Problem Of Cylinder Research Articles

Correction: Solving an electrically conducting nanofluid over an impermeable stretching cylinder problem with a spectral reproducing kernel method

Correction: Solving an electrically conducting nanofluid over an impermeable stretching cylinder problem with a spectral reproducing kernel method

Eigenfunction expansion solution for the radiation problem of a uniform cylinder in front of a partially reflective wall

In this paper, the wave radiation problem of a vertical cylinder in front of a partially reflective vertical wall is solved by combining the eigenfunction expansion method and the mirror image method. To satisfy the partial reflection condition at the vertical wall, a scattering incident wave is introduced, which corresponds to the reduction scattering potential from the mirror image cylinder symmetrically distributed about the partially reflective wall and under symmetrical motion about the vertical wall with respect to the original cylinder. Subsequently, the scattering potentials generated by each of the two cylinders are derived using the eigenfunction expansion method on cylindrical coordinate systems with origins at the centers of the two cylinders. By applying Graf's addition theorem, the wave radiation problem is finally solved by transforming the incident scattering potential in the imaginary cylindrical coordinate system back to the original one of the cylinder itself and satisfying the body surface boundary condition. Using the numerical model developed in this paper, the effects of the parameters of the modulus and phase of the partial reflection coefficients as well as the distance between the partially reflective wall and the center of the cylinder on the added mass and radiation damping are investigated. The numerical results show that there are oscillations present in both the curves of added mass and radiation damping versus nondimensional wavenumber ka, the amplitude of the oscillations increases with the increase in the modulus of the reflection coefficient, and the peaks and troughs of the oscillations move to lower wavenumber ranges with increasing phase shift of the reflection coefficient. In addition, the distance between the cylinder and the vertical wall significantly affects the wavenumber range in which the peaks and troughs of the hydrodynamic coefficient curves appear, and the period of the oscillations decreases as the distance increases.

The hydromechanical coupled numerical method in pseudo-3D axisymmetric domain with cracks extension and coalescence applies to the decompression failure problem

The stress-strain state of the saturated porous media determines the behavior of fracturing, which defines the efficiency of developing tight oil, shale, coalbed, and thermal energy fields. Therefore, reliable hydromechanical coupled simulations with destruction reconstruction are critical.The proposed innovative simulator has a strong interrelation between fluid flow and rock deformation of porous media and realizes a fully coupled pseudo-transient numerical method by high-performance computing (HPC) tools. To increase the detail of the results in the problem, a finite difference numerical algorithm was implemented in the axisymmetric cylindrical domain, which reduces from three to two dimensions without loss of precision. Highly efficient parallelization using CUDA on the GPU computes meshes of up to one billion cells, allowing the simulation of a total core sample to sub-micrometer resolution in an appropriate time. The algorithm has been validated to find the exact solution to the cylinder problem. The proposed model accounts for cracks propagation with their coalescence within a single computational static grid, which keeps timing close to the continuous model.This comprehensive implementation enables solving industrial problems, such as modeling core sample damage during rapid decompression. High-resolution simulations help reconstruct fracture propagation, analyze the initial stress state, and identify critical damage factors. The comparison with the exact solution to the cylinder problem confirmed the reliability of the algorithm. The calculation results show a strong dependence of decompression failure on the coalescence and elongation of cracks, influenced significantly by the rock's cohesion. Microcracks length and distribution play a decisive role in the decompressive destruction behavior of the rock sample. For the first time, the simulations demonstrated the decompressive destruction of a core sample during an uncontrolled, rapid core retrieval operation.

Exploring the inverse line-source scattering problem in dielectric cylinders with deep neural networks

Abstract This study presents a novel approach utilizing deep neural networks to
address the inverse line-source scattering problem in dielectric cylinders. By employing
Multi-layer Perceptron models, we intend to identify the number, positions, and
strengths of hidden internal sources. This is performed by using single-frequency
phased data, from limited measurements of real electric and real magnetic surface fields.
Training data are generated by solving corresponding direct problems, using an exact
solution representation. Through extended numerical experiments, we demonstrate
the efficiency of our approach, including scenarios involving noise, reduced sample
sizes, and fewer measurements. Additionally, we examine the empirical scaling laws
governing model performance and conduct a local analysis to explore how our neural
networks handle the inherent ill-posedness of the considered inverse problems.

