Cylindrical Coordinate System Research Articles

Thin liquid films on a rotary bell atomizer in surface-following coordinates

This article analyzes a published formulation of the Navier–Stokes equations cast into surface-following coordinates and provides some additional mathematical background to follow the article. Ubiquitous in the paint shops of automotive plants around the world, a high-speed rotary bell is succinctly described as a rapidly spinning concave axisymmetric surface with liquid paint supplied from a port coinciding with the center of rotation. The spinning surface transfers momentum to the paint film causing it to flow outward. Upon reaching the bell periphery, it is flung off, subsequently forming an atomized spray transferred to an automotive body through advection and electrostatics. Common analytical frameworks of rotating films were spherical or cylindrical coordinate systems where the wetted surface profile of the bell was constrained to follow a coordinate axis. This led to solutions for films modeled with conical, disk-like, or partial hemispherical profiles. An alternative was a more general case using a surface-following orthogonal curvilinear coordinate system along with its derived vector operators. In the unique case of a thin film, these results validated a simpler pattern found in common coordinate systems.

Buckling analysis of multilayer FG-CNT reinforced nanocomposite cylinders assuming CNT waviness, agglomeration, and interphase effects using the CUF-EFG method

In this article, the Carrera unified formulation (CUF) is developed for the buckling analysis of multilayered functionally graded carbon nanotube (MFG-CNT) reinforced cylinders. For this purpose, the CUF is obtained in the cylindrical coordinate system as a first step. Then, the displacement-based CUF is derived from the principle of virtual work in each individual layer in the framework of the element free Galerkin (EFG) method. The mechanical properties of each CNTs-reinforced layer are estimated using the modified Halpin–Tsai (H-T) micromechanical model and rule of mixture. In this model, the waviness, interphase, and agglomeration of CNTs are accounted using influencing factors in terms of CNTs geometric and processing characteristics. Four types of laminates, which are composed of several reinforced layers with different arrangements (distributions) along the radial direction, are taken into account to examine the effect of the layers’ arrangement on the buckling capacity of the cylinder. The proposed CUF-EFG formulations and solution method are validated by comparing the present buckling loads with those obtained by theoretical formula for the homogeneous slender cylinders. A parametric study is conducted to investigate the effects of CNTs weight fraction, waviness, agglomeration and interphase of CNT, distribution of layers, power-law index, radius-to-thickness ratio, length-to-radius ratio, and boundary conditions (BCs) on the critical buckling loads of MFG-CNT reinforced cylinder. The results show the high performance of the proposed CUF-EFG method for buckling analysis of MFG-CNT reinforced cylinders with a wide range of aspect ratios.

Singular integral equation for an electric dipole taking into account the finite metal conductivity from which it is made

A singular integral equation for an electric dipole has been obtained, which makes it possible to take into account the finite conductivity of the metal from which it is made. The derivation of the singular integral equation is based on the application of the Greens function for free space, written in a cylindrical coordinate system, taking into account the absence of the dependence of the field on the azimuthal coordinate, on a point source located on the surface of an electric dipole. Methods for its solution are proposed. In contrast to the well-known mathematical models of an electric dipole, built in the approximation of an ideal conductor, the use of the singular integral equation obtained in this work makes it possible to take into account heat losses and calculate the efficiency.

Real-time panoramic-deformation measurement of cabin structure of launch vehicle based on camera network

<p indent="0mm">To satisfy the requirement of real-time panoramic-deformation measurement of a cabin structure in a large-diameter launch vehicle, a camera-network deformation-measurement system composed of 24 cameras and real-time three-dimensional (3D) deformation-measurement software based on CPU parallel computing was developed. The 360° full-circle deformation measurement of the inner surface of a cylindrical coordinate system and real-time measurement of the local deformation of a local Cartesian coordinate system were successfully realized. The camera-network measurement system consisted of 12 sets of binocular systems. The field of view of a single set of binocular systems was 3.6 m×3.6 m, and a certain overlap area was set between two adjacent binocular systems to ensure continuity of measurements. Photogrammetry and binocular stereo vision were used to reconstruct the 3D coordinates of the coded points, and coordinate transformation between the local and global coordinate systems was realized using the coded points. Finally, coordinate unification of the 12 sets of binocular systems was performed. A single set of binocular systems could be connected to a computer. By implementing the seed-point-based parallel algorithm and initial guess-estimation-algorithm-based deformation-transfer scheme, real-time 3D displacement and surface-strain measurements at 70000 points per second were successfully realized. On the basis of the 360° full-circle deformation-measurement results in the cylindrical coordinate system, high-precision calculation of the diffusion angle was successfully realized. The standard deviation of the static noise in the three directions was less than 0.01 mm, and the standard deviation of the static noise in the strain was less than 50 microstrains.

