Turbulent Transition Research Articles

Toward Interpreting the IBEX Ribbon with Mirror Diffusion in Interstellar Turbulent Magnetic Fields

We investigate the role of the magnetohydrodynamic (MHD) turbulence measured by Voyager in the very local interstellar medium (VLISM) in modeling the Interstellar Boundary Explorer ribbon. We demonstrate that the mirroring by compressible modes of MHD turbulence dominates over that by the mean magnetic field. Based on the new mirror diffusion mechanism identified by Lazarian & Xu for particles with large pitch angles in MHD turbulence, we find that the mirror diffusion can both confine pickup ions and preserve their initial pitch angles, and thus it accounts for the enhanced intensity of energetic neutral atoms that return to the heliosphere. The ribbon width is determined by both the range of pitch angles for effective turbulent mirroring and the field line wandering induced by Alfvénic modes. It in turn provides a constraint on the amplitude of magnetic fluctuations of fast modes. The field line wandering also affects the coherence of the ribbon structure across the sky. By extrapolating the magnetic energy spectrum measured by Voyager, we find that the injection scale of the turbulence in the VLISM must be less than ∼500 au for the ribbon structure to be coherent.

Laminar to turbulent transition in terms of information theory

Laminar to turbulent transition in terms of information theory

Influence of deep gaps on laminar–turbulent transition in two-dimensional boundary layers at subsonic Mach numbers

Systematic experimental investigations on the influence of deep gaps on the location of laminar–turbulent transition are reported. The tests were conducted in the Cryogenic Ludwieg–Tube Göttingen, a blow-down wind tunnel with good flow quality, at eight different unit Reynolds numbers ranging from Re_1 = {17.5,,times 10^{6},mathrm{{m}^{-1}}} to 80,times,10^{6},mathrm{m}^{-1}, three Mach numbers, M= 0.35, 0.50 and 0.65, and various pressure gradients. A flat-plate configuration, the extended two-dimensional wind tunnel model PaLASTra was modified in order to allow the installation of gaps with nominal widths of 30 upmu m, 100 upmu m and 200 upmu m and a depth of d = {9,mathrm{mm}}. A maximum Reynolds number based on the gap width Re_{w} = Re_1 cdot w approx {16{,}000} was reached. Transition Reynolds numbers ranging from Re_{tr}approx 1 × 106 to 11 × 106 were measured, as a function of gap width, pressure gradient and Mach and Reynolds number. This systematic investigation facilitates a linear approximation of Re_{tr} dependent on the boundary layer shape factor H_{12} for various flow conditions and gap widths. It was therefore possible to conduct an investigation of Re_{tr} depending on Re_{1} and the relative change of the transition location depending on the gap width w. Incompressible linear stability analysis was used to calculate amplification rates of Tollmien–Schlichting waves and determine critical N-factors by correlation with measured transition locations. The change in the critical N-factor varDelta N by installation of the gap is investigated as a function of w and Re_w. It was found that a gap width of 30 upmu m reduces the critical N-factors in the range of varDelta N approx 0.5 pm 0.25, while gap widths of 100 upmu m and 200 upmu m reduce the critical N-factor in the range of varDelta N approx 1.5 pm 1. Interestingly, an increase in gap width from 100 to 200 upmu m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.

Hydrodynamic roughness induced by a multiscale topography

Turbulent flows above a solid surface are characterised by a hydrodynamic roughness that represents, for the far velocity field, the typical length scale at which momentum mixing occurs close to the surface. Here, we are theoretically interested in the hydrodynamic roughness induced by a two-dimensional modulated surface, the elevation profile of which is decomposed in Fourier modes. We describe the flow for a sinusoidal mode of given wavelength and amplitude with Reynolds-averaged Navier–Stokes equations closed by means of a mixing-length approach that takes into account a possible surface geometrical roughness as well as the presence of a viscous sublayer. It also incorporates spatial transient effects at the laminar–turbulent transition. Performing a weekly nonlinear expansion in the bedform aspect ratio, we predict the effective hydrodynamic roughness when the surface wavelength is varied and we show that it presents a non-monotonic behaviour at the laminar–turbulent transition when the surface is hydrodynamically smooth. Further, with a self-consistent looped calculation, we are able to recover the smooth–rough transition of a flat surface, for which the hydrodynamic roughness changes from a regime where it is dominated by the viscous length to another one where it scales with the surface corrugation. We finally apply the results to natural patterns resulting from hydrodynamic instabilities such as those associated with dissolution or sediment transport. We discuss in particular the aspect ratio selection of dissolution bedforms and roughness hierarchy in superimposed ripples and dunes.

