Vertical Velocity Profiles Research Articles

Aeroelastic Experimental Investigation of Hyperbolic Paraboloid Membrane Structures in Normal and Typhoon Winds

The lightweight and flexible membrane structure of roofs are susceptible to wind loads with the risk of damage and failure. Compared with uniform and low-level turbulence flow cases (i.e., normal winds) that have been well investigated, the wind-induced vibration problem of membrane structures in high-level turbulence flows such as typhoons has been paid little attention. To address the gap, this paper aimed at investigating the aerodynamic behavior of hyperbolic paraboloid membrane structures in normal and typhoon winds by a series of wind tunnel tests. Some distinct wind characteristics of upcoming normal and typhoon flows in terms of vertical profiles of wind velocity, turbulence intensity, and power spectrum density of fluctuating winds were well simulated in an automatically controlled wind tunnel. The aeroelastic behavior of a scaled model was analyzed and discussed in terms of displacement time-history responses, probability distribution characteristics, and dynamic characteristics including the natural frequency, mode shape, and damping ratio. Results show that the increasing suction in a typhoon leads to significant growth in maximum deformations and more risks to suffer from aeroelastic instability. Non-Gaussian characteristics appear more remarkable with skewness and kurtosis increasing almost two-fold in typhoons. Structural modal parameters are influenced by both turbulence intensity and wind velocity. This study provides basic insights into the deficiency of dynamic response of membrane structures in typhoons, and promotes the applications of membrane structures in green buildings.

Linear analysis on the non-hydrostatic pressure field of depth-integrated models

In the development of depth-integrated models, certain assumptions are made on the vertical profile of the horizontal velocity, and the pressure field is eliminated through vertical integration of the vertical momentum equation. In this study, analytical forms of the approximated non-hydrostatic pressure field are derived from five most representative depth-integrated models, which include three Boussinesq-type models, a weighted residual type model and a non-hydrostatic model. A Stokes wave-type Fourier analysis is then conducted to examine their capability in reproducing the vertical profile of the non-hydrostatic pressure field, which is compared with linear wave theory. We found the Boussinesq-type models are able to reproduce the non-hydrostatic pressure field from shallower water up to the kd values similar to that of concerning linear wave phase velocity. Specifically, the two-layer Boussinesq model generally outperforms the higher-order (μ4) Boussinesq model, especially for higher kd values. The weighted residual type model can reasonably capture the non-hydrostatic pressure near to the free surface even at high kd values, but undulations appear in the lower part of the water column where non-hydrostatic pressure is close to zero. The non-hydrostatic model shows rapid convergence of linear wave phase velocity by using few vertical layers, however, its capability in reproducing the non-hydrostatic pressure field is limited, especially at the highest layer interface, where nonphysical phenomena of reversed pressure could appear. This suggests that it is necessary to employ more layers when detailed information on the pressure field is needed, e.g. wave–structure interaction problems.

Understanding Changes in the Tropical Circulation under Global Warming Using a Cloud-Resolving Model and a Conceptual Model

Abstract A cloud-resolving model (CRM) is used to investigate how a prototype tropical circulation driven by a sea surface temperature (SST) contrast changes in a warmer climate. The CRM is used to simulate a region of the atmosphere with a positive SST anomaly, and the large-scale circulation in this region is represented using the weak temperature gradient (WTG) and damped gravity wave (DGW) parameterizations, where the large-scale vertical velocity within the domain is related to the deviation of the simulated density profile from a reference profile representative of the tropical mean state. The behavior of the circulation in response to an increase in SST of both the domain and reference state (i.e., uniform warming) is examined. While the vertical velocity shows an increase in its maximum strength with warming, its value in the lower to midtroposphere decreases. Since the water vapor concentration is largest in the lower troposphere, this leads to a dynamic weakening of precipitation under warming. To understand these results, a simple model for the thermodynamic structure of a convecting atmosphere based on a bulk entraining plume is employed. The model uses a fixed entrainment rate and the relative humidity profiles from the CRM to predict the temperature profiles of the domain and reference state. The vertical velocity profiles calculated from these predicted temperature profiles reproduce important aspects of those simulated with the CRM. This simple modeling framework reveals that the effect of entrainment is crucial to understanding the dynamic response of precipitation to warming, providing a stepping stone to understanding the factors driving changes to the tropical precipitation distribution in a future warmer climate.

