Rough Turbulent Research Articles

Evidence that uniform momentum zones originate from roughness sublayer structure interactions in fully rough channel turbulence

Fully rough wall-sheared turbulence is composed of an inner and outer layer, the former occupied by sinuous structures sustained by the well-known autonomous inner cycle, the latter occupied by inclined parcels of momentum deviations relative to the average. The outer-layer structures are also known as uniform momentum zones (UMZs), where the presence of successive UMZs manifests instantaneously with a distinct ‘staircase’ pattern in streamwise velocity. Direct numerical simulation (DNS) of fully rough channel turbulence was recently used to interpret UMZs as wakes originating from antecedent bluff-body-like interactions within the inner layer (Anderson & Salesky, J. Fluid Mech., vol. 906, 2020, A8). Wake-scaling arguments agreed precisely with instantaneous results from DNS. Foremost among these results was evidence that the instantaneous wall-normal gradient of streamwise velocity exhibited scaling of ${\sim }x_3^{-1/2}$ , where $x_3$ is wall-normal location; this is in contrast to logarithmic scaling, which requires the wall-normal gradient of streamwise velocity to scale as ${\sim }x_3^{-1}$ . Herein, wake-scaling arguments have been advanced and compared against results from wall-modelled large-eddy simulation (LES). New results from the ‘bottom up’ wake-scaling arguments agree with LES results, such that the shear associated with the instantaneous staircase-like streamwise velocity follows a clear trend. We have leveraged conditional sampling during LES – predicated upon instantaneous low-frequency, high-magnitude surface stress values known to correspond to large-scale inertial-layer coherence – to further assess the predictive value of the wake-scaling arguments. Model results compare favourably.

Numerical Study on the Turbulent Structure of Tsunami Bottom Boundary Layer Using the 2011 Tohoku Tsunami Waveform

In this study, the tsunami-induced bottom boundary layer was investigated based on actual waveforms obtained by the GPS buoys along the coast of the Tohoku region during the 2011 Great East Japan Earthquake tsunami. The k-ω model was utilized for the numerical analysis in this study. As a result, the tsunami boundary layer thickness was found to be extremely thin compared to the water depth. The velocity distribution was similar to that of the bottom boundary layer under wind-generated waves. The flow regime is located in the transition from smooth turbulence to rough turbulence. Because of this, the gradient of the flow across the layer is much greater than the gradients in the steady flow direction. Therefore, the bottom friction is underestimated if the steady friction factor, such as in the Manning formula, is used. This study proposes a new simple method for calculating the bottom shear stress due to an irregular tsunami based on the wave friction law, and the k-ω model results are used to validate the proposed methods.

Secondary Flow in Smooth and Rough Turbulent Circular Pipes: Turbulence Kinetic Energy Budgets

Direct Numerical Simulations have been performed for turbulent flow in circular pipes with smooth and corrugated walls. The numerical method, based on second-order finite discretization together with the immersed boundary technique, was validated and applied to various types of flows. The analysis is focused on the turbulence kinetic energy and its budget. Large differences have been found in the near-wall region at low Reynolds number. The change in the near-wall turbulent structures is responsible for increase of drag and turbulence kinetic energy. To investigatselinae the effects of wall corrugations, the velocity fields have been decomposed so as to isolate coherent and incoherent motions. For corrugated walls, we find that coherent motions are strongest for walls covered with square bars aligned with the flow direction. In particular, the coherent contribution is substantial when the bars are spaced apart by a distance larger than their height. Detailed analysis of the turbulence kinetic energy budget shows for this set-up a very different behavior than for the other types of corrugations.

Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation

The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, $$\Delta U^+$$ , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re $$_{\tau }$$ . In the present work, the effects of several geometrical parameters on the roughness function, in both transitional and fully rough regimes, are investigated by means of large eddy simulation of channel flows characterized by different wall-roughness textures at different values of Re $$_{\tau }$$ up to 1000. The roughness geometry is generated by the superimposition of sinusoidal functions with random amplitudes and it is exactly resolved in the simulations. A total number of 10 cases are solved. With the aim to find a universal correlation between the roughness geometry and the induced roughness function, we analyzed the effect of more than a single geometrical parameter, including the effective slope, which takes into account both the roughness height and its texture. Based on data obtained from our simulations and a number of data points from the literature, a correlation between the ES and the root mean square of the roughness oscillation, as well as between ES and the mean absolute deviation of the roughness, satisfactorily predicts the roughness function.

Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

This paper provides a new unified formula for Newtonian fluids valid for all pipe flow regimes from laminar to fully rough turbulent flow. This includes laminar flow; the unstable sharp jump from laminar to turbulent flow; and all types of turbulent regimes, including the smooth turbulent regime, the partial non-fully developed turbulent regime, and the fully developed rough turbulent regime. The new unified formula follows the inflectional form of curves suggested in Nikuradse’s experiment rather than the monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula uses switching functions and interchangeable formulas for the laminar, smooth turbulent, and fully rough turbulent flow regimes. Thus, the formulation presented below represents a coherent hydraulic model suitable for engineering use. This new flow friction model is more flexible than existing literature models and provides smooth and computationally cheap transitions between hydraulic regimes.

CALCULATION OF PRESSURE DROP IN NARROW ROTATING ANNULAR CLEARANCES

This paper presents a review of correlations used for pressure drop calculation in narrow annular clearances with rotation of inner cylinder. Based on these review, a new general correlation is proposed to calculate pressure drop through such clearances. Results are compared with experimental data for different flow regimes: laminar, laminar with Taylor vortex, smooth and rough turbulent, with good agreement. The main objective is to develop a simple and general correlation that could be used for backflow calculation in twin-screw multiphase pumps. In this kind of pump, the volumetric efficiency is defined mainly by the backflow rate which occurs in the annular clearance between screw and casing. Usually, the backflow is calculated ignoring the influence of shaft rotation over pressure drop and does not consider the several possible flow regimes. Depending on operational conditions, this simplification can lead to significant errors.

Leak Before Break: Studies in Support of New R6 Guidance on Leak Rate Evaluation

The concept of leak-before-break (LBB) is often used in safety cases for pressure systems, particularly, in the nuclear industry. An important factor in making a LBB case is in the prediction of the leak rate of fluid through a crack. This paper presents a summary of a program of work, which had the aim of improving guidance on leak rate evaluation for the LBB procedures in the R6 defect assessment methodology. Methods of calculating leak rates have been reviewed, and this has led to a crack morphology model being proposed, which represents single-phase isothermal compressible flow through a crack. In the crack morphology model, the flow is assumed by default to be fully rough turbulent, and the effective roughness to vary between a local roughness value for narrow cracks and a global value (i.e., the overall crack contours) for wide cracks. The effect of pressure drops due to changes in the flow direction at crack turns has also been included. Calculations using the model show that the friction factor relation due to Spence et al. (1991, “Leakage Flow Through Small Cracks—Report of Second Stage of Experimental Work,” unpublished) gives better agreement with measured flow rates than that due to Button et al. (1978, “Gas Flow Through Cracks,” ASME J. Fluids Eng., 100, pp. 453–458), which tends to overestimate the flow rate for the examples studied. The inclusion of an inertial pressure term arising from changes in overall flow direction appears to be justified.

The turbulent life of copepods: effects of water flow over a coral reef on their ability to detect and evade predators

The heterogeneous distribution of water flow over structurally complex environments, such as coral reefs, may play an important role in the interactions between copepods and plankti- vorous fish by interfering with the copepods' ability to detect and evade predators. The escape response and capture rates of the copepod Acartia tonsa were examined in laboratory flumes that created both unidirectional and oscillatory flow conditions similar to those found near coral reefs. Two turbulent regimes were produced in each flume: 'smooth' flow was formed using a grid colli- mator and 'rough' flow was generated by placing a branched coral skeleton upstream of the flume's working section. A predator was simulated by a fixed siphon to generate a stimulatory flow field. Copepod detection of the siphon was measured as the distance from the siphon tip to where an escape response was initiated. This reactive distance remained the same in low-flow conditions as in still water, but was reduced by 25% at higher flow speeds, indicating a decline in the copepods' ability to detect velocity gradients formed by the siphon. Rough turbulence regimes intensified the effect of current speeds, resulting in an even shorter copepod reactive distance. Capture rates of copepods by the siphon increased with current speed, wave motion, and in rough flow, while the capture rates of non-evasive prey, Artemia nauplii, did not vary with flume conditions. The differ- ences in capture rates between evasive and non-evasive prey suggest that behavioral shifts in cope- pod escape thresholds may account for increases in predation by reef-dwelling fishes observed in hydrodynamically complex coral environments.