Shape optimization of composite porous vapor chamber with radial grooves: A study on the minimization of maximum pressure drop

Composite porous vapor chamber (CPVC) with uniform radial grooves is a recently developed vapor chamber, exhibiting good temperature uniformity and excellent stability under high heat flux of 280 W/cm2 with the thermal resistance less than 0.15 °C/W. However, the maximum pressure drop in CPVC due to liquid flow is prone to exceed the limits of capillary pressure, and the shape design of the wicks lacks scientific and objective enough criteria. This paper proposes a shape optimization method to optimize the shape of the evaporator wick in CPVC, based on the study on the minimization of the maximum pressure drop. In this method, the discrete adjoint method is utilized to efficiently analyze the sensitivities and find the most rapid descendant directions for the minima problem. The shape of the evaporator wick is updated by the polynomial-based approach based on the sensitivity information. Results indicate that the bottom contours of the wick blocks’ surfaces surrounding the circular cavity contribute the highest sensitivities. Consequently, the mesh deformations near the contours change the shape of the lateral surfaces of wick blocks from rectangular to concave trapezoidal in both Cylindrical and Cartesian coordinate systems. This reduces the maximum velocities and flow resistance in CPVC, due to the smoother structural transition from the condenser wick to the evaporator wick, thus reducing the maximum pressure drop by about 18.5% and 23.3% in Cartesian and Cylindrical coordinate systems, respectively. The proposed method may pave a more objective and scientific alternative to design the shape of the wicks in CPVC.

Analysis of blood flow through curved artery with mild stenosis

Building-up of plaque narrows arteries, decreasing blood flow to the heart, causing chest pain, shortness of breath, or other coronary artery disease signs and symptoms. Implementing Navier–Stokes equations in a cylindrical coordinate system and assuming axial symmetry under laminar flow conditions, the study has been conducted on the two aspects of blood flow dynamics viz., velocity profile and volumetric flow rate of blood around curved stenosis with a variation of curvature of the artery and the stenosis thickness. The blood flow behavior taking different values for the viscosity coefficient has been also studied.

Обобщенные модельные представления теории теплового удара для локально-неравновесных процессов теплообмена

An open problem of the theory of thermal shock in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process was considered. The model simultaneously includes three coordinate systems: Cartesian coordinates - a massive body bounded by a flat surface; spherical coordinates - a massive body with an internal spherical cavity; cylindrical coordinates - a massive body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, medium. The task is set: to obtain an analytical solution, to carry out numerical experiments and to give their physical analysis. As a result, generalized model representations of thermal shock in terms of dynamic thermoelasticity have been developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of curvature of the boundary surface of the thermal shock area substantiates the initial statement of the dynamic problem in displacements using the proposed corresponding "compatibility" equation. The latter made it possible to propose a generalized dynamic model of the thermal reaction of massive bodies with internal cavities simultaneously in Cartesian, spherical and cylindrical coordinate systems under conditions of intense thermal heating and cooling, thermal heating and cooling, heating and cooling by the medium. The model is considered in displacements on the basis of local non-equilibrium heat transfer. An analytical solution for stresses is obtained, a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison with the classical solution is made without taking into account local non-equilibrium. On the basis of the operational solution of the problem, design engineering relations important in practical terms for the upper estimate of the maximum thermal stresses are proposed.

Математичне моделювання полів температури антенних рефлекторів космічних апаратів за допомогою нового інтегрального перетворення

Prediction of the mechanical properties of the reflector, and above all, the deviation of the highly accurate shape of the reflecting surface (RSS) from the given one is the main goal of designing spacecraft antennas. Distortion of the RSS is determined by the stress-deformed state of the elements of the reflector structures under the conditions of orbital operation. At the same time, the main factor determining the distortion of reflectors with RSS in open space is temperature deformation due to the uneven distribution of solar heat fluxes among structural elements. Therefore, the development of methods and models for calculating temperature fields in reflectors during heat flows on the surface is relevant. In the article, for the first time, a new finite integral transformation for the Laplace equation in a cylindrical coordinate system is constructed for a region bounded by several closed piecewise smooth contours. The inverse transformation formula is given. In the article, for the first time, a mathematical model for the calculation of temperature fields in a paraboloid rotating with a constant angular velocity is constructed, taking into account the finite speed of heat propagation in the form of a boundary value problem of mathematical physics for the hyperbolic equation of heat conduction with Dirichlet boundary conditions. With the help of the developed integral transformation, the temperature fields in the paraboloid were found in the form of convergent series according to the Fourier functions. The found solution to the generalized boundary value problem of the heat transfer of the paraboloid of rotation can find application in modulating the temperature fields that arise in the antenna reflectors of space vehicles. The developed integral transformation makes it possible to obtain solutions to complex boundary value problems of mathematical physics.

