Array Of Circular Cylinders Research Articles

Stokes flow past an array of circular cylinders through slip-patterned microchannel using boundary element method

Two-dimensional viscous incompressible, pressure-driven, creeping flow at low Reynold's number (Re ≪ 1) around a series of circular cylinders in a slip-patterned rectangular microchannel is investigated numerically by using the boundary element method (BEM) based on a non-primitive variables approach. The non-primitive variables approach refers to the combination of stream function and vorticity variables. The Stokes equations are used to govern the flow of creeping fluid through a microchannel. We consider the alteration of the slip on both the upper and lower surfaces of the microchannel maintain the same phase (i.e., in-phase configuration). Here, the slip boundary condition refers to Navier's slip boundary condition. We considered both small as well as large patterned slip on both surfaces of the microchannel. Moreover, we have assumed that a number of cylinders of equal diameter are present in the in-line configuration in the path of flow. We studied streamlines, velocity profiles, pressure gradients, and the shear stresses with varied slip-length, and the radius of the cylinder, to get a complete comprehension of flow dynamics. We observed that the velocity and shear stress profiles exhibit significant variability in the case of fine slip patterning. Additionally, the proposed investigation holds several potential applications, such as drug capsule delivery systems, hemodynamics, bio-MEMS technology, and so forth.

Impacts of Biomimetic Mangrove Structures on Wave Attenuation in Kuala Sepetang, Perak

Biomimicry is introduced as an approach to develop an ecologically-informed design solution. The study proposes a regenerative design solution through hydrodynamic effects of the complex mangrove roots system that is applied to a biomimetic structural column design, with consideration on interactions between root porosity, water flows, and sediment transportation. Sangga Besar River, Perak is chosen as the key parameters of the flow. The roots are modelled with a circular array of cylinders (patch) with different porosities and varying spacing ratios. 15 patches are derived from 3 main sets where each set consisted of five patches with varying porosities. The simulation of each case to understand the impacts of different patch porosity on the flow structure is carried out using Ansys Fluent Student Version 2021. The study found that turbulence is impacted, but not directly proportional to the patch porosity where there could be an optimal porosity of the patch that generates maximum yield of turbulent kinetic energy dissipation rate with minimum sediment erosion for the onset of sediment deposition. The patch with φ=40% has the highest turbulence dissipation rate which relatively coherent with the range of porosity that would likely be encountered in natural mangrove ecosystem.

A Bottom-up Transient Theory for Concentration Polarization with Applicability to over-Limiting Current Conditions

