Form-induced Stress Research Articles

Turbulent flow characteristics over rough permeable and impermeable gravel-bed stream- an experimental study

Abstract The study aims to presents flow heterogeneity over rough permeable and impermeable gravel-bed stream. The rough permeable stream is prepared by laying multiple layers of gravel, whereas its impermeable counterpart is presented by a resin-casted gravel-bed. In general, a common approach can be found in literature to mimic an impermeable bed by laying single layer of gravels, therefore some results are compared with single layer gravel-bed stream keeping the hydraulic conditions same. An acoustic Doppler velocimeter was used for flow measurements whereas; double averaging (DA) methodology was adopted for data analysis. The larger flow penetration depth and intense flow mixing in permeable gravel-bed infer sufficient impetus for organized flow turbulence and damping of DA Reynolds shear stresses whereas; the wall-blocking in resin-casted gravel-bed prevents fluid infiltration which leads to follow the linear stress profile away from the crest level. The damping of DA Reynolds shear stress (RSS) is compensated by enhanced DA form-induced shear stress (FISS). The results are further analysed under the light of the energy budget to characterize the mass-momentum exchange as it penetrates the subsurface layers. The energy budget indicates negative pressure energy diffusion rates corroborating gain in turbulence production in the permeable gravel-bed stream.

Double-averaged turbulence statistics of wave current flow over rough bed with staggered arrangement of hemispherical blocks

Double-average turbulence characteristics of combined wave-current flow are studied over a rough bed comprising hemispheres arranged in a staggered pattern with different spacing (p/r = 4, 6, and 8; p = pitch length, r = height). The instantaneous velocity data was collected by Acoustic Doppler Velocimetry for the evaluation of double-average (DA) velocity, turbulence intensity, form-induced intensity, Reynolds stress, and form-induced stresses. The smallest DA velocity was obtained for p/r = 4 at the bottom region, signifying that p/r = 4 offered the maximum resistance to the flow among the tested cases. DA Reynolds stress is decreased for the entire flow depth due to superimposed waves. The advection of momentum-flux of normal stress in stream-wise and bottom-normal directions is increased at the outer layer and decreased at the near-bed region after wave-imposition. Maximum TKE production and diffusion are obtained just above the interfacial sub-layer and the middle of the form-induced sub-layer respectively. The turbulence structure is strongly anisotropic at the bottom region for p/r = 4 and near the outer layer, the tendency towards the return to isotropic state is dominant while with the increase in roughness spacing, a decrease in anisotropy is observed. Furthermore, an increase in wave-frequency decreased the tendency for the return to isotropy at the free surface.

An assessment of turbulence transportation near regular and random permeable interfaces

Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (φ=0.6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry.

Effects of surface roughness topography in transient channel flows

The dynamical effects of roughness geometry on the response of a half-height turbulent channel flow to an impulse acceleration are investigated using direct numerical simulations. Two rough surfaces different in the surface height spectrum are compared between themselves and with a smooth-wall baseline case. Both rough cases develop from a transitionally rough state to a fully rough one. Results show that on rough walls the thickness of the roughness sublayer (RSL), defined as the layer with significant form-induced stresses, stays almost constant. The ensemble-average flows inside the RSL stays close to equilibrium throughout the transient. This is shown by the form-induced perturbations largely scaling with the mean velocity at the edge of the RSL. Inside the RSL, turbulence develops rapidly to the new steady state, accompanied by substantial changes in the Reynolds stress balance. In contrast, the flow above the RSL recovers long after the sublayer is fully developed, without a significant change in Reynolds stress balance. The geometry of the roughness plays an important role in determining the rate of response of turbulence throughout the boundary layer. This work provides detailed explanation of the suppression of reverse transition by surface roughness in response to a mean flow acceleration.

Role of roughness geometry function on spatially averaged form induced shear stresses and pressure energy diffusion rates in gravel-bed stream

ABSTRACT Stream-bed porosity has received substantial interest of research in the field of fluvial hydraulics since few decades and the focus of our present study has been on the respond of gravel-bed porosity on form-induced shear stresses and pressure energy diffusion rates in open channel flows. An inherent parameter called roughness geometry function is introduced to further broaden the aforementioned issues within the frameworks of near-bed turbulent flow characteristics. Laboratory experiments were conducted over three rough beds: (a) uniformly poised gravel bed (b) water-worked bed and (c) uniformly poised sphere bed. The roughness geometry functions of the channel beds are compared to those obtained by water displacement method. An acoustic Doppler velocimeter is used to measure the instantaneous velocity components and double-averaging methodology is applied for data interpretation. Most significantly, the form-induced shear stresses were predicted 30–42% of the double averaged Reynolds shear stresses in case of water-worked bed. The extreme upper limits of the form-induced shear stress distributions in all the three beds corroborated the effects of gravel bed porosity. Furthermore, the negative pressure energy diffusion rates with increasing turbulent production provided additional support offering overwhelming evidence of the effects of gravel bed porosity within the interfacial sub-layer.