Computational semi-analytic code for stress singularity analysis

Problems of stress singularities in single or multi-material corners have been addressed by many authors over the years. Most of the authors presented closed-form corner-eigenequations for special cases, and often there is no easy way to check if the solution is correct. In this work, we present a general computational tool that can solve many different cases of stress singularity problems for multi-material corners under generalized plane strain. The semi-analytic code is based on the matrix formalism presented in Mantič et al. (1997, 2014); Barroso et al. (2003); Herrera-Garrido et al. (2022) and is developed in MATLAB. The following boundary conditions are implemented: stress-free, fixed, some restricted or allowed direction of displacements (defined either in the reference frame aligned with the cylindrical coordinate system or in an inclined reference frame), or frictional sliding. The following interface condition between two consecutive materials are implemented: perfectly bonded, and frictionless or frictional sliding. The code can analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic (with any orientation) constitutive laws. The code has proven to be a reliable, very accurate, robust and easy-to-use tool, which has been verified by comparing the results computed with those obtained by other authors. A summary of the corner singularity problems solved is presented. The results of the corner singularity analysis obtained by the code can be further used for prediction of crack onset at the corner tip by the Coupled Criterion of Finite Fracture Mechanics and FEM, see García and Leguillon (2012) and references therein.

Numerical Simulation of the Nonstationary Process of the Shot Based on the Navier – Stokes Equations

This paper gives a spatial mathematical formulation of the problem of internal ballistics based on the Navier – Stokes equations, taking into account the swirl of the flow due to the rotation of the projectile. The k-e model of turbulent viscosity is used. The control volume method is used for the numerical solution of systems of equations. The gas parameters at the boundaries of the control volumes are determined by the method of S. K. Godunov using a self-similar solution to the problem of the decay of an arbitrary discontinuity. The MUSCL scheme is used to increase the order of approximation of the difference method. For equations written in a cylindrical coordinate system, an orthogonal difference grid is constructed using the complex boundary element method. A comparative analysis of the results obtained with different approaches to modeling the process of an artillery shot is given. Quantitative data are presented on the influence of factors not previously taken into account on the characteristics of the process.

Characteristic and Occurrence Condition of Vehicle Vibration when Running on Particle Ground

In forestry work, vehicles such as heavy industry machines or tractors are used when they carry tools. When the vehicle run on group of particles, vibration occurs on the vehicle that causes deterioration in safety and ride comfort. It is important to clarify the characteristic and occurrence condition of vibration. In this study, Non-smooth DEM is used to analyze the vibration of vehicle. To improve the computational performance, vibration analysis method for a vehicle running on particle ground in a cylindrical coordinate system are proposed. The results of the analysis show that as the wheel speed increases, the amplitude also increases. In the case of multiple particle layers, as the number of particle layers decreases, the vibration becomes lower in frequency. At all damping natural frequencies, the vibration frequency is lower than damping natural frequency. Therefore, it was found that the vibration frequency is lowered by the particle ground.

Second-harmonic generation in the surface layer of a dielectric spheroidal particle: II. Analysis of the solution

The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed. Keywords: second-harmonic generation, spheroidal dielectric particle, symmetry of the spatial distribution of radiation, conditions for the absence of generation, conditions for the generation of linearly polarized radiation.

Генерация второй гармоники в поверхностном слое диэлектрической сфероидальной частицы: II. Анализ решения

The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed.

Комп’ютерне рішення для знаходження поперечних динамічних зміщень товстих пружних плит в умовах невизначеності

