Simplified Numerical Method Research Articles

Adaptability analysis of flow and heat transfer multi-scale numerical method for printed circuit heat exchanger

The printed circuit heat exchanger (PCHE) is a high-efficiency and compact mini-channel heat exchanger. Due to the large number of fine channels, it is difficult to conduct the flow and heat transfer numerical simulation of the entire heat exchanger based on the actual channels, which requires a lot of computational resource and time. In this paper, a simplified multi-scale numerical method with a non-equilibrium porous media model (NOPM) is proposed to study the flow and heat transfer performance of PCHE at high temperature and pressure. The pressure field, velocity field and temperature field of NOPM and actual multi-channel model (MC) under different working conditions are compared to study the adaptability of NOPM for the PCHE. The results indicate that the NOPM can accurately predict the flow and heat transfer performance under PCHE configurations with a large number of channels. However, as the channel number decreases, the relative errors in the temperature and pressure prediction significantly increase due to the increased flow maldistribution. Similarly, the NOPM can well predict the overall temperature distribution of the PCHE solid when the channel number is numerous. This work could support accurate thermal design, and provide accurate temperature field for the thermal stress analysis of PCHE.

Long-term effects including shrinkage and interfacial creep on bond behavior of concrete-filled steel tubes (CFST): Experiment and design

Concrete-filled steel tubes (CFST) are widely used in significant projects due to their high performance stemming from full utilization of combined material advantages. The interfacial bond behavior is the foundation of their high performance, but will deteriorate during the long-term service. Due to the difficulties on carrying out long-term experiments and decoupling the multi-constitutive component bond strength including chemical adhesion, micro-interlocking and friction, there is still a lack of research on long-term interface constitutive models, restricting the safe design of CFST structures throughout their full-lifecycle. Here, push-out tests were carried out on CFST specimens considering long-term effects spanning 850 days including concrete age and duration of long-term interfacial load. The steel plate-concrete specimens, reversed push-out tests and interfacial normal pressure calculation were used to decouple the components of bond stress. the CFST interface database considering long-term effects was established and the mechanism of long-term effects have been revealed. As the duration increases, the bond stress decreases at the beginning, and thereafter stabilizes where the friction component dominates. Compared to that without interfacial load, long-term interfacial load accelerates the damage to chemical adhesion and micro-interlocking at initial stage, but the difference of their effects on bond stress is not significant in the later stage. On this basis, a long-term interfacial constitutive model for its full-lifecycle safe design and a simplified numerical method for long-term effects on bond behavior have been proposed.

Determination of Propeller-Rudder-Hull Interaction Coefficients in Ship Manoeuvring Prediction

Abstract The assessment of ship manoeuvring properties is a crucial part of the process of ship design and is usually first carried out during the model test phase of the project. According to the International Maritime Organisation (IMO), the manoeuvrability of the ship can be assessed on the basis of the standard trial manoeuvres. In order to do this, free running model tests or captive model tests are used, in conjunction with a mathematical model of ship motion; this is considered to be a reliable prediction method. In recent years, numerical-based methods have also been widely used in ship hydrodynamics and constantly improving computing power and more accurate fluid dynamics models have made the simulation of more complex cases possible. The study presented in this paper focuses on the determination of propeller-rudder-hull interaction coefficients based on the Mathematical Modelling Group (MMG) standard method in ship manoeuvring prediction. The identification of the parameters uses both captive model tests and a simplified numerical method, as well as regression formulas. The results of 35° turning and 10°/10° zig-zag manoeuvres, obtained with the use of each prediction method, are then compared. The test case used in the study is the container type cargo ship equipped with a single propeller and rudder. The model scale, for which the referenced model tests were carried out, is equal to 1:25 and a NACA 0020 rudder profile was used. This research highlights the advantages and disadvantages of each presented prediction method and their potential for future improvement.

