Time-averaged Force Research Articles

Flow control around a pitching oscillation circular cylinder using a dielectric barrier discharge plasma actuator

This paper discusses flow control around a stationary and pitching oscillation circular cylinder using a dielectric barrier discharge plasma actuator (PA). The pressure on the cylinder surface was measured to determine the lift and drag forces on the cylinder, and the differences between these values were investigated with and without the PA actuations. The results indicated that the time-averaged lift force increased by up to 140% for the 180° rotating cylinder. Additionally, the effect of the PA on the lift-hysteresis curve of the pitching cylinder were evaluated based on the temporal variation in the surface pressure. Moreover, to investigate the effect of the PA on the flow field, smoke wire and LED-PIV methods were used to visualize the flow around the cylinder. The results showed that PA promotes the mixing between the freestream and separated flow which makes the separated shear layer thicker for both stationary and a pitching oscillating cylinder. For the pitching oscillating cylinder, the flow fields modified by PA actuation are different depending on the direction of the rotation of the cylinder. These results indicate that PA enhances the circulation of the flow around the cylinder.

Numerical Analysis on the Unsteady Radial Load on the Shaft of a Large-Scale Dredge Pump Unit

Vibration and fatigue damage of pump shafts has become a prominent engineering problem, indicating the need for higher-quality reliability analysis of the pump unit in the design stage. In this study, the unsteady flow field in a large centrifugal dredge pump was numerically simulated via the unsteady Reynolds-averaged Navier-Stokes (URANS) method with the SST k-ω model. An experiment was carried out to verify the numerical method. The hydraulic radial force on the impeller and the total radial load were calculated based on computational fluid dynamics. The flow field with a double volute was simulated, analyzed, and compared to the flow field with a single volute. The stress of the pump shaft caused by the radial load was also calculated and discussed. The results show that the impeller gravity determines the time-averaged value and fluctuation frequency of the total radial load on the shaft, which must be considered in the shaft stability analysis. The total radial load fluctuating in asymmetric cycle results in stress cycles with different features at different circumferential locations. The application of a double volute effectively reduces the radial load on the pump shaft, which decreases the time-averaged hydraulic radial force by 38% and its fluctuation amplitude by 3%, decreases the time-averaged total radial load by 20% and its fluctuation amplitude by 28% in the design condition, and decreases the local stress at the narrowest shaft section by 44%. A double volute can be applied to weaken vibration and fatigue damage for a pump shaft if it is acceptable for the pump efficiency to be lowered.

Benefits of controlled inclination for contactless transport by squeeze-film levitation

Developed in this paper is a theoretical description of the fluid flow involved in contactless transport systems that operate using squeeze-film levitation. Regular perturbation methods are employed to solve the appropriate Reynolds equation that governs the viscous, compressible flow of air in the slender film separating the oscillator and the levitated object. The resulting reduced formulation allows efficient computation of the time-averaged levitation force and moment induced by fluid pressure, as well as the accompanying quasistatic thrust force that accounts additionally for shear stresses. Investigated, in particular, is the possibility of combining two distinct methods of thrust generation that have been experimentally demonstrated in previous studies – (i) inclination of the levitated body and (ii) generation of asymmetrical flexural deformations, such as travelling waves, on the oscillator surface – the latter of which is shown to allow a transition from the typically repulsive levitation force to one that is attractive. Computations reveal that systematic control of the inclination angle can provide significant performance benefits for squeeze-film transport systems. In the case of attractive levitation, the amount of improvement that can be obtained appears to correlate closely with the degree of lateral asymmetry exhibited by the flexural oscillations.

REDUCTION OF TOTAL DRAG FOR FINITE CYLINDERS IN TURBULENT FLOW WITH A HALF-C SHAPE UPSTREAM BODY

The effect of an upstream half-C shape body on the reduction of the total drag of a finite circular cylinder is investigated experimentally. Five main cylinders, each with an upstream half-C shape body placed at five upstream positions, a total of 25 different configurations, are considered during the experimentation at a Reynolds number in the range of 1.2 × 10<sup>4</sup> to 1.6 × 10<sup>5</sup>. The aspect ratios of the main cylinders are 1.25, 2.09, 3.03, 3.78, and 4.90 and the upstream bodies are taken as 90° peripheral cut-outs of the respective main cylinder. The total configuration drag coefficient is calculated from the time-averaged drag force on the configuration and compared with the drag coefficient of the respective main cylinder. Results suggest that at least 20% of the total drag of the configuration might be reduced with the upstream half-C shape body, and the reduction varies with the main cylinders' aspect ratio and the upstream body placement distance. The maximum drag reduction is about 55% if the half-C shape body is placed at an upstream distance of 66% of the main cylinder diameter with an aspect ratio of 3.03 and at a Reynolds number of 1.8 × 10<sup>4</sup>. A critical distance ratio is found beyond which drag cannot be reduced by the upstream half-C shape body, and the attribution might be given to a formation of intermittent swirling flow in the cavity mode.

