Uniform Flow Conditions Research Articles

Hydraulics of Time-Variable Water Surface Slope in Rivers Observed by Satellite Altimetry

The ICESat-2 and SWOT satellite earth observation missions have provided highly accurate water surface slope (WSS) observations in global rivers for the first time. While water surface slope is expected to remain constant in time for approximately uniform flow conditions, we observe time varying water surface slope in many river reaches around the globe in the ICESat-2 record. Here, we investigate the causes of time variability of WSSs using simplified river hydraulic models based on the theory of steady, gradually varied flow. We identify bed slope or cross section shape changes, river confluences, flood waves, and backwater effects from lakes, reservoirs, or the ocean as the main non-uniform hydraulic situations in natural rivers that cause time changes of WSSs. We illustrate these phenomena at selected river sites around the world, using ICESat-2 data and river discharge estimates. The analysis shows that WSS observations from space can provide new insights into river hydraulics and can enable the estimation of river discharge from combined observations of water surface elevation and WSSs at sites with complex hydraulic characteristics.

Plasma-Fluid Energy Transfers in Plasma Assisted Ignition

ABSTRACT A three-dimensional model of plasma-fluid coupling is developed, including the Navier-Stokes, the drift-diffusion, and the radiative transfer equations, to investigate the energy transfers between plasma and fluid in repetitive-pulsed discharge ignition. A modal decomposition of the energy transfer is performed to determine the contributions of plasma to the mechanical coupling and pressure losses during ignition. The detailed model is validated against experiments and compared against a well-known empirical approximation. The main findings are that the modal coupling is dependent on the geometry of the electrodes and flat electrodes provide the strongest mechanical transfer into the acoustic modes. Uniform flow conditions decrease the extent of the mechanical coupling due to the decreased pressure velocity correlations in shear flows. Water vapor production reduces the entropic mode of the energy coupling.

Effects of aspect ratio on flow characteristics on free surface-mounted rectangular cylinders

Turbulent flow characteristics around free surface-mounted rectangular cylinders of different streamwise aspect ratios (AR=1, 2, 2.5, 3, 4, 5, and 8 denoted as AR1, AR2, AR2.5, AR3, AR4, AR5, and AR8, respectively) at a Reynolds number based on the freestream velocity and cylinder height, Reh = 11100, were investigated experimentally using a time-resolved particle image velocimetry system. The results reveal distinct flow behaviors for different aspect ratios. The separated shear layer is shed directly into the wake for AR1, while AR2 and AR2.5 exhibits intermittent reattachment on the cylinder and direct shedding into the wake. However, for AR≥3 cylinders, the separated shear layer reattaches onto the cylinder and is later shed into the wake after subsequent separation from the trailing edge of the cylinder. Comparative analysis with previous studies on rectangular cylinders in uniform flow and wall-mounted conditions demonstrates similarities in reattachment behavior on the cylinder to uniform flow cases and wake reattachment mechanism akin to wall-mounted cylinders subjected to a thin turbulent boundary layer. The Reynolds stresses, turbulence production, and vortex shedding patterns examined with frequency spectra and proper orthogonal decomposition of velocity fluctuations exhibit significant dependence on streamwise aspect ratio.

Bed Roughness Incorporated Lift Force Formulation for Sediment Concentration Solutions

