Flow Curvature Research Articles

Study of the flow around cofferdams constructed in running water through computational model

ABSTRACT River closure to provide a dry area for the construction of the works in the river bed must be carefully performed because a failure can lead to serious and costly delays. By means of a computational approach, using the FLOW 3D® software, this paper studies the hydraulic behavior of the flow around a cofferdam constructed in running water. The computational model was validated using results of an experimental investigation. Then the effect of changing the cofferdam configuration on the flow characteristics in this region was analyzed. This study showed that the computational model adequately reproduces this type of flow and that changing the configuration of the cofferdam: increasing the width of the crest or decreasing the embankment slope affects the flow curvature and positively affects the river closure process.

LSPIV Measurements of Two‐Dimensional Flow Structure in Streams Using Small Unmanned Aerial Systems: 2. Hydrodynamic Mapping at River Confluences

AbstractAlthough past field work at stream confluences has relied on velocity information at specific cross sections to examine flow structure, detailed characterizations of spatial and temporal variations in the hydrodynamics of confluences are lacking. This study uses large‐scale particle image velocimetry (LSPIV) obtained from small unmanned aerial systems (sUAS), a method evaluated in a companion paper, to map surficial patterns of mean flow and turbulent structures at two small stream confluences in unprecedented levels of detail. LSPIV reveals two‐dimensional flow patterns within different hydrodynamic zones in each confluence as well as similarities and differences in hydrodynamic conditions between the confluences. As expected based on extant conceptual models of confluence hydrodynamics, the spatial arrangement of characteristic hydrodynamic zones varies with confluence planform geometry and with changes in incoming flow conditions. However, local morphological features, such as bars and irregularities in channel banks, also exert a strong influence on the spatial structure of flow and in some cases influence confluence hydrodynamics to an extent comparable to changes in incoming flow conditions. The usefulness of sUAS‐based LSPIV is demonstrated by the correspondence between patterns of flow curvature revealed by this method and patterns of helical motion documented at cross sections within the confluences using acoustic Doppler velocimetry. The method can also be used to characterize the structure of turbulent vortices within the mixing interface between confluent streams under appropriate conditions. Hydrodynamic mapping using sUAS‐based LSPIV enriches the interpretation of traditional in‐stream velocity data acquired in the field and provides information on surface velocity patterns in rivers at a resolution similar to that of numerical models.

Extra Strain Rates in an unsteady spilling breaking wave

We analyze the extra strain rates that characterize a curved, thin mixing layer induced at an unsteady spilling breaker. We focus on the flow curvature, which induces some extra rates of strain that should be accounted for in algebraic-type turbulence closures. The comparison between the analytical formulation proposed by Brocchini and co-workers for a single-phase turbulent thin layer of fluid and the data, obtained from a Particle Image Velocimetry (PIV) dedicated experimental program, reveals that the order of magnitude of the extra rates of strain induced by the streamline curvature, is comparable with that of the simple shear. This differs from what observed for the geometric curvature terms and from what occurs at hydraulic jumps, typically used to model steady breakers.

Isolator Dynamics During Unstart of a Dual-Mode Scramjet

The phenomenology of unstart in a dual-mode ethylene-fueled scramjet is studied in the presence of inflow distortion using carefully calibrated unsteady Reynolds-averaged Navier–Stokes computations with an emphasis on understanding the large-scale transients over the length scale of the flowpath. The computational approach is validated with experimental data for two combustor operating states that bound the dual-mode and unstart conditions. Unstart is induced via an imposed fuel-staging transient that emulates the experiments. Inlet distortion introduces three-dimensional effects in the isolator, which primarily manifest in the nature of side wall separation and flow curvature; however, localized regions of heat release are shown to contribute to unstart-inducing side wall separation. A wall-pressure-based metric used to track shock-train motion in experiments is adapted to identify a period of constant shock-train speed and an incipient unstart condition. During the constant-velocity phase, separation on the upper wall modulates the supersonic core, resulting in a change from an oblique to a normal-like shock-train configuration. The incipient unstart state precedes the ejection of the shock train from the isolator, which is suggestive of a precursor to unstart. This metric highlights the importance of the side wall corner region during the unstart process and complements other studies of three-dimensional effects in similar isolator geometries.

