Distribution Of Streamwise Velocity Research Articles

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

Experiments investigation on atomization characteristics of a liquid jet in a supersonic combustor

The atomization characteristics of a liquid jet in a supersonic combustor were studied experimentally for the first time. A phase doppler anemometry (PDA) system was utilized for the measurement of droplets properties along the cross-sectional area of spray plumes inside the cavity. The results were obtained under the inflow conditions of Ma = 2.0 supersonic crossflow with a stagnation pressure of 0.55 MPa and a stagnation temperature of 300 K. The size and velocity distribution of droplet inside the cavity are obtained based on the PDA measurements. It was found that the Sauter Mean Diameter (SMD) distribution of droplets inside the cavity ranged from 30 to 55 μm. The average streamwise velocity ranged from −20 to 150 m/s and the average vertical velocity ranged from −20 to 30 m/s. Large droplets distribute in the central area of the cavity. Small droplets spread around the central area of the bottom and sidewall areas of the cavity. The area near the sidewall may be an ideal ignition location due to the lower SMD and velocity of droplets. The time-averaged motion trend of droplets in the cavity is proposed experimentally based on the streamwise and spanwise velocity distribution profiles of droplets. The presence of a recirculation zone within the cavity is confirmed. The recirculation area inside the cavity is mainly distributed in the front half of the cavity. The droplets in the cavity show a good tracking performance. With the effect of the airflow, the droplets in the top area of the cavity move toward the bottom and rear wall of the cavity. In addition, the droplets in the middle and bottom area of the cavity move toward the front wall of the cavity especially for droplets near the sidewall. These universal curves can potentially be used for the modeling of a liquid jet in a supersonic combustor.

Diffusion performance of lobed jet in the developed states consistent across temporally and spatially developing flows

This study demonstrates that temporally developing lobed jets can qualitatively reproduce the diffusion performance in the fully developed states of spatially developing lobed jets in laboratory experiments. The jet exit geometries, Reynolds number [Formula: see text], and turbulence intensity (3% of mean velocity) were set to be the same across the temporally and spatially developing jets. Four types of jet flows were tested, one being a round jet and three being lobed jets with different numbers or curvatures of lobes, referred to as 6L, 6S, and 3L, respectively. The half-width of the mean streamwise velocity distributions and centerline mean streamwise velocity of the four jets in the developed states were consistent between the numerical simulations and experiments. The round jet displayed the highest diffusion performance, followed by 3L, while 6L and 6S were the smallest and were comparable with each other. Despite such consistency in the developed states, the diffusion performance and formation of the streamwise swirling flows did not agree between the numerical and experimental results. These results suggest that unique large-scale structures corresponding to the initial conditions are reproduced in temporally developing jets, which is in good agreement with the spatially developing lobed jets. Therefore, the current study demonstrated that the temporally developing simulations can reproduce similar diffusion processes to those of the spatially developing ones.

Velocity Distribution and Bed Profile Variation for Inbank Flow in a Meandering Channel

Meandering is relatively a common river planform in Malaysia. The sediments transported along the channel due to erosion and deposition are the main reason of meandering river formation. This resulted when the outer bend experienced higher velocities while lower velocities occurred at the inner bend which resulting in sedimentation processes along the river. Hydraulic characteristics in meandering river are considerably more complex and unique as compared to the straight river. Therefore, an experimental investigation was conducted in the Hydraulic Laboratory, UTM Johor Bahru to enhance the understanding of the hydraulics behaviour and morphological changes of an inbank flow in a sand bed meandering channel. Flow classification, streamwise velocity distribution and bed profile changes are addressed in this paper. The findings prevailed that the maximum velocity reduced up to 10% from the upstream to downstream due to the resistance from the meanders. Furthermore, erosion and deposition processes along the channel highly influenced by the velocity distribution. The maximum velocity shifted toward the outer and decreased at the inner of the meander resulting in the deposition and erosion. Higher erosion and deposition were observed at the outer and inner bends, respectively during high flow discharge.