Within the field of sediment transport dynamics, there is an emphasis on the need for providing and improving simplified analytical solutions from which the findings can be extended upon. Typically, solutions have been developed from the understanding and incorporation of vertical velocity components/distribution; however, there remains opportunity for analytical enhancement. Under uniform open channel dilute sediment laden flow conditions, the type II concentration profile reflects the maximum concentration at a distance from the bed. To analytically depict the type II profile, it is essential to describe the vertical velocity components acting within the flow hydrodynamics. Yet, the impact of bed roughness on the vertical velocity distribution influencing a sediment particle has not been articulated. Hence, in this research, the impact of bed roughness is incorporated into the vertical velocity distribution to formulate the lift force acting upon a particle, to provide a sediment concentration solution. The proposed analytical vertical velocity distribution solution is validated against existing formulations, followed by the proposed sediment concentration being validated against existing solutions. Here, the results indicate that analytically incorporating the bed roughness alongside the secondary current induced vortices provides a lift force solution that can depict the type II concentration profile. Under relatively low shear velocity, increasing the sediment diameter allows for a clearer depiction of the near surface region and profile curvature. Furthermore, the proposed sediment concentration solution can accurately depict the near surface region, curvature of concentration, and maximum concentration under relatively large shear velocity data. Importantly, under conditions where both the shear velocity and sediment diameter are relatively large, the maximum concentration is captured with greater accuracy; however, the curvature of the profile and the near surface region accuracy are hindered. It is to be noted, that due to the formulation of the proposed velocity distribution the accuracy of the solution towards the bed decreases due to instability caused as the characteristic depth decreases to zero.

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The impact of the wall on the hydrodynamic forces is accounted for as a function of a multiplication factor on the drag force in case of locally uniform flow, and an additional force contribution for the lift and the torque, modifying the resultant forces experienced by a particle in a locally uniform flow. The changes in the hydrodynamic forces prove to be substantial, emphasizing the necessity of accounting for wall effects across all particle types and flow conditions investigated in this study. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for the drag, lift, and torque coefficients of a non-spherical particle in wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian–Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded shear flow to locally uniform flow conditions.

Numerical investigation of effects of riblets on wind turbine performance

In this study, systematically designed wind tunnel experiments were conducted to characterize the aerodynamic performance of a DU91-W2-250 airfoil with a riblet film. To quantify the impact of the riblet film on wind turbine performance, experimental results were used as input data for numerical simulations. Large-eddy simulations were conducted for the smooth and modified airfoils under uniform and turbulent inflow conditions. For the turbulent inflow simulations, staggered cubes were introduced upstream of the wind turbine to generate velocity fluctuations in the flow. Results from the numerical simulations show that improvements in the aerodynamic performance of the airfoil with riblets enhance the aerodynamic torque that drives the wind turbine, thereby increasing the power output. The improvement in the power coefficient with the use of the riblet film is higher for turbulent incoming wind compared to uniform flow conditions.

Aerodynamic Characterization of the IEA 15 MW Reference Wind Turbine by Code-to-Code Comparison

The consistency of different aerodynamic formulations applied to the analysis of a modern multi-megawatt horizontal axis wind turbine rotor is investigated. The proposed code-to-code comparison involves specific implementations of a hierarchy of solvers based on Blade Element Momentum Theory (AEOLIAN), Actuator Line Modelling (OpenFOAM), free-wake Panel Method (FUNAERO) and blade-resolved Computational Fluid Dynamics (OpenFOAM ). The analysis addresses local and integral aeroloads and flow physical quantities concerning the state-of-the-art IEA 15 MW reference wind turbine in axial uniform flow conditions. The proposed solvers predict consistent rotor performance and blade aeroloads (also in line with data from of IEA Task 47). However, differences emerge close to blade root, where blade-resolved CFD reveals a significant flow separation on the suction side. Furthermore, scattering of induction factors computations is observed, especially in the axial direction. Different methodologies and numerical setup used in blade-resolved simulations allow achieving physically-consistent induction values, especially at blade tip. Finally, flow-field predictions by Computational Fluid Dynamics (CFD) and Panel Method are consistent upstream and close to the disk downstream (except where significant flow separation occurs), whilst a more detailed study on the effect of extending wake refinement zone in CFD simulation is advisable.