CFD simulation of swirling flow induced by twist vanes in a rod bundle

Abstract Swirling flow induced by the twist vanes can enhance the heat transfer in the rod-bundle fuel assembly. In order to investigate accuracy of the k-e models in predicting the swirling flow in a rod bundle subchannel, the CFD simulations with the standard and realizable k-e model are benchmarked with In et al.’s experiment. The nonlinear closure models are utilized with the standard k-e model to account for the curved and rotational flow, while the curvature correction model is employed in the realizable k-e model. Comparison with the experiment indicates that the CFD simulations predict the relatively large core region of swirling flow. Utilization of the nonlinear closure models in the standard k-e model leads to the larger initial angular momentum. The curvature correction in the realizable k-e model reduces the initial angular momentum, but it does not affect the decay rate, which indicates that the curvature correction is effective near the twist vanes where the flow curvature is strong. The decay rate of swirling flow is generally overestimated by all the models. The cross-flow velocity profile in the gap is affected by prediction of swirling flow separation from rod surface. The cubic and quadratic closure model can improve turbulence modelling in the core of swirling flow, especially near the spacer, where the linear closure models significantly underestimate the production of turbulence. However, in the further downstream all the models underestimate the turbulence intensity in the swirling core, as a consequence of low-frequency large-scale flow structure in the core region. Underestimation of turbulence in the annular and wall region will result in the underestimation of wall heat transfer and inter-subchannel mixing.

A dynamic stall model for analysis of cross-flow turbines using discrete vortex methods

Abstract Cross-flow turbine blades operate in an unsteady environment over large ranges of angle of attack and Reynolds number, often enduring dynamic stall. The hydrodynamics are further complicated because the circular orbit of the blades changes their effective curvature. In order to address these technical challenges with modeling cross-flow turbines, this article presents a novel dynamic stall model with flow curvature correction. The dynamic stall model extends Beddoes-Leishman dynamic stall theory, including several effects such as proper asymptotic behavior at large (∼90°) angles of attack, influence of reduced-pitch rate on the stall angle, dynamics of the flow separation point, and changes in effective camber due to flow curvature. Further, the model enables rapid hydrodynamic analysis of cross-flow turbines using free vortex methods. Important design parameters such as blade thickness and camber are explicitly accounted for in the model, which enables parametric study of turbine configurations and therefore makes the model useful for system-level turbine optimization. Numerical predictions are validated by experimental data for several cases, including ranges of blade profile, toe angle, solidity, and tip speed ratio.

Development of a BEM-CFD tool for Vertical Axis Wind Turbines based on the Actuator Disk Model

The present work focuses on the numerical simulation of Vertical Axis Wind Turbines by means of an “in-house” BEM-based User Defined Function to be used 39ith the CFD code ANSYS Fluent. Typical VAWT unsteady and 3D phenomena, such as dynamic stall, flow curvature and tip losses, are taken into account by original and literature-based sub-models. The presence of the blades is mimicked by replacing them with suitable momentum sources.For the present work, the Actuator Cylinder Model has been employed. 3D analysis, of a SANDIA rotor, are carried out in order to assess the accuracy of our model against numerical simulations and experimental data. The current User Defined Function is able to give a satisfactory agreement with the reference cases especially from a qualitative point of view, with a significant computational time reduction to a factor of 10 compared to the case with the moving bodies. A typical wake behavior can be noticed in our simulations even though its recovery is strongly influenced by the lack of turbulence inherent to the chosen actuator model. The torque and the power coefficient of the turbines are also analyzed and compared against the reference cases, finding a remarkable agreement.The model has been successfully applied to predict the transient aerodynamic loads of an offshore 5MW troposkein turbine subjected to the pitching motion of its platform. The operating conditions have been chosen in order to allow a qualitative comparison with a floating 5MW horizontal axis turbine which performance under pitching motion is available in literature.

