Measurements of Turbulent Transport in a Square Channel with One Ribbed Wall

The velocity field of the fully developed turbulent flow in a one-sided ribbed square channel (rib-height-to-channel-height ratio of k/h = 0.0667, rib-pitch-to-rib-height ratio of p/k = 9) were measured at Reynolds numbers (based on the channel height h and the mean bulk velocity uB) of Reh = 50 000 and 100 000 by means of Laser-Doppler-Anemometry (LDA). Triple velocity correlations differed slightly between both Reynolds numbers when normalized by the bulk velocity and the channel height, similarly to the first- and second-order statistical moments of the velocity. Their near-wall behavior reflected the crucial role of turbulent transport near the rib crest and within the separated shear layer. Sweep events occurred with the elongated flow structures of the flapping shear layer and gained in importance towards the channel bottom wall, while strong ejection events near the rib leading and trailing edges coincided with flow structures bursting away from the wall. Despite the predominant occurrence of sweep events close to the ribbed wall within the inter-rib spacing, ejection events contributed with higher intensity to the Reynolds shear stress. Ejection and sweep events and their underlying transport phenomena contributing to the Reynolds shear stress were almost Reynolds number-insensitive in the resolved flow range. The invariance to the Reynolds number can be of benefit for the use of scale-resolving simulation methods in the design process of rib structures for heat exchange applications.

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of full RANS closure. For the non-stratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

Direct Numerical Simulation of Real-gas Effects within Turbulent Boundary Layers for Fully-developed Channel Flows

Real-gas effects have a significant impact on compressible turbulent flows of dense gases, especially when flow properties are in proximity of the saturation line and/or the thermodynamic critical point. Understanding of these effects is key for the analysis and improvement of performance for many industrial components, including expanders and heat exchangers in organic Rankine cycle systems. This work analyzes the real-gas effect on the turbulent boundary layer of fully developed channel flow of two organic gases, R1233zd(E) and MDM - two candidate working fluids for ORC systems. Compressible direct numerical simulations (DNS) with real-gas equations of state are used in this research. Three cases are set up for each organic vapour, representing thermodynamic states far from, close to and inside the supercritical region, and these cases refer to weak, normal and strong real-gas effect in each fluid. The results within this work show that the real-gas effect can significantly influence the profile of averaged thermodynamic properties, relative to an air baseline case. This effect has a reverse impact on the distribution of averaged temperature and density. As the real-gas effect gets stronger, the averaged centre-to-wall temperature ratio decreases but the density drop increases. In a strong real-gas effect case, the dynamic viscosity at the channel center point can be lower than at channel wall. This phenomenon can not be found in a perfect gas flow. The real-gas effect increases the normal Reynolds stress in the wall-normal direction by 7–20% and in the spanwise direction by 10–21%, which is caused by its impact on the viscosity profile. It also increases the Reynolds shear stress by 5–8%. The real-gas effect increases the turbulence kinetic energy dissipation in the viscous sublayer and buffer sublayer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo><</mml:mo><mml:mn>30</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> but not in the outer layer. The turbulent viscosity hypthesis is checked in these two fluids, and the result shows that the standard two-function RANS model (<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ω</mml:mi></mml:math></inline-formula>) with a constant <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>C</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.09</mml:mn></mml:math></inline-formula> is still suitable in the outer layer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>></mml:mo><mml:mn>70</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, with an error in ±10%.

Analyses of wave-phase variation of Reynolds shear stress underneath surface wave using streamline coordinates

The dependence of Reynolds shear stress on wave phase is investigated for initially isotropic turbulence distorted by a progressive surface wave through direct numerical simulations. A wave-following streamline coordinate frame is used to analyse the turbulence dynamics such that the information of the varying direction of wave orbital motions is embedded into the coordinate system, which helps capture the effect of flow curvature on the turbulence and quantify momentum exchange between the near-surface and deep regions in the wavy domain accurately. It is found that the Reynolds shear stress is enhanced under the backward slope of the wave and can be scaled by the wave steepness and the streamwise velocity fluctuations. Analyses of the budget of Reynolds shear stress indicate that such a variation with the wave phase is caused by the variation in the production of the Reynolds shear stress and the effect of pressure fluctuations. Further investigation shows that the production of the Reynolds shear stress is closely associated with the wave surface curvature. A model that includes a correction term for the curvature effect for the pressure–strain correlation term is examined and is found to agree reasonably well with the simulation result. The correction term is found to make an appreciable contribution to the model, further supporting our finding that the wave curvature plays an important role in the turbulence dynamics near the surface.