Underwater radiated noise numerical analysis of polar transport vessels under ship-ice-water-air coupling continuous icebreaking based on the S-ALE algorithm

With the gradual opening of the Arctic channel, the underwater radiated noise induced by the ship-ice collision cannot be ignored. However, the underwater radiated noise induced by ship-ice collision is significantly different from that of ships navigating in open water. To explore the response rule of transient underwater radiation noise induced by ship-ice collision, this paper proposes a simplified numerical analysis method of ship-ice collision-induced transient underwater radiated noise in the full frequency band by combining the explicit dynamic method and acoustic analysis method. The ship-ice-water-air coupled collision analysis method based on the S-ALE algorithm is used to simulate and verify the ice load in the process of ship-ice continuous collision at different speeds. Then, the frequency-domain acoustic analysis method is used to predict the transient underwater radiated noise response in the full frequency band under icebreaking excitation and evaluate it by referring to the steady-state underwater radiated noise standard. The results show that the simplified analysis method can effectively predict the transient underwater radiation noise under icebreaking excitation. Under the icebreaking excitation, the radiation shape is irregularly scattered and the radiation direction is concentrated towards the bottom and bow of the ship with the frequency increase. The influence range of transient underwater radiated noise is mainly within 1000 Hz at different speeds, and the variation in the ship's speed affects the amplitude of the sound power level and the smoothness of the periodic response. The synthesized total sound power levels are 172.56 dB (V = 2.0kn), 174.15 dB (V = 2.5kn), 175.70 dB (V = 3.0kn), and 182.49 dB (V = 4.0kn), respectively. According to the comparison with the evaluation standard, it is found that the transient underwater radiation noise induced by ship icebreaking has a greater impact on marine organisms. It should give more detailed requirements within 10–1000 Hz when using relevant standards to evaluate underwater radiated noise induced by polar icebreaking. This paper can provide a reference for the research of underwater radiated noise induced by ship-ice collision and the formulation of relevant standards.

A simplified numerical method based on anisotropic porous media model for the precooler of the hypersonic precooled engine

The precooler is a key component of hypersonic precooled engine, and its actual structural have a high anisotropy in the axial, circumferential, and radial direction. Considering the non-uniform flow inside the precooler is crucial to study the flow and heat transfer characteristics of the precooler. The previous simplified method for the precooler has not fully considered the flow non-uniformity of the axial, radial and circumferential direction. In this paper, a simplified numerical method based on anisotropic porous media model for the precooler was proposed. The unique aspect of this method is the integration of anisotropic surface porosity of porous media model with the zero-dimensional heat transfer model. In addition, the influence of key structural parameters on the flow and heat transfer characteristics of precooler was studied. It is found that as the tube transverse pitch increases from 2 to 3.5, the total flow rate increases by 11%, and the heat exchange rate decreases by 25%. As the number of tube rows increases from 7 to 13, the heat exchange rate increases by 22%, but the total pressure loss coefficient increases from 0.046 to 0.082. In addition, the decrease of inner diameter of the precooler improves the heat exchange rate, but reduces the flow capacity of the precooler. These results indicate that the simplified numerical method is capable of simulating the behavior of precooler and provides some guidance on the design of precooler.

Study on radon release behaviors of the tubular flow-through radon source with natural radium-bearing materials

To obtain a radon source that is easy to access natural radium-bearing raw material and does not require the approval of relevant departments, the tubular flow-through radon source using radium-bearing ore as the radon-generating material was designed. Based on the theories of radon diffusion-convection migration in porous media, the simplified calculation formula and numerical calculation models of radon activity concentration at the outlet of the tubular flow-through radon source were established, and the radon release rules of the tubular flow-through radon source were studied using a combination of simplified calculation formulas, numerical simulations, and experiments, respectively. The results show that (1) the radon activity concentration at the outlet of the tubular flow-through radon source was dominated by mass (or the volume) of the natural radium-bearing raw material, free radon production rate, and gas flow rate. (2) When the range of radon activity concentration at the outlet is 260–1308 Bq m-3, the relative deviation of the three methods is less than 2.62%. (3) The simplified calculation formula and numerical simulation method proposed in this paper can provide a reference for the design and control of the radon activity concentration of a tubular flow-through radon source.

Flexibility analysis of typical roof diaphragms in steel structures using the equivalent connectors method

Steel structures are invariably analyzed and designed excluding the global stiffening effect of the roof cladding. Including this effect historically required complex design methods or deprecated standards. This paper presents a simplified numerical modeling method which allows this stiffening effect to be included. The method is an extension of the already established Component Method but utilizes only elements commonly available in typical design and analysis software. The results of the models were favorably compared to standardized test cases; an average difference of 0.24 mm maximum displacement was found, corresponding to a 3.4% discrepancy. The consistency of these results implies that the proposed model can be considered to be used for scientific and practical purposes when assessing a building’s most realistic behavior is necessary.

