Search results for: Numerical Schlieren

Authors: Haoxiang Desmond Lim, Jie Wu, Tze How Daniel New, Shengxian Shi

Abstract:

This paper outlines the development of a novel experimental technique in quantifying supersonic jet flows, in an attempt to avoid seeding particle problems frequently associated with particle-image velocimetry (PIV) techniques at high Mach numbers. Based on optical flow algorithms, the idea behind the technique involves using high speed cameras to capture Schlieren images of the supersonic jet shear layers, before they are subjected to an adapted optical flow algorithm based on the Horn-Schnuck method to determine the associated flow fields. The proposed method is capable of offering full-field unsteady flow information with potentially higher accuracy and resolution than existing point-measurements or PIV techniques. Preliminary study via numerical simulations of a circular de Laval jet nozzle successfully reveals flow and shock structures typically associated with supersonic jet flows, which serve as useful data for subsequent validation of the optical flow based experimental results. For experimental technique, a Z-type Schlieren setup is proposed with supersonic jet operated in cold mode, stagnation pressure of 8.2 bar and exit velocity of Mach 1.5. High-speed single-frame or double-frame cameras are used to capture successive Schlieren images. As implementation of optical flow technique to supersonic flows remains rare, the current focus revolves around methodology validation through synthetic images. The results of validation test offers valuable insight into how the optical flow algorithm can be further improved to improve robustness and accuracy. Details of the methodology employed and challenges faced will be further elaborated in the final conference paper should the abstract be accepted. Despite these challenges however, this novel supersonic flow measurement technique may potentially offer a simpler way to identify and quantify the fine spatial structures within the shock shear layer.

Keywords: Schlieren, optical flow, supersonic jets, shock shear layer

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Authors: Shinsuke Udagawa, Masato Yamagishi, Masanori Ota

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The Schlieren method, which has been conventionally used to visualize high-speed flows, has disadvantages such as the complexity of the experimental setup and the inability to quantitatively analyze the amount of refraction of light. The Background Oriented Schlieren (BOS) method proposed by Meier is one of the measurement methods that solves the problems, as mentioned above. The refraction of light is used for BOS method same as the Schlieren method. The BOS method is characterized using a digital camera to capture the images of the background behind the observation area. The images are later analyzed by a computer to quantitatively detect the amount of shift of the background image. The experimental setup for BOS does not require concave mirrors, pinholes, or color filters, which are necessary in the conventional Schlieren method, thus simplifying the experimental setup. However, the defocusing of the observation results is caused in case of using BOS method. Since the focus of camera on the background image leads to defocusing of the observed object. The defocusing of object becomes greater with increasing the distance between the background and the object. On the other hand, the higher sensitivity can be obtained. Therefore, it is necessary to adjust the distance between the background and the object to be appropriate for the experiment, considering the relation between the defocus and the sensitivity. The purpose of this study is to experimentally clarify the effect of defocus on density field reconstruction. In this study, the visualization experiment of underexpanded jet using BOS measurement system with ronchi ruling as the background that we constructed, have been performed. The reservoir pressure of the jet and the distance between camera and axis of jet is fixed, and the distance between background and axis of jet has been changed as the parameter. The images have been later analyzed by using personal computer to quantitatively detect the amount of shift of the background image from the comparison between the background pattern and the captured image of underexpanded jet. The quantitatively measured amount of shift have been reconstructed into a density flow field using the Abel transformation and the Gradstone-Dale equation. From the experimental results, it is found that the reconstructed density image becomes blurring, and noise becomes decreasing with increasing the distance between background and axis of underexpanded jet. Consequently, it is cralified that the sensitivity constant should be greater than 20, and the circle of confusion diameter should be less than 2.7mm at least in this experimental setup.