Numerical investigation of the translational motion of bubbles: The comparison of capabilities of the time-resolved and the time-averaged methods.

In the present study, the accuracies of two different numerical approaches used to model the translational motion of acoustic cavitational bubble in a standing acoustic field are compared. The less accurate but less computational demanding approach is to decouple the equation of translational motion from the radial oscillation, and solve it by calculating the time-averaged forces exerted on the bubble for one acoustic cycle. The second approach is to solve the coupled ordinary differential equations directly, which provides more accurate results with higher computational effort. The investigations are carried out in the parameter space of the driving frequency, pressure amplitude and equilibrium radius. Results showed that both models are capable to reveal stable equilibrium positions; however, in the case of oscillatory solutions, the difference in terms of translational frequency may be more than three fold, and the amplitude of translational motion obtained by the time-averaged method is roughly 1.5 times higher compared to the time-resolved solution at particular sets of parameters. This observation implies that where the transient behaviour is important, the time-resolved approach is the proper choice for reliable results.

Comparison of Electromagnetic Forces Evaluated in Yee-Lattice Finite-Difference Time-Domain and Lattice-Boltzmann Method

Electrodynamic simulations in the Yee-lattice finite-difference time-domain method (YL-FDTDM) require half-unit-cell and half-time-unit offsets between electric and magnetic field components. To evaluate energy, momentum, and force in the YL-FDTDM, electric and magnetic fields must be colocated in both space and time. Colocation operations can be computationally intensive while introducing implementation complexity and numerical error. As an alternative to the YL-FDTDM, the Hauser and Verhey electrodynamic lattice-Boltzmann method (HV ELBM) is implemented on a single lattice representing electric and magnetic fields at the same location and time. Since colocation is not required on a single lattice, its central differences are simpler to implement and more accurate. Continuous plane-wave scattering of electric and magnetic fields from a nondispersive dielectric sphere is solved using the YL-FDTDM, the HV ELBM, and Mie scattering analysis. The YL-FDTDM and HV ELBM are compared in terms of numerical error and computational time representing the analytical Mie solution for the Einstein and Laub time-averaged force density. The HV ELBM requires less computational time to evaluate a time-averaged force density with half the error of the YL-FDTDM. At a similar absolute error, the HV ELBM evaluates a time-averaged force density in less than 10% of the computational time.

Maximizing the thrust performance of flexible caudal fin panels via experimental optimization

This paper discusses the experimental optimization of an artificial caudal fin to maximize thrust production. A combination of direct experimental measurement and Gaussian Process modeling was applied to optimize the time-averaged net thrust force produced by the fin panel. Specifically, this paper investigates the effect of the fin panel’s stiffness and flapping frequency on the thrust force. The Gaussian Process regression is primarily used to model the relationship between the flapping frequency and thrust force, with variations in the fin panel’s stiffness. Results show that the optimum flapping frequency that yields maximum force tends to decrease as the stiffness decreases. Furthermore, increasing the lateral amplitude displacement of the fin base leads to a higher time-averaged net thrust force. Further investigation shows that the phase difference between the trailing and leading edge of the oscillating fin should be about 90°to yield optimum time-averaged net thrust force.

