Layer Separation Research Articles

A nonwoven supported mixed matrix membrane for CH4/N2 separation

Efficiently enriching low-concentration CH4 is pivotal for enhancing the utilization of unconventional energy sources and mitigating greenhouse gas emissions. This study focuses on modifying the overall performance of CH4/N2 separation membranes. A novel mixed matrix membrane (MMM) with a reinforced substrate structure was developed through a straightforward dip-coating technique. This MMM incorporates a polytetrafluoroethylene (PTFE) porous membrane as the supporting framework, while a composite of block polymer (styrene-butadiene-styrene) and metal–organic framework (Ni-MOF-74) forms the selective separation layer. Comprehensive characterization of Ni-MOF-74 and the fabricated membranes was conducted using X-rays diffraction, scanning electron microscope, Brunauer–Emmett–Teller analysis, and gas permeance tests. The findings indicate a robust integration of the PTFE porous support with the membrane layer, enhancing the mechanical stability of the MMM. Under optimal conditions, the mechanical strength of the PM20 membrane (containing 20% Ni-MOF-74) was observed to be 37.7 MPa, representing remarkable increase compared to the non-reinforced MMM. Additionally, the PM20 membrane exhibited an impressive CH4 permeation rate of 92 Barrer (1 Barrer = 3.35×10–16 mol·m·m–2·s–1·Pa–1) alongside a CH4/N2 selectivity of 4.18. These results underscore the MMM's substantial performance and its promising potential in methane enrichment applications.

Two-phase numerical simulation of thermal and solutal transport of zero mass flux conditions over a porous deformable disc: The extension of Jeffrey-Hamel model

In recent times, numerous assertions on the thermophysical properties of nanoliquids in various flow regimes, particularly the laminar flow regimes have been documented in the literature. With this focus, this theoretical investigation is to explore multiple solutions of the laminar two-dimensional Jeffrey fluid describing the Buongiorno nanofluid model and features of heat transport near a stagnation point across a movable radial disc. Also, the study seeks to explore the effects of zero mass flux and velocity of mass transpiration embedded within a Jeffrey fluid. With the help of the ansatz similarity transformations, the study simplifies complex partial differential equations into a set of ordinary differential equations, facilitating numerical dual solutions employing the bvp4c solver. The multiple solutions become apparent in a specific range of the shrinkable parameter. The results of the present study show that the suction parameter intensifies the phenomena of friction factor in the upper solution, whereas an annulment trend is observed in the lower solution. In addition, the shear stress and heat transfer rate decline with higher impacts of the Deborah number for the first solution while a monotonical behaviour is seen for the second solution. Besides, the absolute critical value decreases owing to the change value of the Deborah number, as a result, the separation of the boundary layer accelerates. Moreover, the heat transfer rate declined by about 0.29%, 0.37%, and 0.28% for the FBS and 0.30%, 0.32%, and 0.28% for the SBS with larger values of Nta, Nba and Sca, respectively. Lastly, the outcomes of the present examination with existing data are an excellent match for the limiting cases.

Ship-Radiated Noise Separation in Underwater Acoustic Environments Using a Deep Time-Domain Network

Ship-radiated noise separation is critical in both military and economic domains. However, due to the complex underwater environments with multiple noise sources and reverberation, separating ship-radiated noise poses a significant challenge. Traditionally, underwater acoustic signal separation has employed blind source separation methods based on independent component analysis. Recently, the separation of underwater acoustic signals has been approached as a deep learning problem. This involves learning the features of ship-radiated noise from training data. This paper introduces a deep time-domain network for ship-radiated noise separation by leveraging the power of parallel dilated convolution and group convolution. The separation layer employs parallel dilated convolution operations with varying expansion factors to better extract low-frequency features from the signal envelope while preserving detailed information. Additionally, we use group convolution to reduce the expansion of network size caused by parallel convolution operations, enabling the network to maintain a smaller size and computational complexity while achieving good separation performance. The proposed approach is demonstrated to be superior to the other common networks in the DeepShip dataset through comprehensive comparisons.