FFT-Based Numerical Method for Nonlinear Elastic Contact

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplified to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the finite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efficiency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplified numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

Simplified Numerical Homogenization Method for the Plasticity Problem with Isotropic Hardening

Simplified Numerical Homogenization Method for the Plasticity Problem with Isotropic Hardening

A predictive method for pipe in pipe, cylindrical modules and spherical packed bed latent thermal energy storage systems

Due to the transient operation of latent thermal energy storage (LTES) heat exchangers, methods from classical heat exchanger theory such as the effectiveness number of transfer unit method are not applicable. As a result, the study of these systems lacks a general theoretical framework. Recently, an approximate analytical solution method was developed which integrates phase fraction under a constant boundary condition to an LTES heat exchanger with a varying heat transfer fluid temperature. In this paper, the method is applied to three geometries: pipe in pipe, cylindrical modules and spherical packed bed geometries. The resulting model predicts the phase change fraction and effectiveness as a function of time, based on one-dimensional solutions for the movement of the phase change front. The predictions of the analytical model are compared to results of a simplified numerical method of an LTES heat exchanger. The average deviation of the predicted phase change fraction is 3.3 10−2 %, 4.6 10−1 % and 3.7 10−1 % for the pipe in pipe, cylindrical and spherical module respectively. The difference in model performance stems from the description of the fundamental heat transfer behavior. In a second validation step, the outlet temperature predicted by the model is compared to an experimental dataset for a LTES shell and tube heat exchanger. The predictions of the model can be improved further by including sensible heat, heat losses and allowing time-varying inlet conditions.

Study on the Influence of Window Glass Size on Blast-Resistant Performance

As the most commonly used exterior-protecting components for buildings, window glass, due to its typical brittle characteristics, is more prone to break under the action of blast loads and produce high-speed flying fragments, which can pose a great threat to personal safety. This paper studies the influence of the size of window glasses on their failure characteristics. A simplified numerical simulation-based method for evaluating the P–I (pressure–impulsive) curve of window glass failure under blast loads is proposed. The influences of the length–width ratio, the area, and the thickness of the P–I curves of window glasses are systematically investigated. It was found that smaller a length–width ratio, smaller area, and thicker panel could increase the blast resistance of the window glasses. The empirical prediction formulae for the P–I curves of window glasses with different geometrical dimensions are established, and the validity of the proposed empirical formula is verified.

Engineering Method for Calculating Temperature Deformations of PVC Window Profiles with a Reinforcing Steel Core

In current engineering practice, static calculation of windows for temperature loads is not performed. However, the existing experience in operating PVC windows in environmental conditions of Eastern and Northern Europe shows that the temperature deformation of such structures can reach values comparable to those of wind loads, which leads to a significant reduction in their technical and operational characteristics. Temperature deformations of windows can be assessed during laboratory tests. However, such tests are not representative. In this regard, it is necessary to develop an engineering method for calculating temperature deformations of windows. In this study, the authors present the results of the analysis of temperature deformations of PVC window profiles. The investigations were divided into several stages. First, the authors numerically analysed the character of temperature distribution over the cross section of PVC window profiles. Then, they theoretically substantiated the bending deformations of PVC window profiles disregarding the reinforcing steel core. Next, the authors considered the patterns of bending deformations of PVC window profiles, taking into account the presence of a reinforcing steel core in various schemes of their connection to each other. The authors also analysed the effect of the temperature dependence of the mechanical properties of PVC on the deformation of window profiles. The character of torsional temperature deformations of PVC window profiles was also studied. As a result of this investigation, the authors proposed a simplified analytical and numerical method for calculating the temperature deformations of PVC window profiles with a reinforcing steel core. The authors have used the proposed methods to calculate the temperature deformations of PVC window mullions (vertical bars that divide the window into parts). These theoretical calculations were compared with the experimental investigations data on PVC windows and showed a fine precision of results (the discrepancy was 10.6%).

