Search Results for fluid dynamics equation

This article is a comprehensive collection of fluid dynamic equations for properties of fluids, fluid statics, fluid motion, dimensional analysis, and boundary layer flow. It presents equations for analyzing problems in fluid mechanics, continuity equation, momentum equation, and energy equation for solving various problems related to fluid dynamics.

This article focuses on the basic turbulent flow, and the thermal, mass-transfer, and hydrodynamic phenomena for use in modeling physical processes during induction melting. It provides a discussion on transport phenomena equations that includes the approximation of convective terms in the transport equation and computational schemes for the fluid dynamics equation. The aspects of computational algorithms for specific magnetohydrodynamic problems with mutual influence of the magnetic field and melt flow due to the changing shape of the free surface are also considered. The article illustrates the application of the basic equations and approaches formulated for electromagnetic field and melt turbulent flow for the numerical study of an induction crucible furnace.

Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid generation with complex geometries. It discusses the four-step procedures used in the CFD process for engineering design: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. The article also provides information on the engineering applications of the CFD. It concludes with a discussion on issues and directions for engineering CFD.

Computational fluid dynamics (CFD) is one of the tools available for understanding and predicting the performance of thermal-fluids systems. This article qualitatively describes the basic principles of CFD. The numerical methods, such as geometry description and discretization, used to solve the CFD equations are discussed. The article also demonstrates the application of CFD to a few casting problems.

Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid generation with complex geometries: the use of unstructured grids and the use of special differencing methods on structured grids. The article describes the four-step procedures of the CFD process: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. It provides information on the applications of the engineering CFD. Issues and directions for the engineering CFD are also described.

Computational fluid dynamics (CFD) provides an efficient, alternate, virtual approach for simulating and analyzing quenching processes with an impact on component design, manufacturing process, and quality. This article provides domain insights for quenching researchers and CFD practitioners for the modeling of the industrial quenching process and for supporting the diverse multifunctional needs in an industry, ranging from primary metallurgical companies (steel, aluminum, and other alloys), original equipment manufacturers, engineering companies, captive and commercial heat treating facilities, quench system manufacturers, and quench fluid suppliers. It describes the governing differential equations for the fluid flow and heat-transfer phenomena during quenching. The article also discusses different modeling categories to determine a CFD methodology for quenching.

This article provides information on the classification of various composites manufacturing processes based on similar transport processes. The composites manufacturing processes can be grouped into three categories: short-fiber suspension methods, squeeze flow methods, and porous media methods. The article presents an overview of the modeling philosophy and approach that is useful in describing composite manufacturing processes.

This article provides an overview of experimental, analytical, and numerical tools for temperature evaluation of dry and lubricated systems. It describes the analytical methods and numerical techniques for frictional heating and temperature estimation, as well as viscous heating in full-film lubrication. The article also discusses the viscous heating temperature measurements and numerical analysis of viscous heating.

This article provides a comprehensive review and critical assessment of numerical modeling of heat and mass transfer in fusion welding. The different fusion welding processes are gas tungsten arc welding, gas metal arc welding, laser welding, electron beam welding, and laser-arc hybrid welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty in, numerical models.

This article describes the viscoelastic behavior of plastics in their solid state only, from the standpoint of the material deforming without fracturing. The consequences of viscoelasticity on the mechanical properties of plastics are described, especially in terms of time-dependencies, as well as the dependence of the viscoelastic character of a plastic on chemical, physical, and compositional variables. By examining the viscoelastic behavior of plastics, the information obtained are then applied in situations in which it may be important to anticipate the long-term properties of a material. This includes assessing the extent of stress decay in materials that are pre-stressed, the noise and vibration transmission characteristics of a material, the amount of heat build-up in a material subjected to cyclic deformation, and the extent a material can recover from any prior deformation. Several qualitative graphs are presented, which highlights the possible differences in the viscoelastic behavior that can exist among plastics.