Coupling Effects of a Top-Hinged Buoyancy Can on the Vortex-Induced Vibration of a Riser Model in Currents and Waves

In order to investigate the effects of the top-end dynamic boundary of risers caused by floater motions on their vortex-induced vibration (VIV) characteristics, a combined model comprising a buoyancy can with a relatively simple structural form and a riser is taken as the research object in the present study. The aspect ratios of the buoyancy can and the riser model are 5.37 and 250, respectively. A set of experimental devices is designed to support the VIV test of the riser with a dynamic boundary stimulating the vortex-induced motion (VIM) of the buoyancy can under different uniform flow and regular wave conditions. Several data processing methods are applied in the model test, i.e., mode superposition, Euler angle conversion, band pass filter, fast Fourier transform, and wavelet transform. Based on the testing results, the effect of low-frequency VIM on the high-frequency VIV of the riser is discussed in relation to a single current, a single wave, and a combined wave and current. It is found that the coupling effect of VIM on the riser VIV presents certain orthogonal features at low current velocities. The effect of the cross-flow VIM component on VIV is far more prominent than that of its counterpart, the in-line VIM, with increasing flow velocity. The VIM in the combined wave–current condition significantly enhances the modulation of vibration amplitude and frequency, resulting in larger fluctuation peaks of vibration response and further increasing the risk of VIV fatigue.

Stereo-PIV measurements within the canopy in open-channel flows

Measuring the flow field not just above but also inside the canopy of rough beds in open-channel flows is challenging when optical access from below or the side is not possible. To this end, a new stereo-PIV arrangement was implemented and tested. To optically access the area in between the roughness elements, a top-viewing stereo-PIV system was installed at a steep viewing angle of 70∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}. Furthermore, a glass plate was installed at the water surface to avoid random image distortions from surface waves. Finally, in-house-produced low-cost fluorescent particles were used to filter out laser reflections on the canopy’s surface. To validate the stereo-PIV measurements with respect to the steep viewing angle of the stereo cameras, the instantaneous flow field above a bed of spheres was measured simultaneously with the stereo-PIV system and with a third side-looking camera for standard 2D-PIV processing. Two different water depths and two different Reynolds numbers were investigated under uniform flow conditions. Finally, to assess the influence of the glass plate on the flow, 2D-PIV measurements were performed with and without the glass plate. It is shown that the steep viewing stereo PIV can properly reconstruct the instantaneous, mean and turbulent statistics except for the vertical normal turbulent stresses, which are overestimated due to peak-locking errors. Also, the boundary layer developing below the glass plate induces a slight acceleration in the bulk flow, which can be considered negligible for higher water depths. In all instances, the flow acceleration does not affect the near-bed region.Graphical abstract

Effects of the turbulent incoming flow condition on the wind–snow flow characteristics and accretion distribution in the cutting area of the high-speed railway

In addressing snowdrift disasters in high-speed railway cutting areas, this study utilized the improved delayed detached eddy simulation turbulence model, synthetic eddy method, and Eulerian two-phase flow model (Euler–Euler). Coupled with grid dynamic deformation techniques, the investigation facilitated extracting temporal variations in snow particle accumulation profiles within the cutting areas. The predicting accuracy of the numerical method was validated through the wind tunnel and wind–snow experimental data. Building upon this foundation, the study investigated how uniform and turbulent flow conditions impact snow distribution in the high-speed railway cutting areas. The analysis examined the turbulent flow structures, friction velocity distribution, and snow accretion contours within the cutting area. Findings indicate that the snow mass on the windward slope in the cutting area remains consistent under both flow conditions. However, there are significant differences in the rate of snow mass growth and the characteristics of snow accretion distribution. The disappearance of vortex structures at the base of the leeward slope is crucial for indicating the transition in the accumulation states of the surrounding snow particles. Under turbulent incoming flow conditions, the transition from large-scale vortex systems to vortex pairs on the leeward slope of the cutting is delayed, resulting in a postponed stable growth period for snow accretion. Additionally, strong erosion between the track bed and the leeward slope results in reduced snow accretion mass in these areas. In particular, at the simulation time of t = 150 min, under turbulent incoming flow conditions, the overall snow accumulation in the cutting decreased by 20.8% compared to the uniform incoming flow conditions. The snow mass in the leeward slope area decreased by 38.3%, and the track bed area experienced a 23.3% reduction in snow accumulation. In contrast, the snow quantity on the windward slope remained relatively consistent.