Renewable power sources have drawn interest due to scarcity of fossil fuels and associated pollution during their combustion-based power production. Renewables are projected to produce approximately 60% of US electricity generation by 2050, with an expected contribution of 2000 TW-h from wind power alone. To overcome the mismatch between electricity demand and intermittent supply, such power plants require large-scale energy-storage device integrated with them. In contrast to other technologies, redox flow batteries (RFBs) offer independently scalable power and energy capacity that is demanded for such applications. Despite significant achievement in their designs through experimentation and modeling, limited understanding has been established to date concerning their transient response while operating under irregular charge/discharge scenarios in renewable-powered grids and micro-grids. Under such conditions pore-scale mass transport physics and different mechanisms of concentration polarization can occur, but the conventional film law of mass transfer (FLoMT) using a constant Sherwood number cannot capture time-varying diffusion layer thickness near electrode surfaces. Further, the mean solute advection rate through porous RFB electrodes can deviate from the value expected from product of superficial velocity and average concentration inside the electrode if pore-scale concentration polarization is substantial. Consideration of these effects in the present bottom-up theory makes it applicable to over-limiting conditions, while predicting concentration polarization in agreement with experimental observations. We accomplish this by creating theory with similarity to the theory of Ralph White and co-workers for solid-state, particle-scale diffusion in Li-ion batteries [J. Power Sources, 2012, Vols. 214 and 218], while our theory is instead applied to an arbitrary representative volume element of flowing liquid electrolyte inside electrode pores.Here, we present a theory to incorporate these transient effects into a bottom-up transient model (B-UTM) by using frequency-dependent transfer functions (TFs) that are derived from the Fourier transformed pore-scale mass conservation equations (MCEs). These TFs preserve pore-scale mass transfer physics during their embedding into an up-scaled model. One of these TFs is the spectral Sherwood number that extends the film law of mass transfer to transient conditions and that correlates reactive flux with concentration polarization through an output-input relationship in the frequency domain. Another TF named the advective-flux transfer function captures the acceleration/suppression of solute advection rate that arises from the inhomogeneity in pore-scale concentration distributions. We first present validation of this theory using transient RFB experiments where the introduced B-UTM predicts the time evolution of concentration polarization in good agreement. Meanwhile the conventional FLoMT model that uses time-independent Sherwood number and neglects the solute acceleration/suppression effect shows systematically larger polarization (up to 400%), which restricts such models from simulating charging/discharging with applied current near and above the limiting current.The utility of the introduced bottom-up theory is demonstrated by incorporating it into a multi-scale RFB model in which redox-active electrolyte flows through a porous electrode comprised of an array of circular cylinders in crossflow that mimics commonly used carbon felt. The frequency dependence of the introduced TFs obtained from numerical solution of pore-scale MCEs are analyzed for different electrode porosity and Péclet number, where both the TFs reach a non-zero finite value in the limit of vanishing frequency. The non-zero value of the spectral Sherwood number in this limit is identical to the Sherwood number obtained in the pseudo-steady limit (PSL) where transient effects are negligible. With increasing frequency both the TFs show a transition from lagless response to semi-infinite Warburg response with orders higher values compared to that of the PSL. Finally, these TFs are embedded into an up-scaled model to obtain the time-domain response of RFBs operating under a step impulse applied current with different step durations. Numerically obtained concentration polarization and the average reactant concentration inside electrodes is used to construct non-dimensional regime maps showing a regime of over-limiting current. The results show that fast current fluctuations are sustained even when current exceeds the limiting current, which provides a means to increase the utilization of charge capacity of existing flow-based electrochemical devices that are operated under transient conditions. The theory introduced here can find applicability in other flow-based electrochemical devices including electrochemical separations and CO2 capture. Figure 1

Oscillating viscous flow past a streamwise linear array of circular cylinders.

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Conductivity gain predictions for multiscale fibrous composites with interfacial thermal barrier resistance

Nanocomposites are heterogeneous media with two or more micro‐structural levels. For instance, a nano‐level is characterized by isolated nano‐inclusions, and a micro‐level is represented by the clusters resulting from aggregation processes. Based on the reiterated homogenization method, we present a procedure to study the influence of this aggregation process and interfacial thermal resistance on the effective thermal conductivity for 2‐D square arrays of circular cylinders. First, an effective intermediate thermal property is obtained by taking into account only the influence of the individual nano‐inclusions in the matrix. Second, the final effective thermal coefficient ( ) is calculated considering the clusters immersed in the intermediate effective medium derived in the first step. The conductivity gain ( ) is defined as the quotient ( ) where is the effective thermal coefficient computed considering only one microstructural level with the same volumetric fraction of inclusions. We apply the theory of complex variable functions deriving in an infinite system of equations solvable by truncation method. The analytical formulas of the effective coefficient used in the calculations generalize other well‐known formulas reported in the literature. We also provide formulas for several truncation orders. The main novel contribution is in the reiterative application of the obtained formulas to illustrate the gain effect in nanocomposites, expressed as a function of the Biot number, thermal conductivities, volumetric fibers fraction, and an aggregation parameter. Furthermore, this result can be used to assess numerical computations and for nano‐reinforced fibers and nanofluids applications. An appendix is included showing similarities and differences with a three‐phase model.

