Slippage Coefficients Research Articles

Design method of variable slippage coefficient non‐geodesic filament‐wound composite pressure vessels

AbstractPrevious studies on the design methods of filament winding paths for composite pressure vessels have mainly focused on geodesic and constant slippage coefficient non‐geodesic patterns, neglecting the design of variable slippage coefficients along the fiber path. In this paper, a design method of variable slippage coefficient non‐geodesic filament wound composite pressure vessels is proposed. The study begins by establishing a meridian rotation mapping model and deriving fiber path equations on the shell surface. Subsequently, the fiber paths, curvature characteristics, slippage coefficients, and shell stress responses of the shell under variable geometrical parameters are simulated and analyzed. Next, the winding parameters are optimized while considering bandwidth and stable winding constraints. The optimal winding parameters are determined, and filament winding simulations are conducted on composite pressure vessels. Results demonstrate the feasibility of the proposed method for variable slippage coefficient fiber path winding mode, providing a new and effective filament winding path design approach for composite pressure vessels.Highlights Establishment of meridian rotation mapping model and simulation of shell fiber paths under variable geometric parameters. The fiber paths, curvature characteristics, slippage coefficients, and winding angles of the shell under variable geometrical parameters are simulated and analyzed. Stress response analysis of shells based on Tsai‐Wu failure criterion and classical lamination theory stress field dimensionless modeling. Construction of winding parameter optimization strategies and bandwidth error evaluation based on stable winding and fiber bandwidth constraints. Simulation of variable slippage coefficient non‐geodesic filament winding for composite pressure vessels with different parameters.

An improved Klinkenberg permeability model for tight reservoir cores: Effects of non-linear gas slippage to real gases

Absolute permeability is one of the most fundamental reservoir-rock properties required for reservoir simulation models. Most research studies are focused on the Klinkenberg gas slippage, considering the ideal behavior of the flowing gas under first- and second-order slippage conditions. This paper assesses the non-linear slippage of real gas through the low permeability reservoir rock samples. The cubic equation of state (van der Waals/Soave-Redlich-Kwong/Peng-Robinson), coupled with Taylor series-based non-linear slippage, predicts the apparent permeability for the non-Darcy gas flow in tight reservoir rock. The novelty of the present contribution is to develop a comprehensive mathematical model to describe the temperature- and pressure-dependent non-linear slippage effect accounting for the real gas behavior, which is based on the fundamental principle of momentum balance. The thirty-nine sets of experimental results of different authors using different core samples (e.g., coal seams, tight sandstones, tight carbonates, gas-shale reservoirs) and gases (Air, H2, He, N2, CH4, C2H6, and CO2) are used to authenticate the proposed non-linear slip model for real gases. Results show that (a) the proposed model correctly predicts infinite permeability and non-linear slippage coefficients of eight-tests non-ideal gases with an average absolute deviation of ≤9.69%, (b) non-linear slippage dominates for the core samples having permeability <1.5 mD, and (c) the first- and second-order slippage coefficients vary from 0.76 to 6.22 atm and 0.15–9.30 atm2, respectively. The proposed model is simple and may readily be applied for the reservoir simulation of coal seams, tight sandstones, tight carbonates, gas-shale reservoirs, etc., for reservoir characterization, forecasting future natural gas production, decision-making, and efficient reservoir management practices for enhanced production efficiency and sustainability.

Transient Flow Theory of Multiple-Fractured Horizontal Wells with Complex Mechanisms in Shale Gas Reservoirs

Shale reservoirs have the characterizations of low porosity, low permeability, and hydrocarbon organic matter self-generation and self-storage, resulting in its complex flow mechanisms. Compared with fractured vertical wells, multiple-fractured horizontal wells are widely used due to their advantages of effectively increasing the well control range and further expanding the drainage area. To further study the multiscale flow mechanisms of shale gas, a flow model was established that considered viscous flow in microfractures and inorganic pores, the diffusion of Knudsen in nanoscale porosity, the coexistence of slippage, adsorption-desorption effects under infinity, and closed outer boundary conditions; based on the continuous point source solution, a multiple-fractured horizontal well flow model was established and solved by MATLAB programming. Then, the effects of various factors were investigated. The results show that the Knudsen diffusion and slippage coefficients mainly affect the apparent permeability of the matrix pores. The more the Knudsen diffusion and slippage coefficients are, the earlier the turbulent flow occurs and the higher the gas production is.