Investigation of the Effect of Vegetation on Flow Structures and Turbulence Anisotropy around Semi-Elliptical Abutment

In the present experimental study, the effect of vegetation on flow structure and scour profile around a bridge abutment has been investigated. The vegetation in the channel bed significantly impacted the turbulent statistics and turbulence anisotropy. Interestingly, compared to the channel without vegetation, the presence of vegetation in the channel bed dramatically reduced the primary vortex, but less impacts the wake vortex. Moreover, the tangential and radial velocities decreased with the vegetation in the channel bed, while the vertical velocity (azimuthal angle > 90°) had large positive values near the scour hole bed. Results showed that the presence of the vegetation in the channel bed caused a noticeable decrease in the Reynolds shear stress. Analysis of the Reynolds stress anisotropy indicated that the flow had more tendency to be isotropic for the vegetated bed. Results have shown that the anisotropy profile changes from pancake-shaped to cigar-shaped in the un-vegetated channel. In contrast, it had the opposite reaction for the vegetated bed.

The influence of different morphological units on the turbulent flow characteristics in step-pool mountain streams

The morphology of step-pools is often implemented for ecological restoration and for the creation of close-to-nature fish passes. Step-pools display spatio-temporal variations in bed and flow characteristics due to meso-scale units such as step, tread, base of step, and pool. Exclusive research on the effects of bed variations in step-pools on the flow dynamics is limited. Here, we conducted laboratory experiments on a physical model downscaled from a field site in the Western Ghats, Kerala, India. The results of Kruskal–Wallis ANOVA show significant differences in the velocity and turbulent intensities for the morphological units. A regression equation of the form Power-Allometric1 has been proposed to relate the normalized turbulent kinetic energy with the velocity magnitude. The present study also estimated the range of Reynolds shear stress and energy dissipation factor existent in the step-pool systems. The normalized values of Reynolds shear stress in the x–z plane ranged from − 19.477 to 13.729, and energy dissipation factors obtained for the three step-pool systems are 321, 207, and 123 W/m3; both the results reveal insufficient pool volume for adequate energy dissipation. The study concludes that while designing close-to-nature step-pool fish passes, pool dimensions should be finalized with respect to the target aquatic species.

Determination of Reynolds shear stress from the turbulent mean velocity profile and spectral characteristics of Orr-Sommerfeld -Squire equations

Theoretically, based on a waveguide model, the expression of the tangential stress is formulated for steady, two-dimensional incompressible fluid flow over a flat plate in turbulent boundary layer. It is dependent on some factors, one of them, the behaviour of the last damping mode eigenvalues, and eigenfunctions, that are deduced from solution Orr-Sommerfeld equation by spectral Chebyshev collocation Method. Verification of the latter method is investigated by comparison the deduced formula of turbulent tangential stress with experimental data. In addition to, weight factors in this expression are connected to define the condition of dynamical system solution for multiple 3-wave resonance. This system is solved numerically, and the dynamic invariant is normalized to obtain the time average of the square modulus harmonic, and sub harmonics amplitudes by theorem Birkhoff-Khinchin. Comparison is made between the time-averaged and the phase average for the square modulus of harmonic, and sub harmonic amplitudes that defined on the unit sphere, in the state of multiple 3-wave resonance.

Experimental Investigation of the Reynolds Shear Stress Exceedance Rate for the Injury and Disorientation Biocriteria Boundary in the Pool-Orifice and Vertical Slot Type Fishways

Fragmentation of rivers has a negative impact on river’s ecological status which can be improved by the construction of fishways next to obstacles in rivers that prevent a free migration. Flow field characteristics are key factors in the design process of hydraulically efficient fishways—flow and turbulence patterns in a functional fishway allow fish to enter, progress through and exit with minimum time/energy expenditure. The aim of this paper is an experimental study of the flow field characteristics measured in the physical fishway model with the goal of providing information on the Reynold’s shear stress distribution that would facilitate their design in accordance with the environmental requirements. The focus of the research was on the nominally hydraulically efficient con-figuration pool-type fishways—pool-orifice and vertical slot. Fishway geometry was varied for bottom slope (7.5%, 10% and 12.5%), pool length (45 cm, 60 cm and 90 cm) and orifice size (8 × 8 cm, 10 × 10 cm and 12 × 12 cm) in a model scaled 1:3 to the prototype. Since Reynold’s shear stress has been identified as the main turbulent parameter affecting fish swimming performance and behavior, it is used as the basis for the analyses. The velocity data were collected with Vectrino ADV and processed in all three planes—streamwise, horizontal and vertical. Reynold’s shear stress data were analyzed according to the injury (>50 N/m2) and disorientation (>30 N/m2) biocriteria boundaries defined in the literature. The percentage of the flow field exceeding the boundaries were analyzed depending on the fishway geometry. The results obtained in this research suggest that the critical design parameter is the orifice size for the pool-orifice fishways and the pool length for the VS fishway. The Reynold’s shear stress is generally the highest in the bottom layer for pool-orifice fishways and the surface layer for vertical slot fishways.