A wall-modeled hybrid RANS/LES model for flow around circular cylinder with coherent structures in subcritical Reynolds number regions

In the present paper, a hybrid RANS/LES model with the wall-modelled LES capability (called WM-HRL model) is developed to perform the high-fidelity CFD simulation investigation for complex flow phenomena around a bluff body with coherent structure in subcritical Reynolds number region. The proposed method can achieve a fast and seamless transition from RANS to LES through a filter parameter <i>r</i><sub>k</sub> which is only related to the space resolution capability of the local grid system for various turbulent scales. Furthermore, the boundary positions of the transition region from RANS to LES, as well as the resolving capabilities for the turbulent kinetic energy in the three regions, i.e. RANS, LES and transition region, can be preset by two guide index parameters <i>nr</i><sub>k1-Q</sub> and <i>nr</i><sub>k2-Q</sub>. Through a series of numerical simulations of the flow around a circular cylinder at Reynolds number <i>Re</i> = 3900, the combination conditions are obtained for such two guide index parameters <i>nr</i><sub>k1-Q</sub> and <i>nr</i><sub>k2-Q</sub> that have the capability of high-fidelity resolving and capturing temporally- and spatially-developing coherent structures for such complex three-dimensional flows around such a circular cylinder. The results demonstrate that the new WM-HRL model is capable of accurately resolving and capturing the fine spectral structures of the small-scale Kelvin-Helmholtz instability in the shear layer for flow around such a circular cylinder. Furthermore, under a consistent grid system, through different combinations of these two guide index parameters <i>r</i><sub>k1</sub> and <i>r</i><sub>k2</sub>, the fine structuresof the recirculation zones with two different lengths and the U-shaped and V-shaped distribution of the average stream-wise velocity in the cylinder near the wake can also be obtained.

Numerical study of solution structure and nonlinear behavior of Dean flow with vortex structure in a bending square duct

Fluid flow and heat transfer in bending channels are topics of much research interest because of increasing demand in various fields, particularly in the medical and industrial arenas. This paper presents a numerical study of fluid flow and heat transfer in a bending channel with a square cross section. Numerical calculations using spectral methods were performed for a curvature of 0.001 and a Dean number (Dn) in the range of 0<Dn≤5000. A temperature difference was maintained between the horizontal walls for a Grashof number of Gr = 1000, with the bottom wall heated and the outer and inner walls thermally insulated. Applying Newton–Raphson iteration and path continuation, two branching structures of steady solutions with two to eight vortices were obtained. The first branch comprises multi-vortex up to eight and it occurs at Dn≥3500 while the second branch comprises to multi-vortex up to a maximum of four. The first branch forms symmetric solution while the second branch for its complexity forms asymmetric solutions. For unsteady solutions, time-evolution calculations were performed to investigate the nonlinear behavior, and it was found that with increasing Dn, the unsteady flow experienced various flow instabilities. The time evolution was plotted in phase space to clarify the unsteady flow characteristics. Distinctive contours of the secondary flow patterns, streamwise velocity distributions, and isotherms were also obtained, and the unsteady flow was found to comprise two to six vortices. Finally, convective heat transfer was explored by obtaining temperature contours, and the secondary flow was found to magnify the convective heat transfer significantly. Because of the increase of several secondary vortices in the chaotic solutions, heat transfer occurred markedly in the flow.

Hydrodynamics of turbidity currents evolving over a plane bed

In this paper, we investigate the hydrodynamics of turbidity currents evolving over a plane bed. The analytical framework encompasses the depth-averaged conservation equations for fluid mass, sediment mass, momentum, and turbulent kinetic energy (TKE). The analysis incorporates self-similar distributions of streamwise velocity, sediment concentration, and TKE. Using the self-similar distributions of streamwise velocity and sediment concentration, the distributions of turbulent diffusivity, Reynolds shear stress, and TKE production rate are determined. The analytical model of turbidity currents enables the prediction of streamwise evolutions of flow depth, depth-averaged velocity, depth-averaged sediment concentration, and depth-averaged TKE. The self-acceleration and subsidence of turbidity currents are found to depend on the initial conditions. Additionally, the model results demonstrate the sensitivity of turbidity current hydrodynamics to grain size and longitudinal bed slope. Importantly, increased grain size and longitudinal bed slope contribute to enhanced self-acceleration, leading to a decrease in the subsidence rate of turbidity currents. The model predictions satisfactorily capture the available experimental data.

