameter α/A* is also proposed to scale the uplift coefficients in both smooth uniform and turbulent flows.

Three-dimensional multi-scale fluid distributor assembly minimizing total viscous dissipation

In this paper, a novel multi-scale transport network geometry has been addressed by means of constructal theory. The channel dimensions are given and justified with an engineering criterion into the design itself. The first stage of this work consists of assembly optimization, which is formulated as follows: find the distribution of channel radii and angle that minimizes total viscous dissipation (or pumping power, pressure drop) under the constraints of fixed total volume of channels and tube material consumed. Analytical resolutions of the problem of optimal channel size distribution for tree-like networks used as flow distributors are obtained. In the subsequent stages, a large number of flow configurations are constructed based on the optimal channel size. The resulting structure is an optimized multi-scale flow distributor. Furthermore, for such configuration, the equality of pressure drops ensuring flow rate uniformity at the outlet ports of the distributor is demonstrated theoretically. Finally, CFD simulations are employed to investigate fully developed smooth turbulent flow on different branch junctions. Numerical results are found to be in good agreement with predicted analytical results and support the relationship between the pressure drop and the liquid flow rate at the inlet port of the constructal liquid distributor.

Uncertainties in key transport variables in homogeneous slurry flows in pipelines

Several concentrate and tailing pipelines use leak detection systems to predict system ruptures and minimise response times in case of or before the occurrence of pipeline ruptures. Those of internal type compare a set of model predictions for pressure losses and flows with actual readings from the system. Input data including solids specific gravity, concentration by weight or rheology curves, obtained either from periodic measurement campaigns or from installed instrumentation, are used to define values for rheological parameters such as the viscosity to be considered for such computations of head losses. In the present paper, an analysis of propagation of different error sources on the rheology identification and eventually on the computation of the head losses is proposed to investigate the relevance of system instrumentation accuracy and indirect errors derived by lack of instrument parameter update. A simple model for the calculation of friction losses for homogeneous Bingham fluids in the hydraulically smooth turbulent flow, a common regime found in copper and iron slurries, was considered. Assuming standard models to link the solids volume concentration with viscosity, uncertainties between 7% and 12% on the latter parameter are predicted for various conditions and variants of the referred mixtures. This is predicted to propagate to values between 10% and 20% on unit head loss uncertainties, provided errors between 5% and 10% on flow metering. Results suggest the inconvenience of rheology inference when using indirect leak detection systems, in favour of online or very frequent rheometric measurement during the transport process.

Bottom friction and erosion beneath long-crested and short-crested nonlinear random waves

A practical approach for calculating the bottom shear stress beneath long-crested (2D) and short-crested (3D) nonlinear random waves is provided. The approach is based on assuming the waves to be a stationary narrow-band random process and by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves. Results are presented for laminar, smooth turbulent and rough turbulent flow. Examples are also included to illustrate the applicability of the results for practical purposes using data typical for field conditions; the mobile layer thickness in sheet flow representing rough turbulent flow; erosion of mud representing smooth turbulent flow and deposition of mud representing laminar flow.

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds.

Phototactic Clustering of Swimming Microorganisms in a Turbulent Velocity Field

We study the distribution of swimming microorganisms advected by a two-dimensional smooth turbulent flow and attracted towards a light source through phototaxis. It is shown that particles aggregate along a dynamical attractor with fractal measure whose dimension depends on the strength of the phototaxis. Using an effective diffusion approximation for the flow, we derive an analytic expression for the increase in light exposure over the aggregate and by extension an accurate prediction for the fractal dimension based on the properties of the advection and the statistics of the attracting field.

표면조도가 있는 난류경계층 내 난류구조

Turbulent coherent structures near rod-roughened wall are investigated by analyzing the database of directnumerical simulation of turbulent boundary layer. The surface roughness rods with the height k/δ =0.05 are arranged periodically in Reδ = 9000 . The roughness sublayer is defined as two-point correlations are not independent of streamwise locations around roughness. The roughness sublayer based on the two-point spatial correlation is different from that given by one-point statistics. Quadrant analysis and probability-weighted Reynolds shear stress indicate that turbulent structures are not affected by surface roughness above the roughness sublayer defined by the spatial correlations. The conditionally-averaged flow fields associated with Reynolds shear stress producing Q2/Q4 events show that though turbulent vortices are affected in the roughness sublayer, these are very similar at different streamwise locations above the roughness sublayer. The Reynolds stress producing turbulent vortices in the log layer ( y /δ = 0.15) have almost the same geometrical shape as those in the smooth wall-bounded turbulent flows. This suggests that the mechanism by which the Reynolds stress is produced in the log layer has not been significantly affected by the present surface roughness.