Scaling effects of fixed-wing ground-generation airborne wind energy systems

Abstract. While some airborne wind energy system (AWES) companies aim at small, temporary or remote off-grid markets, others aim at utility-scale, multi-megawatt integration into the electricity grid. This study investigates the scaling effects of single-wing, ground-generation AWESs from small- to utility-scale systems, subject to realistic 10 min, onshore and offshore wind conditions derived from a numerical mesoscale Weather Research And Forecasting (WRF) model. To reduce computational cost, vertical wind velocity profiles are grouped into 10 clusters using k-means clustering. Three representative profiles from each cluster are implemented into a nonlinear AWES optimal control model to determine power-optimal trajectories. We compare the effects of three different aircraft masses and two sets of nonlinear aerodynamic coefficients for aircraft with wing areas ranging from 10 to 150 m2 on operating parameters and flight trajectories. We predict size- and mass-dependent AWES power curves, annual energy production (AEP) and capacity factors (cf) and compare them to a quasi-steady-state reference model. Instantaneous force, tether-reeling speed and power fluctuations as well as power losses associated with tether drag and system mass are quantified.

On the Impacts of Ice Cover on Flow Profiles in a Bend

AbstractWe investigate the impact of ice coverage on flow and bed shear stress profiles in a river bend. We perform field measurements using Acoustic Doppler Current Profiler in a bend of the Red River, North Dakota, the United States. Field campaigns were carried out under both open‐surface and ice‐covered conditions in 2020 and 2021. Our results show that the time‐averaged velocity profile follows closely the quartic solution (Guo et al., 2017, under full ice coverage. While the flow profile under open‐surface condition follows closely the logarithmic law near the bed, it is challenging to identify the logarithmic layers in our measured data under ice‐covered condition. Our results also show that the impact of ice coverage is most significant near both banks where the vertical velocity profile is modified significantly due to the interaction of turbulent flows with the ice cover. Our results suggest that the bend curvature and ice coverage both have significant impacts on the velocity profile as well as the distribution of the bed shear stresses. Our findings provide new insights on sediment transport processes of ice‐covered rivers, especially during the break‐up period when the surface coverage changes rapidly.

Reynolds number and submergence ratio effects on turbulence structures in the shallow wake of a horizontal pipe located on a rough bed

The effects of Reynolds number and submergence ratio on mean velocity, separation length, Reynolds shear stresses (RSS), correlation coefficient, anisotropy, and turbulent kinetic energy (TKE) are evaluated by modifying the free-stream velocity and pipe diameter to understand the fluid–structure interaction in the presence of a rough channel bed. Acoustic Doppler velocimetry is used to acquire three-dimensional velocity data in the experiments. The experimental data demonstrate that the non-dimensional separation length is linearly varying with the Reynolds number up to a critical Reynolds number, and after that, it becomes independent of the Reynolds number. The vertical profiles of the mean velocity, RSS, correlation coefficient, anisotropy, and TKE are not affected by the Reynolds number; however, their profiles are affected by the submergence ratio. The RSS and TKE are found to be larger for the higher submergence ratio below the top level of the pipe throughout the wake region. The reattachment point is found to be the most turbulent as the most pronounced peaks of RSS and TKE are occurring at this point. The quadrant analysis reveals that the RSS contribution of ejection events is higher for a lower submergence ratio, whereas the RSS contribution of the sweep events is higher for a higher submergence ratio. In conclusion, this study provides an in-depth understanding of the turbulent flow characteristics in the wake region of a bed-mounted horizontal circular pipe located on a fixed sand bed, especially the modification of the turbulence properties due to changes in the Reynolds number and submergence ratio.

Assessment of Turbulent Mixing Associated With Eddy‐Wave Coupling Based on Autonomous Observations From the Arctic Canada Basin

AbstractInteraction between mesoscale eddies and near‐inertial internal waves can contribute to enhanced turbulence mixing but quantitative knowledge from in situ observations is still lacking. This study reveals how eddy/near‐inertial wave interactions (ENIs) can affect the variability of turbulent mixing in the ice‐covered Canada Basin of the Arctic Ocean. We use data from five Ice‐Tethered Profiler with Velocity (ITP‐V) systems that autonomously obtained vertical profiles of horizontal velocity as well as temperature and salinity, which enabled quantification of ENI‐caused turbulent mixing using a fine‐scale parameterization. From the ITP‐V observations in 2013–2015, 67 anticyclones were detected, of which 90% had a deep core at 150–250 m depth. The remaining eddies had a shallow core, typically embedded in the Pacific Summer Water (PSW). Just over one third of the eddies showed evidence of ENI with enhanced near‐inertial internal wave amplitude (NIW) near the eddy cores. For these ENI cases, the parameterized turbulence dissipation rate was O (10−10–10−8 W kg−1), the larger estimates being several orders of magnitude greater than the background level. For the deep eddies, the ENI process can largely be accounted for by the classical theory, NIWs are trapped inside the negative relative vorticity core of anticyclones. For one shallow eddy, the NIW signal was greatest below the core. We postulate that a vertically elongated system of NIWs cannot be constrained vertically within such small‐cored eddies. It is also interpreted that the wave enhancement below the core was supported by the isopycnal slope near the PSW through its geostrophic shear.