Impacts of Unsteady Flow Environments on the Propulsive Performance of Oscillating Foils

A numerical study is conducted to understand the impact of an unsteady freestream on the aerodynamic performance of an oscillating airfoil. The unsteady flow environment is generated by placing a stationary inline circular cylinder array upstream of the oscillating airfoil. The dependence of thrust with variation of Reynolds numbers and Strouhal numbers is investigated, and it is revealed that the unsteady flow environment enhances thrust production of a pitching airfoil. This increased thrust production was related to an effective increase in the Reynolds number experienced by the airfoil. With airfoil–vortex interaction analysis, the increase in average thrust coefficient was shown to be caused by constructive interaction of freestream vortex structures and the oscillating airfoil. Drag-inducing interactions were also observed but were less common than thrust-increasing events, resulting in a higher average thrust. A simple scaling law is expanded to include the effects of unsteadiness, where thrust is found to be linearly dependent on turbulence intensity. It is demonstrated that the thrust generated by the pitching airfoil when operating in highly unsteady flow environments is more accurately represented as a function of Reynolds number, Strouhal number, and turbulence intensity.

Applicable Investigation of SPH in Characterization of Fluid Flow in Uniform and Non-Uniform Periodic Porous Media

Today, the use of numerical modeling for characterizing properties of porous media and related concepts has been widely extended, especially in subsurface flow issues such as geological CO2 storage and petroleum recovery. Therefore, in this study, the fundamental problem of laminar fluid flow through uniform or non-uniform and periodic array of cylinders was functionally investigated using the smoothed particle hydrodynamics (SPH) method as a modern and applied method of modeling in order to develop the past studies and introduce a complementary numerical tool alongside laboratory methods. All modeling processes were performed in the form of dimensionless processes for generalization and applicability at different scales. The results were used to characterize properties of porous media and to investigate basic properties such as fluid velocity, permeability, streamlines, and hydraulic tortuosity. Accuracy of modeling was shown in comparison with the results obtained in the literature. In this study, the potential of the method has been investigated in order to show the ability in modeling characteristic laboratory experiments of porous media and the possibility of using it instead of them. For this purpose, three periodic models of uniform and randomly distributed non-uniform porous media with arrays of circular, square, and diamond-shaped cylinders in a porosity range of 30–95%, with different types of cylinder distribution at the pore scale, were investigated. New equations were proposed for permeability as a function of porosity. Moreover, the method of tortuosity calculation was investigated directly through the time history of properties in the SPH method, and shape factors were obtained for the studied porous media models. The results showed that the geometry of a square cylinder with distribution in a square grid led to a higher permeability than circular and diamond-shaped grids. In contrast, diamond-shaped geometry with distribution in a hexagonal grid led to higher permeability than the other two models. Furthermore, diamond-shaped geometry had higher tortuosity, and circular and square geometries had almost identical tortuosity. Increasing the size of the modeling domain and decreasing the size of cylinders (i.e., decreasing resolution) reduces effects of the shape and the geometry of cylinders and achieves the same results. Random and non-uniform distribution of cylinders within porous media reduces fluid velocity, permeability, tortuosity, and shape factor (p) compared to the uniform models.

Hydrodynamic interactions between waves and cylinder arrays of relative motions composed of truncated floating cylinders with five degrees of freedom

The hydrodynamic interactions between waves and a truncated floating circular cylinder array were examined in this work. Each cylinder of the array is allowed to oscillate with five degrees of freedom (DOFs), and there can be relative motions among different cylinders. The hydrodynamic responses of such arrays in the presence of ambient incident waves were studied using a semi-analytical technique, in which, the unknown coefficients of radiation–diffraction velocity potentials caused by array motions were expressed by the linear combination of each cylinder’s to-be-calculated oscillation amplitudes in each direction. Then, for each cylinder in the array, the amplitude of each degree of freedom was computed. Variations in the oscillation amplitudes of the cylinders in the array with wavenumbers for various incidence angles and column spacing, and amplitude distributions of free surface elevation for various wavenumbers were given. Additionally, extensions to the situation of multidirectional irregular waves were presented. Last but not least, we examined the effects of other DOFs (nonheave) on hydrodynamic responses and wave energy extraction performances (capture width w and interaction factor q) by comparing the results obtained by the 5-DOF and the 1-DOF (heave) models. In terms of response amplitude and wave energy extraction performance, the 5-DOF model’s results were significantly different from those of the 1-DOF model. Therefore, it is suggested to use the 5-DOF model to analyze such cylindrical arrays.