Topology optimization of Superhydrophobic Surfaces to delay spatially developing modal laminar–turbulent transition

Super-Hydrophobic Surfaces (SHSs) have been shown to reduce skin friction of an overlying fluid as a consequence of gas pockets trapped within the surface’s microstructure. More recently, they have also been shown capable of delaying laminar–turbulent transition. This article investigates the applicability of topology optimization in designing the macroscopic layout of SHSs in a channel that are able to further delay K-type transition in a spatial setting. Unsteady direct numerical simulations are performed to simulate the transition scenario. This is coupled with adjoint–based sensitivity analysis and gradient based optimization. The optimized designs found through this procedure are capable of moving the transition location further downstream compared to a homogeneous counterpart by inhibiting the growth of secondary instability modes. This article provides the first application of topology optimization to a spatially developing transition scenario.

Simulation of the flow past a circular cylinder from sub-critical to super-critical Reynolds numbers using an intermittency-based hybrid model

In this work, we investigate the prediction of the flow around a circular cylinder from sub-critical to super-critical Reynolds numbers using a hybrid approach which combines a dynamic variational multiscale (DVMS) large-eddy simulation (LES) model and a transitional RANS model. In the proposed hybrid approach, the variational multiscale model, aiming to limit the effects of the subgrid-scale (SGS) model to the smallest resolved scales, is combined with the dynamic procedure which provides a tuning of the SGS dissipation in space and time. For representing laminar to turbulent boundary layer transition, the equations of the RANS part of the hybrid approach are completed with a transition model based on an intermittency transport equation. Results are compared to those of other numerical simulations in the literature and with experimental data. They highlight the overall good prediction capabilities of the proposed hybrid strategy for the simulation of such massively separated flows, even with the use of coarse meshes. In particular, the intermittency-based hybrid model was found to be able to predict the drag crisis of a circular cylinder, as well as the sharp increase in vortex shedding frequency, unlike the equivalent hybrid approach when no laminar-turbulent transition model is introduced.

Numerical Study of the Influence of the Critical Reynolds Number on the Aerodynamic Characteristics of the Wing Airfoil

The paper reports the results of a study concerned with the influence of the size of the leading edge laminar bubble on the aerodynamic characteristics of the HGR01 airfoil. The completely turbulent and transient flows are considered. The mechanism of the appearance and interaction of laminar and turbulent flow separation near the leading and trailing edges of the airfoil is studied in detail. In the paper, the dependence of aerodynamic forces on the critical Reynolds number for the HGR01 airfoil is discussed. It has been established that the separation bubble at the leading edge can only be obtained using the laminar–turbulent transition model. Fully turbulent models are not able to show this feature of the airfoil flow. Graphs of the lift coefficient as a function of the critical Reynolds number, as well as the pressure distribution as a function of the size of the laminar bubble, are shown.

Roughness induced transition delay in a swept-wing boundary layer in presence of freestream disturbances, Part 1: Turbulence effects

Results of experimental investigations on control of the laminar–turbulent transition location in a 45-degree swept-wing boundary layer by the distributed micro-sized roughness (MSR) elements in presence of freestream perturbations are discussed in this two-part work. Part 1 of this study (the present paper) is devoted to the freestream turbulence effects, while Part 2 (Borodulin et al., 2023) concentrates on consideration of the acoustic waves’ effects. The present paper (Part 1) contains: (i) a brief description of previous studies in the field, (ii) description of the experimental setup and techniques of the measurements (based on infrared thermography), (iii) the results of optimization of parameters of the MSR-elements, and (iv) results of studies of freestream turbulence effects on the MSR transition control. The MSR-elements are shown to excite in the boundary layer controlled stationary vortices, which are able to modify significantly both the base flow and its stability characteristics. Variation of the height and the period of the MSR-elements allowed us to find the most stabilizing effect on the boundary layer flow compared to the case without MSR as a reference one. A significant downstream shift in the position of the laminar–turbulent transition caused by the MSR has been detected and documented in detail. The robustness of this flow control method to freestream turbulence has been studied by increasing the turbulence level by means of turbulence generating grids. At enhanced freestream turbulence levels, the laminar–turbulent transition was found to move upstream, while the MSR-elements lost their effectiveness in the transition control.

