Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

The objective of this article is investigation of dynamic response of thick multilayer functionally graded (FG) beam under generalized dynamic forces. The plane stress problem is exploited to describe the constitutive equation of thick FG beam to get realistic and accurate response. Applied dynamic forces are assumed to be sinusoidal harmonic, sinusoidal pulse or triangle in time domain and point load. Equations of motion of deep FG beam are derived based on the Hamilton principle from kinematic relations and constitutive equations of plane stress problem. The numerical finite element procedure is adopted to discretize the space domain of structure and transform partial differential equations of motion to ordinary differential equations in time domain. Numerical time integration method is used to solve the system of equations in time domain and find the time responses. Numerical parametric studies are performed to illustrate effects of force type, graduation parameter, geometrical and stacking sequence of layers on the time response of deep multilayer FG beams.

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear elements BEM depending on the type of interpolation used at the elements. Its popularity is steadily growing because of its advantages over other numerical methods most important of which being that it only involves obtaining data at the boundary and computation of the solution in the domain is merely a case of post processing through the use of an identity. This results in the reduction of the problem dimension by unity. Although there is a reduction in dimension when we use BEM, the method usually results in full matrices which can be expensive to solve. This makes the method costly for problems that require very fine grids like those with hot spots as in the example of impressed current cathodic protection systems (ICCP). The BEM is a global method in nature in that the solution in one node depends on the solutions in all the other nodes of the grid. Hence an error in one node can pollute the solution in all the other nodes. In this thesis, we first focus our attention on defining and studying both the local and global errors for the BEM. This is not a completely new study as the literature suggests, however, our approach is different. We use the basic foundations of the the method to define the errors. Since the method is a global method, first we use the interpolation error on each element to define what we have called a sublocal error. Then using the sublocal error we have defined the local error. Understanding the local errors enabled us study the global error. Theoretical and numerical results show that these errors are second order in grid size for both the constant and linear element cases. Then, having explored errors, we study a method for adaptive grid refinement for the BEM. Rather than using a truly nonuniform grid, we present a method called local defect correction (LDC) that is based on local uniform grid refinement. This method is already developed and documented for other numerical methods such as finite difference and finite volume methods but not for BEM. In the LDC method, the discretization on a composite grid is based on a combination of standard discretizations on several uniform grids with different grid sizes that cover different parts of the domain. At least one grid, the uniform global coarse grid, should cover the entire boundary. The size of the global coarse grid is chosen in agreement with the relatively smooth behaviour of the solution outside the hot spots. Then several uniform local fine grids each of which covers only a (small) part of the boundary are used in the hot spots. The grid sizes of the local grids are chosen in agreement with the behaviour of the continuous solution in that part of the boundary. The LDC method is an iterative process whereby a basic global discretisation is improved by local discretisations defined in subdomains. The update of the coarse grid solution is achieved by adding a defect correction term to the right hand side of the coarse grid problem. At each iteration step, the process yields a discrete approximation of the continuous solution on the corresponding composite grid. We have shown how this discretisation can be achieved for the BEM. We apply the discretisation to an academic example to demonstrate its implementation and later show how to use it for an application as the ICCP system. The results show that it is a cheaper method than solving on a truly composite grid and converges in a single step.

This paper presents a numerical investigation for laminar forced convection flow of a radiating gas in a rectangular duct with a solid element that makes a backward facing step. The fluid is treated as a gray, absorbing, emitting and scattering medium. The governing differential equations consisting the continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques. Since the present problem is a conjugate one and both gas and solid elements are considered in the computational domain, simultaneously, the numerical solution of Laplace equation is obtained in the solid element for temperature calculation in this area. Discretized forms of these equations are obtained using the finite volume method and solved by the SIMPLE algorithm. The radiative transfer equation (RTE) is also solved numerically by the discrete ordinate method (DOM) for computation of the radiative term in the gas energy equation.The streamline and isotherm plots in the gas flow and the distributions of convective, radiative and total Nusselt numbers along the solid-gas interface are presented. Besides, the effects of radiation conduction parameter and also solid to gas conduction ratio as two important parameters on thermo hydrodynamic characteristics of such thermal system are explored. It is revealed that the radiative Nusselt number on the interface surface is much affected by RC parameter but the radiation conduction parameter has not considerable effect on the convective Nusselt number. Comparison between the present numerical results with those obtained by other investigators for the case of non-conjugate problems shows good consistency.