Design improvement of interference-type locking cylinder

Abstract The wear of the cylinder and locking-sleeve, generate during operation, is one of the main problems of interference-locking cylinder. In order to solve this problem, the operating principle and traditional design method of interference-locking cylinder are introduced briefly, the causes of wear are found based on its force state. And then an improved design method of interference-locking cylinder is proposed, the magnitude of interference is divided into two parts. A simplified finite element model of interference-fit is established and simulations are conducted to verify the effectiveness of the improved design method, the results indicate that the improved design method reduces the wear of the cylinder and locking-sleeve, and also can improve the service life of the interference-locking cylinder.

A multivariate piecewise interpolation model for viscosity representation and its application to the numerical simulation of non-isothermal polymer melt flow

In this study, a multivariate piecewise interpolation model is introduced to represent melt viscosity based on temperature and shear rate. The model does not require a predefined functional form for the entire data range, instead finding a suitable line between adjacent measured viscosity data points to obtain viscosity as a function of shear rate and temperature. To assess the effect of viscosity representation on polymer melt flow, a two-dimensional (2D) flow past a cylinder problem and a three-dimensional (3D) single screw extruder problem are numerically solved using different viscosity models. The pressure drop (ΔP) from the shift-factor model deviates by more than 10% at an average velocity (Uav) of 1 m/s due to overestimation of viscosity in the high shear rate region. The dimensionless thicknesses of the thermal boundary layer near the channel wall (δT/H) at wall temperature (Tw) of 210 °C are also misevaluated by more than 4% using both the shift-factor model and the Klein model, reflecting their poor viscosity evaluation. It is noteworthy that in all viscosity models, a high Tw leads to the formation of a thin thermal boundary layer, which adversely affects the heat transfer. In single screw extruder applications, viscosity misevaluation in high shear rate regions causes issues in pure drag flow cases, while misevaluation in low shear rate regions causes issues in pure back-pressure flow cases. These analyses highlight the accuracy and versatility of our multivariate piecewise interpolation model compared to existing viscosity models.

Meshless Error Recovery Parametric Investigation in Incompressible Elastic Finite Element Analysis

The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and global), convergence rates, and adaptive mesh improvement for triangular/quadrilateral discretization schemes. It uses meshless moving least squares (MLS) interpolation with rectangular and circular support regions and solves benchmark plate and cylinder problems. It is observed that a circular influence region, a cubic spline weight function, and regular mesh patterns yield a better performance of than an MLS-based error recovery method. The study also concludes that lower dilation index values with rectangular influence regions are preferable for regular meshes, while higher dilation index values with radial influence regions are suitable for preferable meshes to enhance MLS error recovery.

Reducing spatial discretization error on coarse CFD simulations using an openFOAM-embedded deep learning framework

AbstractWe propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.

Treatment of anastomotic leak in colorectal surgery by endoluminal vacuum therapy with the VACStent avoiding a stoma - a pilot study

PurposeAnastomotic leak (AL) represents the most relevant and devastating complication in colorectal surgery. Endoscopic vacuum therapy (EVT) using the VACStent is regarded as a significant improvement in the treatment of upper gastrointestinal wall defects. The innovative concept of the VACStent was transferred to the lower GI tract, gaining initial experience by investigating safety and efficacy in 12 patients undergoing colorectal resections.MethodsThe pilot study, as part of a German registry, began with 2 patients suffering from AL, who were treated with the VACStent after stoma placement. Subsequently, 6 patients with AL were treated with the VACStent omitting a stoma placement, with a focus on fecal passage and wound healing. Finally, the preemptive anastomotic coverage was investigated in 4 patients with high-risk anastomoses to avoid prophylactic stoma placement.ResultsIn total 26 VACStents were placed without problems. The conditioning and drainage function were maintained, and no clogging problems of the sponge cylinder were observed. No relevant clinical VACStent-associated complications were observed; however, in 2 patients, a dislodgement of a VACStent occurred. The 6 patients with AL but without stoma had a median treatment with 3 VACStents per case with a laytime of 17 days, leading to complete wound healing in all cases. The 4 prophylactic VACStent applications were without complications.ConclusionThe clinical application of the VACStent in the lower GI tract shows that successful treatment of anastomotic colonic leaks and avoidance of creation of an anus praeter is possible.Trial registration numberClinicaltrials.gov NCT04884334, date of registration 2021-05-04, retrospectively registered.