Experimental Study of Secondary Flow in Narrow and Sharp Open-Channel Bends

Secondary flow is a prominent feature of channel bends; it alters the streamwise velocity and bed shear stress distributions. Experiments were conducted to investigate the complex pattern of secondary flow in a narrow and sharp open-channel bend and the underlying mechanism of generation of multiple circulation cells. Compared with the moderate bends, the sharp bends are characteristic of multiple circulation cells from the 90° section. In addition to the curvature-induced circulation cell (S1) and turbulence-induced counter-rotation circulation cell (C1) near the outer bank, another circulation cell (S2) was observed near the inner bank and was attributed to flow separation. A term-by-term analysis of the vorticity equations indicates that the centrifugal term favours S1 and C1 while opposing S2. The turbulence-related term accounts for the formation of C1 and S2. The advective transport term redistributes vorticity and maintains the existence of S2. The dependence of secondary flow structure on Reynolds number and aspect ratio was also explored. With an increase in the Reynolds number from 23000 to 37000, both the strength and size of C1 are reduced by 50%, whereas the size of S2 increases by 20%, and its strength slightly decreases. With a decrease in the aspect ratio from 3.3 to 2, the strengths of S1, S2, and C1 are doubled, and the sizes of C1 and S2 increase by 90% and 20%, respectively.

A simplified CFD approach for bluff-body aerodynamics under small scale free stream turbulent flow

The study of free stream turbulence (FST) effects on bluff bodies by means of computational approaches has been addressed so far mainly applying scale resolving methods adopting a three-dimensional domain, which is cumbersome and complex. The development of an alternative more affordable approach capable of providing reliable data, at least qualitatively, about the impact of FST in aerodynamic responses of interest would be very beneficial for the penetration of CFD techniques in industrial applications. In this work, a 2D URANS approach is adopted to numerically replicate the well-known rod-induced small scale turbulent flow in wind tunnel testing. A square cylinder is selected as canonical application case to study the effects caused by ambient turbulence (0.7%), and 3.3% and 6.8% FST levels. The numerical results for the force coefficients, base pressure coefficient, mean and fluctuating pressure coefficient distributions, time-averaged flow structures, mean streamwise velocity and Reynolds stresses distributions are reported along with experimental data in the literature for exhaustive validation. The agreement between the proposed CFD approach and the wind tunnel data is remarkable as not only qualitative agreement has been reached, but in many cases consistency between numerical and experimental data has been obtained. The proposed approach, once its feasibility and accuracy has been satisfactorily assessed, may be applied for affordably study FST-dependent aerodynamics problems of interest in wind engineering.

Analytical modeling of vertical distribution of streamwise velocity in open channels using fractional entropy

Following the work of Chiu based on classical Shannon entropy, several kinds of generalized entropies have been explored in literature for studying open-channel flow. In this work, we explore a new kind of entropy, namely fractional entropy, which is based on the popular fractional calculus, to derive the vertical distribution of streamwise velocity in open channels. The velocity profile is derived analytically using the series approximation for the Lambert function. Also, the entropy index (i.e., the order of the fractional derivative) is considered a varying parameter and is computed along with the Lagrange multipliers by solving a nonlinear system using the second-order moment constraint, i.e., the momentum balance equation. The derived velocity equation is validated with selected laboratory and field data and compared with the Shannon, Tsallis, and Renyi entropy-based velocity profiles. It is observed that the proposed model can predict the measured values well for all the cases and the model corresponding to the entropy-based momentum coefficient formula is superior to all the abovementioned models. Further, the effects of Lagrange multipliers and the entropy index on the velocity profile are discussed. Also, the entropy index values for all the data are not close to zero, which specializes the entropy into the classical Shannon entropy, and hence, the approach justifies the applicability of the fractional entropy over the Shannon entropy in the context of open-channel flow velocity. Moreover, the methodology is developed based on an approximation of the series, which is based on a convergence criterion. This criterion needs to be verified against each of the data sets and, therefore, may become a difficult task for handling large data sets. To address this issue, this study provides a possible way of reformulating the mathematical model in terms of a nonlinear system with inequality constraint as a scope for future research. Finally, it is expected that the study can be further extended to study other kinds of important hydraulic variables such as sediment concentration, shear stress, etc.