Non-uniform inlet flow definition for highly skewed model propeller by geometric partitioning

Ship design involves many calculations to provide a propulsion system with the appropriate speed. Prioritizing speed-resistance calculations affects main engine, gearbox, propeller, and other auxiliary system selection. Here, the propeller is most intriguing. Since the propeller operates in a fluid domain, internal and external factors affect it. Despite being designed for service speed, water flow can affect the efficiency of a propeller at the ship's stern. Under open-water circumstances, a ship's hull affects a propeller's hydrodynamic performance. The effect usually decreases propeller efficiency, so it's important to know how ship hull and propeller design interact before production. To overcome this issue, researchers test towing tanks extensively. Computational Fluid Dynamics, which is efficient and cost-effective, is also commonly used. This study examines the hydrodynamics of a fishing vessel's highly skewed model propeller. The objective of this study was to assess the propeller's efficiency under uniform and non-uniform flow conditions and investigate an alternative method for dividing the inlet area, which has not been studied in the literature. The study has effectively met its goals, producing satisfactory error margins for both operating conditions. This research significantly contributes to understanding the relationship between hull configuration and propeller design, particularly in non-uniform flow scenarios.

Evaluation and optimization of outdoor wind environment in block based on space syntax and CFD simulation.

The wind environment quality at the height of pedestrians can significantly affect the thermal comfort and physical and mental health of pedestrians, promote the diffusion of air pollutants and inhibit the formation of urban heat island effect, and has been paid more and more attention in the field of urban and rural planning. This paper takes Jianlan Road commercial pedestrian Street as an example to maximize the thermal comfort of pedestrians. Based on CFD numerical simulation technology and space syntax theory, the pedestrian wind environment of the accessible space of the block is selected for quantitative research. Through numerical simulation, the influence of block spatial form on the wind environment at pedestrian height under the initial condition of uniform air flow is analyzed, and some suggestions are put forward for the optimization of block spatial form. Finally, the block optimization scheme is verified and simulated. The visualization results show that the wind environment quality of the optimized high-accessibility space is significantly improved, the proportion of comfort zone is increased from 58.2% to 86%, and the static wind rate is reduced from 41.8% to 14%. The wind environment optimization effect is obvious.

POD-LSTM model for predicting pressure time series on structures

A novel method for predicting wind pressure time series on structures is proposed by combining long short-term memory network (LSTM) with proper orthogonal decomposition (POD). POD-LSTM predicts the pressure time series on any circumferential locations of a structure using data from limited pressure taps. The wind tunnel test data of pressure on a single square cylinder and the downstream cylinder of two tandem square cylinders is utilized to evaluate the performances of POD-LSTM, LSTM, and POD-BPNN (back-propagation neural network). Results of pressure time series, aerodynamic parameters, and pressure moments are presented. POD-LSTM takes advantage of LSTM in time series prediction and POD in extracting essential features, resulting in a better performance than POD-BPNN and LSTM. The similarity of pressure on nearby taps affects the accuracy of POD-LSTM. A larger error is observed at the rear corners of a single cylinder where intermittent flow reattachment occurs. The predicted results for mean and fluctuating pressure coefficients are satisfactory, but POD-LSTM underestimates the absolute value of skewness and kurtosis at structural surfaces where the non-Gaussian property of pressure is significant. Compared with the uniform flow condition, the prediction accuracy decreases when the structure is in the wake of upstream structures.

Chezy’s Resistance Coefficient in a Round-cornered Rectangle Channel

Abstract The determination of resistance coefficients, such as Chezy’s or Manning’s coefficients, requires a great deal of sensible thought in order to express these coefficients better and more extensively in free-surface channels and aqueducts. This can be achieved if the expression of the resistance coefficient is well stated and takes into account the maximum number of parameters for governing flows in channels. However, in most practical cases, if these coefficients are not expressed by implicit models, they are generally taken as constant and arbitrary. To this end and in a rational manner, the dimensioning and design of channels requires the expression of the resistance coefficient in an easily and explicit form by adopting numerous flow parameters, namely the roughness of the walls, the aspect ratio, the slope of the channels and essentially the viscosity of the liquid. To achieve this aim, the Chezy’s resistance coefficient C is identified using the rough model method (RMM), which gives the discharge under uniform flow conditions appropriate to a round-cornered rectangle channel.