This article focuses on four industrial additive manufacturing approaches that are used to create polymer parts. The first section focuses on material extrusion, providing information on lumped-parameter material flow models and higher-fidelity models developed to estimate temperature distribution. The second section covers polymer powder-bed sintering/ fusion, discussing the different levels of scale used to address modeling and the impact of process settings: thermodynamics at the powder-bed surface, consolidation of adjacent particles in the fusion process, and fusion and molecular-level behavior within particles. The third section on vat photopolymerization (VPP) discusses two primary approaches to modeling VPP processes, namely a lumped-parameter approach to estimate cured regions in the vat, known as the Jacobs model, and a high-fidelity, continuum approach that uses finite-element methods. The final section is devoted to material jetting, focusing on simulations used to study droplet generation at the nozzle and droplet impact.

Agitation is one of the most critical areas of quench system design. This article provides an overview of the impact of agitation on quench uniformity, followed by a general discussion of the selection and use of various types of agitators, including recirculation pumps, jet mixers, forced air (sparging), and impellers. A brief overview of heat-exchanger types and their selection criteria is also provided, along with simplified calculations for approximating heat-exchange requirements. The methods of selecting a quenchant are provided. Recommendations for system maintenance are also described. Much effort is placed on the proper design of the furnace for temperature and atmosphere uniformity, proper temperature control, and exact carbon potential. However, the design of the quench tank can have a drastic effect on the overall system performance, with proper design ensuring proper mechanical properties (hardness, strength, and fracture toughness) as well as distortion control.

This article presents the modes of heat transfer and the stages of cooling during quenching. It provides an overview on the wetting process and then focuses on the evaluation of heat transfer during quenching. It also presents the challenges of thermal process evaluation based on an inverse heat conduction analysis. The article contains a compilation of best practice examples on heat transfer evaluation, which are intended to represent the practical aspects and applicability of the methods aiming the prediction of heat-transfer coefficients.

This article examines the critical features of four key areas of modeling transport phenomena associated with casting processes. These include heat and species transport in a metal alloy, flow of the liquid metal, tracking of the free metal-gas surface, and inducement of metal flow via electromagnetic fields. Conservation equations that represent important physical phenomena during casting processes are presented. The article provides a discussion on how the physical phenomena can be solved. It provides information on a well-established array of general and specific computational tools that can be readily applied to modeling casting processes. The article also summarizes the key features of the conservation equations in these tools.

Computational modeling assists in addressing the issues of solid/liquid interface dynamics at the microlevel. It also helps to visualize the grain length scale, fraction of phases, or even microstructure transitions through microstructure maps. This article provides a detailed account of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models.

This article provides an overview of cavitation erosion with a specific focus on the estimation of mass loss. It describes the mechanisms of cavitation erosion and the types of laboratory devices to evaluate the resistance to cavitation erosion of materials. The laboratory devices include rotating disks, vibratory devices, cavitating liquid jets, and high-speed cavitation tunnels. The article discusses materials selection and surface protection to prevent cavitation erosion. It reviews the fluid-structure interaction that plays a role in cavitation erosion particularly for compliant materials. The article provides information on the numerical prediction of cavitation erosion damage by the finite element method (FEM).

This article provides information on the various stages of quenching, sources of distortion, and factors that affect the creation of thermal gradients. It reviews the various determinations of heat-transfer coefficients by the thermal conductivity and diffusivity method, analytical and empirical methods, application of cooling curves, computational fluid dynamics, and the inverse conduction calculation and measurement of parts. Suitable examples are also provided.

This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification. The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport equations.

This article focuses on the concepts involved in heat-transfer modeling, thermomechanical modeling, and microsegregation modeling of hot tearing. It discusses the modeling of solidification defects, namely, inclusion entrapment, segregation, shrinkage cavities, gas porosity, mold-wall erosion, and hot-tear cracks.

This article discusses the fundamentals of friction stir welding (FSW) and presents governing equations and an analytical solution for heat transfer. It provides the solutions for structural distortion in FSW. The article describes various techniques that have been adopted to solve the equations and simulate the FSW process. The techniques include modeling without convective heat transfer and modeling with convective heat transfer in a workpiece. The article concludes with information on active research topics in the simulation of FSW.