The complex Maxwell stress tensor theorem: The imaginary stress tensor and the reactive strength of orbital momentum. A novel scenery underlying electromagnetic optical forces

We uncover the existence of a universal phenomenon concerning the electromagnetic optical force exerted by light or other electromagnetic waves on a distribution of charges and currents in general, and of particles in particular. This conveys the appearence of underlying reactive quantities that hinder radiation pressure and currently observed time-averaged forces. This constitutes a novel paradigm of the mechanical efficiency of light on matter, and completes the landscape of the optical, and generally electromagnetic, force in photonics and classical electrodynamics; widening our understanding in the design of both illumination and particles in optical manipulation without the need of increasing the illuminating power, and thus lowering dissipation and heating. We show that this may be accomplished through the minimization of what we establish as the reactive strength of orbital (or canonical) momentum, which plays against the optical force a role analogous to that of the reactive power versus the radiation efficiency of an antenna. This long time overlooked quantity, important for current progress of optical manipulation, and that stems from the complex Maxwell theorem of conservation of complex momentum that we put forward, as well as its alternating flow associated to the imaginary part of the complex Maxwell stress tensor, conform the imaginary Lorentz force that we introduce in this work, and that like the reactive strength of orbital momentum, is antagonistic to the well-known time-averaged force; thus making this reactive Lorentz force indirectly observable near wavelengths at which the time-averaged force is lowered. The Minkowski and Abraham momenta are also addressed.

Base wake dynamics and its influence on driving stability of passenger vehicles in crosswind

The unsteady flow around a travelling vehicle induces fluctuating aerodynamic loads. Automotive manufacturers usually set targets on the time-averaged lift forces to ensure good straight-line stability performance at high speeds. These targets are generally sufficient in preventing unstable vehicle designs. Yet, small changes in averaged values occasionally yield unexpectedly large differences in the stability performance, indicating that the changes in averaged normal loads cannot solely explain these differences. The unsteady aerodynamic effects on driving stability are, therefore, an interesting topic to study. The objective of the present work is to investigate the differences in wake dynamics and fluctuating aerodynamic loads for two variants of a roof spoiler on a sports utility vehicle: a baseline that was known to cause stability issues and an improved design which resolved them. The vehicle designs were investigated using accurate time-resolved CFD simulations for a set of crosswind conditions. The unsteady aerodynamic response was coupled to a vehicle dynamics model to analyse the resulting impact on driving stability. It was shown that in crosswinds the baseline spoiler, contrary to the improved spoiler, has bi-stable wake dynamics that induce lift force fluctuations at frequencies close to the 1st natural frequency of the rear suspension.

Hydrodynamic characteristics and wake evolution of a submarine pipe with the presence of gas leakage at a low Reynolds number of 160

Hydrodynamic characteristics and wake structures of a submarine gas transmission pipe with the presence of gas leakage are of significance from a scientific and practical viewpoint. In this paper, we present a numerical investigation of flow past a leaking pipe at a low Reynolds number of 160 using the Eulerian–Eulerian multi-fluid volume of fluid model. The focus is on the effects of gas buoyancy and the location of the leak hole on the wake flow structures, bubble–vortex interference, and hydrodynamic forces. The variation of drag and lift coefficients is highly associated with the evolution of gas bubbles and the interaction between the bubble-induced vortices and the shear layers. When the gas buoyancy is ignored, the alterations of the main vortex structure and hydrodynamic forces are not sensitive to the location of the leak hole. The bubble-induced vortices are encompassed by the two shear layers and quickly dissolved in the main vortices. Finally, the released gas bubbles are locked in the center of main vortices and convected downstream with them. In contrast, when the buoyancy is considered, the gas bubbles line up in the upper shear layer, strongly interfering with the formation of the upper main vortex. Each gas bubble introduces a pair of small vortices that experience complicated merging or splitting during the migration. Consequently, the upper main vortex is suppressed at θ = 90° and vanished at θ = 180° and θ = 270° (θ is measured clockwise from the forward stagnation point), leading to the negative time-averaged lift force and the same-frequency oscillation of drag and lift coefficients. Due to the upward migration of gas bubbles from both front and rear surfaces at θ = 270°, the evolution of bubble-induced vortices is more complicated and the oscillation of hydrodynamic forces is significantly enhanced in comparison with other cases.

Fast computation of the Lorentz force induced by longitudinal electromagnetic stirring

In this work, we revisit a recent transient three-dimensional (3D) model for longitudinal electromagnetic stirring in the continuous casting of rectangular steel blooms. Whereas the earlier work was able to demonstrate accurate approximations to the solutions in two asymptotic limits, both of which gave economical alternatives to time-consuming 3D computations, here we show that the original governing equations can be manipulated to a form that allows for rapid computation even outside of these asymptotic limits. The resulting formulation requires the numerical solution of two steady-state complex Helmholtz-like equations in two dimensions that are coupled via a non-standard internal interface condition that is reminiscent of that occurring in the study of Marangoni convection; these equations are then solved numerically using the finite-element software Comsol Multiphysics. With this formulation, it is possible to compute the time-averaged Lorentz force components in a way that requires around four orders of magnitude less computational time than the fully 3D approach.

