Simple Numerical Model Research Articles

Simplified Numerical Models of the Unsteady Tip Leakage Flow in Compressor

Simplified Numerical Models of the Unsteady Tip Leakage Flow in Compressor

Moisture absorption of an aerogel-based coating system under different wetting scenarios

Aerogel-based coating mortars (ACM-systems) provide energy-efficient retrofitting solutions for masonry buildings, with thermal conductivities (30–50 mW/(m·K)) comparable to traditional insulation materials. However, limited knowledge on their moisture absorption under rainwater wetting hinders the moisture-safe design of building envelopes incorporating these mortars. Thus, this study investigated the moisture absorption of an ACM-system under three laboratory-created wetting scenarios. A small-scale setup was developed to simulate runoff wetting based on typical wind-driven rain intensities in Sweden, enabling continuous monitoring of moisture conditions during wetting and drying. Two complementary capillary suction experiments under zero (free suction) and elevated hydrostatic pressure explored additional wetting scenarios. The impact of water-repellent paint and surface cracks was also assessed, as previous testing focused on undamaged ACM-systems. Among the three wetting scenarios, runoff wetting resulted in the lowest moisture absorption by the undamaged ACM-system. Water-repellent paint (sd = 0.01 m) reduced moisture uptake by up to 15% during runoff and 50% during free capillary suction for the same system. Horizontal or vertical surface cracks of 1 ± 0.5 mm width increased water absorption by 3–5 times during prolonged runoff wetting, comparable to suction at elevated hydrostatic pressure. Furthermore, a trial was done to verify a simplified numerical moisture transport model using the runoff experiment. The results highlighted the necessity for future model refinement and advanced moisture transport modeling in the ACM-system. The developed small-scale setup facilitated easy use and real-time monitoring of moisture conditions during wetting and drying. Future development should include wind-driven rain simulation alongside the existing runoff wetting scenario.

Investigation of heat transfer at the outer combustor wall on self-sustained thermoacoustic oscillations in a Rijke tube

Thermoacoustic oscillations have plagued combustion systems for decades and are becoming increasingly relevant as engines become more powerful, more compact, and more eco-friendly. These oscillations arise from constructive coupling between unsteady heat release and acoustic pressure waves, and result in strong pressure oscillations that can inhibit flame stability and induce component failure. In this work, a simple numerical model is used to study the effects of the temperature distribution of the outer combustor wall on the thermoacoustic stability of a Rijke tube. A Galerkin series expansion of the linearized acoustic governing equations is coupled with a classical G-equation premixed flame model to determine the minimum energy required to maintain stability for various system configurations, and results are compared against computational fluid dynamics simulations for select cases.

Dynamics and acoustics of bubbly plumes

Transient bubbly plume dynamics including their effects on the free surface were studied numerically using a simple numerical model based on integral theory [1, 2] and Eulerian–Eulerian coupled large Eddy simulation (EE-LES) method. The EE-LES model was validated with the interfacial closures evaluated for drag, lift and virtual mass forces. The simulation data showed good agreement with both numerical predictions and experimental measurements in the literature. The spectrum of the surface pressure fluctuations and acoustical pressure induced by a bubbly plume were extracted from numerical simulations [3]. The effect of interaction of two plumes is discussed. [1] B.R. Morton, G.I. Taylor, J.S. Turner, Turbulent gravitational convection from maintained and instantaneous sources, Proc. R. Soc. Lond. A234, 1–23 (1956) [2] A. Skvortsov, T. DuBois, M. Jamriska, M. Kocan, Scaling laws for extremely strong thermals, Phys. Rev. Fluids 6, 053501 (2021) [3] S.J. Zhu, A. Ooi, R. Manasseh, A. Skvortsov, Prediction of gas holdup in partially aerated bubble columns using an EE-LES coupled model, J. Chem. Eng. Science 217, 115492 (2020)

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams with arbitrarily axially varying cross-sections, materials, foundations, loads, and general boundary conditions. These spatially varying properties are all approximated by high-order Chebyshev expansions, and discretized by Gauss–Lobatto sampling. The discrete governing equation of non-uniform axially functionally graded beams resting on variable Winkler–Pasternak foundations subjected to non-uniformly distributed loads is derived based on the Euler–Bernoulli beam theory. A projection matrix method is employed to simultaneously assemble spectral elements and impose general boundary conditions. Numerical experiments are performed to validate the proposed method, considering different inhomogeneous materials, boundary conditions, foundations, cross-sections, and loads. The results are compared with those reported in the literature and obtained by the finite element method, and excellent agreement is observed. The convergence, accuracy, and efficiency of the proposed method are demonstrated.