This paper presents the implementation of an algebraic frosting model into a general-purpose Navier-Stokes computational fluid dynamics (CFD) solver. The selected frosting model, derived from the energy and mass conservation equations, is used to predict the growth of the frost zone in space and time, and the resulting modification of the local flow characteristics within the non-frosted part of the domain. This implementation is used for a CFD analysis of the frosting behavior of a heat pump evaporator (represented through all relevant geometrical features) under realistic operating conditions. The obtained simulation results are compared with the findings of the experimental investigation of the fin-and-tube heat exchanger frosting, coming from the air-to-water heat pump measurements.

This thesis investigates the flexibility associated to Discontinuous Galerkin (DG) discretization on very general meshes obtained by means of agglomeration techniques. The work begins with a brief overview of the main tools that have been extended or specifically developed to deal with arbitrarily shaped elements in the DG context. Then two different implementations of the BRMPS scheme introduced by Bassi, Rebay, Mariotti, Pedinotti and Savini in [16] for the DG discretization of the Laplace operator on arbitrarily shaped elements have been presented. The validation of the scheme on a Poisson problem shows that the discrete polynomial space preserves optimal convergence properties. The discretization of the second order differential operator has been directly extended to the Navier-Stokes equations and the Reynolds Averaged Navier-Stokes (RANS) equations coupled with the k-w turbulence model of Wilcox [54]. In this regard, an implicit time integration strategy has been considered and assessed on classical validation test cases for the compressible f uid dynamics. Then a simple alternative approach to high-order mesh generation is presented. Indeed, once a standard fine grid able to provide an accurate domain discretization has been produced by means of standard low-order grid generation tools, a computational mesh suitable for the desired accuracy and computationally affordable can be obtained via agglomeration while keeping the boundary resolution of the fine grid. The effectiveness of this approach in representing the geometry of the domain is numerically assessed both on a Poisson model problem and on challenging inviscid and viscous test cases. Finally, the freedom in simply defining the topology of agglomerated meshes leads to a nonstandard approach to h-adaptivity that exploits adaptive agglomeration coarsening of a properly fine underlying grid. The effectiveness of this approach has been assessed on test cases involving both error-based and fl ow feature-based simple estimators.

Coupling Mortar Finite Element and Boundary Element Methods for 2D Navier-Stokes Equations Courant Element: Before and After Iterative Methods for Solving Stiff Elliptic Problems Straight and Curved Finite Elements of Class C1 and Some Applications to Thin Shell Problems Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary Conditions Cubic Version of FEM in Elliptic Problems with Interfaces and Singularities Least Squares Mixed Finite Elements Turbulence Modelling in Finite Element Industrial Applications Necessary and Sufficient Conditions for the Numerical Approximation of a Partial Differential Equation Depending on a Small Parameter Efficient Solution Methods for Compressible Flow Computations Parallel Finite Volume Algorithms for Solving the Time-Domain Maxwell Equations on Nonstructured Meshes Coupling Between Nonlinear Maxwell and Heat Equations for an Induction Heating Problem: Modelling and Numerical Methods Solving the 3D Harmonic Maxwell Equations with Finite Elements, Lagrange Multipliers, and Iterative Methods Some Applications of the Hierarchic High Order MITC Finite Elements for Reissner-Mindlin Plates Domain Decomposition for Immiscible Displacement in Single Porosity Systems An Error Estimator for Nonconforming Approximations of a Nonlinear Problem Some Observations on Raviart-Thomas Mixed Finite Elements in p Extension for Parabolic Problems Mixed Finite Element Methods in Fluid Structure Systems A Black-Box Solver for the Solution of General Nonlinear Functional Equations by Mixed FEM A Remark on the Asymptotic Behaviour of Parabolic Variational Inequalities and Their Finite Element Approximation by the Courant Element Domain Decomposition vs. Adaptivity Material Optimization of Composites. Part Contents.