Ideal and non-ideal planar compressible fluid flows in radial equilibrium

Two-dimensional compressible flows in radial equilibrium are investigated in the ideal dilute-gas regime and the non-ideal single-phase regime close to the liquid–vapour saturation curve and the critical point. Radial equilibrium flows along constant-curvature streamlines are considered. All properties are therefore independent of the tangential streamwise coordinate. A differential relation for the Mach number dependency on the radius is derived for both ideal and non-ideal conditions. For ideal flows, the differential relation is integrated analytically. Assuming a constant specific heat ratio $\gamma$ , the Mach number is a monotonically decreasing function of the radius of curvature for ideal flows, with $\gamma$ being the only fluid-dependent parameter. In non-ideal conditions, the Mach number profile also depends on the total thermodynamic conditions of the fluid. For high molecular complexity fluids, such as toluene or hexamethyldisiloxane, a non-monotone Mach number profile is admissible in single-phase supersonic conditions. For Bethe–Zel'dovich–Thompson fluids, non-monotone behaviour is observed in subsonic conditions. Numerical simulations of subsonic and supersonic turning flows are carried out using the streamline curvature method and the computational fluid dynamics software SU2, respectively, both confirming the flow evolution from uniform flow conditions to the radial equilibrium profile predicted by the theory.

Influence of upstream and downstream flow on different packed bed configurations in phase change process

One approach to storing latent heat in large quantities is through PBSS (Packed bed storage system) with spheres filled with PCM (Phase Change Materials). In these storage systems, an HTF (heat transfer fluid) flows over the spheres. So, both the sphere wall temperature and the heat flux can vary depending on the geometric conditions of the bed of spheres, the PCM thermodynamic conditions, and the HTF thermal conditions. Thus, this work aims to verify the influence of the thermal conditions of the external flow on the PBSS filled with PCM in the melting process. Cases with variable heat flux as well as uniform temperature and uniform heat flux conditions were tested. Three sphere positions, 4 sphere spacing ratios (blockage ratio), and three temperature differences between HTF and PCM phase change temperature were also analyzed, for two external flow directions (upstream and downstream), totaling 74 different configurations. The study found that the uniform temperature condition resulted in a 33 % faster total melting time than the uniform heat flow condition. Additionally, the upstream flow showed a total melting time that was approximately 24 % shorter than the flows in the opposite direction. The relationship between the total melting time and the temperature differences was found to be non-linear. Moreover, the blockage ratio showed a non-linear dependence with total melting time. The configuration with a blockage ratio of 1.125 demonstrated the shortest total melting time, with values on average 22.4 % shorter than the blocking ratio of 0.550, which had the longest melting times. These results demonstrate that optimizing external flow thermal conditions is crucial for improving the performance of PBSS with PCM-filled spheres in large-scale latent heat storage systems.

An experimental investigation on the effect of in-flow distortions of propeller noise

Propellers usually operate in non-uniform flow conditions, leading to significant levels of noise generation due to interaction with the leading edges of the propeller blades. Under these flow conditions, the noise generated can be substantially different from the rotor-alone self-noise generated under uniform mean flow conditions. This paper presents an experimental investigation aimed at studying the far-field noise due to a two-bladed propeller immersed in a controlled non-uniform flow with known characteristics. This paper presents the results of a parametric study with different degrees of flow non-uniformity generated from different geometric obstructions located in the jet nozzle, while maintaining constant thrust. Measurements of the radiated noise show that the incoming mean flow non-uniformities under investigation in this study cause a significant increase in tonal amplitudes of the blade passing frequencies of harmonic orders greater than 2. At the first two blade passing frequencies the tones are dominated by the rotor-alone ‘Gutin-type’ tones resulting from the steady blade loading.The measured noise spectra are compared with predictions from a simple frequency-domain flat plate model. The analytical model will be shown to capture the main features of the interaction tonal noise spectrum and directivity.