Novel three-dimensional simplified numerical simulation method of a compact precooler for hypersonic precooled air-breathing engine

The revolutionary thermal cycle of precooled air-breathing engines has led to the application of a compact tubular precooler. A novel three-dimensional simplified numerical simulation method for a compact tube precooler is proposed. The unique aspect of this method is the integration of low-dimensional design method of the precooler with three-dimensional simulation technique. The method includes a segmented model to discretize the precooler into sub-precoolers, with corresponding performance calculation programs for circumferential uniform and non-uniform airflows in the circumferential direction. The heat transfer and pressure drop are then simulated using a combination of the distributed heat source method and porous model. The developed method was verified with previous experiments, and showed good agreement. In addition, the flow and heat transfer characteristics of the precooler were investigated under both circumferential uniform and non-uniform inlet conditions. The results show that the radial total temperature distortion intensity at the outlet of the precooler is 0.087 and 0.073 under uniform and non-uniform inlet conditions, respectively. Additionally, the intensity of circumferential total temperature distortion increases from 0.004 under uniform inlet conditions to 0.029 under non-uniform inlet conditions. Overall, this method provides an accurate evaluation of the precooler during the engineering design phase.

A simplified numerical method for modelling the wind flow and ventilation at urban-scale street network

Street networks serve as the main open corridors for wind flow within urban areas, so understanding their ventilation performance and capacity of removing pollutants helps improve urban air quality. However, conventional modelling methods using an exact building model (EBM) are hard-pressed to simulate urban-scale areas, due to their extremely high computing load. To reduce time and cost of numerical simulations, and accurately predict the flow field and ventilation within the street network, a simplified modelling approach (i.e., EBM&PMM) is proposed, in which only the first row of buildings flanking the street is modelled by EBM and the rest of the urban buildings are modelled by a porous media model (PMM). The performance of EBM&PMM is evaluated by three common modelling approaches, i.e., EBM, PMM, and sealed concrete model (SCM) in which the building complexes with gaps are treated as an enclosed entity. A typical crossing street network flanked by four communities (building arrays) is used for this study. The age of air (τP) and ventilation flux (Q) obtained from the four modelling methods are compared. The results show that EBM&PMM predicts τP and Q well, and the flow pattern by this model agrees well with EBM. PMM significantly underestimates τP but exaggerates Q in street networks, and it fails to give the detailed flow patterns. SCM over-predicts τP, and Q between the community and street is zero. Furthermore, the first row of buildings facing the street plays a decisive role in flow pattern and ventilation effectiveness of the street network.

Numerical analysis method of ship-ice collision-induced vibration of the polar transport vessel based on the full coupling of ship-ice-water-air

As the Arctic Channel continues to be developed, collisions between polar navigation vessels and sea ice are inevitable, which will directly affect structural safety and vibration comfort. However, the numerical analysis method of ship–ice collision-induced vibration is not perfect, and the effect of fluid coupling is not typically considered. In this paper, a simplified numerical analysis method for ship–ice collision-induced vibration is proposed, in which a reliable ice load is obtained by first performing ship–ice–water–air coupled collision calculations, followed by ship–ice–water coupled vibration calculations to obtain the vibration response of the structure. In addition, this paper investigates the full coupling method and the modeling ranges and meshing sizes involved in the analysis ship–ice collision-induced vibration, and the computational efficiencies of the traditional ALE algorithm and S-ALE algorithm are compared. The results indicate that the simplified simulation analysis method and gradient meshing model improve the calculation accuracy and efficiency in ship-ice collision and vibration response analysis. Moreover, the modeling range of the water and air models cannot be less than 6 times the ship width, 2 times the ship length, and 1 times the ship depth, and the S-ALE algorithm saves 47.86% time compared to the ALE algorithm. The research results in this paper can provide a reference for the numerical simulation of ship–ice collision-induced vibration.

A Simplified Numerical Method for Simulating the Generation of Linear Waves by a Moving Bottom

In this study, simplified linear numerical method that can simulate wave generation and transformation by a moving bottom is introduced. Numerical analysis is conducted in wave number domain after continuity equation, linear dynamic and kinematic free surface boundary conditions and linear kinematic bottom boundary condition are Fourier transformed, and the results are expressed in space domain by an inverse Fourier transform. In the wavenumber domain, the dynamic free water surface boundary condition and the kinematic free water surface boundary condition are numerically calculated, and the velocity potential in the mean water level (<i>z</i> = 0) satisfies the continuity equation and the kinematic bottom boundary condition. Wave generation and transformation are investigated when the triangular and rectangular shape of bottoms move periodically. The results of the simplified numerical method are compared with the results of previous analytical solutions and agree well with them. Stability of numerical results according to the calculation time interval (△<i>t</i>) and the calculation wave number interval (△<i>k</i>) was also investigated. It was found that the numerical results were appropriate when △<i>t</i>≤<i>T</i>(period)/1000 and △<i>k</i>≤π/100.

