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The freezing phenomenon of a falling droplet is a frequently encountered phenomenon in various applications, such as spray crystallization, hail formation and artificial snowmaking. Therefore, this paper aims to understand the freezing processes of a falling droplet without and with initial horizontal velocity in a cold space.

The freezing processes of a falling droplet were characterized using a modified enthalpy-based lattice Boltzmann method.

The temperature field, streamlines and freezing process of the falling droplet were investigated and analyzed. The lower part of the droplet was frozen earlier than the upper part. The freezing trend slowed down in the later stage of the freezing process. The droplet shape was related to the initial vertical velocity, nucleation temperature and initial horizontal velocity.

A modified enthalpy-based lattice Boltzmann method is proposed. In the model, the improved pseudo-potential model is used and the radiation is considered. This method was firstly used to simulate the freezing process of a falling droplet. By examining these freezing processes in detail, the freezing trend and the effect factors of droplet deformation and freezing time were obtained, respectively.

This paper aims to present an algorithm for local mesh refinement of finite elements in a two‐dimensional compressible fluid flow.

The algorithm works on a principle of maximum gradient of fluid variables, e.g. pressure, velocity and density. The simulation of two‐dimensional, transient, viscous, compressible, adiabatic flow of turbulent fluid through a De Laval nozzle was performed by the finite element method. The pressure gradient was used as a condition for mesh refinement.

With the gradient method faster numerical calculations can be obtained. Boundary layer separation and locations of normal shock waves can be described on locally refined mesh.

Further development of the algorithm is required, especially the determination of the gradient criterion.

The paper provides a new approach to mesh refinement. The mesh is refined automatically. Calculation time and required computer memory are decreased.

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid and the viscous (boundary layer) fluid dynamic equations are coupled by an iterative solution procedure. Non‐equilibrium, equilibrium and perfect gas boundary layer equations are included. The non‐equilibrium gas boundary layer equations assume a binary mixture (two species; atoms and molecules) of chemically reacting perfect gases. Conservation equations for each species include finite reaction rates applicable to high temperature air. The equilibrium gas boundary layer equations assume infinite rate reactions, while the perfect gas equations assume no chemical reactions. Projectile near‐wall and surface flow profiles (velocity, pressure, density, temperature and heat transfer) representing converged solutions to both the inviscid and viscous equations can be obtained in less than two minutes on minicomputers. A technique for computing local reverse flow regions is included. Computations for yawed projectiles are accomplished using a coordinate system transformation technique that is valid for small angle‐of‐attack. Computed surface pressure, heat transfer rates and aerodynamic forces and moments for 1.25 &le Mach No. &le 10.5 are compared to wind tunnel and free flight measurements on flat plate, blunt‐cone, and projectile geometries such as a cone‐cylinder‐flare.

A fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations.

Different values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation.

The use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results.

The developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered.

The paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

This paper is useful for researchers in the area of external compressible flows. This work is original.

The purpose of this paper is to carry out a systematic energy analysis for predicting the first and second law efficiencies and the entropy generation during a laser surface alloying (LSA) process.

A three‐dimensional transient macroscopic numerical model is developed to describe the turbulent transport phenomena during a typical LSA process and subsequently, the energy analysis is carried out to predict the entropy generation as well as the first and second law efficiencies. A modified k–ε model is used to address turbulent molten metal‐pool convection. The phase change aspects are addressed using a modified enthalpy‐porosity technique. A kinetic theory approach is adopted for modelling evaporation from the top surface of the molten pool.

It is found that the heat transfer due to the strong temperature gradient is mainly responsible for the irreversible degradation of energy in the form of entropy production and the flow and mass transfer effects are less important for this type of phase change problem. The first and second law efficiencies are found to increase with effective heat input and remain independent of the powder feed rate. With the scanning speed, the first law efficiency increases whereas the second law efficiency decreases.

The top surface undulations are not taken care of in this model which is a reasonable approximation.

The results obtained will eventually lead to an optimized estimation of laser parameters (such as laser power, scanning speed, etc.), which in turn improves the process control and reduces the cost substantially.