Thermal Features of mixed convection from an inline periodic array of circular cylinders in non-Newtonian power-law fluids

Mixed convection heat transport from multi-cylinders finds numerous applications in chemical, petroleum, and food industries. This study presents the mixed convection characteristics of an inline array of heated circular cylinders in non-Newtonian power-law fluids for the following governing parameters: fluid volume fractions; 0.70≤ φ f ≤0.99, power-law index; 0.4≤ n ≤ 1.8, Reynolds number; 1≤ Re D ≤40, Prandtl number; 1≤ Pr D ≤50 and Richardson number; 0≤ Ri D ≤2. Mathematical model equations are solved using the Finite Volume Method within the framework of Boussinesq approximations. Thermal features are explored using isotherms, local and averaged Nusselt numbers. Qualitatively, isotherms display a complex relationship with the governing parameters. Local and average Nusselt numbers improve with increasing Reynolds, Prandtl and Richardson numbers, shear-thinning natures. An opposite nature is noted for shear-thickening fluids. Nusselt numbers were further improved with increased fluids volume fractions contrary to decrease in forced convections cases. At maximum Reynolds, Prandtl and Richardson numbers, Nusselt number increased by 30.53% and 13.11% for shear-thinning (n = 0.4) fluids, respectively for φ f = 0.70 and 0.99. An unsteady nature was also found in shear-thinning regions at larger volume fractions. Lastly, statistical analysis is presented for the average Nusselt numbers to depict additional physical insights of the numerical outcomes.

Computational analysis of cross‐flow of power‐law fluids through a periodic square array of circular cylinders

AbstractThe steady flow of non‐Newtonian power‐law fluids across a periodic square array of infinitely long circular cylinders is studied numerically using an unstructured finite volume method. The local and global flow characteristics have extensively been explored by the systematic variations of the pertinent dimensionless parameters as follows: fluid volume fraction (ϕf = .70–.99), Reynolds number (Re = 1–40), and power‐law index (n = .4–1.8). Qualitatively, the dense and curved streamlines are seen with the increasing inertial forces and shear‐thinning behavior across all the fluid volume fractions. Further, the pressure coefficient over the surface of periodic cylinders is significantly influenced by the governing parameters and found to be maximum and minimum for the upstream and downstream cylinders, respectively. The individual and total drag coefficients have shown complex dependence on n, ϕf, and Re. For shear‐thinning fluids (n < 1), the pressure drag coefficient dominates over the friction drag coefficient, whereas an opposite response is seen for the shear‐thickening fluids (n > 1) except at Re = 40. Further, both individual and total drag coefficients are observed to increase and decrease in the ranges of ϕf of .70–.90 and .92–.99, respectively, with increasing n. The strong interactions between the periodic cylinders, at smaller ϕf, diminish with a corresponding increase in ϕf. In addition, simple predictive correlations for the pressure, friction, and total drag coefficients have been developed to gain further physical insights into the detailed flow kinematics. Finally, the present findings display a good agreement with the available literature.

Efficient Analysis of Radiation From a Dipole Source in Woodpile EBG Structures

An efficient and rigorous approach to analyze the radiation from an electric dipole placed in 3-D woodpile electromagnetic bandgap material (EBG) structures consisting of layered periodic arrays of circular cylinders is presented. The response in the spectral domain of the woodpile EBGs excited by a dipole source is calculated using one-dimensional lattice sums, the 3-D transition matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The closed-form expression of the radiated field is rigorously obtained by a finite integral of the spectral response. Comparisons with the far fields calculated using reciprocity both with the present approach and with a fully independent commercial EM software package are presented showing excellent agreement with the proposed method and demonstrating the high computational efficiency of the semianalytical formalism.