Winding path design based on mandrel profile updates of composite pressure vessels

A novel design approach has been proposed to generate winding paths for composite pressure vessels with unequal dome parts. The experiments were carried out to obtain the mandrel profiles after each update of composite layers, and then the winding paths were generated to accommodate the updated profiles. To evaluate the effect of mandrel profiles updated by composite layers on the winding paths, the variety of winding angles and dome thickness distribution as well as the slippage coefficients corresponding to different winding paths were investigated. Further, the burst pressure was predicted using the progressive failure method, and the performance factors were calculated to evaluate the effect of the profile-update-based winding paths on the structural performance of the pressure vessels. The results illustrate that the winding angles have a significant change as the number of updated layers increases. The thickness accumulation on dome parts is reduced and the fiber stability is further improved, therefore, the precision of fiber paths is improved using updates of mandrel profiles. The improvement of the performance factor indicates that the present method is able to provide a useful tool for improving the performance of composite pressure vessels.

Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime: Application to plane boundaries.

The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over distinct wall slippage conditions, namely, no-slip, first-order slip, and second-order slip. The modeling of channel walls is discussed at both lattice-aligned and non-mesh-aligned configurations: the first case illustrates the numerical slip due to the incorrect modeling of slippage coefficients, whereas the second case adds the effect of spurious boundary layers created by the deficient accommodation of bulk solution. Finally, the slip-flow solutions predicted by LBM schemes are further evaluated for the Knudsen's paradox problem. As conclusion, this work establishes the parabolic accuracy of slip velocity schemes as the necessary condition for the consistent LBM modeling of the slip-flow regime.

Application of variable slippage coefficients to the design of filament wound toroidal pressure vessels

The non-geodesics using variable slippage coefficients along the winding trajectories are gaining increasing attention for composite pressure vessels. The aim of this paper is to evaluate the influence of several slippage coefficient distributions on fiber trajectories and the resulting mass of toroidal pressure vessels. The distributions of slippage coefficients are represented in terms of three functions satisfying C1 continuity. The governing equations for designing non-geodesics on a toroid are formulated using the given functions of slippage coefficients. For each function, the initial fiber angle and the shell thickness are considered as the design variables, and the minimum mass is taken as the objective. With the aid of the classical lamination theory and the SQP algorithm, the optimal fiber trajectories are respectively determined for the given three slippage coefficient distributions, and the corresponding masses of the toroids are then obtained and compared to each other. The results indicate that toroids produced using variable slippage coefficients show improved performance than toroids using constant slippage coefficients; this is mainly due to the maximum utilization of the laminate strength. It is also revealed that the weight efficiency of toroidal vessels can be significantly improved using the quadratic distribution function of fiber slippage coefficients.

Fiber Trajectories Design of Ellipsoid Component Based on Topological Mapping Methodology

This paper presents a topological mapping algorithm for ellipsoid component winding trajectory. The sphere with double opposite holes was used as initial winding trajectory design model. The double opposite holes ellipsoid winding trajectory was obtained form that of the double-holes-sphere based on topological mapping algorithm. The basic equation of equilibrium for ellipsoidal mapping trajectory was given and its slippage coefficients were calculated using the non-geodesic law and differential geometry. The variation of slippage coefficients with holes-radius and ellipsoid rate were analyzed. The results show that, when ellipsoidal rate get close to 1 gradually, the better stability of fiber trajectories was obtained by topological mapping function. The ellipsoid component with lager holes-radius requires lower coefficient of friction between the fiber bundle and the ellipsoid surface. This fiber trajectory mapping function in the paper presents a useful tool for designing the double opposite holes ellipsoid filament-wound component trajectory.