Keywords: BOS method, underexpanded jet, abel transformation, density field visualization

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Authors: Abdul Wajid Ali

Abstract:

Supersonic flight promises speed, but the design of the air inlet faces an obstacle: shock waves. They prevent air flow in the mixed compression ports, which reduces engine performance. Our research investigates this using supersonic wind tunnels and schlieren imaging to reveal the complex dance between shock waves and airflow. The findings show clear patterns of shock wave formation influenced by internal/external pressure surfaces. We looked at the boundary layer, the slow-moving air near the inlet walls, and its interaction with shock waves. In addition, the study emphasizes the dependence of the shock wave behaviour on the Mach number, which highlights the need for adaptive models. This knowledge is key to optimizing the combined compression inputs, paving the way for more powerful and efficient supersonic vehicles. Future engineers can use this knowledge to improve existing designs and explore innovative configurations for next-generation ultrasonic applications.

Keywords: oblique shock formation, boundary layer interaction, schlieren images, double wedge surface

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Authors: Vishnu Asokan, Zaid M. Paloba

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Flow over cavities is an important area of research due to the significant change in flow physics caused by cavity aspect ratio, free stream Mach number and the nature of upstream boundary layer approaching the cavity leading edge. Cavity flow finds application in aircraft wheel well, weapons bay, combustion chamber of scramjet engines, etc. These flows are highly unsteady, compressible and turbulent and it involves mass entrainment coupled with acoustics phenomenon. Variation of flow dynamics in an angled cavity with a heated and cooled pylon upstream to the cavity with spatial combinations of heat flux addition and removal to the wall studied numerically. The goal of study is to investigate the effect of energy addition, removal to the cavity walls and pylon cavity flow dynamics. Preliminary steady state numerical simulations on inclined cavities with heat addition have shown that wall pressure profiles, as well as the recirculation, are influenced by heat transfer to the compressible fluid medium. Such a hybrid control of cavity flow dynamics in the form of heat transfer and pylon geometry can open out greater opportunities in enhancement of mixing and flame holding requirements of supersonic combustors. Addition of pylon upstream to the cavity reduces the acoustic oscillations emanating from the geometry. A numerical unsteady analysis of supersonic flow past cavities exposed to cavity wall heating and cooling with heated and cooled pylon helps to get a clear idea about the oscillation suppression in the cavity. A Cavity of L/D 4 and aft wall angle 22 degree with an upstream pylon of h/D=1.5 mm with a wall angle 29 degree exposed to supersonic flow of Mach number 2 and heat flux of 40 W/cm² and -40 W/cm² modeled for the above study. In the preliminary study, the domain is modeled and validated numerically with a turbulence model of SST k-ω using an HLLC implicit scheme. Both qualitative and quantitative flow data extracted and analyzed using advanced CFD tools. Flow visualization is done using numerical Schlieren method as the fluid medium gives the density variation. The heat flux addition to the wall increases the secondary vortex size of the cavity and removal of energy leads to the reduction in vortex size. The flow field turbulence seems to be increasing at higher heat flux. The shear layer thickness increases as heat flux increases. The steady state analysis of wall pressure shows that there is variation on wall pressure as heat flux increases. Shift in frequency of unsteady wall pressure analysis is an interesting observation for the above study. The time averaged skin friction seems to be reducing at higher heat flux due to the variation in viscosity of fluid inside the cavity.

Keywords: energy addition, frequency shift, Numerical Schlieren, shear layer, vortex evolution

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Authors: H. Hentati, R. Abdelmoula, Li Jia, A. Maalej

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In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time.

Keywords: fracture mechanics, optimization, variation approach, mechanic

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Authors: Kazumasa Kitazono, Hiroshi Fukuoka, Nao Kuniyoshi, Minoru Yaga, Eri Ueno, Naoaki Fukuda, Toshio Takiya

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The unsteady supersonic jet formed by a shock tube with a small high-pressure chamber was used as a simple alternative model for pulsed laser ablation. Understanding the vortex ring formed by the shock wave is crucial in clarifying the behavior of unsteady supersonic jet discharged from an elliptical cell. Therefore, this study investigated the behavior of vortex rings and a jet. The experiment and numerical calculation were conducted using the schlieren method and by solving the axisymmetric two-dimensional compressible Navier–Stokes equations, respectively. In both, the calculation and the experiment, laser ablation is conducted for a certain duration, followed by discharge through the exit. Moreover, a parametric study was performed to demonstrate the effect of pressure ratio on the interaction among vortex rings and the supersonic jet. The interaction between the supersonic jet and the vortex rings increased the velocity of the supersonic jet up to the magnitude of the velocity at the center of the vortex rings. The interaction between the vortex rings increased the velocity at the center of the vortex ring.