Effect of Rigid Vegetation Arrangement on the Mixed Layer of Curved Channel Flow

Curved channels and aquatic vegetation are commonly present in the riverine environment. In this study, the effects of vegetation density and distribution on the hydrodynamic characteristics of a mixed layer developed over a 180-degree curved channel were investigated through flume experiments. Wooden sticks were used to simulate rigid vegetation distributed along the half side of the channel, and a 200 Hz acoustic Doppler velocimeter (ADV) was employed to measure the three-dimensional instantaneous velocity at five selected cross sections along the curved channel. Experimental results show that the vegetation covering the half of the channel significantly affects the hydrodynamic structure of the curved channel flow, and the unequal vegetation resistance induces the K-H instability at the vegetation and non-vegetation interface, resulting in a standard hyperbolic tangent function of streamwise velocity distribution along the lateral direction. The influence of curve position on turbulence kinetic energy is far greater than that of vegetation density and vegetation distribution. The peak value of turbulent kinetic energy is comprehensively affected by vegetation density and distribution, and the peak position of turbulent kinetic energy at the interface is changed by different vegetation distribution. The combined effect of the curve and the partly covered vegetation increases the mixing between the water bodies, enhancing turbulent kinetic energy, and vegetation along the concave bank plays a more significant role. For turbulent bursting, the inward and outward interactions are mainly bursting events in the vegetation area, while ejections and sweeps are dominant in the non-vegetation area. However, the critical vegetation condition to initiate large-scale coherent structure (LSS) in the mixed layer and the influence of flexible vegetation need to be further studied in the future.

Characterizing the Three‐Dimensional Flow in Partially Vegetated Channels

AbstractPartially obstructed shear flows, such as flows over submerged vegetation patches in river systems, are common in natural environments. Here, a model of a patchily‐vegetated river flow, using staggered arrays of rigid wooden dowels, is used to experimentally characterize the flow. Three‐component point velocity measurements in the cross sectional plane are used to investigate the highly nonuniform, 3D flow field in patchy vegetation and its effect on mass and momentum exchange. The cross‐sectional distribution of mean streamwise velocity varies as a consequence of the bed heterogeneity, being highly dependent on vegetation density. Asymmetric shear layers form at the vertical and lateral edges of the canopy, having different scales within the canopy and in the unvegetated region. Secondary flow cells form in the cross‐plane, with a size that decreases with increasing canopy density. The strength of the upward and downward motions is found to be greater for denser canopies. In addition to the secondary flow, additional rotating cells are observed both above the patch and next to it with increasing canopy density. A triple‐averaging procedure allowed for the quantification of the vertical advective dispersive stresses, which are up to 21% of the total shear stress. This demonstrates the significant role of secondary circulation generated by patchy vegetation in interfacial momentum exchange. Finally, the secondary circulation contribution to vertical scalar transport is estimated to be of the same order as that due to turbulent diffusion, highlighting the importance of understanding the impact of the secondary flow field on aquatic ecosystem function.

Numerical Investigation of Very Low Reynolds Cross Orifice Jet for Personalized Ventilation Applications in Aircraft Cabins

This study focuses on the numerical analysis of a challenging issue involving the regulation of the human body's microenvironment through personalized ventilation. We intended to first concentrate on the main flow, namely, the personalized ventilation jet, before connecting the many interacting components that are impacting this microenvironment (human body plume, personalized ventilation jet, and the human body itself as a solid obstacle). Using the laminar model and the large eddy simulation (LES) model, the flow field of a cross-shaped jet with very low Reynolds numbers is examined numerically. The related results are compared to data from laser doppler velocimetry (LDV) and particle image velocimetry (PIV) for a reference jet design. The major goal of this study is to evaluate the advantages and disadvantages of the CFD approach for simulating the key features of the cross-shaped orifice jet flow. It was discovered that the laminar model overestimated the global jet volumetric flow rate and the flow expansion. LES looks more suitable for the numerical prediction of such dynamic integral quantities. In light of the computational constraints, it quite accurately mimics the mean flow behavior in the first ten equivalent diameters from the orifice, where the mesh grid was extremely finely tuned. From the perspective of the intended application, the streamwise velocity distributions, streamwise velocity decay, and volumetric flow rate anticipated by the LES model are rather well reproduced.