This paper provides essential information for modelling solid–liquid phase transition as well as a systematic analysis for entropy generation prediction.

Cyclic phase change involves the successive freezing and melting of a region driven by a boundary temperature that cycles above and below the solid/liquid phase change temperature. In this paper, a recently proposed fixed grid phase change enthalpy method is modified and applied to cyclic solid/liquid phase change problems. The basic approach is demonstrated on application to a one‐dimensional, heat conduction controlled phase change. Then the method is used to investigate a cyclic phase change problem that involves fluid flow. The interaction of the melting and freezing with the phase change leads to some interesting predictions for the location and shape of the solid/liquid interface. The results also indicate that melting cycles are more effective than freezing cycles.

The present paper is about numerical simulations of one‐ and two‐dimensional lean hydrogen combustion at an equivalence ratio of 0.7. The initial flat two‐dimensional flames show unstable behavior. The instabilities generate flame wrinkling and flame induced turbulence. As a result, cusp‐like structures arise that both merge and break up in new cusps. Therefore, physically, the laminar burning velocity associated to an adiabatic flat flame does not exist. Instead, a statistical effective burning velocity and flame width develop in which the cusp like structures and their effects are included. The purpose of this paper is to describe the phenomena with a reduced chemical approach.

Simulations are performed with detailed kinetics, to study the main properties and dynamics of the wrinkling. An attempt is made to reduce the chemistry employing flamelet generated manifolds to make a step towards large‐scale, low cost simulations, which are still able to capture the physics. Here the manifold was built of premixed flames with variations of stretch, unburnt temperature and equivalence ratio. A priori correlations are presented, together with results from actual reduced chemistry simulations.

It was found that with introduction of variation of equivalence ratio into the manifold the main physical phenomena are captured. Moreover, an effective inclusion of differential diffusion was succesfully tested and applied. Results of effective burning velocities and flame widths are presented.

The paper shows the potential of performing accurate simulations using the chemical reduction technique of flamelet generated manifolds for pure lean hydrogen flames.

The paper aims to be a first step toward the efficient, yet accurate, solution of detailed combustion fields using the lattice Boltzmann (LB) method, where applications are still limited due to both the stiffness of the governing equations and the large amount of fields to solve.

The suggested methodology for model reduction is developed in the setting of slow invariant manifold construction, including details of the while. The simplest LB equation is used in order to work out the procedure of coupling of the reduced model with the flow solver.

The proposed method is validated with the 2D simulation of a premixed laminar flame in the hydrogen‐air mixture, where a remarkable computational speedup and memory saving are demonstrated.

Because of the chosen detailed LB model, the flow field may be described with unsatisfactory accuracy: this motivates further investigation in this direction in the near future.

A new framework of simulation of reactive flows is available, based on a coupling between accurate reduced reaction mechanism and the LB representation of the flow phenomena. Hence, the paper includes implications on how to perform accurate reactive flow simulations at a fraction of the cost required in the detailed model.

This paper meets an increasing need to have efficient and accurate numerical tools for modelling complex phenomena, such as pollutant formation during combustion.

The buoyancy‐driven magnetohydrodynamic flow in a cubic enclosure was investigated by three‐dimensional numerical simulation. The enclosure was volumetrically heated by a uniform power density and cooled along two opposite vertical walls, all remaining walls being adiabatic. A uniform magnetic field was applied orthogonally to the gravity vector and to the temperature gradient. The Prandtl number was 0.0321 (characteristic of Pb–17Li at 300°C), the Rayleigh number was 10⁴, and the Hartmann number was made to vary between 0 and 2×10³. The steady‐state Navier–Stokes equations, in conjunction with a scalar transport equation for the fluid's enthalpy and with the Poisson equation for the electrical potential, were solved by a finite volume method using a purposely modified CFD code and a computational grid with 64³ nodes in the fluid. Emphasis was laid on the effects of increasing the Hartmann number on the complex three‐dimensional flow and current pattern.