Keywords: computational fluid dynamics, shock-wave, unsteady jet, vortex ring

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Authors: Mohsen Zahraei

Abstract:

‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Chin-Yun Chen

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Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

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Authors: Panagiotis Svarnas, Polykarpos Papadopoulos

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Atmospheric-pressure cold plasmas continue to gain increasing interest for various applications due to their unique properties, like cost-efficient production, high chemical reactivity, low gas temperature, adaptability, etc. Numerous designs have been proposed for these plasmas production in terms of electrode configuration, driving voltage waveform and working gas(es). However, in order to exploit most of the advantages of these systems, the majority of the designs are based on dielectric-barrier discharges (DBDs) either in filamentary or glow regimes. A special category of the DBD-based atmospheric-pressure cold plasmas refers to the so-called plasma jets, where a carrier noble gas is guided by the dielectric barrier (usually a hollow cylinder) and left to flow up to the atmospheric air where a complicated hydrodynamic interplay takes place. Although it is now well established that these plasmas are generated due to ionizing waves reminding in many ways streamer propagation, they exhibit discrete characteristics which are better mirrored on the terms 'guided streamers' or 'plasma bullets'. These 'bullets' travel with supersonic velocities both inside the dielectric barrier and the channel formed by the noble gas during its penetration into the air. The present work is devoted to the interpretation of the electro-hydrodynamic effects that take place downstream of the dielectric barrier opening, i.e., in the noble gas-air mixing area where plasma bullet propagate under the influence of local electric fields in regions of variable noble gas concentration. Herein, we focus on the role of the local space charge and the residual ionic charge left behind after the bullet propagation in the gas flow field modification. The study communicates both experimental and numerical results, coupled in a comprehensive manner. The plasma bullets are here produced by a custom device having a quartz tube as a dielectric barrier and two external ring-type electrodes driven by sinusoidal high voltage at 10 kHz. Helium gas is fed to the tube and schlieren photography is employed for mapping the flow field downstream of the tube orifice. Mixture mass conservation equation, momentum conservation equation, energy conservation equation in terms of temperature and helium transfer equation are simultaneously solved, leading to the physical mechanisms that govern the experimental results. Namely, we deal with electro-hydrodynamic effects mainly due to momentum transfer from atomic ions to neutrals. The atomic ions are left behind as residual charge after the bullet propagation and gain energy from the locally created electric field. The electro-hydrodynamic force is eventually evaluated.

Keywords: atmospheric-pressure plasmas, dielectric-barrier discharges, schlieren photography, electro-hydrodynamic force

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Authors: M. Reyes, R. Sastre, P. Gabana, F. V. Tinaut