An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation

Aquatic submerged vegetation is widespread in rivers. The transverse distribution of flow velocity in rivers is altered because of the vegetation. Based on the vegetation coverage, the cross-section of the ecological channels can be divided into the non-vegetated area and the vegetated area. In the vegetated area, we defined two depth-averaged velocities, which included the water depth-averaged velocity, and the vegetation height-averaged velocity. In this study, we optimized the ratio of these two depth-averaged velocities, and used this velocity ratio in the Navier–Stokes equation to predict the lateral distribution of longitudinal velocity in the open channel that was partially covered by submerged vegetation. Based on the Navier–Stokes equations, the term “vegetation resistance” was introduced in the vegetated area. The equations for the transverse eddy viscosity coefficient ξ, friction coefficient f, drag force coefficient Cd, and porosity α were used for both the non-vegetated area and the vegetated area, and the range of the depth-averaged secondary flow coefficient was investigated. An analytical solution for predicting the transverse distribution of the water depth-averaged streamwise velocity was obtained in channels that were partially covered by submerged vegetation, which was experimentally verified in previous studies. Additionally, the improved ratio proposed here was compared to previous ratios from other studies. Our findings showed that the ratio in this study could perform velocity prediction more effectively in the partially covered vegetated channel, with a maximum average relative error of 4.77%. The improved ratio model reduced the number of parameters, which introduced the diameter of the vegetation, the amount of vegetation per unit area, and the flow depth. This theoretical ratio lays the foundation for analyzing the flow structure of submerged vegetation.

Numerical Investigation of Flow Structure and Turbulence Characteristic around a Spur Dike Using Large-Eddy Simulation

Spur dikes provide significant control for flow regimes in river regulation engineering, which can help in the regeneration of stream habitats. However, the narrowing of the flow by spur dike changes the turbulence characteristics. To clarify the turbulence characteristics around the spur dike, the method of large eddy simulation (LES) was used to investigate the horizontal turbulence structure around spur dikes with different discharges in an open-channel flume. The simulations were an exact reproduction of large-scale laboratory experiments, which showed agreement with the experimental results. The distributions of time-averaged streamwise velocity, bed shear stress, and second-order turbulence statistics obtained from the LES were analyzed. An examination of the time series of velocity fluctuation as the probability density function, quadrant analysis, the power density spectra, flow instability, and the vortex separation created in the detached shear layer were estimated. The results accurately revealed the flow field under flow separation, the turbulence statistics inside the separated shear layer, and the vortex structure and emphasized the variation in the different water depths. The results demonstrated that the form of turbulence was not significantly affected by discharge. Moreover, vortex and energy transmission displayed the same periodicity, despite variances in the structural form of turbulence at different water depths. Overall, the results of the study provide an efficient basis for understanding the turbulence around spur dikes, which is crucial for their safe design.

Modeling velocity in a compound channel with co-existing emergent and submerged vegetation

Vegetation on a floodplain, which contains both emergent vegetation and submerged vegetation, has a considerable influence on the velocity profile of the channel. In this study, a modified analytical model, which considers interactions within the vegetation, is developed based on the Shiono and Knight method (SKM) and the concept of the two-layer model to obtain the transverse distribution of the depth-averaged streamwise velocity in a compound channel with emergent and submerged vegetation. This analytical model includes the influence of secondary flows, lateral shear stress, bed friction, and the drag force caused by the vegetation. The aforementioned model is then employed in a straight compound channel, which contained various types of vegetation. Using suitable boundary conditions, the calculated data are found to be consistent with the experimental data. Subsequently, the effects of dimensionless eddy viscosity coefficient (λ), the depth-averaged secondary flows coefficient, and the impact coefficient β on the model are analyzed. It finds that the λ has a clear effect on the main channel region, but the depth-averaged secondary flows coefficient (K¯) has only a definite effect in the slope sub-region. The β value is significantly less than 1 for the condition of the vegetation with a variable frontal width. The model proposed in the present work can provide a guidance for the investigation of the flow characteristics of the various vegetated channel.