The article poses the task of finding the function of dynamic transverse displacements of thick elastic plates under the action of axisymmetric external dynamic disturbances acting on the surface of such plates. When setting the problem, it is indicated that some initial-boundary observations are known for the state of the plate, but their number is insufficient to solve this problem by classical methods of mathematical physics or numerical integration. Therefore, it is possible to apply to this problem the method of mathematical modeling of externally distributed dynamic processes under conditions of uncertainty, i.e. under insufficient number of initial and boundary conditions. For such a method, it is necessary to have an integral mathematical model and its main components - kernels, that is, integral functions for which there is a finding method. Or they can be calculated using numerical methods of computer algebra systems. With the built integral model of the dynamics of thick elastic plates, taking into account its kernels, the method of mathematical modeling of the dynamics of spatially distributed processes leads to the result - a set of solutions that accurately satisfy the integral and differential models and agree with the initial boundary conditions according to a certain criterion. The article selects one of the many solutions to the problem of finding the function of transverse dynamic displacements, which is found according to the methodology of mathematical modeling of the dynamics of spatially distributed processes and thanks to the calculation of the integral function of the mathematical integral model. For the problem, the elastic characteristics and density of the slab corresponding to some material are fixed, some specific external dynamic disturbances and initial-at-the-edge observations are determined, which are represented by certain conditions at specific points. Under such assumptions, graphs of the functions of transverse dynamic displacements are constructed at different values of the transverse coordinate z and at the value 0 of the radial coordinate r of the cylindrical coordinate system.

Pulsatile Flow of Copper Suspended Nanofluid Venture Through a Bifurcated Artery

With an aim to investigate the pulsatile flow of blood through a bifurcated artery with mild stenosis in the parent lumen in the manifestation of heat transmission. The blood is treated to be copper suspended nanofluid. The arteries forming bifurcation are assumed to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The highly nonlinear momentum and energy equations of nanofluid model are simplified by considering the mild stenosis case and a radial coordinate transformation is initiated to map irregular geometry into a rectangular grid. The solution for flow rate, impedance, shear stress are found by using the finite difference scheme in a cylindrical coordinate system. An extensive quantitative analysis has been performed based on numerical computations in order to estimate the effects of pertinent parameters on various physical quantities near the apex by means of their graphical representations so as to validate the applicability of the proposed mathematical model.

Construction of the solutions of the Helmholtz equation in cylindrical system of coordinates in the form of homogeneous polynomials by two biorthogonal systems of functions

Construction of the solutions of the Helmholtz equation in cylindrical system of coordinates in the form of homogeneous polynomials by two biorthogonal systems of functions

Development of mathematical models for predicting dimensional stability of furniture boards using the finite element method

An approach for predicting the properties of furniture boards made of common beech wood (Fagus sylvatica L.) based on the finite element method is proposed. It has been found that in the constructions of furniture panels made of beech wood, an orthogonal, cylindrical or transversal calculation scheme of anisotropy can be attributed depending on the dimensions of the furniture panels and the orientation of the fibers in the rails. A model of the physical and mechanical properties of monolithic or jointed slats made of beech wood during the finite element analysis of furniture boards based on the cylindrical coordinate system of the anisotropy of constant elasticity is proposed. It has been established that the practical use of the cylindrical anisotropy scheme when solving the problems of the mechanics of a rigid deformed body for the calculation of furniture boards made of beech wood is expedient when it is not possible to ignore the curvature of the annual layers, that is, when analyzing the dimensional stability of furniture boards and monolithic or jointed reibukaak made of beech wood with swelling and shrinkage. An applied methodology for calculating furniture boards made of beech wood has been developed, which makes it possible to take into account the peculiarities of the anisotropy of the physical and mechanical characteristics of the rails, taking into account their shrinkage and swelling when the temperature and humidity conditions of the environment change. The substantiation of new designs of furniture boards made of beech wood, which is based on the use of finite element analysis systems, allows identifying the shortcomings of these products at the conceptual stage of the project and correcting them before the start of production, taking into account the specified technical conditions. An optimal arrangement scheme of annual layers in adjacent slats of furniture panels made of beech wood is proposed, which ensures improvement of dimensional stability (reduction of gouging) of the structure while simultaneously reducing the stresses that arise when the humidity of the product increases during operation. Mathematical models are proposed that predict (describe) the strength and dimensional stability of furniture boards made of common beech wood. The developed model can be used for research and optimization of furniture boards of new designs according to the conditions of strength and deformability.

Electro-magnetic vibration behavior of smart curved micro-/nanoshells

This paper investigates dynamic results of a small-scale-dependent panel subjected to a combination of mechanical, electrical, and magnetic loads using the shear defamation theory. Modified couple stress theory (MCST) is used for accounting small-scale effects in small sizes. Governing equations of motion are derived based on Hamilton’s principle in the cylindrical coordinate system. The micro panel is composed of an elastic core integrated with two piezoelectric/piezomagnetic layers at top and bottom. Microlength scale parameter is included in the couple stress tensor and symmetric curvature tensor to capture size dependency. The analytical solution is applied for the solution of the motion equations. The extended parametric results are provided to show natural frequencies in terms of main significant input parameters such as initial electric/magnetic loads, span angle, length to thickness, radius to thickness, and length to radius ratio. Furthermore, the effect of higher mode numbers along the axial and circumferential directions is studied on the responses. The numerical results indicate that the natural frequencies are increased with an increase in initial magnetic potential and a decrease in initial electric potential.