Post-growth tuning of detachable Ge membranes adhesion strength via porous Ge transformation

Single crystal germanium (Ge) membranes have recently gained increasing interest for lightweight and low-cost solar cells and flexible optoelectronic devices. These membranes achieved similar material quality as bulk Ge substrate. However, the control of the membrane detachment is still challenging. In this work, we explore post-growth engineering of the adhesion strength of a Ge membrane on a porous germanium (PGe) substrate by inducing morphological transformations in the separation layer through Thermal Budget (TB) control. Indeed, the pillars formed through PGe sintering during epitaxy are found to evolve with post-growth thermal annealing. Scanning electron microscopy (SEM) based analysis of the residue of the post-detachment broken pillars has been performed showing that the pillar's diameter and density can be tuned by thermal annealing. Depending on the post-growth annealing temperature, the membrane adhesion strength can be successively tailored from 0.5 to up to 3.5 MPa while ensuring 100 % detachment yield. The experimental results have been correlated with Finite Element Modeling (FEM) considering realistic pillar distribution revealing that pillar size and density are the dominant factors influencing the membrane adhesion strength.

Geofoam integrated separation layer for enhancing seismic resilience in modified piled raft foundations

Geofoam integrated separation layer for enhancing seismic resilience in modified piled raft foundations

High-order discretization–based self-adaptive turbulence eddy simulation for supersonic base flow with PHengLEI software

PurposeThe purpose of the present study is to develop a new numerical framework that can predict the supersonic base flow more accurately, including the development of axisymmetrically separated shear layer and recompression shock. To this end, two aspects are improved and combined, i.e. a newly self-adaptive turbulence eddy simulation (SATES) turbulence modeling method and a high-order discretization numerical scheme. Furthermore, the performance of the new numerical framework within a general-purpose PHengLEI software is assessed in detail.Design/methodology/approachSatisfactory prediction of the supersonic separated shear layer with unsteady wake flow is quite challenging. By using a unified turbulence model called SATES combining high-order accurate discretization numerical schemes, the present study first assesses the performance of newly developed SATES for supersonic axisymmetric separation flows. A high-order finite differencing-based compressible computational fluid dynamics (CFD) code called PHengLEI is developed and several different numerical schemes are used to investigate the effects on shock-turbulence interactions, which include the monotonic upstream-centered scheme for conservation laws (MUSCL), weighted compact nonlinear scheme (WCNS) and hybrid cell-edge and cell-node dissipative compact scheme (HDCS).FindingsCompared with the available experimental data and the numerical predictions, the results of SATES by using high-order accurate WCNS or HDCS schemes agree better with the experiments than the results by using the MUSCL scheme. The WCNS and HDCS can also significantly improve the prediction of flow physics in terms of the instability of the annular shear layer and the evolution of the turbulent wake.Research limitations/implicationsThe small deviations in the recirculation region can be found between the present numerical results and experimental data, which could be caused by the inaccurate incoming boundary layer condition and compressible effects. Therefore, a proper incoming boundary layer condition with turbulent fluctuations and compressibility effects need to be considered to further improve the accuracy of simulations.Practical implicationsThe present study evaluates a high-order discretization-based SATES turbulence model for supersonic separation flows, which is quite valuable for improving the calculation accuracy of aeronautics applications, especially in supersonic conditions.Originality/valueFor the first time, the newly developed SATES turbulence modeling method combining the high-order accurate WCNS or HDCS numerical schemes is implemented on the PHengLEI software and successfully applied for the simulations of supersonic separation flows, and satisfactory results are obtained. The unsteady evolutions of the supersonic annular shear layer are analyzed, and the hairpin vortex structures are found in the simulation.