A dip-corrected discharge estimation method for a river system

This work proposes a novel dip corrected velocity distribution model in combination with the entropy theory for discharge estimation in a braided river. A modified form of the dip correction factor is derived by considering the topographical complexities and applied for assessing velocity profiles in river cross-sections. The velocity profiles at different verticals are computed by employing Shanon's entropy theory. The depth-averaged velocities at different cross-sections are estimated from the computed vertical velocity profiles and substituted in the area-velocity method for the discharge calculation. The model is applied to two study areas, Majuli and Umananda of the Brahmaputra River, having both simple and braided sections. The validation of the model is performed using the observed discharge data available at the nearby gauge site for low flow condition. Results indicate that the integration of bed rugosity factor in dip corrected velocity distributions improves the accuracy of discharge estimations.

DYNAMICAL EFFECTS OF A HOT DISK ON THE DEVELOPMENT OF A NATURAL CONVECTION FLOW BETWEEN CYLINDRICAL WALLS

This study numerically investigates the problem of natural convection flow ina vertical cylinder. The importance of this issue mainly stems from thermal systems (e.g. chimneys, hot air generators, solar collectors, and many others.). Despite the numerous studies on the modeling of free convection flow between two perpendicular plates, there are very few studies that have investigated regarding the convective flow between two cylindrical walls. Therefore, the study is limited to vertical cylinders with different heating modes.The first configuration includes heated walls of thermosiphon flow in a cylindrical channel.The second configuration introduces a circular heat source at the channel entrance, and the third configuration includes an ended vertical cylinder with a heat source centered in the cylinder (zs = 0.04). The flow comparison from the three configurations demonstrates how the hot disk affects the flow from a dynamic point of view.Furthermore, details about the flow and dynamical fields can be obtained from the solution equation of the conservation of momentum and energy, considering the differences between the boundary conditions of the studied configurations. The study covers Rayleigh numbers and focuses on the effect of the cylinders geometry on the characteristic of the flow as well as dynamical and thermal field characteristics and variations in Nusselt number. The studied flow is natural convection, laminar, steady, two-dimensional, and incompressible flow. Solutions were obtained using a numerical model based on the finite volume method and the Navier–Stokes equations. The velocity–pressure coupling was resolved using the SIMPLER algorithm. The temperature and vertical velocity profiles of the flow showed the existence of a boundary layer regime along the heated channel wall without a heat source. The layer continued along the cylindrical wall with the introduction of the heat source at the channel inlet. However, introducing the heat source caused a considerable change in the flow structure at the channels central part.Calculations were performed for the channel aspect ratio R* = 0.2 and different Rayleigh numbers (Ra = 105, 107, 108, 109 and 1010). Numerical results included velocity, temperature, and Nusselt number profiles.

Methodology for multidimensional approximation of current velocity fields around offshore aquaculture installations

Consistent growth of the marine aquaculture industry over the past decades calls for potential deployments of large-scale aquaculture structures to produce finfish, shellfish and macroalgae in varying inshore and offshore environments. Numerical simulations for engineering design applications become more challenging with increase of scale since current velocity fields are no longer uniform, complicating accurate hydrodynamic load calculations. Horizontal and vertical velocity profiles in this case are spatially (depth and particular location within the deployment site) and temporary (date and time) dependent. Thus, proper representation of the current velocity field in numerical models becomes crucial for accurate predictions of structural performance of aquaculture installations. In this paper, an advanced multidimensional approximation method based on discrete current velocity data is formulated. The approach implies presenting the continuous current velocity function as a superposition of weighted radial basis functions extended by a linear polynomial. To address overfitting issues, the thin plate regularization is applied in the method. The approximation is then constrained in order to fit the velocity values on the domain boundaries. The method is implemented in finite element software Hydro-FE and its performance is compared to other approximation methods on the example of a kelp grow line deployed at the Wood Island research site, Maine, USA. It was found that the difference between regular (mean or linearly interpolated) velocity profiles and the velocity profiles approximated with the radial basis function method can reach up to 34–38 % in terms of grow line mooring tensions, and 6–18% in terms of grow line displacement.