Simultaneous identification of mechanical properties of functionally graded plates under the Kirchhoff and Tymoshenko models

The paper presents models of deformation of functional-gradient round plates in the framework of the hypotheses of Kirchhoff and Timoshenko. Based on the equations of oscillations and boundary conditions obtained earlier using the Hamilton - Ostrogradsky variational principle, the formulations of problems in a cylindrical coordinate system are written, taking into account the variability of the functions of cylindrical stiffness and density along the radial coordinate. The plates was considered rigidly clamped along the edge. The case of steady-state vibrations caused by a load applied to the surface was considered. A scheme for solving direct problems calculating vibrations of plates based on the Galerkin method is constructed. An analysis of the influence of the functions of cylindrical stiffness and density on the amplitude-frequency characteristics (AFC, acoustic response) was carried out, which revealed that both functions significantly affect the AFC, and the greatest influence is observed in the vicinity of resonant frequencies. The results of the analysis made it possible to formulate new inverse problems of simultaneous identification of the functions of cylindrical stiffness and density of an inhomogeneous circular plate using additional information about the acoustic response for both hypotheses. To solve them, a special projection technique was built, based on the expansion of unknown functions of mechanical characteristics, as well as dynamic quantities (functions of deflection and angle of rotation of the normal) in terms of some systems of linearly independent functions that satisfy the boundary conditions. The coefficients of these expansions are determined from the solution of special systems of linear and nonlinear equations obtained from the formulated weak statements of both problems. As a result, it is possible to identify the desired characteristics in the given classes of functions. The identification results are illustrated with a set of computational experiments for various functions.

Radiative bioconvection nanofluid squeezing flow between rotating circular plates: Semi-numerical study with the DTM-Padé approach

Modern biomedical and tribological systems are increasingly deploying combinations of nanofluids and bioconvecting microorganisms which enable improved control of thermal management. Motivated by these developments, in this study, a new mathematical model is developed for the combined nanofluid bioconvection axisymmetric squeezing flow between rotating circular plates (an important configuration in, for example, rotating bioreactors and lubrication systems). The Buongiorno two-component nanoscale model is deployed, and swimming gyrotactic microorganisms are considered which do not interact with the nanoparticles. Thermal radiation is also included, and a Rosseland diffusion flux approximation is utilized. Appropriate similarity transformations are implemented to transform the nonlinear, coupled partial differential conservation equations for mass, momentum, energy, nanoparticle species and motile microorganism species under suitable boundary conditions from a cylindrical coordinate system into a dimensionless nonlinear ordinary differential boundary value problem. An efficient scheme known as differential transform method (DTM) combined with Padé-approximations is then applied to solve the emerging nonlinear similarity equations. The impact of different non-dimensional parameters i.e. squeezing Reynolds number, rotational Reynolds number, Prandtl number, thermophoresis parameter, Brownian dynamics parameter, thermal radiation parameter, Schmidt number, bioconvection number and Péclet number on velocity, temperature, nanoparticle concentration and motile gyrotactic microorganism density number distributions is computed and visualized graphically. The torque effects on both plates, i.e. the lower and the upper plate, are also determined. From the graphical results, it is seen that momentum in the squeezing regime is suppressed clearly as the upper disk approaches the lower disk. This inhibits the axial flow and produces axial flow retardation. Similarly, by enhancing the value of squeezing Reynolds number, the tangential velocity distribution also decreases. More rigorous squeezing clearly therefore also inhibits tangential momentum development in the regime and leads to tangential flow deceleration. Tables are also provided for multiple values of flow parameters. The numerical values obtained by DTM-Padé computation show very good agreement with shooting quadrature. DTM-Padé is shown to be a precise and stable semi-numerical methodology for studying rotating multi-physical flow problems. Radiative heat transfer has an important influence on the transport characteristics. When radiation is neglected, different results are obtained. It is important therefore to include radiative flux in models of rotating bioreactors and squeezing lubrication dual disk damper technologies since high temperatures associated with radiative flux can impact significantly on combined nanofluid bioconvection which enables more accurate prediction of actual thermofluidic characteristics. Corrosion and surface degradation effects may therefore be mitigated in designs.