Solving an electrically conducting nanofluid over an impermeable stretching cylinder problem with a spectral reproducing kernel method

In this paper, a nonlinear mechanical system of ordinary differential equations (ODEs) with multi-point boundary conditions is considered by a novel type of reproducing kernel Hilbert space method (RKHSM). To begin, we define the unknown variables in terms of the reproducing kernel function. The roots of the Shifted Chebyshev polynomials (SCPs) are then utilized to collocate the resulting system. Finally, Newton’s iterative method is employed to find the unknown expansion coefficients. The solutions of this system of equations, which arise from the flow of an electrically conducting nanofluid over an impermeable stretching cylinder, are numerically analyzed, and convergence analysis is discussed to demonstrate the reliability of the presented method (PM). Tables and figures are provided to further discuss the solutions and assess the effectiveness of the method in comparison to other techniques in the literature.

Predicting pressure fields from incomplete velocity fields based on deep convolutional neural network

Acquisition of an instantaneous pressure field in a flow field is essential for experimental fluid dynamics research because pressure is associated with various flow phenomena. Machine learning has performed well in various fluid mechanics studies in recent years due to its nonlinearity. In this paper, we use the machine learning method to predict the pressure fields from incomplete velocity fields while reconstructing the missing velocity information, as exemplified by the stationary circular cylinder flow and circular cylinder undergoing forced oscillating problems, in which the incompleteness of the velocity field is caused by the optical path occlusion in experiments. We propose a network model based on convolutional neural networks. The experimental results show that the error of machine learning methods is around 4%, and even if the resolution of the training set is reduced, it does not affect the prediction accuracy of the network. For statistical averaging of prediction results, the network has high accuracy in predicting first-order quantities, but its ability to predict second-order quantities is limited. We also explore the effects of the amount of noise on the performance of networks. When applying the model to the forced oscillating cylinder problem, we use transfer learning to train the network given the similarity of the two problems, and the training error yields faster convergence and more minor convergence results. In addition to this, we use flow field data with a single vibration frequency to construct a single dataset, and flow field data with multiple vibration frequencies to construct a mixed dataset, and study the effect of different datasets on the prediction accuracy, which shows that it is difficult for neural networks to achieve both accuracy and generalization.

Semi-Analytical Solution for a Single-Phase Thermal Conduction Problem of a Hollow Cylinder with a Growing or Receding Inner Radius

Abstract A semi-analytical solution for the thermal conduction of a single phase, homogeneous, circular, hollow-cylinder with a growing or receding inner radius at a constant rate under unit-loading was derived using conformal mapping, Laplace transformation, and a Zakian series representation of the inverse Laplace transform. All solutions allow for convection on the fixed outer radius. Predictions were compared to finite-element simulations with excellent agreement observed. Given the changing thickness, thermal transients could not reach true steady-state equilibrium, especially for faster growth or recession rates. Indeed, the temperature states become somewhat linear with respect to time, reflecting the constant velocity of growth or recession. In practice, the resulting solutions can be used to determine temperatures during machining, wear, erosion, corrosion, and/or additive manufacturing, especially for lower temperature solid-state methods such as cold-spray.

Thermoelastic response of multilayer cylinders: The direct integration and single-solid approach

An approach for solving the plane nonaxisymmetric thermoelasticity problems in multilayer cylinders is suggested from the single-solid standpoint, which implies considering a multilayer structure as a single unity with a step-wise variation of material properties. The direct integration method was used to the advantage of our approach by applying toward the compatibility equation in terms of strains instead of the one in terms of stresses. As a result, the governing equation is derived without involving generalized derivatives by the radial coordinate and then reduced to an integral equation of the second kind. Using the resolvent-kernel for solving the latter equation, the thermal stresses are computed as the Fourier series whose constituents are explicitly determined by the corresponding constituents of the thermal loading.

