Lock-in regime Time periodic flow and heat transfer a b s t r a c t Heat convection from the uniformly heated walls of a straight channel in presence of a rotationally oscillating cylinder (ROC) is simulated at Re ¼ 100. Heat transfer enhancement due to vortex shedding from the ROC is investigated. Systematic studies are performed to explore the rotation angle and frequency influences on heat transfer by varying the latter in range of the lock-in regime and the former from 0 to 2p/3. All simulation results are based on the numerical solutions of two-dimensional, unsteady, incompressible NaviereStokes and energy equations using an h/p type finite element algorithm. Considering time periodicity of the resulting flow and temperature fields, time averaged wall Nusselt number is reported to quantify the heat transfer enhancement for Pr ¼ 0.1, 1.0, 5.0 and 10.0 fluids. Performance analyses of the ROC device based on its total power consumption and heat transfer enhancement are also presented.
Heat-transfer enhancement in a uniformly heated slot mini-channel due to vortices shed from an adiabatic circular cylinder is numerically investigated. The effects of gap spacing between the cylinder and bottom wall on wall heat transfer and pressure drop are systemically studied. Numerical simulations are performed at Re = 100, 0.1 Pr 10and a blockage ratio of D/H = 1/3. Results within the thermally developing flow region show heat transfer augmentation compared to the plane channel. It was found that when the obstacle is placed in the middle of the duct, maximum heat transfer enhancement from channel walls is achieved. Displacement of circular cylinder towards the bottom wall leads to the suppression of the vortex shedding, the establishment of a steady flow and a reduction of both wall heat transfer and pressure drop. Performance analysis indicates that the proposed heat transfer enhancement mechanism is beneficial for low-Prandtl-number fluids.
A detailed laboratory study was conducted to examine the effects of particle size on hysteretic sediment transport under time‐varying rainfall. A rainfall pattern composed of seven sequential stepwise varying rainfall intensities (30, 37.5, 45, 60, 45, 37.5, and 30 mm h−1), each of 20 min duration, was applied to a 5 m × 2 m soil erosion flume. The soil in the flume was initially dried, ploughed to a depth of 20 cm and had a mechanically smoothed surface. Flow rates and sediment concentration data for seven particle size classes (<2, 2–20, 20–50, 50–100, 100–315, 315–1000, and >1000 µm) were measured in the flume effluent. Clockwise hysteresis loops in the sediment concentration versus discharge curves were measured for the total eroded soil and the finer particle sizes (<2, 2–20, and 20–50 µm). However, for particle sizes greater than 50 µm, hysteresis effects decreased and suspended concentrations tended to vary linearly with discharge. The Hairsine and Rose (HR) soil erosion model agreed well with the experimental data for the total eroded soil and for the finer particle size classes (up to 50 µm). For the larger particle size classes, the model provided reasonable qualitative agreement with the measurements although the fit was poor for the largest size class (>1000 µm). Overall, it is found that hysteresis varies amongst particle sizes and that the predictions of the HR model are consistent with hysteretic behavior of different sediment size classes.
The scaling relation between the drainage area and stream length (Hack's law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for channelized fluvial regions. We report here on a laboratory experiment on an eroding unconsolidated sediment for which no channeling occurred. Laser scanning was used to capture the morphological evolution of the sediment. High-intensity, spatially nonuniform rainfall ensured that the morphology changed substantially over the 16-hr experiment. Based on the surface scans and precipitation distribution, overland flow was estimated with the D8 algorithm, which outputs a flow network that was analyzed statistically. The above-mentioned scaling and exceedance probability relationships for this overland flow network are the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of experiment. Plain Language SummaryIn spite of different climates, vegetation, and land properties, the geometry of river networks is characterized by near-identical scaling laws. Can we expect similar statistical metrics for surface flow over unchanneled morphologies at small scales? To answer this question, the morphology of uncohesive sediment was measured at high resolution in a laboratory flume and under nonuniform rainfall. Based on this morphology, the overland flow network was determined. The results showed that even at small scale (2 m by 1 m) and in absence of rills, the flow network has the same statistical characteristics as large-scale river networks. In other words, the shallow overland flow could be represented by a network that dynamically changed while preserving catchment scaling laws.
Unlike sediment transport in rivers, erosion of agricultural soil must overcome its cohesive strength to move soil particles into suspension. Soil particle size variability also leads to fall velocities covering many orders of magnitude, and hence to different suspended travel distances in overland flow. Consequently, there is a large range of inherent timescales involved in transport of eroded soil. For conditions where there is a constant rainfall rate and detachment is the dominant erosion mechanism, we use the Hairsine-Rose (HR) model to analyze these timescales, to determine their magnitude (bounds) and to provide simple approximations for them. We show that each particle size produces both fast and slow timescales. The fast timescale controls the rapid adjustment away from experimental initial conditions-this happens so quickly that it cannot be measured in practice. The slow timescales control the subsequent transition to steady state and are so large that true steady state is rarely achieved in laboratory experiments. Both the fastest and slowest timescales are governed by the largest particle size class. Physically, these correspond to the rate of vertical movement between suspension and the soil bed and the time to achieve steady state, respectively. For typical distributions of size classes, we also find that there is often a single dominant timescale that governs the growth in the total mass of sediment in the non-cohesive deposited layer. This finding allows a considerable simplification of the HR model, leading to analytical expressions for the evolution of suspended and deposited layer concentrations.Abbreviations: HR, Hairsine-Rose.
Despite numerous applications of physically-based models for incised landscapes, their applicability for overland flow on unchanneled surfaces is not known. This work challenges a widely used landscape evolution model for the case of non-uniform rainfall and absence of rills using laboratory flume experiment. Rainfall with an average intensity of 85 mm h−1 was applied for 16 h during which high resolution laser scans of the morphology were captured. The overland flow was modeled as a network that preserves the water flux for each cell in the discretized domain. This network represented the gravity-driven surface flow and determined the evolution direction. The model was calibrated using the first 8 h of the experiment and was then used to predict the second 8 h. The calibrated model predicted, as expected, a smoother surface morphology (and less detailed overland flow network) than that measured. This difference resulted from quenched randomness (e.g., small pebbles) within the experimental soil that emerged during erosion and that were captured by the laser scans. To investigate the quality of the prediction, a low-pass filter was applied to remove the small-scale variability of the surface morphology. This step confirmed that the model simulations captured the main characteristics of the measured morphology. The experimental results were found to satisfy a scaling relation for the exceedance probability of discharge even in absence of rills. However, the model did not reproduce the experimental scaling relation as the detailed surface micro-roughness was not accounted for by the model. A lower cutoff on the scale of applicability of the general landscape evolution equation is thus suggested, complementing other work on the upper cutoff underpinned by runoff-producing areas.
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