An assessment of turbulence transportation near regular and random permeable interfaces

Turbulent channel flow with a porous wall is investigated using direct numerical simulation, where the porous media domain consists of regular or random circular cylinder arrays. We compare the statistics and structure of the mean flow and turbulence in the channel flow with a bulk Reynolds number of 2500 and two porosities (φ=0.6 and 0.8) for the porous media. It is shown that the random interface significantly affects the dynamics of turbulence and the time-averaged flow. More intense mixing is observed near the random interface due to augmented form-induced shear stresses. Due to the strong dependence of induced flow direction on the interface geometry, we segmented the flow field into two types of areas based on the slope angle formed by the top-layer cylinders: the windward area and leeward area. The conditional average of turbulence kinematic energy budget over each type of area reveals their respective role in turbulence transportation more explicitly. In addition, we use finite-time Lyapunov exponents to inspect the Lagrangian coherent structures in the flow fields, which reveal the preferential fluid trajectories in the random porous medium geometry.

Analytical solution based on BEM to oblique waves scattering by thin arc-shaped permeable barrier applied for array of aquaculture cages

In this paper, linear oblique wave incident to a thin arc-shaped permeable barrier and an array of permeable circular cylinders was studied analytically. Two unique research objectives of this work include, considering the thickness for permeable material and the wavefield inside surrounded region by the permeable structure. The conventional boundary element method (BEM) is used to solve the governing equations of the problem. The mathematical relation between Bessel functions leads to representing the BEM-related integrals in the Fourier modes of Hankel function. This approach is useful as the singular integrals are accounted indirectly. Two basic geometries made by the permeable material are studied, including an arc-shaped and a circular geometry. The first geometry can represent a wave-breaking barrier in shallow water, while the latter can represent a floating fish farm in deep water. For the floating fish farm, the study is extended to the interaction between an array of cages. To quantify the amount of wave energy passed through the object, the Energy Transmission Index or ETI concept is introduced. ETI can be used as an indicator for permeable barriers performance.The results indicate that ETI is mostly a function of permeability rather than the wavenumber. In addition, the imaginary part of the permeability parameter plays an essential role in the problem of wave incident to permeable barrier, and it is necessary to be determined with enough accuracy. Furthermore, the shear force and bending moment on the base of the barrier and drift force and heeling moment on circular cylinders are studied. The results show, the drift force decreases as permeability and wavenumber increase. The results of this research are useful in the design of rigid circular offshore aquaculture fish cages and coastal barriers.

An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders

This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.

On the acoustical performance of plenum window installed with rigid circular cylinders at low frequency

The low-frequency acoustical performance of plenum window with an array of rigid circular cylinders installed is analysed with the Finite Element Method (FEM) in the current study. This study includes the effect of vibrational glass boundaries, cavity resonance, the opening width of the window, and the arrangement of cylinders, on the sound transmission loss (TL) of the plenum window. The relationship between the above factors with TL is also investigated statistically and simple optimization of the geometry has been done based on the results. Results have shown that including the mechanical vibration of glass does not result in a significant difference with previous results, but an average decrease of 1 dB in TL is observed near the eigenfrequencies of the glass boundary. The effect of opening width on TL is not trivial but frequency-dependent due to the cavity resonance formed between the overlapping regions. Lastly, the introduction of rigid cylinders causes a shift of significant TL to lower frequency regardless of the opening width. The installation of them also seems to have destroyed the formation of cavity resonance, which results in much smaller TL.

Analytical Solution of Earthquake-Induced Hydrodynamic Pressure on Arrays of Circular Cylinders Considering High-Order Scattered Waves

AbstractThe earthquake-induced pressures on arrays of cylinders have received less concern, although pile groups have been widely adopted in real practice. This paper develops an analytical method ...