Reynolds number variation in oscillatory boundary layers: Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.

A Dynamic Boundary Condition for Bedload Sediment Transport in Non-Uniform, Hydraulically Rough Turbulent Boundary Layers

Spatially and temporally averaged constraints on the extraction of momentum at the sediment boundary are inadequate to describe the episodic and spatially variable nature of bedload sediment transport. A model is proposed for the instantaneous transport of bedload sediment i a turbulent boundary layer having an arbitrary near-bed structure. The instantaneous force on individual grains is calculated. based upon a function for the reduction of velocity caused by upstream, protruding grains. Instantaneous forces calculated in this manner are in agreement with the highly spatially-and temporallyvarying drag forces measured of particles in sediment beds. When coupled with a simulation of the motion of all grains comprising a three-dimensional bed, the dynamic boundary condition predicts reasonable transport rates.

Life and Death in Moving Fluids: Hydrodynamic Effects on Chemosensory‐Mediated Predation

Previous studies in taxonomically diverse marine animals have established the general existence, and importance, of the olfactory sense in a wide variety of behavioral processes. Evidence suggests that the sense of smell mediates predatory search in many marine animals. Past investigations have not, however, been designed to link either the degree of successful olfactory—mediated search or guidance mechanisms with the hydraulic environment in which predatory activities naturally take place. In an effort to examine the interaction between hydrodynamics and chemoreception, we investigated predatory success and search strategies of blue crabs foraging in controlled hydrodynamic environments generated in a flume. Hydrodynamics were characterized by quantifying boundary layer shear velocity (°) and roughness Reynolds number (Re°), two measures that describe the structure of boundary layer flows. Flow properties affected the ability of crabs to orient to odor plumes emanating from actively pumping infaunal bivalves (Mercenaria mercenaria). High flow speed or large sediment particle size increased boundary layer turbulence, thereby decreasing the success of crab chemo—orientation ability. In addition, high flow speed also lessened the probability that crabs contacted odor plumes. Thus, habitats with high flows can provide hydrodynamic refuges from olfactory—mediated predation. Because search ability is contingent on the magnitude of boundary layer turbulence, olfactory—mediated predation may also be ineffective in slow flows, if bottom roughness elements can generate sufficient turbulence. Further, search ability in blue crabs is extremely sensitive to small changes in benthic boundary layer structure. The presence of a thick viscous sublayer, dominated by quasilaminar flow, seems especially critical for successful location of an odor source by crabs. Benthic estuarine crustaceans inhabit an environment where flows are transitional between smooth—and rough—turbulence conditions. Accordingly, chemosensory systems appear geared primarily to extracting information from hydraulically smooth flows. These results indicate that mechanisms governing the physical transport of odor signals can have profound influences, not only on the development of sensory and behavioral mechanisms, but also on biotic interactions such as predation, which, in turn, can mediate community structure.