A Fluidic Culture Platform for Spatially Patterned Cell Growth, Differentiation, and Cocultures.

Stem cell cultures within perfusion bioreactors, while efficient in obtaining cell numbers, often lack the similarity to native tissues and consequently cell phenotype. We develop a three-dimensional (3D)-printed fluidic chamber for dynamic stem cell culture, with emphasis on control over flow and substrate curvature in a 3D environment, two physiologic features of native tissues. The chamber geometry, consisting of an array of vertical cylindrical pillars, facilitates actin-mediated localization of human mesenchymal stem cells (hMSCs) within ∼200 μm distance from the pillars, enabling spatial patterning of hMSCs and endothelial cells in cocultures and subsequent modulation of calcium signaling between these two essential cell types in the bone marrow microenvironment. Flow-enhanced osteogenic differentiation of hMSCs in growth media imposes spatial variations of alkaline phosphatase expression, which positively correlates with local shear stress. Proliferation of hMSCs is maintained within the chamber, exceeding the cell expansion in conventional static culture. The capability to manipulate cell spatial patterning, differentiation, and 3D tissue formation through geometry and flow demonstrates the culture chamber's relevant chemomechanical cues in stem cell microenvironments, thus providing an easy-to-implement tool to study interactions among substrate curvature, shear stress, and intracellular actin machinery in the tissue-engineered construct.

Aerodynamic modeling methods for a large-scale vertical axis wind turbine: A comparative study

Abstract Vertical axis wind turbines (VAWTs) are experiencing a renewed interest for large-scale offshore wind energy generation. However, the three-dimensional (3D) modeling of VAWT aerodynamics is a challenging task using computational fluid dynamics (CFD), owing to the high computational costs entailed. To alleviate this computational burden and improve design process efficiency, an alternative low-order model (LOM) is presented that incorporates key VAWT aerodynamic effects. These coupled sub-models account for the influence of dynamic stall, tower shadow, parasitic drag, flow curvature and finite blade effects. A two-step approach is adopted to investigate two-dimensional (2D) and 3D VAWT aerodynamics separately with experimental data. A CFD model was created and both modeling strategies were compared. The LOM showed good agreement with the CFD model and the measurements with a low computational cost requirement. The CFD results identified that as the tip-speed ratio (TSR) was increased, the tower's downwind wake became increasingly more skewed. Finally, both the LOM and the CFD model were employed in predicting the VAWT aerodynamic efficiency. It was established 3D effects must be included to provide an accurate prediction of VAWT performance especially at high TSRs. For VAWT analysts, modeling recommendations and limitations are discussed regarding the LOM.

Laminar flow and heat transfer in U-bends: The effect of secondary flows in ducts with partial and full curvature