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In this work, an optical characterization of the ethanol-air laminar combustion is presented in order to investigate the origin of the instabilities developed during the combustion, the onset of the cellular structure and the laminar burning velocity. Experimental tests of ethanol-air have been developed in an optical cylindrical constant volume combustion bomb equipped with a Schlieren technique to record the flame development and the flame front surface wrinkling. With this procedure, it is possible to obtain the flame radius and characterize the time when the instabilities are visible through the cell's apparition and the cellular structure development. Ethanol is an aliphatic alcohol with interesting characteristics to be used as a fuel in Internal Combustion Engines and can be biologically synthesized from biomass. Laminar burning velocity is an important parameter used in simulations to obtain the turbulent flame speed, whereas the flame front structure and the instabilities developed during the combustion are important to understand the transition to turbulent combustion and characterize the increment in the flame propagation speed in premixed flames. The cellular structure is spontaneously generated by volume forces, diffusional-thermal and hydrodynamic instabilities. Many authors have studied the combustion of ethanol air and mixtures of ethanol with other fuels. However, there is a lack of works that investigate the instabilities and the development of a cellular structure in ethanol flames, a few works as characterized the ethanol-air combustion instabilities in spherical flames. In the present work, a parametrical study is made by varying the fuel/air equivalence ratio (0.8-1.4), initial pressure (0.15-0.3 MPa) and initial temperature (343-373K), using a design of experiments type I-optimal. In reach mixtures, it is possible to distinguish the cellular structure formed by the hydrodynamic effect and by from the thermo-diffusive. Results show that ethanol-air flames tend to stabilize as the equivalence ratio decreases in lean mixtures and develop a cellular structure with the increment of initial pressure and temperature.

Keywords: ethanol, instabilities, premixed combustion, schlieren technique, cellularity

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Authors: Ahlem Mougaida, Hedi Bel Hadj Salah

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Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Pawel Flaszynski, Piotr Doerffer, Jan Holnicki-Szulc, Grzegorz Mikulowski

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Results of numerical simulations for transonic flow in a piezoelectric valve are presented. The valve is the main part of an adaptive pneumatic shock absorber. Flow structure in the valve domain and the influence of the flow non-uniformity in the valve on a mass flow rate is investigated. Numerical simulation results are compared with experimental data.

Keywords: pneumatic valve, transonic flow, numerical simulations, piezoelectric valve

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Zuodong Liang, Dong-Sheng Jeng

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Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: pore pressure, 3D wave model, seabed liquefaction, pipeline

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Authors: Amal Machtalay

Abstract:

In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: Peng Li, Er-xiang Song

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Numerical analysis of longitudinal tunnel seismic response due to spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical methods for analysis of tunnel longitudinal response under asynchronous seismic wave is extensively studied, including the improvement of the 1D time-domain finite element method, three dimensional numerical simulation technique for the site asynchronous earthquake response as well as the 3-D soil-tunnel structure interaction analysis. The study outcome will be beneficial to aid further research on the nonlinear meticulous numerical analysis and seismic response mechanism of tunnel structures under asynchronous earthquake motion.

Keywords: asynchronous input, longitudinal seismic response, tunnel structure, numerical simulation, traveling wave effect

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Authors: Bartosz Olszanski, Zbigniew Nosal, Jacek Rokicki

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An experimental study of cold-jet (nitrogen) reaction control jet system has been carried out to investigate the flow control efficiency for low to moderate jet pressure ratios (total jet pressure p0jet over free stream static pressure in the wind tunnel p∞) and different angles of attack for infinite Mach number equal to 2. An investigation of jet influence was conducted on a flat plate geometry placed in the test section of intermittent supersonic wind tunnel of Department of Aerodynamics, WUT. Various convergent jet nozzle geometries to obtain different jet momentum ratios were tested on the same test model geometry. Surface static pressure measurements, Schlieren flow visualizations (using continuous and photoflash light source), load cell measurements gave insight into the supersonic crossflow interaction for different jet pressure and jet momentum ratios and their influence on the efficiency of side jet control as described by the amplification factor (actual to theoretical net force generated by the control nozzle). Moreover, the quasi-steady numerical simulations of flow through the same wind tunnel geometry (convergent-divergent nozzle plus test section) were performed using ANSYS Fluent basing on Reynolds-Averaged Navier-Stokes (RANS) solver incorporated with k-ω Shear Stress Transport (SST) turbulence model to assess the possible spurious influence of test section walls over the jet exit near field area of interest. The strong bow shock, barrel shock, and Mach disk as well as lambda separation region in front of nozzle were observed as images taken by high-speed camera examine the interaction of the jet and the free stream. In addition, the development of large-scale vortex structures (counter-rotating vortex pair) was detected. The history of complex static pressure pattern on the plate was recorded and compared to the force measurement data as well as numerical simulation data. The analysis of the obtained results, especially in the wake of the jet showed important features of the interaction mechanisms between the lateral jet and the flow field.