Role of secondary components in the numerical analysis and in-plane seismic performance assessment of glass curtain walls

Glass façades are complex mechanical systems, in which brittle and vulnerable glass panels interact with metal members and secondary components. Under extreme design actions, such as seismic events, glass failure in tension (cracking) or compression (crushing) is a critical condition for structural performance assessment. Compared to full-scale experiments, in this regard, Finite Element (FE) numerical tools can offer a robust support in design. Besides, many primary and secondary façade components should be properly taken into account, because responsible of possible major approximations in their expected mechanical interactions. In this paper, the in-plane seismic response of glass curtain walls is investigated with geometrically accurate and detailed (“MREF”) or simplified and efficient (“MSIMP”) numerical models. Comparative results are critically discussed, based on dynamic numerical simulations, with a primary attention which is focused on the mechanical performance of glass panels.

A Method for Teaching Overinvestment and Underinvestment Problems in Corporate Finance Courses

One of the most important concepts in corporate finance is agency theory. When the financiers of a firm are not also the managers of the firm, the incentives of different financiers (lenders and owners) often conflict. One of the biggest problems in agency theory is that of overinvestment and underinvestment due to misalignment of shareholder and bondholder incentives. While this problem has many real applications, the underlying concepts frequently seem quite abstract to business students. This paper presents an implementation of a simple numerical spreadsheet model that can clearly illustrate the conflicting incentives of lenders and owners that lead to overinvestment and underinvestment.

A Seismic Risk Assessment of Concrete-Filled Double-Skin Steel Tube (CFDST) Frames with a Beam-Only-Connection for Reinforced Concrete Shear Walls (BRWs)

The beam-only connected reinforced concrete shear wall (BRW) is used as a reinforcing component to enhance the seismic performance of concrete-filled, double-skin steel tube (CFDST) frames. The effects of the BRW on seismic risks of CFDST frames are investigated. Three performance levels of limit states are defined and described according to the typical failure of test specimens and the existing definition of current guidance. A simplified numerical model is calibrated for CFDST frame-BRW structures, and test results validate it. Nonlinear dynamic analyses on a nine-story CFDST-BRW building are performed to investigate the effects of BRW on reducing the seismic risk of CFDST buildings. The results show that the BRW reduces the probability of collapse of the CFDST frame to 2.76% in 50 years, which can effectively reduce the probability of different degrees of damage in the service cycle of the structure. The results provide information for risk-informed decision-making on the design of CFDST frame-BRW structures.

Prediction of the discharging time of a latent heat thermal energy storage system with a UA approach

Designing latent heat thermal energy storage systems is a cumbersome task and the estimation of the performance of such a storage system normally involves experiments and detailed numerical simulations. Analytical, empirical and simplified numerical models are much faster but subject to large uncertainties. Even the prediction of the performance of an existing latent heat thermal energy storage system under different boundary conditions is often not possible in an easy way. Therefore, we present an analytical method – the UA approach – to predict the discharging (solidification) time of a flat plate latent heat thermal energy storage system. A special feature of the UA approach is that one can incorporate experimental or numerical results to improve the prediction of the performance under a variety of boundary conditions or material properties. The UA approach was tested for a variation of the Stefan number (Ste), the Biot number (Bi), the number of transfer units (NTU) and the heat transfer fluid and was compared to the results of a validated numerical model. The results are promising, especially for small Ste. In addition, the prediction of performance for a high thermal heat conductivity of the phase change material based on a numerical reference solution with a low thermal conductivity worked remarkable well.