The present study numerically explores the flow and heat transfer in “U-type” curved pipes of either partial or full curvature, which are often used as integral parts of heat exchangers and heat sinks in industrial applications such as solar thermal systems, among many others. Specifically, the case of a high-Prandtl-number Newtonian fluid (thermal oil) in laminar forced convection inside partially and fully curved “U-bends” is investigated, in order to illustrate the effect of the generated secondary flows on the various local and global scales. The 3D steady-state simulations are performed using the free and open source computational fluid dynamics software “OpenFOAM”. The analysis of the computational results is initially based on data at selected characteristic locations of interest; they are properly established and further explored by extracting internal field variables, in the form of 2D contours of quantities of interest, such as temperature and vorticity. A parametric study on the flow rate and curvature impact, namely in terms of increasing Re and De numbers (Re = 100, 1000, 2000), on the heat transfer process inside the U-bends is conducted comparatively for both geometries. The presence of secondary flows is confirmed and the differences between the geometries under investigation are visually illustrated. For moderate and high Re numbers, the presence of multiple counter-rotating secondary cells is generally observed, while the partially curved U-bend (“composite”) displays a more complex flow topology. This behavior is projected on heat transfer through the examination of temperature distribution on inner and outer arcs of both geometries. It is shown that the composite bend causes an abrupt decrease and oscillations on temperature distributions, which are found to be related with phenomena like flow impingement, separation and re-attachment.The Pr number effect is illustrated through a comparison with a lower Pr fluid and its impact is demonstrated both inside and downstream of the U-bends. The averaged Nusselt distribution along the length of both curved ducts further highlights the impact of these phenomena on local heat transfer and provides initial evidence in favor of the composite bend. The overall performance of the investigated curved geometries is compared based on a “performance factor” criterion and a superior performance of the composite U-bend is further established, attaining a value of almost 45% for higher flow rates. Finally, the effect of each U-bend on the straight pipe downstream of their respective exit is quantified. High divergence from the regular “combined hydrodynamic and thermal entrance flow” is found for the forced convection inside the downstream pipe. A characteristic overshoot of the downstream-to-upstream ratio Nusselt number is found for moderate and higher flow rates at small lengths from entrance (z*). The partially curved U-bend downstream effect seems to be greater for the investigated cases of Re = 100, 2000, while the fully curved outperforms the composite for the moderate Re case (Re = 1000). The source of this discrepancy cannot be clearly identified through this work and further investigation is needed on this matter. All in all, the simulations performed here show that partially curved U-bends can potentially be advantageous, in terms of performance, compared to the standard fully-curved pipes for laminar forced convection applications. These results can provide a good starting point for the optimal design of such ducts for several heat transfer operations.

Identification of flow classes in the wake of a simplified truck model depending on the underbody velocity

An experimental study of the near wake of a simplified truck model with an aspect ratio between the height and the width greater than one is presented. The influence of the underbody velocity at a constant ground clearance height is considered. The evolution of the model base pressure and of the near wake as a function of the underbody velocity permits to identify four classes of flow. For large values of underbody velocity, typically above 60% of the free stream velocity, the near-wake structure is similar to what obtained in bluff-body characterizations where the underbody flow momentum is sufficient to prevent its detachment from the ground. For smaller values of underbody velocity, of particular interest when considering real truck applications, base pressure mean value and near wake characteristics strongly depend on the underbody velocity; three different classes are defined through the values of time-averaged rear pressure as well as a qualitative analysis of the near-wake structure. Quantitatively, a momentum budget in the near-wake together with the characterization of the curvature of the underbody flow near the model end provide ad-hoc indicators for discriminating between the different flow classes.

Upper bound analysis of differential velocity sideways extrusion process for curved profiles using a fan-shaped flow line model

An analytical model for predicting the shapes of rectangular bars with variable curvatures along their lengths through a novel forming method, differential velocity sideways extrusion (DVSE), previously proposed by the authors, has been developed on the basis of the upper bound method. A new flow line function was presented to describe its deformation field. The plastic deformation zone (PDZ) was assumed to be fan-shaped, where the trajectory of the material flow within the PDZ had an elliptic shape. The proposed continuous flow line function was validated using finite element simulations. The flow patterns, extrusion pressure, curvature, and effective strain predicted by the analytical solutions agreed well with modelling results. Compared to the classical discontinuous simple shear model of channel angular extrusion (CAE) with a 90° die, the new approach was shown to predict the effective strain more closely.

A Global Climatology of Tropospheric Inertial Instability

Abstract A climatology of tropospheric inertial instability is constructed using the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) at 250, 500, and 850 hPa. For each level, two criteria are used. The first criterion is the traditional criterion of absolute vorticity that is opposite in sign to the local Coriolis parameter. The second criterion, referred to as the gradient criterion, is the traditional criterion with an added term incorporating flow curvature. Both criteria show that instability, on all pressure levels, occurs most frequently in the tropics and decreases toward the poles. Compared to the traditional criterion, the gradient criterion diagnoses instability much more frequently outside the tropics and less frequently near the equator. The global distribution of inertial instability also shows many local maxima in the occurrence of instability. A sample of these local maxima is investigated further by constructing composites of the synoptic-scale flow associated with instability. The composites show that instability occurs in association with cross-equatorial flow in the North Atlantic Ocean, the Somali jet, tip jets off northern Madagascar, the western Pacific subtropical high, gap winds across Central America, upper-level ridging over western North America, and the North Atlantic polar jet. Furthermore, relatively long-lived synoptic-scale regions of instability are found within the midlatitude jet streams.