Numerical analysis on the moment redistribution behavior of prestressed continuous beams considering the effect of construction method

The design method for the prestressed continuous beams (PCBs) in the current design codes usually neglects the effect of construction method, which determines the distribution of initial internal forces caused by dead load in the PCBs. To fully investigate the moment redistribution behavior of the PCBs constructed by monolithic casting (MC), simply supported-continuous (SC), and cantilevered-continuous (CC) methods, a simplified but effective numerical analysis method was proposed by combining the modified force method and incremental method, in which the effect of initial internal forces and secondary moment were isolated and discussed. The proposed numerical method was first calibrated by the test results, and then used to predict the mechanical behavior of 27 PCBs during the whole loading process with the parameters of construction method, the effective prestressing stress in the prestressing tendons (fpe), the degree of prestressing (PPR), and the relative neutral axis depth (ξ). Based on the analysis results, it was observed that the initial negative and positive bending moment in the PCBs produced by different construction methods helps improving the moment redistribution ability of the sections with maximum negative and positive bending moment, respectively. Besides, the current design codes generally overestimate and underestimate the ultimate bearing capacity of the simply supported-continuous and cantilevered-continuous PCBs, respectively.

Optimisation of railway noise barrier design using finite element and boundary element modelling methods

The prediction of environmental noise barrier insertion loss (IL) is commonly undertaken from widely available empirical methods derived from measurements and geometrical acoustic approximations. The accuracy of these methods is limited when analysing non-standard design parameters, such as geometry; characteristics and location of sound absorbing materials; or diffraction effects close to the barrier. This article presents a new methodology to optimise the design of a railway noise barrier using a simplified numerical method. The numerical method is based on a two-dimensional hybrid finite element and boundary element analysis. The numerical method has been calibrated and tested against measurements of high speed trains. The model assumes an infinitely long train with pre-defined sound sources (e.g. rolling source, body aerodynamic, etc.). The numerical model quantifies the effect of various parameters upon the barrier IL including material properties; area and location of sound absorbing materials; diffraction over the barrier top; and analysis of energy build-up between train and barrier. These parameters are not easily quantifiable using standard methods and hence the innovation aspect of the methodology. The outcome of this study can be used to optimise and improve confidence in the detailed design of complex noise barriers.

Load-bearing characteristics of marine complex sandwich composites considering unequal elastic modulus in tension and compression

The panel and core materials of sandwich composite usually have the characteristics of unequal elastic modulus in tension and compression. However, in the numerical calculation of sandwich composite, it is usually considered as the material with the same tensile modulus or compression modulus, which often leads to larger calculation errors. The test results show that when the elastic modulus of tension and compression is about 10 times different, the maximum calculated stress and maximum deflection will be more than twice different. In view of the complexity of sandwich composite structure, based on the bi-modulus model of laminated plates, a simplified theoretical formula and numerical calculation method are proposed for bi-modulus sandwich composite structures in this paper. Furthermore, the accuracy of the proposed numerical calculation method of bi-module is verified by the experimental study of composite single-layer plate structure and sandwich composite cabin structure. The results show that the error between the improved numerical calculation method and the experimental measurement results is basically within 6%. Meanwhile, the numerical method based on field variables has wide application range and high convergence, and can be used to calculate complex marine composite structures.

Numerical analysis of bridge piers under earthquakes considering pile‒soil interactions and water‒pier interactions

Previous investigations have shown that both pile‒soil interactions and water‒pier interactions have a significant effect on the seismic performance of bridge piers. However, there is a lack of systematic research on the influence of pile‒soil and water‒pier interactions simultaneously on the seismic responses of real bridge piers. This study was conducted to narrow this knowledge gap through a series of numerical analysis. A simplified numerical modelling method for the soil-water-structure system was proposed and validated with results of a centrifuge shaking table test, which considered water‒pier interactions by the additional mass method and pile‒soil interactions by a fine finite element model. The verified numerical modelling method was used to analyse a real bridge pier under near-field and far-field earthquakes. The obtained results show that both pile‒soil interaction and water‒pier interaction increase the pier displacements, and internal forces of the pier decrease by pile‒soil interaction and increase by water‒pier interaction. The effect of water‒pier interaction on the seismic responses of the pier is smaller than that of pile‒soil interaction. The water‒pier interaction significantly increases the bending moments of the base pier considering pile‒soil interactions and shear forces of the base pier without considering pile‒soil interactions.