On the aerodynamic loads and flow statistics of airfoil with deformable vortex generators

The aerodynamic performances and flow statistics for a Delft University-91-W2-250 airfoil with deformable vortex generators (DVG) were experimentally studied in a wind tunnel across various angle of attacks and wind speeds. A high-resolution force sensor was used to measure the time-averaged lift force, while a planar particle image velocimetry system was applied to characterize the mean velocity and vortex shedding over airfoil surface. The results highlighted that, similar to conventional rigid vortex generators (RVG), DVG can effectively enhance lift coefficient after the stall angle of airfoil with clean surface under low incoming winds. However, the deformation of DVGs increased with the growth of wind speed; this suppressed the effectiveness of wake mixing where the aerodynamic performance of DVGs gradually converged to clean surface configurations. The flow measurements demonstrated that the deformation of DVG can lead to significant decrease in near-wall flow velocities close to the airfoil trailing edge and generate more dispersed vorticity distributions. To further investigate the linkage between DVG deformation and its wake mixing effectiveness, complementary tomographic particle image velocimetry measurements were conducted. The results indicated that the vorticity strength presented monotonic decay with the bending angle of DVG within both near and intermediate wake regions. The capability of DVGs passively adjusts their bending angle, and therefore, the airfoil lift coefficients provide a novel approach to reduce aerodynamic load fluctuations for aircraft within unsteady flows.

Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels

Direct numerical simulations (DNS) are used to systematically investigate the applicability of the minimal-channel approach (Chung et al., J. Fluid Mech., vol. 773, 2015, pp. 418–431) for the characterization of roughness-induced drag on irregular rough surfaces. Roughness is generated mathematically using a random algorithm, in which the power spectrum (PS) and probability density function (p.d.f.) of the surface height can be prescribed. Twelve different combinations of PS and p.d.f. are examined, and both transitionally and fully rough regimes are investigated (roughness height varies in the range $k^+ = 25$ –100). It is demonstrated that both the roughness function ( ${\rm \Delta} U^+$ ) and the zero-plane displacement can be predicted with ${\pm }5\,\%$ accuracy using DNS in properly sized minimal channels. Notably, when reducing the domain size, the predictions remain accurate as long as 90 % of the roughness height variance is retained. Additionally, examining the results obtained from different random realizations of roughness shows that a fixed combination of p.d.f. and PS leads to a nearly unique ${\rm \Delta} U^+$ for deterministically different surface topographies. In addition to the global flow properties, the distribution of time-averaged surface force exerted by the roughness onto the fluid is calculated. It is shown that patterns of surface force distribution over irregular roughness can be well captured when the sheltering effect is taken into account. This is made possible by applying the sheltering model of Yang et al. (J. Fluid Mech., vol. 789, 2016, pp. 127–165) to each specific roughness topography. Furthermore, an analysis of the coherence function between the roughness height and the surface force distributions reveals that the coherence drops at larger streamwise wavelengths, which can be an indication that very large horizontal scales contribute less to the skin-friction drag.

Study of Underwater and Wave Gliders on the Basis of Simplified Mathematical Models

Both underwater and wave gliders are known as autonomous unmanned energy-saving vehicles which have recently found applications for monitoring the world ocean. The paper under consideration discusses simplified mathematical models of these platforms enabling the straightforward parametric investigation into relationships between their parameters and performance. In its first part the paper discusses equations describing the motion of an underwater glider (UG) in a vertical plane as a basis for derivations relating geometric, kinematic and hydrodynamic characteristics of UG and its lifting system with relative differential buoyancy and pitch angle. Obtained therewith are formulae for the estimation of the UG glide path speed, lift-to-drag ratio, range of navigation and endurance. The approach is exemplified for typical cases of the UG conceived as winged bodies of revolution and flying wings. The calculated results feature dependencies of the UG speed on its configuration and volume as well as on the angle of attack for different magnitudes of relative buoyancy. Also considered is an optimal mode of operation, based on the maximization of the lift-to-drag ratio. The second part of the paper is dedicated to the estimation of the thrust and speed of a wave glider (WG), comprising a surface module (float) and underwater module represented by a wing, with the use of a simplified mathematical modeling intended to clarify the influence of the parameters upon the performance of the WG. The derivations led to an equation of forced oscillations of the vehicle accounting for the interaction of the upper and lower modules, connected by a rigid umbilical. The exciting impact of progressive waves of a given length and amplitude is found through the calculation of the variation of a buoyancy force in accordance with the Froude–Krylov hypothesis. The derivatives of time-varying lift with respect to kinematic parameters, entering the equation of vertical motion of the WG, as well as coefficients of instantaneous and time-averaged thrust force, are found by resorting to the oscillating hydrofoil theory. The derivation of the available thrust and the approximate calculation of the drag of the vehicle with account of wave and viscous components enable the evaluation of the speed of the WG for the prescribed geometry of the craft and wave motion parameters.