Predicting Liquid Re-Entrainment in Horizontal Separators

Summary The design procedure for horizontal-separator sizing results in a range of configurations of vessel diameter and length that will perform adequate-liquid separation. The actual diameter chosen depends on a trade-off between smaller, more economic diameters and the larger diameters needed to preventre-entrainment of previously separated liquid droplets that can break away from the gas/liquid interface. The lower diameter limit has been determined previously by design guidelines based on the slenderness ratio of the vessel. This article presents a procedure for determining the lower diameter limit and calculating the maximum gas capacity of a horizontal separator on the basis of liquid re-entrainment. The method is based on correlations for predicting the onset of liquid re-entrainment developed by Ishii and Grolmes. The procedure uses known and predicted liquid and gas properties and may be used in conjunction with normal design procedures for more economic horizontal-separator designs. Introduction Entrainment refers to liquid droplets breaking away from a gas/liquid interface to become suspended in the gas phase. The term re-entrainment is used in horizontal-separator design because it generally is assumed that droplets have settled to the liquid phase and then are returned to the gas phase. Liquid re-entrainment is caused by high gas velocities. Momentum transfer from the gas to the liquid and associated pressure variations on the gas/liquid interface cause disturbances in the two-phase boundary. These disturbances manifest themselves as waves and ripples. Gas-to-liquid momentum transfer to a disturbed interface is more efficient than to a smooth surface, which allows droplets to break away from the liquid phase. Re-entrainment must be avoided in horizontal separators because it is the reverse of the gas/liquid separation desired. This necessity imposes an upperlimit on the gas velocity allowed across the liquid surface in the gravity settling section of the separator, which places a lower limit in the vessel on the cross-sectional area for gas flow. Vessel design therefore is limited by a combination of minimum vessel diameter and maximum liquid level because these determine the cross-sectional area. Previously, such rules of thumb as a maximum slenderness ratio of 4:5 have been used to avoid re-entrainment.1 This article presents a procedure for predicting when re-entrainment is possible on the basis of previously developed correlations and discusses modifications to design procedures to produce more economical horizontal-separator designs. Re-Entrainment Theory Re-entrainment is a physical phenomenon of two-phase stratified fluid flow. The onset of re-entrainment occurs at the boundary of the stratified wavy and annular mist two-phase flow regimes at relatively high gas/liquid velocities, as Fig. 12 shows. Re-entrainment is caused by rapid momentum transfer from gas to liquid. For the purposes of this article, only the onset of re-entrainment must be predicted because no amount of re-entrainment can be allowed in a horizontal separator. Ishii and Grolmes3 and Ishii and Kaichiro4 proposed correlations for predicting the minimum velocity required for re-entrainment of liquid into gas for concurrent flow. The equations (see Appendix) are based on interpretation of experimental data taken from several gas/liquid systems, including water or oil and nitrogen or helium. The correlations use the Reynolds film number and an interfacial viscosity number to characterize the two-phase flow. These are defined asEquation 1and Equation 2 N Ref is a measure of the turbulence of the liquidphase and indicates which mechanism of re-entrainment is most likely for the flow conditions considered. Ishii and Grolmes3 proposed three distinct mechanisms forre-entrainment. For NRef<160, a wave undercut mechanism was proposed where gas impinges on the gas/liquid interface, undercutting it and breaking displaced liquid away from the interface. Athigher NRef, roll wave shear, where the tops of waves are sheared off by high relative velocities between gas and liquid, becomes the dominant mechanism. NRef>1,635 indicates a highly turbulent condition dominated by interfacial properties. AsNRef increases, the liquid surface becomes rougher, and the importance of NRef diminishes asymptotically. These mechanisms occur in three flow regimes, called low Reynolds number(<160), transition (160 to 1,635), and rough turbulent (>1,635).Re-entrainment is more likely at high NRef. N μ is a measure of the resiliency of the liquid surface under turbulent conditions. In physical terms, it is the ratio of viscous forces induced in the liquid by flow to the surface tension maintaining the gas/liquid interface. Re-entrainment becomes more likely with higherNμ. The tendency of liquids to re-entrain increases appreciably as Nμ exceeds 1/15.

Formation of ripples in erodible channels

Formation of ripples and dunes in erodible channels is analyzed by using the hydrodynamic model developed by Kobayashi and Madsen (this issue). Applying the continuity equation of sediment, the propagation velocity of the wavy bed is expressed in terms of the net fluxes of bed load along the wavy bed and suspended sediment out of the bed load transport layer. The spatial variation of the bed load transport rate is derived by analyzing the balance of forces acting on a representative bed load particle on a sloping bed. The net flux of the suspended sediment out of the bed load transport layer is obtained by solving the diffusion equation for the suspended sediment near the bed. The stability analysis predicts that a perturbation that is either fairly short or long relative to the depth of flow will initially grow, depending on whether the flow is hydraulically smooth or fully rough. Thus the model explains why ripples are not observed in experiments involving fairly coarse sediments, since in these cases the flow is rough turbulent.