Direct numerical simulations of turbulence and hyporheic mixing near sediment–water interfaces

The effects of bed roughness, isolated from those of bed permeability, on the vertical transport processes across the sediment–water interface (SWI) are not well understood. We compare the statistics and structure of the mean flow and turbulence in open-channel flows with a friction Reynolds number of 395 and a permeability Reynolds number of 2.6 over sediments with either regular or random grain packing at the SWI. The regular sediment interface is formed by cubic packing of spheres aligned with the mean-velocity direction. It is shown that, even in the absence of any bedform, the subtle details of the particle roughness alone can significantly affect the dynamics of turbulence and the time-mean flow. Such effects translate to large differences in penetration depths, apparent permeabilities, vertical mass fluxes and subsurface flow paths of passive scalars. The less organized distribution of mean recirculation regions near the interface with a random packing leads to a more isotropic form-induced stress tensor. The augmented wall-normal form-induced fluctuations play a significant role in increasing mixing and wall-normal mass and momentum exchange.

Scales of turbulence in open-channel flows with low relative submergence

The present work aims at studying the turbulence structure developed over a highly rough bed in open-channel flows (OCFs) by varying the relative submergence through the use of three sediment sizes ranging from gravels to pebbles. The second-order moments were analyzed and compared with those already observed for canonical turbulent OCFs having similar values of relative submergence. Particular attention was paid to the turbulent Reynolds stresses, and the viscous and the form-induced shear stresses in the near bed region. The violation of the Taylor hypothesis was verified through an alternative method, by comparing two time scales, namely, the large scale advection time and the eddy characteristic nonlinear time. Moreover, an analysis of the large eddies was performed with the spectral analysis. The premultiplied spectra provide a way to quantify the contribution of different eddy scales (peaks in the premultiplied spectra) and indicate wavelengths in which a significant amount of energy resides. In order to locate the normalized wavelengths associated with the peaks in the premultiplied spectra, a systematic procedure is presented.

Water-Worked Gravel Bed: State-of-the-Art Review

In a natural gravel-bed stream, the bed that has an organized roughness structure created by the streamflow is called the water-worked gravel bed (WGB). Such a bed is entirely different from that created in a laboratory by depositing and spreading gravels in the experimental flume, called the screeded gravel bed (SGB). In this paper, a review on the state-of-the-art research on WGBs is presented, highlighting the role of water-work in determining the bed topographical structures and the turbulence characteristics in the flow. In doing so, various methods used to analyze the bed topographical structures are described. Besides, the effects of the water-work on the turbulent flow characteristics, such as streamwise velocity, Reynolds and form-induced stresses, conditional turbulent events and secondary currents in WGBs are discussed. Further, the results form WGBs and SGBs are compared critically. The comparative study infers that a WGB exhibits a higher roughness than an SGB. Consequently, the former has a higher magnitude of turbulence parameters than the latter. Finally, as a future scope of research, laboratory experiments should be conducted in WGBs rather than in SGBs to have an appropriate representation of the flow field close to a natural stream.

Influence of permeable beds on hydraulically macro-rough flow

In this study, macro-rough flows over beds with different permeability values are simulated using the large-eddy simulation, and the results are analysed by applying the double-averaging (DA) methodology. Spheres of different sizes and arrangements were used to form the beds, which are deemed to be permeable granular beds. The influence of bed permeability on the turbulence dynamics and structure is investigated. It was observed that the scales of the spanwise vortical structures over more permeable beds are larger than those over less permeable beds. This is attributed to large-scale spanwise-alternate strips of varying Reynolds shear stress (RSS), emerging from the surface of macro-rough elements for the permeable beds. The DA stress balance suggests that the time-averaged spanwise vortical structure leads to a damping in DA RSS and an unusual peak of the form-induced stress in the main flow. In the streamwise direction, both large turbulent structures that originate from the Kelvin–Helmholtz-type instability and small turbulent structures that are associated with the turbulent transport across the gaps of the roughness elements are more prevalent over highly permeable beds. Near the bed, the relative magnitude of turbulent events shows a transition from a ejections-dominating to sweeps-dominating zone with vertical distance. Further, several hydrodynamic characteristics normalized by inner scales (kinematic viscosity to shear velocity ratio) show a greater dependency on permeability Reynolds number than those normalized by sediment size. The study provides an insight into the mechanism of mass transfer near the fluid–particle interface, which is vital to benthic and aquatic ecology.