Numerical Simulation of Turbulent Fluid Flow in Rough Rock Fracture: 2D Case

We investigate both laminar and turbulent flow regimes in a rough-walled rock fracture via numerical CFD simulations. While previous studies were limited to either fully viscous Darcy or inertial Forchheimer laminar flow regimes, we chose to cover the widest possible Reynolds number range of 0.1–10^6. We introduce CFD simulation of a turbulent flow for rough-walled fractures, implementing RANS approach to turbulence modeling. We focus on 2D fracture geometries and implement changes in both shear displacement and wall roughness, systematically examining their effect on fracture permeability and friction factor in a manner similar to the fundamental studies of the flow in rough-walled pipes. For a curvilinear fracture, laminar flow becomes non-stationary between Re , {sim } , 10^2–10^3, earlier for larger shear displacement and wall roughness. Laminar–turbulent transition starting at Re_{textrm{cr}} , {sim } , 2300 may lead to a sharp drop in permeability depending on the fracture geometry; this gap vanishes for larger shear displacement and wall roughness. Depending on the fracture geometry, bottlenecks closing with shear become a major negative factor for the overall permeability.

Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics. Part I: Expanding Observational Evidence of Occurrence and Environmental Influences

Abstract Multiple recent observations in the mesosphere have revealed large-scale Kelvin–Helmholtz instabilities (KHI) exhibiting diverse spatial features and temporal evolutions. The first event reported by Hecht et al. exhibited multiple features resembling those seen to arise in early laboratory shear-flow studies described as “tube” and “knot” (T&K) dynamics by Thorpe. The potential importance of T&K dynamics in the atmosphere, and in the oceans and other stratified and sheared fluids, is due to their accelerated turbulence transitions and elevated energy dissipation rates relative to KHI turbulence transitions occurring in their absence. Motivated by these studies, we survey recent observational evidence of multiscale Kelvin–Helmholtz instabilities throughout the atmosphere, many features of which closely resemble T&K dynamics observed in the laboratory and idealized initial modeling. These efforts will guide further modeling assessing the potential importance of these T&K dynamics in turbulence generation, energy dissipation, and mixing throughout the atmosphere and other fluids. We expect these dynamics to have implications for parameterizing mixing and transport in stratified shear flows in the atmosphere and oceans that have not been considered to date. Companion papers describe results of a multiscale gravity wave direct numerical simulation (DNS) that serendipitously exhibits a number of KHI T&K events and an idealized multiscale DNS of KHI T&K dynamics without gravity wave influences. Significance Statement Kelvin–Helmholtz instabilities (KHI) occur throughout the atmosphere and induce turbulence and mixing that need to be represented in weather prediction and other models of the atmosphere and oceans. This paper documents recent atmospheric evidence for widespread, more intense, features of KHI dynamics that arise where KH billows are initially discontinuous, misaligned, or varying along their axes. These features initiate strong local vortex interactions described as “tubes” and “knots” in early laboratory experiments, suggested by, but not recognized in, earlier atmospheric and oceanic profiling, and only recently confirmed in newer, high-resolution atmospheric imaging and idealized modeling to date.

EAF-WGAN: Enhanced Alignment Fusion-Wasserstein Generative Adversarial Network for Turbulent Image Restoration

Because of optical distortion induced by atmospheric turbulence and the limitations of optical devices, acquired images of space objects are blurred and degraded. This effect results in anamorphosis in the output of two-dimensional imaging systems. In this work, we present a novel Enhanced Alignment Fusion-Wasserstein Generative Adversarial Network, called EAF-WGAN, for turbulent image restoration. This model is characterized by the innovative use of two modules, including the Align Module (AM) and the Feature Fusion Module (FFM) in the generator, especially in the process of feature fusion, in which 3D convolution is used. Through 3D convolution, the temporal and spatial information of the input image is obtained. Therefore, the formation mode and intensity of turbulence are not considered and the image can be reconstructed. The ability of EAF-WGAN is proved by algorithmically simulated data, physically simulated data, and real-world data.