Controlling amine monomers via UiO-66-NH2 defect sites to enhance forward osmosis membrane performance for lithium recovery

The excessive thickness of the separation layer and the presence of cracks cause low water flux and poor lithium recovery in conventional forward osmosis (FO) membranes. According to the influence of the diffusion behavior of amine monomers in interfacial polymerization, the use of an interlayer optimizes the separation layer structure of traditional thin-film composite FO membrane. However, it is difficult to accurately control the separation layer structure by simply adjusting the amount of the interlayer material loaded. Herein, FO membranes with defect-containing metal–organic framework (MOF) interlayers were constructed. By adjusting the concentrations of competitive ligands, the MOFs showed different degrees of linker loss, which exposed the metal ions in the MOFs to different extents. The defective sites of the constructed MOFs increased the interaction between the interlayer and m-phenylenediamine (MPD), and density functional theory (DFT) simulations also revealed an increase in the binding energy of the two materials. Therefore, MPD attachment and diffusion were controlled by changing the proportion of defects in the MOFs, thereby finely regulating the separation layer structure. Additionally, tannic acid (TA) was predeposited to improve the stability of the interlayer. The prepared membrane exhibited water fluxes of 33.84 and 65.81 LMH and reverse salt fluxes of 0.58 and 2.38 gMH in the active layer facing feed solution (AL-FS) and active layer facing draw solution (AL-DS) modes, respectively. Excellent lithium ion recovery and fouling resistance was also demonstrated in battery wastewater treatment.

Turbulent vortex pair at equilibrium and its interaction with the ground at

A turbulent two-vortex system (T-2VS) is obtained by inserting analytical model wake vortices into very weak homogeneous isotropic turbulence (HIT) and by evolving them in time using large-eddy simulation until a turbulent state at statistical equilibrium is reached. The T-2VS is characterised as follows: circulation distribution of the vortices; energy of the mean and fluctuating fields; energy dissipation rate. It is also verified that essentially the same T-2VS is obtained when varying the initial model or initial HIT perturbation. A wall-resolved simulation of the T-2VS further interacting with a smooth ground is then performed at $Re_\varGamma = 2 \times 10^5$ ; this is $10 \times$ higher than in previous works, which allows us to better capture the high Reynolds number behaviour. The high release height of the T-2VS also ensures a physically correct approach to the ground. The results are compared with the literature and also to what is obtained for the case of non-turbulent vortices interacting with the same ground at the same Reynolds number. The flow topologies are discussed, and significant differences are highlighted regarding the separation of the boundary layer generated at the ground, and the way this secondary vorticity interacts with the primary vortices and makes them decay. The vortex trajectories are also measured, together with their circulation distribution and global circulation evolution, and the differences are discussed.

Detection of pneumonia in chest X‐ray image based on separable convolutional neural network

SummaryPneumonia disease progress rapidly leading to missed diagnosis and diagnosis error. However, it is significant to be diagnosed accurately as well as adopted timely treatments, particularly for children and elderly people over 65. In the first place, we propose a novel method for data augmentation to expand non‐case samples in order to solve the problem of imbalance of the raw data. Then we have designed a neural network based on separable convolution layers, using deep learning to classify between Pneumonia cases and normal cases from chest X‐ray images. Finally, well‐known performance measures are utilized to evaluate our model, obtaining the following results: Accuracy (0.97), AUC (0.99), Sensitivity (0.98), Specificity (0.98), Precision (0.95), F1‐Score (0.97), and Youden Index (0.90). Simultaneously, we highlighted the proposed neural network recognition area via Class Activation Method for the purpose of providing an explainable diagnosis. Compared with the‐state‐of‐art models, our model performed better, and it may be regarded as an alternative in countries or regions lack of the relevant equipment and professional radiologists.

Small object intelligent Detection method based on Adaptive Cascading Context

With the technology advances, deep learning-based object detection has made unprecedented progress. However, the small spatial ratio of object pixels affects the effective extraction of deep details features, resulting in poor detection results in small object detection. To improve the accuracy of small object detection, an adaptive Cascading Context small (ACC) object detection method is proposed based on YOLOv5. Firstly, a separate shallow layer feature was proposed to obtain more detailed information beneficial to small object detection. Secondly, an adaptive cascade method is proposed to fuse the output features of the three layers of the pyramid to adaptively filter negative semantic information, while fusing with shallow features to solve the problem of low classification accuracy caused by insufficient semantic information of shallow features. Finally, an adaptive context model is proposed to use a deformable convolution to obtain spatial context features of shallow small objects, associating the targets with the background, thereby improving the accuracy of small object detection. The experimental results show that the detection accuracy of the proposed method has been improved by 6.12%, 3.35%, 3.33%, and 5.2%, respectively, compared with the source code on the PASCAL VOC, NWPU VHR-10, KITTI, and RSOD datasets, which fully demonstrate the effectiveness of our method in small object detection.