Analysis of axisymmetric hollow cylinder under surface loading using variational principle

In this work, a variational principle–based approach has been adopted to analyze one of the classical linear elasticity problem of the axisymmetric cylinder under surface loading. The use of variational principle results in a set of governing partial differential equations with associated boundary conditions. The equations have been solved using the separation of variable approach and the Frobenius method. A general solution has been derived and used to solve two test cases. The proposed solution is capable of meeting all the boundary conditions. The solution has been validated by comparing it with a finite element–based numerical solution and considering a special limiting condition of a solid cylinder, for which results are available in the literature. Further various studies have been carried out to understand the robustness and limitation of the presented solution.

Flow and heat transfer in annuli owing to inner shrinking and outer stationary cylinder

The scope of the present work is to investigate the motion of the fluid flow and heat exchange within two concentric cylinders. It is assumed that the inner cylinder is moving (shrunk) and the outer cylinder is stationary. It derives the physical phenomenon, which can find industrial practical applications. The gap between the cylinders, curvature of cylinders, and Prandtl number are three physical parameters controlling the hydro-thermal flow motion. Asymptotic solutions are available when the gap size is moderately small. These and other solutions based on the numerical simulations clearly indicate that there are critical gap sizes beyond which either no solutions or dual solutions are possible. The common salient characteristic of solutions is that the axial fluid dragged into the cylinder as a result of surface shrinkage is thrown radially out through the outer cylinder. The non-existence of solutions after identifying critical gap sizes explains why the shrinking sheet and shrinking cylinder problems with an unbounded flow zone could not have been treated in the literature so far. This is the prime reason that with infinite gap size, other controlling mechanisms like surface transpiration, unsteadiness, velocity slip or magnetic field need to be included in the mathematical model to get a solvable problem under the surface shrinking process often studied among researchers. One of the solutions called branch I solution, has rational profiles with small pertinent physical quantities like skin friction, vertical/radial thrown velocity, and heat transfer rate. However, from a stability analysis, it can be shown that the branch II solution, possesses comparatively larger such quantities, making them questionable to appear in real physics with unstable eigenvalues.

Asymptotic behavior of a viscous incompressible fluid flow in a fractal network of branching tubes

<p>We considered a viscous incompressible fluid flow in a varying bounded domain consisting of branching thin cylindrical tubes whose axes are line segments that form a network of pre-fractal curves constituting an approximation of the Sierpinski gasket. We supposed that the fluid flow is driven by volumic forces and governed by Stokes equations with boundary conditions for the velocity and the pressure on the wall of the tubes and inner continuity conditions for the normal velocity on the interfaces between the junction zones and the rest of the pipes. We constructed local perturbations, related to boundary layers in the junction zones, from solutions of Leray problems in semi-infinite cylinders representing the rescaled junctions. Using $ \Gamma $-convergence methods, we studied the asymptotic behavior of the fluid as the radius of the tubes tends to zero and the sequence of the pre-fractal curves converges in the Hausdorff metric to the Sierpinski gasket. Based on the constructed local perturbations, we derived, according to a critical parameter related to a typical Reynolds number of the flow in the junction zones, three effective flow models in the Sierpinski gasket, consisting of a singular Brinkman flow, a singular Darcy flow, and a flow with constant velocity.</p>

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured deep operator network (DeepONet) framework that effectively combines low- and high-fidelity datasets, leveraging the strengths of each. In our methodology, we begin by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network’s output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts. The bi-fidelity learning framework, built upon the physics-guided Fourier-featured deep operator, accurately forecasts the time trajectories of lift and drag coefficients. A thorough evaluation of the proposed bi-fidelity framework confirms that our approach closely matches the high-fidelity solution, with an error rate under 2%. This confirms the effectiveness and reliability of our framework, particularly given the limited high-fidelity dataset used during training.