Flow simulation in 3D fractured porous medium using a generalized pipe-based cell-centered finite volume model with local grid refinement

The presence of fractures in porous media strongly influences the fluid flow behavior. This work presents an efficient and simple numerical model to address the hydrodynamic behavior of complex fractured porous media, aiming at balancing computational efficiency and accuracy. Fractures are mapped to a set of cells having implicit aperture, where local grid refinement (LGR) is adopted around the fracture to improve accuracy with lower computational burden. The fluid flow in the matrix, fracture, and exchange between fracture-matrix, are described by a generalized equivalent pipe-network model. The numerical scheme and implementation are verified against established numerical solutions. Results show that this method is efficient in capturing main phenomena of the fluid transport in fractured porous media, without sacrificing computational accuracy. Heterogeneous and anisotropic features of fluid flow are well captured. Particularly, the convergence of the LGR is in a higher order than the global grid refinement (GGR). This model also provides great flexibility in handling a multitude of fracture input data, e.g., planar fractures obtained from statistical data and non-planar fractures from digital images represented with point clouds. Balancing computational accuracy and efficiency, this method provides an effective approach for simulating flow transport in fracture porous medium.

Experimental investigation of the tire wear process using camera-assisted observation assessed by numerical modeling

This paper presents a novel experimental method to study the abrasion mechanism of car tires. It is based on the detection of microscopic movements associated with material damage (cracking) on the rubber tread. This is referred to as degrading layer relaxation. It correlates with the wear rate and, interestingly, the direction of the pattern’s movement is opposite to the lateral forces during cornering. To measure and analyze the microscopic movements, a new camera-based method with feature point matching using video stabilization was developed. Besides extensive experimental investigation, the formation and propagation of microcracks are investigated using a simplified numerical model in which a phase field approach coupled with a viscoelastic constitutive behavior is implemented in a finite element framework.

On the Capacity of Beams with U Cross Section Subjected to Bending and Torsion

AbstractBeams with singly symmetric U cross sections are often subjected to bending about the strong axis and simultaneously to scheduled torsion, since the shear center is outside the section geometry. The member capacity of such sections, which is strongly influenced by effects of lateral torsional buckling, can therefore hardly be represented with the common design regulations based on reduction factors χLT of EN 1993‐1‐1. However, numerical approaches allow analyzing deeply the structural behavior of corresponding beams. In the present study, different numerical finite element simulations (GMNIA) including simplified numerical models based on the plastic zones theory are incorporated to determine member capacities and to derive corresponding reduction factors for simplified verifications. As the load‐bearing capacity of members susceptible to stability is strongly influenced by imperfections, the straightness according to manufacturing tolerances as well as approaches for the acquisition of structural imperfections (residual stresses) are considered in the numerical analyses. The investigations are carried out for selected structural systems with different sets of parameters, such as for the member lengths and cross section types. Concluding, a capacity curve is derived and compared to different reduction factors χLT specified in EN 1993‐1‐1.

THE EFFECT OF WIND STRESS ON WAVE OVERTOPPING ON VERTICAL SEAWALL

Onshore wind can significantly affect wave overtopping process and increase mean overtopping discharge. Thus, the wind should be an important variable in coastal design process. However, despite many researches have analyzed the influence of wind on the overtopping, there is still a lack of exhaustive knowledge about this phenomenon. To further analyze the wind effects, the CFD model FLOW-3D has been used to investigate wave overtopping at vertical seawalls. The single-fluid approach has been adopted, i.e. the presence of wind has been simulated via the wind shear stress on the sea surface. The main aim of this work is to verify the ability of this simplified numerical modelling to capture the macro-processes involved in the phenomenon of wave overtopping. The presence of wind shear stress has led to physically consistent results. It confirmed that as the mean overtopping discharge decreases, as the wind effect increases. Furthermore, numerical results have shown that the advection of water droplets behind the structure by the wind is the key mechanism for the enhancement of wave overtopping. Finally, by gathering numerical results and laboratory data carried out by Durbridge (2021), a new predictive formula to estimate the wind factor is provided.