Impact of Low Freestream Turbulence and Surface Roughness on the Flat-Plate Boundary Layer Transition Under a High-Lift Airfoil Pressure Gradient

Abstract Effects of low incoming freestream turbulence level (Tu < 1%) and surface roughness on the transition of flat-plate boundary layers under a high-lift airfoil pressure gradient have been investigated. Time-resolved streamwise and wall-normal velocity fields with surface roughness values of Ra/C = 0.065 × 10−5, 4.417 × 10−5, and 7.428 × 10−5 have been measured at a fixed Reynolds number of 5.2 × 105 and freestream turbulence intensity of 0.2%. For the reference smooth surface of Ra/C = 0.065 × 10−5, a laminar separation bubble forms from about 64% to 83% of the chord length. Increasing surface roughness has little impact on the laminar boundary layer separation onset but reduces the height and length of the separation bubble and induces earlier transition. For Ra/C = 4.417 × 10−5, displacement thickness during transition is slightly thinner and the overall momentum deficit is slightly lower than those for Ra/C = 0.065 × 10−5. For Ra/C = 7.428 × 10−5, the separation bubble becomes hardly visible as the transition mode approaches the attached mode, and turbulent mixing by the wall-bounded turbulence becomes dominant. In addition, the portion of turbulent wetted area increases due to earlier transition, and momentum deficit increases more rapidly in the turbulent wetted area. Thus, the overall momentum deficit for Ra/C = 7.428 × 10−5 is larger than that for Ra/C = 0.065 × 10−5.

Laser Patterning of Porous Support Membranes to Enhance the Effective Surface Area of Thin-Film Composite-Facilitated Transport Membranes for CO2 Separation.

Although thin-film composite membranes have achieved great success in CO2 separation, further improvements in the CO2 permeance are required to reduce the size and cost of the CO2 separation process. Herein, we report the fabrication of composite membranes with high CO2 permeability using a laser-patterned porous membrane as the support membrane. High-aspect-ratio micropatterns with well-defined micropores on their surface were carved on microporous polymer supports by a direct laser writing process using a short-pulsed laser. By using a Galvano scanner and optimizing the laser conditions and target materials, in-plane micropatterns, such as microhole arrays, microline grating, microlattices, and out-of-plane hierarchical micropatterns, were created on porous membranes. An aqueous suspension of hydrogel microparticles doped with an amine-based mobile carrier was sprayed onto the patterned surface to form a defect-free thin separation layer. The surface area of the separation layer on the patterned support is up to 80% larger than that of flat pristine membranes, resulting in a 52% higher CO2 permeance (1106 GPU) with a CO2/N2 selectivity of 172. The laser-patterned porous membranes allow the development of inexpensive and high-performance functional membranes not only for CO2 separation but also for other applications, such as water treatment, cell culture, micro-TAS, and membrane reactors.

Positively charged nanofiltration membranes with gradient structures for enhancing separation properties

Creating a gradient structure in a separation layer is an effective approach for enhancing separation performance of thin film composite membranes. Here we present the preparation of a positively charged nanofiltration membrane with a gradient structure. An inner layer consisting of a loose polyester separation layer with large pores was formed through the interfacial polymerization (IP) reaction between triethanolamine (TEA) and trimesoyl chloride (TMC). And a dense and thin top layer composed of a polyamide separation layer was obtained by secondary interfacial polymerization (SIP) reaction using polyethyleneimine (PEI) along with unreacted TMC and residual acyl chloride groups of IP reaction. The influences of TEA concentration, PEI concentration and SIP time on the physicochemical properties and separation performances of the membrane were systematically analyzed. Our results show that the presence of the gradient structure optimized mass transfer pathways and reduced mass transfer resistance, resulting in significantly improved permeability of 13.0 ± 0.5 L·m−2·h−1·bar−1 (over 3 times compared with control-PEI), high MgCl2 rejection of 91.7 ± 0.6 %, and an excellent stability and anti-fouling performance. Our work provides valuable insights and guidance for developing high-performance positively charged NF membrane with gradient structures.