On the Interaction between Moist Convection and Large-Scale Ascent in the Tropics

Abstract A simple steady-state model is constructed for the interaction between moist convection and large-scale ascent in the tropics. The model is based on a bulk-plume representation of convection, and it is coupled to the large-scale circulation using methods developed for limited-area numerical models that are consistent with the weak temperature gradient approximation. Given the midtropospheric temperature anomaly in the ascent region, the model solves for the profiles of temperature, relative humidity, and large-scale vertical velocity in this region, as well as the tropical-mean profiles of temperature and relative humidity, as a function of two parameters representing the importance of entrainment and condensate re-evaporation in moist convection. According to the simple model, the ascent region is characterized by an anomalously moist and stable free troposphere with a top-heavy vertical velocity profile that peaks in the upper troposphere. These results are shown to be consistent with simulations using a cloud system–resolving model in which the large-scale circulation is parameterized. Furthermore, it is shown that, due to the effect of entrainment on the tropospheric lapse rate, the predicted vertical velocity profile is more top-heavy than the first-baroclinic mode profile used in previous reduced-complexity models of tropical dynamics. The simple model therefore provides a framework to link mixing and microphysical processes in moist convection to the large-scale structure of the tropical overturning circulation.

Mixed convection in an insulated rectangular enclosure with two obstacles subject to various configurations using multi-relaxation-time lattice Boltzmann method

Mix convection heat transfer is studied in a rectangular lid-driven cavity comprising two obstacles. One of the obstacles is isothermally heated and the other is isothermally cooled. The mass flow and transfer are simulated, taking regular, incompressible, Newtonian, and viscid fluid using Numerical techniques. The fluid follows the Boussinesq approximation. The effect of pertinent parameters like Richardson number (Ri = 0.01, 0.1, 1, 5, 10, 100), Grashof number (), and Prandtl number (Pr = 0.71, 1, 7) is studied. Two aspect ratios of the lid-driven cavity are taken to study the fluid behavior. The effect of centric and eccentric locations of the heated blockages and the effect of different sizes of the obstruction on the fluid flow and thermal transportation are reported. and models of MRT-LBM are implemented for the simulation of flow and heat transfer regimes respectively. Also, Local and Average Nusselt numbers along the walls of a heated obstacle for different dimensionless parameters are calculated. The contour plots for the flow's horizontal and vertical velocity profiles are also discussed. The validation of our result is also checked by the grid independence test. The convergence of against different grid sizes shows that our code is valid.

Lateral Variation of Tidal Mixing Asymmetry and Its Impact on the Longitudinal Sediment Transport in Turbidity Maximum Zone of Salt Wedge Estuary

The lateral bathymetry in the estuary results in different degrees of tidal mixing asymmetry, which has significant impacts on the longitudinal sediment transport by changing the temporal variation of vertical eddy diffusion. This study focus on the lateral variation of tidal mixing asymmetry and longitudinal sediment transport at the landward boundary of turbidity maximum zone in the North Channel of Yangtze estuary, which is a typical time-dependent salt wedge estuary. A transect survey was carried out in December, 2018; five vertical profiles of flow velocity, salinity and suspended sediment concentration were simultaneously measured covering a spring tidal cycle. Analysis of the data revealed that, after the maximum ebb, the stratification in the main and secondary channel was stronger than that on the shoal. In the channel, during ebb tide, the stronger stratification restrained the turbulent mixing induced by vertical shear, vertical mixing during the flood tide was stronger than that during ebb tide and vertical mixing coefficients ranged from 0.06 to 0.12, showing regular tidal mixing asymmetry over a flood–ebb tidal cycle. Therefore, stronger eddy diffusion caused by vertical mixing resulted in higher suspended sediment concentrations during flood tide, the larger landward tidally averaged sediment transport rate was induced by tidal pumping with the transportation of flood tidal current and the net sediment transport over a flood–ebb tidal cycle in the channel was landward. Meanwhile, on the shoal, under the effect of vertical shear, the vertical mixing during flood tide was weaker than that during ebb tide; vertical mixing coefficients ranged from −0.27 to −0.02, showing the reversed tidal mixing asymmetry. Higher suspended sediment concentration was transported seaward by the ebb current, the tidally averaged sediment transport rate by both tidal pumping and advection was seaward and the net sediment transport was seaward. Furthermore, large river discharge increased the seaward advection sediment flux on the surface layer in the main channel, resulting in the seaward tidally averaged sediment flux. Strong resuspension increased the seaward advection sediment flux near the bottom in the main and secondary channel, resulting in the seaward tidally averaged sediment flux.