Analysis of Vaneless Diffuser Stall Instability in a Centrifugal Compressor

Numerical simulations based on the large eddy simulation approach were conducted with the aim to explore vaneless diffuser rotating stall instability in a centrifugal compressor. The effect of the impeller blade passage was included as an inlet boundary condition with sufficiently low flow angle relative to the tangent to provoke the instability and cause circulation in the diffuser core flow. Flow quantities, velocity and pressure, were extracted to accumulate statistics for calculating mean velocity and mean Reynolds stresses in the wall-to-wall direction. The paper focuses on the assessment of the complex response of the system to the velocity perturbations imposed, the resulting pressure gradient and flow curvature effects.

On a Comprehensive Topological Analysis of Moore Spiegel Attractor

A topological analysis of the attractor associated with the Moore–Spiegel nonlinear system is performed, following the basic idea laid down by Gilmore and Lefranc (2002, The Topology of Chaos, Wiley, Hoboken, NJ). Starting with the usual fixed point analysis and their stability, we proceed to study in detail the process of chaotic orbit extraction with the help of close return map. This is then used to construct the symbolic dynamics associated with it, which is helpful in understanding the sequential change taking place inside the attractor. In the next part, we show how to characterize the evolution of the attractor from its birth to the crisis by finding out the homoclinic orbit and the corresponding unstable manifold. In the concluding part of the paper, we show how all the pertinent information of the attractor can be encoded in the template, leading to the explicit realization of linking numbers and the relative rotation rates. In the concluding section, we have touched upon a new approach to chaotic dynamics, using the flow curvature manifold to display the relative positioning of the attractor in relation to the fixed points and the null lines.

Flow derivatives and curvatures for a normal shock

A detached bow shock wave is strongest where it is normal to the upstream velocity. While the jump conditions across the shock are straightforward, many properties, such as the shock’s curvatures and derivatives of the pressure, along and normal to a normal shock, are indeterminate. A novel procedure is introduced for resolving the indeterminacy when the unsteady flow is three-dimensional and the upstream velocity may be nonuniform. Utilizing this procedure, normal shock relations are provided for the nonunique orientation of the flow plane and the corresponding shock’s curvatures and, e.g., the downstream normal derivatives of the pressure and the velocity components. These algebraic relations explicitly show the dependence of these parameters on the shock’s shape and the upstream velocity gradient. A simple relation, valid only for a normal shock, is obtained for the average curvatures. Results are also obtained when the shock is an elliptic paraboloid shock. These derivatives are both simple and proportional to the average curvature.

Experimental investigation of Görtler vortices in hypersonic ramp flows

A sharp leading-edge ramp model with 15°, 20°, and 25° ramp angles is experimentally investigated at a freestream Mach number 7.7 and a unit Reynolds number 4.2 × 106 m−1 in the Aachen Shock Tunnel TH2. The objective of this paper is to analyze Gortler vortices in terms of shear layer length, flow curvature, and vortex related parameters. The spanwise heat flux variation caused by it and the streamwise heat flux enhancement during its tenure are also studied. Thermocouples, pressure sensors, schlieren imagery, and infrared imaging are used for the investigation. The boundary layer on the flat plate until separation is laminar. An important outcome is that the arc length at reattachment is constant irrespective of the ramp angle. Characteristic boundary layer thicknesses at different Mach number show that the momentum thickness is insensitive to compressibility and is used to determine the Gortler number. A model is presented to determine the Gortler number in terms of ramp angle and a constant based on separation angle, arc length, momentum thickness, and Reynolds number. The half of the vortex wavelength is equal to the boundary layer thickness just before reattachment. The length scale required for breakdown of Gortler vortices decreases with rising ramp angle and is analogous to peak heating length. The streamwise heat flux enhancement occurs during the tenure of Gortler vortices and the enhancement rises with ramp angle. Although the visibility of Gortler vortices through temperature variation is distinct, the spanwise heat flux variation is not too high. Moreover, the spanwise heat flux variation rises marginally with ramp angle.