Narrow Width Farley‐Buneman Spectra Above 100 km Altitude

AbstractFor spectra associated with full turbulence the observed mean phase velocity of unstable Farley‐Buneman waves has been found not to exceed the ion‐acoustic speed, cs. This has been attributed to various nonlinear processes. However, weakly turbulent modes are also excited on the edge of the “instability cone.” These modes have to be actual eigenmodes predicted by linear instability theory near‐threshold conditions. Unlike the modes that are associated with strong turbulence, these weakly turbulent modes are affected by the ion drift. This can make the Doppler shift of narrow spectra reach as high as the E × B drift velocity in the upper portion of the unstable layer at small aspect angles. Slow narrow spectra are also predicted nearer the E direction. We have produced a model of the Doppler shift of narrow‐width spectra under various electric field conditions above 100 km altitude. While the fluid dispersion relation is used to clarity the physics, we have also found the eigenmodes from an accepted kinetic dispersion relation. The calculations include a new model of the ion‐acoustic speed based on an empirical model of the electron temperature and of ion frictional heating under strong electric field conditions. The model provides an explanation for various VHF observations of the Doppler shift of narrow spectra that have been called “Type III spectra” and “Type IV spectra” in the existing literature.

Study of Wear Resistance of a Radial Bearing Covered by a Polymer Coating with an Axial Groove on a Nonstandard Base Surface

This paper is devoted to study of increasing the wear resistance of a radial plain bearing. The operation of a bearing is considered in the hydrodynamic mode by means of application of an antifriction polymer composite coating with an axial groove and the micropolar properties on a nonstandard bearing surface adapted to the friction conditions of a bearing bush. The effect of pressure and temperature in the turbulent friction mode on the rheological properties of the lubricant is taken into account. Based on the equation for the micropolar fluid flow in a “thin layer” as well as on the dependence of the micropolar lubricant on the pressure and temperature and on the continuity equation, a self-similar solution has been found taking into account the axial groove on the surface of a bearing bush and without taking into account the axial groove. As a result, the velocity and pressure fields in the axial groove and on the surface of a polymer antifriction composite coating have been determined as has the load capacity and friction force, which make it possible to increase the load capacity, reduce the friction coefficient (increase wear resistance), and also increase the duration of the hydrodynamic mode. The results of numerical analysis of theoretical models and experimental evaluation of the suggested design are presented to verify and confirm the efficiency of the models obtained.

Aerodynamic drag reduction through a hybrid laminar flow control and variable camber coupled wing

This paper presents computational fluid dynamics (CFD) results of a transonic transport aircraft wing, featuring a hybrid laminar flow control (HLFC) and variable camber (VC) technology coupling. The goal of the paper is a quantitative assessment of synergistic effects for aerodynamic drag reduction, when combining the possibility of actively shaping the surface pressure distribution of the wing through VC with the passive natural laminar flow aspect of HLFC. Modeling approaches for both VC integration, achieved through deflections of an Adaptive Dropped Hinge Flap (ADHF), and boundary layer suction into a CFD workflow are presented. Transition prediction is accomplished with the γ−Reθ+Cross-flow(CF) transition turbulence model, and linear stability theory (LST) coupled to a two-N-factor transition prediction method. Both methods reflect synergy-driven effects. While the extent of laminar flow predicted by the γ−Reθ+CF model is limited, both favorable ADHF settings and boundary layer suction lead to an overall drag reduction. This is correspondingly reflected through the analyses via LST. Furthermore, the latter predicts a pronounced downstream shift in transition position with increasing suction strength, where the inherent differentiation of transition mechanisms in the two-N-factor method between Tollmien-Schlichting (TSI) and cross-flow instabilities (CFI) reflects a marked reduction in TSI N-factors with increasing ADHF deflection angles. Even though N-factors associated to CFI partially increase through ADHF deflections, the intended synergistic effects are represented throughout the investigated parameter range, leading to an increase in the extent of laminar flow for adequate ADHF deflection angles.