Densification of activated sludge for better settling performances: experimental characterization in batch column and model parameters calibration.

Conventional activated sludge (CAS) and densified sludge obtained using hydro-cyclone selective wasting were compared at a full-scale water resources recovery facility. The densified tested sludge, containing around 30-50% of aerobic granules, showed enhanced settleability with low and stable sludge volume index (SVI) compared to CAS, which suffered recurrent filamentous bulking. Further in-depth batch settling tests were carried out using a 40 cm diameter column fitted with ultrasonic transducers to monitor both sludge blanket height and vertical velocity profiles. Hindered settling and compression parameters were calibrated from the experiment for latter modelling use. Test sludge displayed more than doubled settling velocities compared to CAS, with hindered settling velocities remaining >3 m·h-1 even at high solids concentrations of 6.85 g·L-1. The compression regime was attained at much higher critical concentration for the test sludge. It also displayed enhanced thickening properties, with concentrations obtained after 30 min of settling being 20.9 and 8.5 g·L-1 respectively for test and control sludge. This allows for a substantial reduction of recirculation rates in practice. These results open perspectives in optimizing existing plant operation as well as clarifier design and modelling using densified sludge.

Validation of near‐shore wind measurements using a dual scanning light detection and ranging system

AbstractThis paper reports results from a 2‐month validation campaign of near‐shore wind measurements taken by a dual scanning light detection and ranging (LiDAR) system at a coastal site in Japan. A meteorological mast and a vertical profiling LiDAR device were deployed at an offshore research station approximately 1.5 km from the coast. Offshore winds at heights of 66, 120, and 180 m above sea level were observed by the scanning LiDAR system. Comparisons with a sonic anemometer found that the radial velocities had a coefficient of determination of more than 0.99 without unreasonable bias. The accuracy of 10‐min mean wind speeds and directions was then evaluated. The 10‐min values from the dual scanning LiDAR system were accurate enough to satisfy the acceptance criteria used for floating LiDAR systems. In addition, the vertical velocity and direction profiles from the dual scanning LiDAR system were compared with those from a vertical profiling LiDAR device. The performance of turbulence intensity (TI) measurements was also evaluated. Although the TIs from the dual scanning LiDAR system were slightly lower than those from the sonic anemometer, they were equivalent to those from the cup anemometers. This investigation concluded that the near‐shore wind measurements using the dual scanning LiDAR system are beneficial for reducing near‐shore wind measurement costs, because the system can measure not only 10‐min wind speed and direction, but also parameters associated with assessing site‐specific conditions without installing offshore meteorological masts.

Experimental investigation of the near-surface flow dynamics in downburst-like impinging jets

Downbursts are strong downdrafts that originate from thunderstorm clouds and create vigorous radial outflows upon hitting the ground. This study is part of the comprehensive experimental research on downburst outflows produced as large-scale impinging jets in the WindEEE Dome simulator at Western University, Canada. The 2800 tests carried out form the largest database of experimental measurements on downburst winds developed thus far, which is made available to the public in its whole and described in detail in a complementary study. Therefore, the current manuscript merely focuses on the data post-processing outcomes and interpretation of results from a selected subset of measurements. Impinging jets are here simulated as transient phenomena in which velocity time series are characterized by a sudden ramp-up of velocity, followed by the velocity peak, a short statistically stationary region, and the final velocity slowdown, as it is expected to occur in the actual downbursts. A dominant velocity peak that was systematically observed in all velocity records is associated with the radial advection of the primary vortex in the outflow. Depending on the radial distance from the downdraft, the primary vortex was sometimes preceded by a secondary, much smaller, vortex close to the surface. Vertical profiles of mean velocity and turbulence intensity are for the first time characterized through the extent of a downburst-like event in the spatiotemporal domain. Particularly, these profiles rapidly change in relation to the passage of the primary vortex and consequent variation of the surface layer thickness. This study lays out a foundation for an experimental model of non-stationary downburst outflows to come.