Experimental Investigation and Modeling of Catheter Temperature in Atherectomy

Atherectomy, which is generally featured by a high-speed grinding, is a common intervention process to treat atherosclerosis and simultaneously restore the blood flow. The friction, generated among the rotational drive shaft, the stationary sheath, and guidewire in the catheter, usually causes the blood temperature rise, which may result in the thermal damage to the artery tissue. This paper is devoted to investigating the catheter temperature in atherectomy. In this study, experiments were conducted to investigate the effects of rotational speed, saline flow, and catheter curvature on the catheter temperature rise. A thermal model to calculate the temporal and spatial distribution of catheter temperature rise was developed to predict the potential thermal damage and the safety interventional parameters in atherectomy. The catheter temperature increases with the time, the length of the catheter, and rotational speed. The curvature induced catheter temperature rise is less than 0.3 °C, which is negligible. Temperature rise under the clinical condition can potentially reach 12 °C at 175,000 rpm. The proposed thermal model can be used to predict the saline temperature within a variation of 0.4 °C. The heat generated in the catheter may cause potential thermal damage to the blood and artery tissues in atherectomy. Furthermore, the safety process time is less than 6 s and safety minimum saline flow rate is 33 ml/min under all recommended rotational speeds. Increasing the saline flow rate is a method to reduce the temperature rise effectively and lower the thermal damage to blood and tissues.

Effect of nonuniform electric field on the electrohydrodynamic motion of a drop in Poiseuille flow

The effect of a nonuniform electric field on the electrohydrodynamic motion of a leaky dielectric suspended drop in the presence of background Poiseuille flow is investigated analytically. Considering the nonuniform electric field to be a linear combination of uniform and quadrupole fields, the velocity of a force-free drop positioned at the flow centerline is obtained. The drop velocity is strongly influenced by the surface charge distribution and drop shape. In the Stokes flow limit, we employ an asymptotic method considering weak surface charge convection and small shape deformation. The present study shows the importance of type of nonuniform electric field (converging or diverging in the direction of the Poiseuille flow), strength of the electric field relative to the Poiseuille flow, and material property ratios on the magnitude and direction of drop motion in the presence of flow curvature. In the presence of a nonuniform electric field, the flow curvature can increase or decrease the drop velocity as compared with a uniform flow case. The converging electric field always drives a perfectly conducting drop in the direction of the Poiseuille flow with increased velocity, while the diverging electric field can drive the drop in either direction, depending on the relative strength of the applied electric field. Shape deformation increases the velocity of a perfectly conducting drop in the converging electric field, while shape deformation increases/decreases the velocity magnitude of a perfectly conducting drop in the diverging electric field. The converging electric field always drives a perfectly dielectric drop in the direction of the Poiseuille flow with increased (or decreased) velocity when the drop phase permittivity is greater (or less) than the medium phase permittivity. The diverging electric field can move a perfectly dielectric drop in either direction, depending on the strength of the electric field relative to the Poiseuille flow and drop-to-medium permittivity ratio. Shape deformation increases the velocity magnitude of a perfectly dielectric drop for larger permittivity ratios. For leaky dielectric drops, both surface convection and shape deformation can increase or decrease the drop velocity in nonuniform electric field, depending on the electrohydrodynamic properties of the drop and the suspending medium.

A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. Recently, a data-driven turbulence modeling approach via machine learning has been proposed to predict the Reynolds stress anisotropy of a given flow based on high fidelity data from closely related flows. In this work, the closeness of different flows is investigated to assess the prediction confidence a priori. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. The flow over periodic hills at Re=10595 is used as the test set and seven flows with different configurations are individually used as training set. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of the data source and to assess the prediction confidence for data-driven turbulence modeling.