Keywords: flow visualization techniques, pressure measurements, reaction control jet, supersonic cross flow

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

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Authors: Yu Liang, Wei Wei

Abstract:

Spatial representation of numbers and numerical magnitude are important for preschoolers’ mathematical ability. Mental number line, a typical index to measure numbers spatial representation, and numerical comparison are both related to arithmetic obviously. However, they seem to rely on different mechanisms and probably influence arithmetic through different mechanisms. In line with this idea, preschool children were trained with two tasks to investigate which one is more important for approximate arithmetic. The training of numerical processing and number line estimation were proved to be effective. They both improved the ability of approximate arithmetic. When the difficulty of approximate arithmetic was taken into account, the performance in number line training group was not significantly different among three levels. However, two harder levels achieved significance in numerical comparison training group. Thus, comparing spatial representation ability, symbolic approximation arithmetic relies more on numerical magnitude. Educational implications of the study were discussed.

Keywords: approximate arithmetic, mental number line, numerical magnitude, preschooler

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Authors: Ridha Zgolli, Hatem Kanfoudi

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Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A 2D numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier-Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density which is expressed as function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term TEM. The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in details. The numerical simulations are in good agreement with the experimental data for steady flow.

Keywords: cavitation, injection nozzle, numerical simulation, k–ω

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Authors: A. Chellil, A. Nour, S. Lecheb, H.Mechakra, A. Bouderba, H. Kebir

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In this paper, the numerical study for the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor is developed. The use of the composite material for the rotor, offers a good Stability. Numerical calculations on the model develop of three dimensions prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed to determine the vibratory responses due to various excitations.

Keywords: rotor, composite, damage, finite element, numerical

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Authors: Ogunrinde Roseline Bosede

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Piotr Ciuman, Barbara Lipska

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The aim of presented research was to improve numerical predictions of air parameters distribution in the actual natatorium by the selection of calculation formula of mass flux of moisture emitted from the pool. Selected correlation should ensure the best compliance of numerical results with the measurements' results of these parameters in the facility. The numerical model of the natatorium was developed, for which boundary conditions were prepared on the basis of measurements' results carried out in the actual facility. Numerical calculations were carried out with the use of ANSYS CFX software, with six formulas being implemented, which in various ways made the moisture emission dependent on water surface temperature and air parameters in the natatorium. The results of calculations with the use of these formulas were compared for air parameters' distributions: Specific humidity, velocity and temperature in the facility. For the selection of the best formula, numerical results of these parameters in occupied zone were validated by comparison with the measurements' results carried out at selected points of this zone.

Keywords: experimental validation, indoor swimming pool, moisture emission, natatorium, numerical calculations CFD, thermal and humidity conditions, ventilation

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Authors: H. Ahmed, A. Schlenkhoff

Abstract:

Recently, permeable breakwaters have been suggested to overcome the disadvantages of fully protection breakwaters. These protection structures have minor impacts on the coastal environment and neighboring beaches where they provide a more economical protection from waves and currents. For regular waves, a numerical model is used (FLOW-3D, VOF) to investigate the hydraulic performance of a permeable breakwater. The model of permeable breakwater consists of a pair of identical vertical slotted walls with an impermeable upper and lower part, where the draft is a decimal multiple of the total depth. The middle part is permeable with a porosity of 50%. The second barrier is located at distant of 0.5 and 1.5 of the water depth from the first one. The numerical model is validated by comparisons with previous laboratory data and semi-analytical results of the same model. A good agreement between the numerical results and both laboratory data and semi-analytical results has been shown and the results indicate the applicability of the numerical model to reproduce most of the important features of the interaction. Through the numerical investigation, the friction factor of the model is carefully discussed.