Experimental study of the shear flow effect on tidal turbine blade loading variation

Tidal turbine arrays are planed to be installed in areas with strong currents where the flow can often be sheared throughout the water column. To study the shear flow effects on tidal turbine, four vertical velocity profiles are generated in a flume tank and are imposed to a three-bladed horizontal axis turbine model. Results show that the sheared velocity profiles do not impact the turbine average performance but are responsible for an increase of blade root streamwise load variations. Blade root streamwise load is moreover linked to the turbine rotational frequency and its harmonics. The velocity perceived by the blades during their rotation is estimated over the rotor area and is compared to the angular phase average of the streamwise load measured on the blades. The phase average of the load and the velocity perceived by the blades are highly correlated even if a varying phase lag has been noticed between these two quantities. This phase lag is dependent on the rotational speed of the turbine, on the incoming flow shear, and is probably caused by the turbine induction effects. This experimental study is a first step to understand the effect of shear velocity profiles on tidal turbines better.

Uncovering the Large-Scale Meteorology That Drives Continental, Shallow, Green Cumulus Through Supervised Classification.

One of the major sources of uncertainty in climate prediction results from the limitations in representing shallow cumulus (Cu) in models. Recently, a class of continental shallow convective Cu was shown to share distinct morphological properties and to emerge globally mostly over forests and vegetated areas, thus named greenCu. Using machine‐learning supervised classification, we identify greenCu fields over three regions, from the tropics to mid‐ and higher‐latitudes, and establish a novel satellite‐based data set called greenCuDb, consisting of 1° × 1° sized, high‐resolution MODIS images. Using greenCuDb in conjunction with ERA5 reanalysis data, we create greenCu composites for different regions and reveal that greenCu are driven by similar large‐scale meteorological conditions, regardless of their geographical locations throughout the world's continents. These conditions include distinct profiles of temperature, humidity and large‐scale vertical velocity. The boundary layer is anomalously warm and moderately humid, and is accompanied by a strong large‐scale subsidence in the free troposphere.

Study on the Methods to Estimate the Bed Shear Stresses in Yangtze Estuary

High spatial and temporal current resolution velocities were measured by use of an acoustic Doppler velocimeter (ADV) in the tidal bottom layer of North Passage Deep water Navigational Channel (DNC) of Yangtze Estuary in China. And the vertical profiles of mean velocity were measured by using a pulse-coherent acoustic Doppler profiler (PC-ADP). The measured data show the vertical profiles of mean velocity are almost logarithmic. For discussing, the turbulent kinetic energy (TKE) method based on the velocity for ADVs-based is chosen and a new logarithmic profile (LP) method ignoring the influence of complex variation of the parameter Z 0 is suggested to estimate the bed shear stresses respectively. The calculated results show that the bed shear stresses estimated by LP method are larger than the ones estimated by TKE method mostly in Yangtze estuary. At the moment of ebb peak, the maximum error can be about twice occurring and the error of ebb tide is almost greater than the one of flood tide. These phenomena are explained in this study by the deduction of formula for steady and unsteady flow. It is concluded that the vertical logarithmic profile of velocities will be influenced by unsteady flow and there is not the same bed shear stress even if there is the same logarithmic velocity profile in vertical. Generally, this has led to a necessary adjustment of the drag coefficient Cd of steady flow in flow model to avoid overestimating the bed stress for unsteady flow in estuary based on the observed data.

Self-similar velocity and solid fraction profiles in silos with eccentrically located outlets

We examine the gravity-induced flow of dry and cohesionless granular media through an outlet placed eccentrically in a planar silo, employing computations based on a soft-sphere discrete element method. The vertical velocity profiles, measured at the outlet, are self-similar when the eccentric position of an outlet is given in terms of the smallest gap (s) between its corners and the lateral walls. On the other hand, the self-similarity of vertical velocity does not always hold for all eccentricities (e) given by the distance between the centers of an outlet and the silo base, which is a typical metric of eccentricity. For the former measure of the eccentric location, the flow conditions are observed to be similar for different outlet sizes. In contrast, we observe, the latter leads to differing flow patterns for the highest eccentricity wherein the largest outlet touches the sidewall and the rest are located at a distance. The effect of using s on the self-similarity of solid fraction profiles is observed to be minor in comparison to e. This study establishes the importance of s compared to e from the viewpoint of the self-similarity of the vertical velocity profiles at the outlet and generalizes the notion of the scaling of velocity and solid fraction reported by Janda et al. [“Flow rate of particles through apertures obtained from self-similar density and velocity profiles,” Phys. Rev. Lett. 108, 248001 (2012)] in a silo with a centric exit to the one with eccentric granular discharge. Finally, we propose expressions for the scaled vertical velocity and solid fraction in terms of s.