Study on the validation of ring filament winding methods for unidirectional preform ply manufacturing

Ring filament winding enables processing of continuous fibers for manufacturing unidirectional non-crimp unidirectional preform plies on straight-, curved-, or closed-mandrel geometries. However, unidirectional processing of tows can lead to increased lateral tow slippage. The objective of the present study is thus to validate unidirectional winding methods for ring filament winding, performing geodesic and non-geodesic trajectories analytically and experimentally. Implementation of geodesic paths investigates the influence of the tensile force and take-up velocity on the winding angle reproducibility. Non-geodesic winding paths are conducted here dependent on winding methods, slippage coefficients, and the mandrel’s surface materials, evidencing the occurrence of lateral tow slippage by measurements of nip-point forces. Findings indicate an excellent reproducibility of geodesic paths independent of the process velocity. Non-geodesic paths were partially validated because of the occurrence of lateral tape-slippage and a tape side-inclination effect, correlating an increased stick behavior to higher local normal pressure.

Minimum weight design of helically and hoop wound toroidal hydrogen storage tanks with variable slippage coefficients

AbstractThis article determines the optimal winding parameters for helically and hoop overwound toroidal hydrogen storage tanks, based on the application of variable slippage coefficients. First, an optimality condition between helical winding angle and hoop‐to‐helical thickness ratio is derived from the minimum strain energy density criterion. The winding angle distributions are then obtained with the aid of the optimality condition, taking into account the shell thickness variation along the meridional direction. The general criteria for fiber trajectory stability on a torus are presented, and the relationship for the slippage coefficient and the helical winding angle is formulated according to the windability and manufacturability. The helical winding angle and thickness at the equator are considered as design variables, whereas the minimum weight acts as the objective function. A design example with a toroidal hydrogen storage tank is outlined to demonstrate the favorable performance of the present method. The results show that the present method using variable slippage coefficients leads to a better distribution of the fiber stress in the toroidal shell and an efficient utilization of the laminate strength. The obtained winding parameters can thus be regarded as optimal for filament‐wound toroidal hydrogen storage tanks. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers

A novel design solution for improving the performance of composite toroidal hydrogen storage tanks

This paper presents a novel design approach combining isotensoidal structures with non-geodesic winding patterns, which is able to significantly improve the geometric flexibility and structural performance of composite toroidal hydrogen storage tanks. The fiber trajectories are allowed to deviate from geodesics and the slippage coefficient is introduced to enlarge the design opportunities of toroidal pressure vessels. With the aid of the netting theory and fiber slippage law, the governing equations for specifying the meridian profiles of non-geodesic-isotensoids are derived based on the condition of uniform fiber stress. The desired toroids are then obtained by forcing the non-geodesic isotensoidal meridian profiles to become closed. The resulting cross-sectional shapes and winding angle distributions are outlined, corresponding to various slippage coefficients of non-geodesics. The vessel performance factors are determined to demonstrate the better structural efficiency that the application of non-geodesics can achieve. The results show that the vessel performance improves by using non-geodesics, due to the overall decrease in winding angles of the fiber trajectories. It is also concluded that the structural performance of isotensoidal toroids can be further improved with increasing the slippage coefficient of the non-geodesic trajectories.

Stability of fiber trajectories for winding toroidal pressure vessels

In this paper the fiber trajectory stability of filament wound toroidal pressure vessels is evaluated for two most frequently used patterns: single helical winding, helical and hoop winding. The basic equations of equilibrium for fibers on a torus are given based on netting analysis. The governing equations that determine helical winding angles along the meridional direction are derived for the two winding patterns. The slippage coefficients of the obtained fiber trajectories are calculated using the non-geodesic law and differential geometry. The condition between the hoop-to-helical thickness ratio and the relative bend radius of the toroid is also formulated to prevent fiber bridging on the concave surface. The fiber slippage and bridging tendencies are outlined and compared, corresponding to various relative bend radii and hoop-to-helical thickness ratios. The results show that the single helical winding process provides better stability of fiber trajectories, in terms of both fiber slippage and bridging, than the helical and hoop winding. The toroidal vessel with larger relative bend radius requires lower coefficient of friction between the fiber bundle and the supporting surface. The present analysis for fiber trajectory stability affords a useful reference tool for designing filament-wound toroidal pressure vessels.