Numerical simulation of a toroidal single-phase natural circulation loop with a k-kL-ω transitional turbulence model

The wall friction correlations of oscillatory natural circulation loops are highly loop-specific, making it difficult to perform 1-D system simulations before obtaining specific experimental data. To better predict the friction characteristics, the nonlinear dynamics of a toroidal single-phase natural circulation loop were numerically investigated, and the transition effect was considered. The k-kL-ω transitional turbulence and k-ω SST turbulence models were used to compute the flow characteristics of the loop under different heating powers varying from 0.48 to 1.0 W/cm2, and the results of both models were compared with previous experiments. The mass flow rates and friction factors predicted by the k-kL-ω model showed a better agreement with the experimental data than the results of the k-ω SST model. The oscillation frequencies calculated using both models agreed well with the experimental data. The k-kL-ω transitional turbulence model provided better friction-factor predictions in oscillatory natural circulation loops because it can reproduce the temporal and spatial variation of the wall shear stress more accurately by capturing the movement of laminar, transition turbulent zones inside unstable natural circulation loops. This study shows that transition effects are a possible explanation for the highly loop-specific friction correlations observed in various oscillatory natural circulation loops.

Roughness induced transition delay in a swept-wing boundary layer in presence of freestream disturbances, Part 2: Acoustic stabilization

Results of experimental investigations on control of the laminar–turbulent transition location in a 45-degree swept-wing boundary layer by the distributed micro-sized roughness (MSR) elements in presence of freestream perturbations are discussed in this two-part work. Part 1 of this study Borodulin et al. (2023) is devoted to the freestream turbulence effects, while Part 2 (the present paper) concentrates on consideration of the acoustic waves’ effects. This paper contains: (i) a complementary description of the experimental setup and measurement techniques related to the acoustic excitation and (ii) the results of studies of the freestream acoustic-field effects on the MSR transition control. The robustness of the MSR transition-control mechanism has been studied by altering the wind-tunnel flow quality: by introducing a significant background sound and/or by simultaneous variation of both the freestream turbulence level and the level of the acoustic wave excitation. At enhanced freestream turbulence, the laminar–turbulent transition is found to move upstream regardless of the sound level and frequency, while the MSR-elements lost their effectiveness in transition control in all cases. At low freestream turbulence levels and in absence of the MSR, the acoustic waves did not affect basically the transition location. However, if the laminar–turbulent transition was delayed by the MSR, the sound of a certain frequency was found to be able to cause a significant additional transition delay.

Numerical investigation of the dynamic stall reduction on the UAS-S45 aerofoil using the optimised aerofoil method

AbstractThis paper investigates the effect of the optimised morphing leading edge (MLE) and the morphing trailing edge (MTE) on dynamic stall vortices (DSV) for a pitching aerofoil through numerical simulations. In the first stage of the methodology, the optimisation of the UAS-S45 aerofoil was performed using a morphing optimisation framework. The mathematical model used Bezier-Parsec parametrisation, and the particle swarm optimisation algorithm was coupled with a pattern search with the aim of designing an aerodynamically efficient UAS-45 aerofoil. The $\gamma - R{e_\theta }$ transition turbulence model was firstly applied to predict the laminar to turbulent flow transition. The morphing aerofoil increased the overall aerodynamic performances while delaying boundary layer separation. Secondly, the unsteady analysis of the UAS-S45 aerofoil and its morphing configurations was carried out and the unsteady flow field and aerodynamic forces were analysed at the Reynolds number of 2.4 × 106 and five different reduced frequencies of k = 0.05, 0.08, 1.2, 1.6 and 2.0. The lift ( ${C_L})$ , drag ( ${C_D})$ and moment ( ${C_M})\;$ coefficients variations with the angle-of-attack of the reference and morphing aerofoils were compared. It was found that a higher reduced frequencies of 1.2 to 2 stabilised the leading-edge vortex that provided its lift variation in the dynamic stall phase. The maximum lift $\left( {{C_{L,max}}} \right)$ and drag $\left( {{C_{D,max}}} \right)\;$ coefficients and the stall angles of attack are evaluated for all studied reduced frequencies. The numerical results have shown that the new radius of curvature of the MLE aerofoil can minimise the streamwise adverse pressure gradient and prevent significant flow separation and suppress the formation of the DSV. Furthermore, it was shown that the morphing aerofoil delayed the stall angle-of-attack by 14.26% with respect to the reference aerofoil, and that the ${C_{L,max}}\;$ of the aerofoil increased from 2.49 to 3.04. However, while the MTE aerofoil was found to increase the overall lift coefficient and the ${C_{L,max}}$ , it did not control the dynamic stall. Vorticity behaviour during DSV generation and detachment has shown that the MTE can change the vortices’ evolution and increase vorticity flux from the leading-edge shear layer, thus increasing DSV circulation. The conclusion that can be drawn from this study is that the fixed drooped morphing leading edge aerofoils have the potential to control the dynamic stall. These findings contribute to a better understanding of the flow analysis of morphing aerofoils in an unsteady flow.