Energetic particle dynamics in a simplified model of a solar wind magnetic switchback

Context.Recent spacecraft observations in the inner heliosphere have revealed the presence of local Alfvénic reversals of the magnetic field, while the field magnitude remains almost constant. These are called magnetic switchbacks (SBs) and are very common in the plasma environment close to the Sun explored by the Parker Solar Probe satellite.Aims.A simple numerical model of a magnetic field reversal with constant magnitude is used in order to explore the influence of SBs on the propagation of energetic particles within a range of energy typical of solar energetic particles.Methods.We model the reversal as a region of space of adjustable size bounded by two rotational discontinuities. By means of test particle simulations, beams of mono-energetic particles can be injected upstream of the SB with various initial pitch- and gyro-phase angles. In each simulation, the particle energy may also be changed.Results.Particle dynamics is highly affected by the ratio between the particle gyroradius and the size of the SB, with multiple pitch-angle scatterings occurring when the particle gyroradius is of the order of the SB size. Further, particle motion is extremely sensitive to the initial conditions, implying a transition to chaos; for some parameters of the system, a large share of particles is reflected backwards upstream as they interact with the SB. These results could have a profound impact on our understanding of solar energetic particle transport in the inner heliosphere, and therefore possible comparisons with in situ spacecraft data are discussed.

Developing simplified numerical calculation and BP neural network modeling for the cooling capacity in a radiant floor cooling system

ABSTRACT To upgrade the computational efficiency and ensure the accuracy of calculated cooling capacity of radiant cooling floor, this study proposed a simplified three-dimensional modeling by combining with a user-defined function compilation. The cooling capacity and minimum floor temperature were taken as evaluation indices considering different radiant floor thicknesses, layers’ thermal conductivities, pipe diameters, pipe spacing, and floor surface sizes. Moreover, a backpropagation neural network model and a prediction program were developed to quickly predict minimum floor temperature and cooling capacity. The results demonstrate that the established backpropagation neural network model can predict the values of cooling capacity and minimum floor temperature well, and the coefficients of determination were 0.9117 and 0.9435, respectively. With the thickness increase of cover layer and filling layer, the minimum floor temperature respectively increases by 10.97% and 11.01%. With the heat transfer coefficient increase of cover layer and filling layer, cooling capacity respectively increases by 30.56% and 23.46%. This study proposes an artificial intelligence method for the rapid prediction of cooling capacity and minimum floor temperature, and provides their theoretical support for engineering application.

Volume of fluid based modeling of thermocapillary flow applied to a free surface lattice Boltzmann method

Thermocapillary flow, also termed as thermal Marangoni convection, is an important material transport mechanism in many technical processes. Thus, it has to be considered in the corresponding simulations. In this work, a novel numerical model for the implementation of thermocapillary flow into a volume of fluid based free surface lattice Boltzmann method is presented. It is based on the idea of discretizing the surface normal vector in accordance to the discretization scheme of the velocity space. This approach is used to interpolate the temperature at the surface and to calculate the local surface gradients.The result is a simple and efficient numerical model, which is able to calculate the Marangoni stress along a liquid surface with sufficient accuracy and without the need to explicitly reconstruct the interface. We show that the Marangoni stress can readily be incorporated into a free surface lattice Boltzmann model by adjusting the boundary condition at the surface. In doing so, no additional forcing scheme has to be applied.In order to verify the presented model, it is tested using several simulation setups. As the lattice Boltzmann method is particularly suitable for complex geometries, a special attention is paid to the behavior at curved surfaces. Additionally, a simple test case for thermocapillary flow that can be regarded as a modified version of the Couette flow problem, is presented.