Stochastic Effects of 2D Random Arrays of Cylinders on Rarefied Gas Permeability Using the Lattice Boltzmann Method

A large set of 2D random arrays of circular cylinders is generated to perform a statistical study on rarefied gas flow through micro-porous media. The flow regimes in this work lie for Knudsen numbers (Kn) ranging from the continuum to the transition regimes. Arrays are built by randomly placing cylinders with constant diameter with a uniform distribution without overlapping, and are generated for three target porosities. Fluid flow is assumed to be incompressible and isothermal. A modified lattice Boltzmann model is adopted to account for discrete effects, with slip-velocity boundary conditions and a Kn-dependent multi-relaxation time collision operator. The apparent permeability is modeled with Darcy’s law with a Klinkenberg-type relationship and compared with existing correlations. Velocity fields highlight the increasing contribution of fluid flow through small pores with increasing Kn. Numerical results show that porous media randomness leads to an uncertainty on rarefied gas permeability calculation despite the same structural characteristics and may not strictly follow a specific correlation. The influence of a local collision operator based on a local Kn instead of a global one in the numerical model is also studied. Results show that the permeability in rarefied regimes undergoes significant deviation when applying the local collision operator compared to the global one. These differences could result from a more accurate capture of the pore-scale behavior with a local Kn. Thus, it emphasizes the sensitivity of the model and the apparent permeability calculation to the appropriate definition of Kn.

Permeability prediction of fibrous porous media by the lattice Boltzmann method with a fluid-structure boundary reconstruction scheme

The D3Q27 lattice Boltzmann method (LBM) combined with the fluid-structure boundary reconstruction (fsBR) scheme and the interpolated bounce back (IPBB) method is extensively evaluated to predict the permeability of nonwoven fibrous porous media. The fsBR-IPBB method transfers digitally defined step-like boundary data, e.g. the three-dimensional structure data obtained by the X-ray computed tomography, to continuous smooth boundary data via level-set functions. It leads to highly accurate calculations despite low lattice resolutions of thin fibers with circular cross-sectional shapes, compared to the conventional half-way bounce back (HWBB) method. The fsBR-IPBB method is first applied to predict the permeability of two different arrays of impermeable circular cylinders and verified by comparing the results with the data in the literature. We then validate the method referring to the numerically and experimentally obtained permeability of six types of nonwoven fabrics prepared by the industrial hydroentanglement process. Finally, the discussion on the applicability and the limitation of the macroscopic correlation models to estimate permeability of porous media is carried out. The results show that although the calculated permeability is in reasonable agreement with the measured one with an error of 8.1–16.3%, analytical or empirical correlation models fail to give the correct trend due to the highly inhomogeneous and anisotropic properties of hydroentangled nonwoven fabrics.

Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation

Turbulence transportation across permeable interfaces is investigated using direct numerical simulation, and the connection between the turbulent surface flow and the pore flow is explored. The porous media domain is constructed with an in-line arranged circular cylinder array. The effects of Reynolds number and porosity are also investigated by comparing cases with two Reynolds numbers (Reapprox 3000,6000) and two porosities (varphi =0.5,0.8). It was found that the change of porosity leads to the variation of flow motions near the interface region, which further affect turbulence transportation below the interface. The turbulent kinetic energy (TKE) budget shows that turbulent diffusion and pressure transportation work as energy sink and source alternatively, which suggests a possible route for turbulence transferring into porous region. Further analysis on the spectral TKE budget reveals the role of modes of different wavelengths. A major finding is that mean convection not only affects the distribution of TKE in spatial space, but also in scale space. The permeability of the wall also have an major impact on the occurrence ratio between blow and suction events as well as their corresponding flow structures, which can be related to the change of the Kármán constant of the mean velocity profile.

Analytical Technique for Synthesizing a Leaky-Wave Antenna with a Semitransparent Wall of Metal Cylinders

We have developed an analytical technique for synthesizing a leaky-wave antenna in the form of an irregular hollow rectangular metal waveguide with a narrow wall in the form of an array of circular metal cylinders using an approximate expression for the reflection coefficient of a plane wave from a fine-periodic lattice of circular metal cylinders and the dispersion equation for a waveguide with a partially transparent wall. As an example of the application of this technique, two leaky-wave antennas are synthesized: with a uniform and sinusoidal distribution of the field amplitude along the antenna. We have performed electrodynamic modeling of synthesized antennas using the finite element method. For a synthesized antenna with a uniform amplitude distribution, the results of a numerical experiment are compared with the results of measurements of an experimental sample in the centimeter wavelength range.