Comprehensive investigation of thermal induced reorganization of porous-germanium structures

Porous germanium (PGe) substrates have recently attracted significant attention for the development of lightweight and flexible solar cells and optoelectronic devices. A reliable approach for releasing epitaxial layers based on Germanium and reusing the substrate involves utilizing a bilayer structure of PGe. The growth of such detachable devices holds great potential for integration onto the Si platform. The used structure of PGe is made of a low-porosity layer serving as epitaxial seed on top of high-porosity one used as a weak separation layer. In this work, we investigate the impact of thermal annealing on the PGe morphology for deeper understanding of the mechanisms involved in the formation of the epitaxial seed layer and the voided weak layer underneath. Indeed, thermal-induced reconstruction has been investigated at various annealing temperatures and times for PGe layers with differing porosity levels, encompassing low, high, and gradual porosity profiles. Our findings reveal the formation of a modified substrate at low annealing temperatures, resulting in a suspended membrane on top of the fragile separation layer, rendering it suitable for detachment and subsequent substrate reuse.

Coupling Global Parameters and Local Flow Optimization of a Pulsed Ejector for Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs), as an important utilization of hydrogen energy, contribute to the sustainable development of global energy. Pulsed ejectors have a high potential for improving the hydrogen utilization of PEMFCs in the full operating range by circulating unconsumed hydrogen. In this study, a pulsed ejector applied to a 120 kW fuel cell was designed, and the flow characteristics were analysed using computational fluid dynamics (CFD). Based on the data from the CFD model, the global optimization of the ejector was carried out using the Gaussian process regression (GPR) surrogate model and the grey wolf optimization (GWO) algorithm. The local structure was then further optimized using an adjoint method coupling streamlining modification that takes into account the local flow characteristics. The CFD results showed that, under a fixed structure, increasing the pressure difference between the secondary flow and the ejector outlet would promote boundary layer separation, shorten the shockwave chain length, change the effective flow area of the secondary flow, and lower the entrainment ratio (ER). The analytical results from the GPR model indicated significant interactions among the structural parameters. The globally optimized ejector using GPR and GWO improved the hydrogen entrainment ratio from 1.42 to 3.12 at the design point. Furthermore, the results of streamlining local optimization show that the entrainment ratio increased by 1.67% at the design point and increased by up to 3.99% over the full operating range compared to the optimized ejector by global optimization.

Unsteady axisymmetric hybrid graphene-copper nanofluid slip flow over a permeable radially shrinking disk with the Soret and Dufour effects

This study investigates the unsteady axisymmetric flow of a hybrid graphene-copper nanofluid over a permeable radially shrinking disk, accounting for velocity slip, Dufour, and Soret effects. Examining such boundary layer flows of hybrid nanofluids is crucial for understanding the underlying fluid mechanics and thermophysical behavior. The fluid flow model is solved using a finite difference scheme in MATLAB to generate the numerical solutions. Since dual solutions are attainable, stability analysis is performed to analyze the nature of the solutions. The existence of dual solutions enables exploring flow separation dynamics through selected control parameters. Results indicate that higher copper volume fraction and velocity slip effectively prevent the boundary layer separation. The 2 % copper volume fraction delays the boundary layer separation approximately 6 % better compared to the usage of 1 % copper volume fraction. The heat transfer is improvable by reducing the shrinking intensity of the disk and maximizing the velocity slip and Soret parameters. The comprehensive mathematical model presented herein lay a solid foundation for future research endeavors, particularly in the field of hybrid nanofluids and their applications in thermal management systems.