Mixing enhancement of supersonic flow induced by splitter plate cavity

Fast and efficient mixing of fuel and oxidizer in a RBCC combustor is crucial for the efficiency improvement of engine propulsion system. Whereas, the existence of compressibility effects of high-speed flow notably suppresses the mixing process. In present work, the strategy of splitter plate cavity is proposed to promote mixing. The influences of splitter plate cavity with different length to depth ratio (r) on mixing process are researched. Fine vortex structures are well captured and the newly found T-shaped structures and their evolution dynamics induced by the cavity instability are thoroughly analyzed. The results indicate that tremendous growth of the mixing layer in flow transition region is realized. For the dimensionless streamwise velocity distribution, the recognized appearance of multiple peaks at far flow field for splitter plate cavity with r=4 and 8 leads to great velocity gradient in local position, which can promote mixing process of upper and lower streams. The distributions of streamwise turbulence intensity, turbulent kinetic energy and transversely integrated turbulent kinetic energy suggest that vigorous dynamic behaviors of T-shaped structures can obviously increase local turbulence, especially for splitter plate cavity with r=8. The structure topology analysis results reveal that larger size of the evolutionary T-shaped structure and more intense rotation process of these structures can undoubtedly engulf more main stream into the mixing region to achieve mixing augmentation.

Numerical Simulation of Slope–Gully–Stream Sediment Transport Process with Water and Gravity Erosion

Soil erosion has become a global problem with serious consequences. It is the source of sediment in rivers, and the subsequent sediment transport is important. Water erosion and gravity erosion, as common forms of soil erosion, have different subsequent sediment transport processes. Numerical simulations can reflect these processes well under different sediment yield types. This study applied the computational fluid dynamics and discrete element method (CFD-DEM) to examine the sediment transport following water erosion and gravity erosion. During the sediment transport process, the solid-phase particles in the gravity erosion case move at a greater speed during the initial stage. In the case of water erosion, a decrease in particle velocity on the slope occurs due to the accumulation of particles. The streamwise velocity distribution of the liquid phase conforms to the logarithmic distribution before the sediment transport process starts. Influenced by the solid-phase particles, the flow velocity near the bottom decreases significantly. The sediment transport rate peak in gravity erosion cases is greater than that in water erosion cases. Furthermore, in water erosion cases, when the slope is steep, there is no peak in the sections located at the inlet and outlet of a gully. The sediment transport rate in river sections shows a step form in the declining process.

DSMC Study of Strong Shear Nonequilibrium Phenomenon in Hypersonic Knudsen-Layer Flows

A series of plane Couette flows of rarefied argon gas under different flowfield settings are simulated by the direct simulation Monte Carlo method. The relaxation process of strong shear nonequilibrium is systematically studied. The results show a qualitatively platform-shaped distribution of molecular streamwise velocity under the conditions of small wall spacing (roughly in the Knudsen layer), and large shear rate and wall speed. The analysis of this phenomenon will help understand the relaxation process of hypersonic Knudsen-layer flow and provide some references for future modelling research.

Influence of Strouhal number and phase difference on the flow behavior of a synthetic jet array

A computational study is presented to characterize the flow behavior of independently controlled multiple synthetic jet actuators (SJA). For fixed geometric configuration and Reynolds number (Re) 300, the influence of Strouhal number (St=0.028–0.172) and phase difference (∅=0°–180°) between the actuators on the evolution, and interaction of the vortices are highlighted. Directivity plots are employed to illustrate the effect of ∅ on the vectoring behavior of a synthetic jet array (SJ array). It has been observed that a high jet vectoring angle (β) is achieved while operating the SJ array at low St. The vectoring angle seems to be independent of ∅ for the low and high St. However, for an intermediate St=0.086, the vectoring angle varies with the ∅. The phase averaged vorticity contour for St=0.028 reveals that the evolution of the anti-clockwise vortex from the leading actuator (SJA1) decides the vectoring of the jet. By contrast, for higher Sts(0.115 and 0.13), the remnant vortices play a significant role in vectoring the jets toward the leading actuator. Based on the cross-stream distribution of time-averaged streamwise velocity, three distinct flow regimes are characterized: near-field, intermediate-field, and far-field. The strength of the jet is quantified by the downstream distribution of the jet momentum flux. Proper evolution of the vortices results in the enhancement of the jet momentum flux. It is recommended to operate the SJ array at an intermediate St (0.086) to vary the jet vectoring angle with phase differences as well as to achieve maximum jet momentum flux.