Erosion and deposition of mud beneath random waves

A systematic approach for predicting the mean erosion and mean deposition rates of mud beneath random waves is derived. This has been accomplished by applying formulas valid for regular waves and by describing the waves as a stationary Gaussian narrow-band random process. The present approach covers flow in the laminar, smooth turbulent and rough turbulent flow regimes. Examples are given, using data typical for field conditions representing laminar and smooth turbulent flow conditions, which are the most common flow regimes over mud beds.

하수관 등류수심 양해법 산정식

등류수심의 산정은 수로 설계 및 흐름 해석에 있어 매우 중요하다. 하수관은 삼각형 또는 사각형의 인공 개수로와 달리 원형, U형과 같이 곡률을 갖는 경우가 일반적이며, 이 경우 수심에 따른 통수단면적 및 동수반경의 변화가 일정하지 않으므로 등류수심 산정 또는 수식 유도에 있어 상당한 어려움을 갖는다. 그러나 단면적과 관경의 비 또는 동수반경과 관경의 비를 수심대 관경의 비로 표기하여 지수형으로 나타내면 수식의 전개과정이 매우 용이해지며, 양해법 산정식의 개발이 가능해진다. 따라서 본 고에서는 우선 실무에서 가장 많이 사용하고 있는 원형 개수로와 U형 개수로에 대한 등류수심 양해법 산정식을 제시하며, 완난류 지수형 마찰계수 산정식과 더불어 실무에서 주로 사용되는 Hagen (Manning) 산정식을 이용한 등류수심 산정식도 제시하였다. The computation of normal depth is very important for the design of channel and the analysis of water flow. Drainage pipe generally has the shape of curvature like circular or U-type, which is different from artificial triangular or rectangular channel. In this case, the computation of normal depth or the derivation of equations is very difficult because the change of hydraulic radius and area versus depth is not simple. If the ratio of the area to the diameter, or the hydraulic radius to the diameter of pipe is expressed as the water depth to the diameter of pipe by power law, however, the process of computing normal depth becomes relatively simple, and explicit equations can be obtained. In the present study, developed are the explicit normal depth equations for circular and U-type pipes, and the normal depth equation associated with Hagen (Manning) equation and friction factor equation of smooth turbulent flow by power law is also proposed because of its wide usage in engineering design.

Bottom friction caused by boundary layer streaming beneath random waves for laminar and smooth turbulent flow

The effect of boundary layer streaming on the sea bed shear stresses, beneath random waves, is investigated for laminar flow as well as smooth turbulent flow. It is demonstrated how bottom friction formulas for regular waves can be used to obtain the bed shear stresses resulting from steady streaming under random waves. As a result, friction factors for steady streaming under random waves are provided, and the effect of streaming versus the effect of linear waves is discussed. For laminar flow the effect of second order Stokes waves is also included. Examples are included to illustrate the applicability of the present practical method, and results are obtained using data typical for field conditions.

Wind Tunnel Study on Rough and Smooth Surface Turbulent Approach Flow and on Inclined Windscreens

The floor of a wind tunnel was provided with isolated roughness elements in the form of small wooden blocks to increase the boundary layer thickness. Since previous experiments were carried out with a smooth floor, the results of the previous research on vertical screens with smooth surface turbulent flow could be compared with the results of the current research on vertical screens with rough surface turbulent flow. It follows that windbreaks are less effective for rough than for smooth turbulent flow, although differences depend on the open area of the windbreak. Furthermore, experiments in the wind tunnel were carried out to compare the effects on wind velocity reduction of vertical and inclined screens. Windscreens were inclined at 30, 45 and 60° with the vertical, either with or against the wind. Except the 30° windward inclined screen with an open area of 49·1% (material C), all other inclined screens were less effective compared with their vertical position, purely through the smaller vertical height of the inclined screens. In general, screens inclined against the wind were more effective than screens inclined with the wind. However, the effectiveness of the windward inclination of the less permeable windbreaks (materials A and B) was more pronounced.

Blasius: A life in research and education

The Blasius boundary layer solution is a basic feature of fluid mechanics, and the first application of Prandtl's boundary layer concept as a significant issue in engineering. This work highlights the contributions of Blasius to hydrodynamics over a period of only six years, which marked the initiation of boundary layer theory. His main papers relating to aerodynamics and smooth turbulent pipe flow are also reviewed, and a biography puts his career into the general environment of Germany over the period of two World Wars. A complete bibliography of Blasius is provided.