Magnus Effect over Aerodynamic Components of Spinning Missile

To reveal the flow mechanism of the Magnus effect of the spinning missile, the flow field under supersonic conditions was numerically simulated based on the unsteady Reynolds-time-averaged Navier–Stokes equation, and the implicit dual-time stepping method and sliding mesh method were used. Validation was performed to ensure the reliability of the numerical methods. The results of the numerical simulation and the wind-tunnel experimental data coincided quite well. The aerodynamic characteristics of various configurations while spinning were calculated. The effect of aerodynamic components and aerodynamic interference between components on the Magnus effect were analyzed. The results indicate that for the projectile body, the interference of the canard enlarges the time-averaged side force; when the slenderness ratio becomes large, from the view of the base, the left leeward separation vortex is close to the surface, resulting in a low-pressure region, and the direction of the side force and yawing moment are changed. The fin installation angle can weaken the body Magnus effect to some extent. For the projectile fin, the influence of leeward separation vortices on the fin depends on their relative positions. The fin installation angle can weaken and even cause the reversal of the side force direction.

Numerical Study of the Aerodynamics of a Hovering Hummingbird’s Wing with Dynamic Morphing

To deepen our understanding of the aerodynamics by which hummingbirds use flexible wings to hover efficiently during flapping flight, a three-dimensional wing model with dynamic morphing was developed according to the morphological and kinematic data of a hovering hummingbird’s wing. Navier-Stokes equations were solved on a dynamically deforming grid to study wing aerodynamics. In numerical simulations, boundary-based smoothing and overset methodologies were used in combination to update the interior nodes of cells in the computational domain, allowing those nodes to accommodate the motion of the flexible wall. This study showed that the leading edge vortex (LEV) attached to the wing was stable during the downstroke but extremely unstable and shed continuously during the upstroke. In the results of the downward stroke, the different vortices separated from the surface and formed a vortex ring. The difference is that the leading edge vortex induced a vortex ring near the root and a smaller and weaker vortex ring near the wingtip during the upstroke. A significant enhancement in aerodynamic forces was found during the downstroke, along with a large number of power consumptions. We found that the asymmetry in the time-averaged vertical force between the two half strokes was 3.5, and the value was higher than that reported earlier. Aerodynamic force coefficients and efficiency matched well with those of another hummingbird wing (the ruby-throated hummingbird). It is worth noting that hummingbirds can maintain a similar wingtip speed by flapping their wings, but different strategies are adapted to hover efficiently due to the differences in size and body weight. The results of this study help to better understand the aerodynamics of the hovering hummingbird.

Optical Magnus radiation force and torque on a dielectric layered cylinder with a spinning absorptive dielectric core.

A dielectric cylindrical shell material with an inner stationary absorptive core (or, equivalently, a concentric layered cylinder) illuminated by an axisymmetric wave field (in 2D) with arbitrary polarization will experience a time-averaged radiation force along the direction of wave propagation, whereas the transverse component vanishes as required by symmetry. Counterintuitively, the present analysis shows that when the inner absorptive core material rotates with an initial angular velocity Ω0 around its main geometrical axis, a transverse radiation force component arises (in addition to a longitudinal force) as well as an axial radiation torque component in plane waves. This phenomenon is the analog of the classical hydrodynamic Magnus effect. In this analysis, the instantaneous rest-frame theory and the modal series expansion method in cylindrical coordinates are utilized to formulate the EM/optical scattering from a cylindrical shell with arbitrary thickness, and to compute the optical radiation force and torque vector components. Particular emphases are given on the size parameter of the cylindrical shell, the layer thickness, the angular rotation of the inner absorptive core, and the polarization (TM or TE) of the incident plane waves. Numerical computations illustrate the analysis and explicate the behaviors of the longitudinal, transverse, and axial radiation force and torque components. Related applications for the optical Magnus effect in radiation force and torque investigations can benefit from the results of the present analysis in spin-optics, rotational Doppler shift for optical waves, optical tweezers, optical manipulation of elongated spinning objects, and particle rotation.