Free surface flow over square bars at intermediate relative submergence

ABSTRACTResults from large-eddy simulations and complementary flume experiments of turbulent open channel flows over bed-mounted square bars at intermediate submergence are presented. Scenarios with two bar spacings, corresponding to transitional and k-type roughness, and three flow rates, are investigated. Good agreement is observed between the simulations and the experiments in terms of mean free surface elevations and mean streamwise velocities. Contours of simulated time-averaged streamwise, streamfunction and turbulent kinetic energy are presented and these reveal the effect of the roughness geometry on the water surface response. The analysis of the vertical distribution of the streamwise velocity shows that in the lowest submergence cases no logarithmic layer is present, whereas in the higher submergence cases some evidence of such a layer is observed. For several of the flows moderate to significant water surface deformations are observed, including weak and/or undular hydraulic jumps which affect significantly to the overall streamwise momentum balance. Reynolds shear stress, form-induced stress and form drag are analysed with reference to the momentum balance to assess their contributions to the total hydraulic resistance of these flows. The results show that form-induced stresses are dominant at the water surface and can contribute significantly to the overall drag, but the total resistance in all cases is dominated by form drag due to the presence of the bars.

Turbulence over cube-mounted rough bed using spatiotemporal averaging approach

The paper describes an experimental study carried out in a laboratory flume to investigate the turbulent characteristics of cube mounted rough bed (3D flow). The three-dimensional (3D) velocity data are analyzed within the framework of double time-space averaging approach. The study particularly focuses on the changes induced in the mean velocities, turbulent intensities, Reynolds shear stresses, and form-induced normal and shear stress profiles both in time and space domains. The mean velocity profile shows two distinct distributions: linear distribution below the roughness crest and logarithmic distribution above the roughness crest. Within the roughness layer near the bottom, the form-induced stress changes significantly with roughness spacing. To highlight the stress terms and associated turbulent events, the quadrant analysis is performed using form-induced velocity fluctuations. Further, the turbulent kinetic energy budget is also analyzed to examine the bursting events comprehensively.

Turbulence in a Gravel-Bed Stream with an Array of Large Gravel Obstacles

AbstractThis experimental and analytical study investigates the double-averaged (DA) turbulent flow characteristics within an array of large gravel obstacles found atop a porous gravel bed. Analysis of the experimental data reveals that the DA streamwise velocity preserves the logarithmic law above the form-induced sublayer, while a linear law and a third-degree polynomial function apply within the form-induced and interfacial sublayers, respectively. The form-induced shear stress is 70% of the DA Reynolds shear stress (RSS) occurring at the virtual bed level. The DA turbulent kinetic energy (TKE) components, streamwise and vertical, attain their peak values at the obstacle crest level, while they diminish sharply below the virtual bed level. The fluxes of the TKE streamwise and vertical components, however, change their signs slightly below the crest level, indicating a changeover of the dominance of the bursting events. For the TKE budget, the TKE production, diffusion, and pressure energy diffusion rat...

Turbulent Flows within Random Arrays of Rigid and Emergent Cylinders with Varying Distribution

AbstractThe spatial distribution of emergent vegetation in rivers is frequently nonuniform. Here, spatial nonuniformity is simulated in the laboratory by varying longitudinally the stem areal number density (m). Time- and space-averaged flow variables, corresponding to different values and gradients of m and different stem Reynolds numbers, are calculated from instantaneous velocity maps obtained with particle image velocimetry (PIV). Results show that Reynolds stresses are completely determined by the local spatially averaged number of stems per unit area; they are not sensitive to local spatial gradients of m. These variables seem to adjust locally to the spatial variations of the stem distribution. Contrarily, the spatial distribution of the time-averaged flow is influenced not only by the local value of m but also by its spatial gradients. Form-induced stresses express this influence. They reveal a subsistence of flow complexity generated by the upstream stem distribution as a form of spatial memory. ...