A model for residually stressed viscoelastic bodies and its application to some boundary value problems

A model for residually stressed viscoelastic bodies undergoing finite deformations is developed and applied to the study of time-dependent responses of spheres and cylinders to various stress and strain controlled tests. An approach based on the notion of natural configurations is employed. An appropriate free energy function is used, and a suitable dissipation function is adopted to obtain a constitutive model. This constitutive model is applied to the study of different boundary value problems of thick spheres and cylinders. The responses to various strain controlled tests are investigated, which includes the stress-relaxation test and a test for a time-dependent inflation–deflation cycle. Also, the response to creep test and step-stress test in thick viscoelastic spheres is investigated. Furthermore, the stretch-controlled responses of residually stressed viscoelastic cylinders to pure torsion and axial stretch are studied. Pure torsion involves an axial extension or compression known as the Poynting effect. The Poynting effect in residually stressed viscoelastic bodies, which does not appear to be studied in the literature, is investigated in detail here. It is noted that the magnitude of the angle of twist has a significant influence (sometimes involving a change of sign) on the observed Poynting effect.

Exact solution of magneto-elastoplastic problem of functionally graded cylinder subjected to internal pressure

With the development of composite material technology, the multi-field coupling analysis of functionally graded (FG) structures has attracted extensive attention. For FG cylindrical pressure vessels, due to the non-uniform distribution of stresses filed in the structure, plastic deformation occurs irreversibly under external load, and Lorentz's force under static magnetic field is also one of the key factors affecting the elastoplastic state. Assuming that the elastic modulus of FG cylinder changes as a power function along the thickness and Poisson's ratio is constant, the hollow cylinder under the combined action of applied magnetic field and internal pressure may have four deformation states containing pure elastic deformation, partial plastic deformation yielding from the inner surface, partial plastic deformation yielding from the outer surface, and full plasticity. In this paper, analytical solutions of stress and displacement fields of the FG cylinder under these four different elastoplastic states are given, and the critical load conditions corresponding to the transition between these four different states are proposed. The correctness of the present analytical solution in this paper is verified by comparing it with the existing results of related simplified problems. In addition, the analytical solution of residual stress distribution caused by unloading internal pressure is discussed for self-reinforcing processing. Based on the analytical solution in this paper, the influence of FG parameter, applied magnetic field and internal pressure on the elastoplastic state, plastic zone size, stresses and displacements distribution of FG cylinder is analyzed in detail. This study shows that for this magneto-elastoplastic problem of FG cylinder, plastic deformation may appear from the inner surface or outer surfaces. With the increase of FG parameter, the first yielding position of FG cylinder changes from the inner surface to the outer surface. In addition, the existence of an applied magnetic field reduces the critical internal pressure required for FG cylinders to yield, making the FG hollow cylinder more prone to plastic deformation.

Wake control of a square cylinder: Impinging the vortex cores with dual flexible splitter plates

Numerous works have been conducted to study the wake control of a bluff body and more efficient strategies are still what we seek for. This paper studies the complex fluid–structure interaction (FSI) problem of a square cylinder mounted with dual flexible splitter plates from a new perspective: impinging the vortex core with flapping plate tip. The Reynolds number (Re) based on the side length of the square cylinder is fixed at 332.6. The splitter plates are attached at both sides of the square cylinder. Structural parameters, such as plate length and bending stiffness, are considered to achieve an optimal arrangement of this configuration. Compared to the traditional single splitter plate arrangement, only a short splitter length is needed for this dual splitter plates configuration. Flow visualization indicates that the drag reduction is associated with the increase of base pressure and the lift suppression is related to the inhabitation of the interaction of the shear layer and split effect of the tip vortices. The dimensionless bending stiffness plays a vital role in determining the behavior of the splitter plate. Two vibration modes, i.e., off-center vibration and asymmetry vibration modes are captured and the up and down splitter plates tend to vibration in-phase. The Lissajous trajectories of the free tip mainly exhibits arc-shape and sickle-shape. Given the performance of the square cylinder-dual splitter plates configuration, splitter length of l/L=1.5 is an optimal configuration, which is less affected by flexural rigidity. The maximum drag reduction could reach 23.1% and the lift force exerting on this configuration does not increase significantly, which is beneficial for the structural stability.