Evaluation of Model Predictions of the Unsteady Tidal Stream Resource and Turbine Fatigue Loads Relative to Multi-Point Flow Measurements at Raz Blanchard

The next stage of development of the tidal stream industry will see a focus on the deployment of tidal turbines in arrays of increasing device numbers and rated power. Successful array development requires a thorough understanding of the resource within potential deployment sites. This is predictable in terms of flow speeds, based upon tidal constituents. However, the operating environment for the turbine is more complex than the turbine experiencing a uniform flow, with turbulence, shear and wave conditions all affecting the loading on the turbine components. This study establishes the accuracy with which several alternative modelling tools predict the resource characteristics which define unsteady loading—velocity shear, turbulence and waves—and assesses the impact of the model choice on predicted damage equivalent loads. In addition, the predictions of turbulence are compared to a higher fidelity model and the occurrence of flow speeds to a Delft3D model for currents and waves. These models have been run for a specific tidal site, the Raz Blanchard, one of the major tidal stream sites in European waters. The measured resource and predicted loading are established using data collected in a recent deployment of acoustic Doppler current profilers (ADCPs) as part of the Interreg TIGER project. The conditions are measured at three locations across the site, with transverse spacing of 145.7 m and 59.3 m between each device. Turbine fatigue loading is assessed using measurements and model predictions based on an unsteady blade element momentum model applied to near-surface and near-bed deployment positions. As well as across-site spatial variation of loading, the through life loading over a 5-year period results in an 8% difference to measured loads for a near-surface turbine, using conditions purely defined from a resource model and to within 3% when using a combination of modelled shear with measured turbulence characteristics.

Fluid-based microbial processes modeling in Trichodesmium colony formation

In tropical and subtropical ocean gyres, Trichodesmium colonies account for up to half of the total N2 fixation in the ocean, making it one of the most ecologically significant N2-fixing cyanobacteria. The processes whereby Trichodesmium colonies and large-scale surface blooms form have not been investigated thoroughly. In particular, the effects of fluid motion have not been included in previous studies. As the first step toward understanding the mechanical processes associated with Trichodesmium colony synthesis, we propose a shear-related flow-based growth model to enlighten how fluid dynamics affect bacteria colony formation and growth. To investigate the possibility that early growth characteristics are strongly dependent on the shear rate, a two-way coupled fluid-colony interaction is developed using the lattice Boltzmann method for a porous colony. This model captures the exponential growth trend during the colony formation phase found in experiments. Our results show that the flow field significantly impacts both the colony growth rate and shape. In pure shear conditions, colonies grow in circular shapes, whereas in uniform flow, they take filament-like forms. Additionally, the Reynolds number (Re) plays a crucial role in shaping the colonies, especially in uniform flow conditions where its effect is more profound.

Theoretical derivation of hydraulic geometry equations for a gravel bed river channel

The geomorphic relations of hydraulic geometry at-a-station and downstream, expressed as power laws, are derived for a straight, single thread, gravel river channel. The cross-section has a plane central bed, narrow or wide, flanked by curved sides or banks. The analysis employs mechanistic formulae for fixed and mobile bed flow resistance, downchannel bedslope, bedload transport and the novel introduction of bedload ratings all expressed as power laws. Steady uniform flow and equilibrium bedload transport conditions are assumed to occur above the central section. Water discharge and sediment size are assumed to be the only known variables. Exponents of the relations of hydraulic geometry are fixed and are consistent with reported theoretical estimates and field measurements. Coefficients are also explicitly derived and are consistent with field measurements and vary owing to the presence of independent variables in their definition. Here aspect ratio has the major influence. The derived equations can provide coarse estimates for the design of canal and river control works. Conditional separate relations between both width and depth, and bed material size or bed slope are also determined for the occurrence of at-many-stations hydraulic geometry. To improve generality, future work should consider the hydraulic geometry of straight gravel channels with bedload transport, but having an irregular cross-section.