Spatially-averaged turbulent flow over cubical roughness in wave-current co-existing environment

The paper describes an experimental study carried out in a laboratory flume to investigate the interaction of surface-wave with unidirectional current over cube mounted rough-bed (3D flow). The cubes were made of wood and were positioned at the channel-bed with different spacing. The spacing was chosen to represent different roughness types under different spacing conditions as: isolated roughness flow, wake interference flow and skimming flow. The three-dimensional velocity field was measured by an acoustic Doppler velocimetre (ADV). The study particularly focused on the changes induced in the spatially-averaged velocity profiles, turbulence intensities and Reynolds shear stress due to the superposition of waves of different frequencies on current-induced flow. Spatially-averaged velocity profiles show two distinct distributions: linear or exponential distribution below the roughness crest and logarithmic distribution above the roughness crest. It is found that the shift of the velocity profile depends strongly on the spacing of roughness elements. The profile of stream-wise turbulence intensity changes significantly below the roughness crest due to presence of surface wave, whereas bottom-normal spatially-averaged turbulence intensity does not change much with increase in wave frequency. Within the roughness crest near the bottom, the form-induced shear stress changes significantly from negative to positive value with change in roughness spacing, but is not affected much due to the presence of surface-wave.

Form-induced stress in non-uniform steady and unsteady open channel flow over a static rough bed

This paper presents a series of 18 steady and 45 unsteady flow experiments over an artificial, rough surface, obtained by a novel molding technique for gravel beds. Velocity data are obtained by a Particle Image Velocimetry (PIV) system. The vertical distributions of the form-induced stresses 〈u˜2〉 and −〈u˜w˜〉 are compared for all experiments. Furthermore, quadrant maps are drawn to analyze the near bed spatial velocity fluctuations u˜ and w˜ in a vertical plane parallel to the flow direction. All experiments were done under non-uniform flow. It is shown that (1) the qualitative shape of the vertical form-induced stress distributions 〈u˜2〉 and −〈u˜w˜〉 is independent from the discharge, as stated in the literature, as well as from the unsteadiness of the flow. (2) The magnitude of the form-induced stress 〈u˜2〉 and −〈u˜w˜〉 in the roughness layer increases with increasing discharge for non-uniform flow, while uniform flow experiments in the literature report the form-induced stresses to be independent from the discharge. A hypothesis is, therefore, proposed, that the independence of the form-induced stress magnitude from the discharge is only valid for uniform flow. (3) Quadrant maps, describing the distribution of the spatial fluctuations u˜ and w˜ in a two-dimensional plane are independent from discharge and unsteadiness of the flow.

Relative impact of uniaxial alignment vs. form-induced stress on differentiation of human adipose derived stem cells

ADSCs are a great cell source for tissue engineering and regenerative medicine. However, the development of methods to appropriately manipulate these cells in vitro remains a challenge. Here the proliferation and differentiation of ADSCs on microfabricated surfaces with varying geometries were investigated. To create the patterned substrates, a maskless biofabrication method was developed based on dynamic optical projection stereolithography. Proliferation and early differentiation of ADSCs were compared across three distinct multicellular patterns, namely stripes (ST), symmetric fork (SF), and asymmetric fork (AF). The ST pattern was designed for uniaxial cell alignment while the SF and AF pattern were designed with altered cell directionality to different extents. The SF and AF patterns generated similar levels of regional peak stress, which were both significantly higher than those within the ST pattern. No significant difference in ADSC proliferation was observed among the three patterns. In comparison to the ST pattern, higher peak stress levels of the SF and AF patterns were associated with up-regulation of the chondrogenic and osteogenic markers SOX9 and RUNX2. Interestingly, uniaxial cell alignment in the ST pattern seemed to increase the expression of SM22α and smooth muscle α-actin, suggesting an early smooth muscle lineage progression. These results indicate that geometric cues that promote uniaxial alignment might be more potent for myogenesis than those with increased peak stress. Overall, the use of these patterned geometric cues for modulating cell alignment and form-induced stress can serve as a powerful and versatile technique towards controlling differentiation in ADSCs.