Design and numerical analysis of Cross-Laminated bamboo (CLB) buildings with different rocking wall configurations

Engineering bamboo attracts increasing attention due to its renewable, low-carbon properties as well as the high strength-to-weight ratio. This paper proposed a displacement-based design (DBD) method for cross-laminated bamboo (CLB) rocking wall buildings based on experimental tests. The DBD was to control the story drift limitation considering the collapse prevention (CP) hazards level. The DBD accounted for the detailed design of prestressed tendons (PT) and conventional friction dampers (CFD). Segmented and monolithic rocking wall configurations were designed based on DBD and applied in the building. The simplified numerical models (SNM) for those two rocking walls were established in ABAQUS using cartesian connectors. Then two three-story CLB building models, i.e., X-LamBR1 with segmented rocking wall and X-LamBR2 with monolithic rocking wall were developed. Modal analysis and time history analysis were conducted with these two models. Smaller inter-story displacement, acceleration, and shear force were observed in X-LamBR2. Simulation results indicated that building with a monolithic rocking wall configuration performed better under earthquake excitation.

Simplified numerical modeling and analysis of electrolyte behavior in multiple physical fields for lithium-ion batteries

The electrolyte plays an important role in lithium-ion batteries, affecting their state and safety. However, the internal states of the electrolyte in the battery full domain are not easy to obtain directly. The electric field distribution, to which less attention has been paid, is as important as the concentration distribution, even related to battery safety. In this paper, an accurate and real-time simplified model for electrolyte is developed at the mesoscale, based on the Nernst-Planck equation and the continuum equation with some simple and reasonable assumptions. The analytical solutions of steady-state distribution for concentration and electric fields are obtained by theoretical derivation. Then, based on the assumption of internal uniformity of electrode, the numerical solution of the transient-state process is derived under full working conditions. The potential distribution and the overpotentials within electrolytes can be further calculated. Finally, the accuracy of the developed model is verified by the experiment of constant current terminal voltage and the accurate finite volume method. Besides, simulations are carried out to analyze the effects on the variables of electrolytes by varying the parameters in the model. The design suggestions of electrolyte concentration, thickness and porosity of each component in the battery are given.

Experimental and numerical investigation of seismic response of access floors based on shake-table tests using 2-story steel moment frame

In this study, a full-scale shake-table test was conducted utilizing a 2-story steel moment frame to evaluate the seismic performance of access floors (or raised floors). A total of four access floor specimens were fabricated that are typically used in offices and computer/server rooms. Based on test results, critical failure modes and nonlinear behavior of access floors were discussed in detail. Specimen utilizing a flexible 600 mm-high access floor (FH600-F) exhibited several cracks in its joint connection plates (or pedestal heads) before the specimen eventually collapsed under the 60% RRS intensity test (PFA = 0.65 g). Due to a partial pull-out of the pedestal heads from their supporting columns, a highly pinched hysteretic response was also observed. A simplified SDOF numerical model was presented that can effectively capture the complex pinching behavior of access floor specimens. Based on the calibrated numerical analysis, it was identified that the partial pull-out of pedestal heads caused about 60% strength loss during the reverse cyclic phase of the specimen, which was the main source of the high pinching. The specimen also exhibited severe stiffness-degradation, which may have resulted from the cracks that developed in a significant number of its joints. The initial stiffness of the specimen was reduced by about 30% before its eventual collapse. Extensive numerical analyses were also conducted to evaluate the effects of pinching and stiffness-degradation on the acceleration response of access floors based on the floor motions obtained from the time history analysis of four multi-story building models.

Numerical Simulation of Ship-Pack Ice-Water Interaction and Motion of Pack Ice Based on CFD-DEM Method

When a ship sails in pack ice area, it not only collides with the ice but also interacts with the water, generating ship-generated waves. The role and influence of ship-generated waves on the ship-ice-water interaction have not been thoroughly studied. In this study, a numerical model with ship-generated waves is established using a coupled Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM), and an appropriate contact model is selected for numerical simulations. Meanwhile, a simplified numerical model without ship-generated waves is proposed. By comparing the simulation results under the same simulation conditions with and without ship-generated waves, the effects of ship-generated waves on the phenomena of ship-ice-water interaction, longitudinal and lateral contact forces between the ship and pack ice, and ice resistance are analysed, along with the underlying mechanisms. The results indicate that the ship-generated waves can mitigate and reduce the collision intensity and contact frequency between the ship and pack ice, resulting in a decrease in the contact forces and ultimately achieving a significant reduction in ice resistance. Furthermore, this mitigation effect becomes more pronounced with increasing ship speed.