Keywords: coastal structures, permeable breakwater, slotted wall, numerical model, energy dissipation coefficient

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Authors: Young Hee Geum

Abstract:

We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding

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Authors: Piotr Wisniewski, Sławomir Dykas

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Condensation has a negative impact on turbomachinery efficiency in many energy processes.In technical applications, it is often impossible to dry the working fluid at the nozzle inlet. One of the most popular working fluid is atmospheric air that always contains water in form of steam, liquid, or ice crystals. Moreover, it always contains some amount of suspended particles which influence the phase change process. It is known that the phenomena of evaporation or condensation are connected with release or absorption of latent heat, what influence the fluid physical properties and might affect the machinery efficiency therefore, the phase transition has to be taken under account. This researchpresents an attempt to evaluate the impact of solid and liquid particles suspended in the air on the expansion of moist air in a low expansion rate, i.e., with expansion rate, P≈1000s⁻¹. The numerical study supported by analytical and experimental research is presented in this work. The experimental study was carried out using an in-house experimental test rig, where nozzle was examined for different inlet air relative humidity values included in the range of 25 to 51%. The nozzle was tested for a supersonic flow as well as for flow with shock waves induced by elevated back pressure. The Schlieren photography technique and measurement of static pressure on the nozzle wall were used for qualitative identification of both condensation and shock waves. A numerical model validated against experimental data available in the literature was used for analysis of occurring flow phenomena. The analysis of the suspended particles number, diameter, and character (solid or liquid) revealed their connection with heterogeneous condensation importance. If the expansion of fluid without suspended particlesis considered, the condensation triggers so called condensation wave that appears downstream the nozzle throat. If the solid particles are considered, with increasing number of them, the condensation triggers upwind the nozzle throat, decreasing the condensation wave strength. Due to the release of latent heat during condensation, the fluid temperature and pressure increase, leading to the shift of normal shock upstream the flow. Owing relatively large diameters of the droplets created during heterogeneous condensation, they evaporate partially on the shock and continues to evaporate downstream the nozzle. If the liquid water particles are considered, due to their larger radius, their do not affect the expanding flow significantly, however might be in major importance while considering the compression phenomena as they will tend to evaporate on the shock wave. This research proves the need of further study of phase change phenomena in supersonic flow especially considering the interaction of droplets with the aerodynamic waves in the flow.

Keywords: aerodynamics, computational fluid dynamics, condensation, moist air, multi-phase flows

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Authors: Dejin Chen, Bin Lin, Xiaohui LI, Haobin Tian

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In order to acquire stable impact performance of cover, the factors influencing the impact force of the cover were analyzed and researched. The influence of impact factors such as impact velocity, impact weight and fillet radius of warhead was studied by Orthogonal experiment. Through the range analysis and numerical simulation, the results show that the impact velocity has significant influences on impact force of cover. The impact force decreases with the increase of impact velocity and impact weight. The test results are similar to the numerical simulation. The cover broke up into four parts along the groove.

Keywords: fragile cover, numerical simulation, impact force, epoxy foam

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Authors: Hariti Rafika, Fekih Malika, Saighi Mohamed

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During the period storage of liquefied natural gas, stability is necessarily affected by natural convection along the walls of the tank with thermal insulation is not perfectly efficient. In this paper, we present the numerical simulation of heat transfert by natural convection double diffusion,in unsteady laminar regime in a storage tank. The storage tank contains a liquefied natural gas (LNG) in its gaseous phase. Fluent, a commercial CFD package, based on the numerical finite volume method, is used to simulate the flow. The gas is just on the surface of the liquid phase. This numerical simulation allowed us to determine the temperature profiles, the stream function, the velocity vectors and the variation of the heat flux density in the vapor phase in the LNG storage tank volume. The results obtained for a general configuration, by numerical simulation were compared to those found in the literature.

Keywords: numerical simulation, natural convection, heat gains, storage tank, liquefied natural gas

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