Influence of relative submergence on spatial variance and form-induced stress of gravel-bed flows

[1] Spatial flow variance has a strong control on sediment transport, sediment-water interface exchange mechanisms, and the distribution and behavior of aquatic organisms in rivers. Thus, being able to quantify spatial flow variance, and how it varies with different water levels, is important for understanding how fluvial processes change during periods of time varying flow. In this paper, laboratory flume measurements of near-bed flow velocity were used to quantify spatial flow variance and form-induced stress, and their variation with flow submergence, within and above the surface of porous, gravel beds with differing grain roughness. The analysis revealed spatial flow variance was usually four or five times higher within the roughness layer than above. A rise in relative submergence resulted typically in a decrease in spatial variance—relative to bed shear velocity—in streamwise form-induced intensity, streamwise turbulence intensity, and form-induced momentum flux, both within and above the roughness layer. Flow submergence had no consistent influence on spatial variance in the vertical flow direction and in Reynolds stress. Form-induced stress was significant within the roughness layer, more so at shallow depths. The greater significance was driven primarily by higher spatial flow variance in time-averaged streamwise velocity at these depths. The implication is the relative role of momentum transfer mechanisms within the roughness layer, and thus, sediment-water interface exchange processes in rivers will change during periods of time varying flows.

Momentum transport and laminar friction in rough-wall duct flows

A large number of experiments and numerical simulations have proved that friction factors in laminar channel flows are roughness-dependent provided that the ratios between roughness and channel height (i.e., the relative roughness) exceed some threshold values. However, it is not yet clear what are the causes that lead to this anomalous behaviour. In order to shed light into this issue, this study presents results from two-dimensional Lattice-Boltzmann simulations of laminar flows in channels with rough walls. The Reynolds number, the geometry of the roughness elements and the relative roughness were varied extensively in order to provide a comprehensive set of data. The analysis and interpretation of the data were carried out within the framework of the Spatially Averaged Navier-Stokes equations, which are ideal to investigate momentum transfer mechanisms in flows over rough walls. The results show that for most of the investigated roughness geometries, the pressure gradient driving the flow is balanced by form-drag, viscous drag, and viscous shear stress whereas form-induced stresses remain largely negligible. Furthermore, it was observed that the higher the ratio between the drag acting upon the roughness elements and the total drag, the more friction factors deviate from classical theory. On the basis of these observations, we propose a formula, which predicts the shear stress partitioning and we discuss its relevance within the context of biomedical applications.

Gravel-Bed Hydrodynamics: Double-Averaging Approach

AbstractThis study focuses on the double-averaged (DA) turbulence characteristics and the local flow characterization in the flow zones over and within the flow-gravel-bed interface. The cumulative running averaged (CRA) value of a turbulence quantity for a given interval (in this study, half of the gravel size) of flow measurement is the prerequisite to determine a complete DA value of that quantity. The CRA turbulence quantities within the interfacial sublayer require a longer distance to become spatially independent. A method is proposed to fit the log law for the DA velocity over the bed and a polynomial law within the interfacial sublayer. The form-induced shear stress is 40% of the DA Reynolds shear stress occurring at the virtual bed level. The spatial velocity fluctuations diminish more rapidly than the temporal velocity fluctuations below the virtual bed level. In the inertial subrange of turbulent kinetic energy (TKE), the eddy size decreases significantly near the virtual bed level, and in the ...

Relative impact of form-induced stress vs. uniaxial alignment on multipotent stem cell myogenesis

Tissue engineering strategies based on multipotent stem cells (MSCs) hold significant promise for the repair or replacement of damaged smooth muscle tissue. To design scaffolds which specifically induce MSC smooth muscle lineage progression requires a deeper understanding of the relative influence of various microenvironmental signals on myogenesis. For instance, MSC myogenic differentiation has been shown to be promoted by increases in active RhoA and FAK, both of which can be induced via increased cell–substrate stress. Separate studies have demonstrated MSC myogenesis to be enhanced by uniaxial cell alignment. The goal of the present study was to compare the impact of increased peak cell–substrate stresses vs. increased uniaxial cell alignment on MSC myogenic differentiation. To this end, MSC fate decisions were compared within two distinct multicellular “forms”. A “stripe” multicellular pattern was designed to induce uniaxial cell alignment. In contrast, a second multicellular pattern was designed with “loops” or curves, which altered cell directionality while simultaneously generating regional peak stresses significantly above that intrinsic to the “stripe” form. As anticipated, the higher peak stress levels of the “loop” pattern were associated with increased fractions of active RhoA and active FAK. In contrast, two markers of early smooth muscle lineage progression, myocardin and SM-α-actin, were significantly elevated in the “stripe” pattern relative to the “loop” pattern. These results indicate that scaffolds which promote uniaxial MSC alignment may be more inductive of myogenic differentiation than those associated with increased peak, cell–substrate stress but in which cell directionality varies.