Investigation of the effects of managed ice field characteristics on a dynamic positioning AHTS vessel using physical modelling techniques

This paper presents the tools, techniques and outcomes of a model testing program of a dynamically positioned (DP) Ice-1A classed Anchor Handling Tug Supply (AHTS) vessel called the “Magne Viking” in different managed ice environments with ice thickness, concentration, floe size, floe distribution, drift speed, and ice encroachment direction as test variables. A total of 168 test runs were carried out in 7 ice sheets to evaluate the vessel's thruster forces and moment on the horizontal plane and the vessel's 6-DOF motions and accelerations. The time series and probability of exceedance plots of thruster forces and yawing moments are presented, along with the vessel's positioning relative to a set-point in various managed ice conditions. In addition, investigations are carried out to evaluate the influence of various ice field parameters on the time-averaged and time-dependent thruster forces and moment. Both measurements and video recordings confirmed complex and stochastic ice-ship-basin wall interactions and different ice failure modes. Overall, the study demonstrated the capability of the DP-controlled ship to maintain the station for most head-on tests and the oblique ice tests not exceeding 15°. The dataset and video recordings acquired through the testing have improved the understanding of the dynamic ice-vessel interactions.

Hydrodynamic performance of an unconstrained flapping swimmer with flexible fin: A numerical study

Flexible tail fins are commonly found in undulatory swimmers which can propel freely in omni-direction with flapping-wing-based propulsion. In this work, the hydrodynamic performance of an unconstrained flapping foil equipped with a flexible tail fin at different length is investigated numerically. As the fin length Lfin changes from 0.2c to c with c being the cord length, the propelling speed of the system first increases and then decreases after maximum propelling speed is achieved when the fin length is 0.8c. There are two kinds of wake vortical structures observed with bending stiffness kb = 2.0: (i) the regular reverse Bénard–von Kármán vortex configuration for foil with short fin and (ii) the aligned vortices with two-layered street at downstream for foil with long fin (Lfin≥ 0.6c). Control volume analysis reveals that for both types of vortical structures, the time-averaged thrust force is mainly related to the momentum flux contribution from the downstream face. Besides, the wake symmetry of a pitching foil with flexible tail fin is sensitive to the vertical phase velocity of vortices, where it can be used to predict whether the wake symmetry of the unconstrained system is preserved. Moreover, the bending stiffness effectively affects the hydrodynamic performance, and the breaking of wake symmetry greatly reduces the propulsive efficiency. The results obtained shed some new light on the role of flexible structures in the self-propulsive biological system and furthered our understanding of flexible self-propulsion system.

The Dielectric Surface Conductivity Effect on the Dielectric Barrier Discharge Actuator Characteristics

The effect of the surface conductivity on the electrical and mechanical characteristics of the surface dielectric barrier discharge actuator has been numerically investigated in this study. Two typical ac-surface dielectric barrier discharge actuators, wire-to-plate and plate-to-plate, have been considered to control airflow alongside a flat dielectric plate. A sinusoidal high voltage of varied frequencies and amplitudes is supplied to the active electrode, and the passive electrode, which is grounded, is encapsulated inside a dielectric plate. Two-species ion transport model, involving generic positive and negative ions, coupled to the electrostatics model is assumed. The electrostatic field is affected by both the space and the surface charges. The surface charge is accumulated due to ion deposition, but its distribution varies due to the surface ohmic conduction. The Navier–Stokes equations for the flow simulation, which include the time-averaged electrohydrodynamic force determined from the discharge model, are solved to analyze the flow field and the boundary layer morphology. The numerical algorithm has been implemented in the COMSOL commercial package. The significance of the dielectric surface conductivity on the discharge behavior and the flow field has been shown. The dielectric surface conductivity behaves nonmonotonically and affects the flow field by altering the electrohydrodynamics force strength, direction, and distribution.