Integral Design for Filament-Wound Composite Pressure Vessels

The most important issues for the integral design of a filament-wound pressure vessel reflect on the determination of the dome shape and applied winding patterns. The goal of this paper is to determine the meridian profiles of continuum-based domes for pressure vessels, and to demonstrate that the utilization of non-geodesic trajectories forms a favorable alternative to the dome design. An integral methodology for the design of such dome structures is outlined, with emphasis on the application of the non-geodesic winding law and the classical lamination theory. Based on the condition of equal shell strains, the governing equation for the shape of the dome meridian and the differential equation describing non-geodesic trajectories on the dome surface are derived. The meridian profiles of non-geodesics-based carbon-epoxy domes are obtained for various slippage coefficients; the structural efficiency of geodesics and non-geodesics-based domes for various polar radii are then calculated and compared to each other. The results concluded that filament-wound domes of pressure vessels designed using the non-geodesics provide better performance than geodesics-based ones.

Design of filament–wound domes based on continuum theory and non-geodesic roving trajectories

In this paper the optimal shapes and fiber architectures of non-geodesics-based domes for pressure vessels are determined upon the condition of equal shell strains. Based on the continuum theory and the non-geodesic law, the system of differential equations governing the optimal meridian profiles is derived. A specific function is chosen to describe the slippage coefficient distribution for the desired non-geodesic path, in order to ensure C 1 continuity of the roving paths when passing the dome–cylinder conjunction. Next, the meridian profiles are determined for various material anisotropies; the related winding angle developments of non-geodesic trajectories are also presented. The performance factors of non-geodesics-based optimal domes are obtained using various slippage coefficients and polar opening radii. The results show that the structural efficiency of the dome improves with increasing slippage coefficient. It is concluded that the non-geodesics-based dome designed using the present method gains better performance than the one relying on geodesics.

Giant slip lengths of a simple fluid at vibrating solid interfaces

It has been shown recently [A. Siria, A. Drezet, F. Marchi, F. Comin, S. Huant, and J. Chevrier, Phys. Rev. Lett. 102, 254503 (2009)] that in the plane-plane configuration, a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier-Stokes equations with partial slip boundary conditions at the solid-fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect-slip regime, the abovementioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results to those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. We show that the plane-plane geometry is more sensitive than the sphere-plane geometry for the measurement of slippage coefficients. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nanoelectromechanical systems.

Shape optimization of filament wound articulated pressure vessels based on non-geodesic trajectories

Abstract The most important issue for the design of articulated pressure structures reflects on the determination of the optimal meridian profile. In this paper, the optimal design for determining non-geodesics-based meridian profiles is outlined, subjected to geometrical limitations, stability-ensuring winding conditions and the Tsai–Wu failure criterion. The stress field is modeled using classical lamination theory, and the non-geodesic trajectories are employed to enlarge the design space and improve the structural performance. The searched optimal meridian profile is here approximated by cubic splines, which are based on equidistant knots. The objective is to maximize the performance factor using nonlinear optimization techniques. Two design problems are solved: firstly the optimal meridian profile determined using the present method is compared with the geodesic-isotensoid under the given opening radius. Secondly, the different optimal profiles with various slippage coefficients are obtained to demonstrate the effect non-geodesic trajectories have on the geometry and performance of articulated vessels. Results indicate that the articulated structure designed using the present method shows better performance, mainly triggered by increased internal volume as compared to that of the geodesic–isotensoid. Results also show that the structural performance of the articulated pressure vessel can further be improved with increasing slippage coefficients.

Design of filament-wound isotensoid pressure vessels with unequal polar openings

Abstract Previous studies on filament-wound isotensoids are mostly based on geodesic winding. However, the geometry of geodesics is certainly limiting the available design space. A typical restriction is the inability to create isotensoids with unequal openings at both ends. In this paper, a simplified method for designing isotensoid pressure vessels with unequal polar opening is outlined, using non-geodesic trajectories. Firstly we present the non-geodesic equations on general shells of revolution. Next, a direct relation among the shell curvatures, roving force, internal pressure and slippage coefficient, as a basis for determining non-geodesics-based isotensoid shapes, is provided. The governing equations for specifying meridian profiles are derived in terms of the slippage coefficient. The meridian profiles of non-geodesics-based isotensoids corresponding to various opening radii and slippage coefficients are determined, and the performance factors of the obtaining domes are calculated to demonstrate the effect the application of non-geodesics has on the structural efficiency. A stable and easily accessible solution procedure is proposed to determine the slippage coefficients fulfilling the winding requirements. Results show that the present method is suitable for the design of isotensoid structures with unequal polar openings. Results also indicate that the non-geodesics-based isotensoid domes show better performance than the geodesic–isotensoid.