Nonlinear Slippage of Tensile Armor Layers of Unbonded Flexible Riser Subjected to Irregular Loads

The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear hysteresis phenomenon, which is a research hotspot and difficulty. In this paper, on the basis of a typical eight-layer unbonded flexible riser model, the nonlinear slippage of a tensile armor layer and the corresponding nonlinear behavior of an unbonded flexible riser subjected to irregular external loads are studied by numerical modeling with detailed cross-sectional properties of the helical layers, and are verified through a theoretical method considering the coupled effect of the external loads on the unbonded flexible riser. Firstly, the balance equation of each layer considering the effect of external loads is established based on functional principles, and the overall theoretical model of the unbonded flexible riser is set up in consideration of the contact between adjacent layers. Secondly, the numerical modeling of each separate layer within the unbonded flexible riser, including the actual geometry of the carcass and pressure armor layer, is established, and solid elements are applied to all the interlayers, thus simulating the nonlinear contact and friction between and within interlayers. Finally, after verification through test data, the behavior of the unbonded flexible riser under the cyclic axial force, torsion, bending moment, and irregular external and internal pressure is studied. The results show that the tensile armor layer can slip under irregular loads. Additionally, some suggestions related to the analysis of unbonded flexible risers under irregular loads are drawn in the end.

Turbulence and mixing from neighbouring stratified shear layers

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$ , approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$ , billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$ , neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

High-temperature ablation behavior and failure mechanism of (Hf0.25Zr0.25Ti0.25Ta0.25)C high-entropy carbide in wide temperature range

The ablation behavior of (Hf0.25Zr0.25Ti0.25Ta0.25)C was investigated using a plasma flame gun over a wide temperature range of 2070–2600℃. The structural transformation during ablation and the effect of temperature on the failure mechanism were discussed. Results showed a sharp increase in mass and linear ablation rates from 0.23 mg·cm−2·s−1 and 4.6 μm·s−1 at 2070℃ to 4.6 mg·cm−2·s−1 and 37 μm·s−1 at 2600℃. This variation was attributed to the temperature's impact on on the microstructure and composition of the oxide layer. During ablation, Hf/Zr-rich oxycarbides preferentially nucleated within the amorphous Hf-Zr-Ti-Ta-C-O layer, leading to phase separation of the oxide layer. With increasing ablation temperature, the filler and binder oxides with low melting point (e.g., (Hf,Zr)TiO4, TaZr2.75O8) were rapidly consumed. The skeleton oxides (e.g., (Hf,Zr)O2) failed to bond and peeled off. The transiently formed (Hf,Zr,Ti,Ta)Ox layer was repeatedly destroyed and reconstructed, resulting in the continuous damage and eventual failure of the matrix.

Axial Tensile Ultimate Strength of an Unbonded Flexible Riser Based on a Numerical Method.

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed to different configurations to adapt to harsh marine environments, and is a key equipment in transporting oil and gas resources from Ultra Deep Waters (UDWs) to offshore platforms. The helical interlayer of an unbonded flexible riser makes the structural behavior difficult to predict. In this paper, the axial tensile behavior and the axial tensile ultimate strength of an unbonded flexible riser are studied based on a typical 2.5-inch eight-layer unbonded flexible riser model, and verified through a theoretical method considering the contact between adjacent layers. First, the balance equation of separate layers is deduced by a functional principle, and then the overall theoretical model of an unbonded flexible riser is established considering the geometric relationship between adjacent layers. Then, the numerical model considering the detailed geometric properties of an unbonded flexible riser is established to simulate the axial tensile behavior. Finally, after being verified through the experimental results, the axial tensile stiffness and axial tensile strength of an unboned flexible riser considering the elasticity of the tensile armor layer are studied using the proposed two methods. Additionally, the effect of frictional coefficients is conducted. The numerical and theoretical results show good agreement with the test results, and the friction between adjacent layers would increase the axial tensile stiffness of an unbonded flexible riser.