Tidal boundary layer measurements in the presence of waves

Measurements of tidal current and wave velocity made at 0.69 and 1.85 m above a rough seafloor exhibit large current gradients (boundary layer) in the water column. The logarithmic boundary layer flow model was fitted to the measurements, and thus roughness (z0) and friction velocity (u∗) parameters were derived. The roughness parameter values were generally consistent with the observed upstream physical roughness. The values of both parameters for conditions in the rough turbulence flow regime are generally larger (much larger for ebb) than earlier published values for similar measurements of currents in the absence of significant waves but are comparable to values from recent measurements of currents in the presence of storm waves. The high parameter values here appear to relate more to the magnitude of the current and to the upstream physical bottom roughness than to the magnitude of the seastate. Large boundary layers in the flow at the seabed have a profound effect on the design of offshore structures such as offshore pipelines.

Erratum for “Oscillatory Rough Turbulent Boundary Layers”

Erratum for “Oscillatory Rough Turbulent Boundary Layers”

Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer

Heat transfer behavior of a fully rough turbulent boundary layer subjected to favorable pressure gradients was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Stanton numbers and profiles of mean temperature, turbulent Prandtl number, and turbulent heat flux are reported. Three equilibrium acceleration cases (one with blowing) and one non-equilibrium acceleration case were studied. For each acceleration case of this study, Stanton number increased over zero pressure gradient values at the same position or enthalpy thickness. Turbulent Prandtl number was found to be approximately constant at 0.7–0.8 across the layer, and profiles of the non-dimensional turbulent heat flux showed close agreement with those previously reported for both smooth and rough wall zero pressure gradient layers.

Field observations of the threshold of sand motion in a transitional wave boundary layer

Field experiments have been performed to study the threshold of sediment movement by irregular surface swell waves on both rippled and flat sand beds. Measurements of the fluid velocity were made in the free stream flow, and simultaneous observations of the sediment movement were made with an underwater television camera. This information has been used to make deductions about the bed shear stress at the threshold of sediment motion. For the case of the rippled bed, the analysis is based upon a decoupling of the problems of the frictionless flow over the ripple profile and of the flow in the boundary layer itself. For the low wave Reynolds numbers in the experiments, it is argued that the flow in the boundary layer was transitional, not smooth or rough turbulent, and that it is therefore legitimate to treat the boundary layer as an “almost laminar” flow governed by a linear equation. The instants in the measured wave cycles corresponding to the onset of sediment motion are well explained on this basis, and the predicted threshold stress for the mobile coarse sand ( D 50 = 0.14 cm ) is roughly the same as that obtained from Shields curve.

CONSIDERATION ON FRICTION COEFFICIENT FOR SEA BOTTOM

A bottom friction is an effective factor which will prove the deformation of progressive waves in shallow water, and many investigators have obtained the friction coefficients from field observations. However, they have not considered the effect of turbulent loss due to sand ripple at a sea bottom. The authors, first of all, study on the friction coefficient for artificial fixed ripple by using the boundary layer theory of rough turbulence, and a new formula on the friction coefficient is proposed. The proposed friction coefficients are compared with Zhukovets' experimental results which were performed on a movable bed, and it is found that the theoretical friction coefficients for artificial fixed ripple have to be modified in order to apply for the natural beach. Lastly, the wave deformation due to the bottom friction on the movable bed is calculated by the modified friction coefficient and the effect of bottom friction on the wave deformation is discussed.

EXPERIMENTAL AND THEORETICAL INVESTIGATIONS IN AN OSCILLATORY TURBULENT BOUNDARY LAYER

The oscillatory flow near the sea bed under a wave motion is always rough turbulent in a coastal zone. This type of an oscillatory boundary layer (or “wave boundary layer”) was therefore chosen as a subject for detailed velocity measurements, from which characteristics such as shear stresses, eddy viscosities, energy loss, and boundary layer thickness were determined.

Turbulent Flow in Smooth and Rough Pipes

Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.