Bifurcation Analysis Software and Chaotic Dynamics for Some Problems in Fluid Dynamics Laminar–Turbulent Transition

The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a difficult problem. Analytical and numerical approaches must be used to deal with this problem. Numerical methods include solving some of the hardest problems in computational mathematics, which include system spectral and algebraic problems, specific nonlinear numerical methods, and computational implementation on parallel architectures. The software structure that is required to perform numerical bifurcation analysis for large-scale systems was considered in the paper. The software structure, specific features that are used for successful bifurcation analysis, globalization strategies, stabilization, and high-precision implementations are discussed. We considered the bifurcation analysis in the initial boundary value problem for a system of partial differential equations that describes the dynamics of incompressible ABC flow (3D Navier–Stokes equations). The initial stationary solution is characterized by the stability and connectivity to the main solutions branches. Periodic solutions were considered in view of instability transition problems. Finally, some questions of higher dimensional attractors and chaotic regimes are discussed.

Computational Fluid Dynamics Turbulence Model and Experimental Study for a Fontan Cavopulmonary Assist Device.

Head-flow HQ curves for a Fontan cavopulmonary assist device (CPAD) were measured using a blood surrogate in a mock circulatory loop and simulated with various computational fluid dynamics (CFD) models. The tests benchmarked the CFD tools for further enhancement of the CPAD design. Recommended Reynolds-Averaged Navier-Stokes (RANS) CFD approaches for the development of conventional ventricular assist devices (VAD) were found to have shortcomings when applied to the Fontan CPAD, which is designed to neutralize off-condition obstruction risks that could contribute to a major adverse event. The no-obstruction condition is achieved with a von Karman pump, utilizing large clearances and small blade heights, which challenge conventional VAD RANS-based CFD hemodynamic simulations. High-fidelity large eddy simulation (LES) is always recommended; however, this may be cost-inhibitive for optimization studies in commercial settings, thus the reliance on RANS models. This study compares head and power predictions of various RANS turbulence models, employing experimental measurements and LES results as a basis for comparison. The models include standard k-ϵ, re-normalization group k-ϵ, realizable k-ϵ, shear stress transport (SST) k-ω, SST with transitional turbulence, and Generalized k-ω. For the pressure head predictions, it was observed that the standard k-ϵ model provided far better agreement with experiment. For the rotor torque, k-ϵ predictions were 30% lower than LES, while the SST and LES torque values were near identical. For the Fontan CPAD, the findings support using LES for the final design simulations, k-ϵ model for head and general flow simulation, and SST for power, shear stress, hemolysis, and thrombogenicity predictions.

Study of Wear Resistance of a Radial Bearing Covered by a Polymer Coating with an Axial Groove on a Nonstandard Base Surface

This paper is devoted to study of increasing the wear resistance of a radial plain bearing. The operation of a bearing is considered in the hydrodynamic mode by means of application of an antifriction polymer composite coating with an axial groove and the micropolar properties on a nonstandard bearing surface adapted to the friction conditions of a bearing bush. The effect of pressure and temperature in the turbulent friction mode on the rheological properties of the lubricant is taken into account. Based on the equation for the micropolar fluid flow in a “thin layer” as well as on the dependence of the micropolar lubricant on the pressure and temperature and on the continuity equation, a self-similar solution has been found taking into account the axial groove on the surface of a bearing bush and without taking into account the axial groove. As a result, the velocity and pressure fields in the axial groove and on the surface of a polymer antifriction composite coating have been determined as has the load capacity and friction force, which make it possible to increase the load capacity, reduce the friction coefficient (increase wear resistance), and also increase the duration of the hydrodynamic mode. The results of numerical analysis of theoretical models and experimental evaluation of the suggested design are presented to verify and confirm the efficiency of the models obtained.