The objective of the present study is to investigate low Reynolds number aerodynamics of a harmonically pitching NACA0012 airfoil. To this mean, the influence of some unsteady parameters; amplitude of oscillation, d, reduced frequency, k, and Reynolds number, Re, on the aerodynamic performance of the airfoil is investigated. Computational Fluid Dynamics (CFD) is utilized to solve Navier-Stokes equations discretized based on Finite Volume Method (FVM). The instantaneous lift coefficients are obtained and compared with analytical data from Theodorsen’s equations. The simulation results reveal that d, k, and Re are of great importance in the aerodynamic performance. They affect the maximum lift coefficients, hysteresis loops, strength and number of generated vortices within the harmonic motion, and the extent of the figure-eight phenomenon region. Thus, the optimum aerodynamic performance demands a careful selection of these parameters.

A novel computational approach to combine the optical and thermal modelling of Linear Fresnel Collectors using the finite volume method

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-state Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65° swept, sharp-edged, cropped delta wing of zero thickness at 20° angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 106, the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown.\nThe effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied.\nComparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2 π eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment.\nThe second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65° swept model and an 80° swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock.\nComparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

A CFD — Finite volume method to generate a deterministic model: Application to stirred tank reactors

The investigation of Computational Fluid Dynamics (CFD) focuses on the mechanical properties of a Rabinowitsch fluid model that was constructed with the help of a stenosed elliptic conduit using the well-known Finite Volume Method (FVM). If you are interested in studying physiology or biomedicine, you will find that the Rabinowitsch fluid model in peristalsis is very helpful. This is because it is used to move blood around the heart and lungs, as well as in sanitary fluid transport systems, the transfer of corrosive fluids and innovative pharmaceutical delivery systems. By using the Cartesian coordinates, it is feasible to get the elliptic domain for this duct model. Additionally, the equation of an ellipse is used in the boundary conditions for this duct in order to maintain the elliptic cross-section for this duct in its current state. The Partial Differential Equations (PDEs) for the velocity profile may be determined as soon as the issue is recast in a form that does not need any dimensions to be specified. With the assistance of boundary conditions that are provided, these PDEs are solved over elliptical cross-sections, and after that, numerical solutions are obtained for them. A dilatant fluid represents state [Formula: see text], a Newtonian fluid represents state [Formula: see text] and a pseudoplastic fluid represents state [Formula: see text] in this model, making it significant. The desired model is computed numerically. FVM is used to study the results at a low Reynolds number (around [Formula: see text]. The goal is to theoritically analyze the transmission of heat and fluid resistance to the flow. The CFD findings with experimental data are compared to confirm the model predictions. A CFD model based on the FVM and experimental data from a flow cell is used to study how fluid moves through the ducts. This study focuses on the pressure, velocity and temperature fields of a fluid moving through a stenosed duct.

The problem of the diffraction of sound by two-dimensional rigid cylindrical objects has been formulated in generalized curvilinear coordinates. The governing equations for the aeroacoustic field are derived by perturbing the unsteady Euler equations and then extracting the steady mean flow equations from them. The governing equations are then solved by an explicit, four-stage Runge-Kutta, time-marching, finite-volume numerical scheme. The scheme has been implemented with far-field radiation and time-accurate wall boundary conditions. The cases of diffraction by a knife edge and a cylinder have been computed and compared against their corresponding analytical solutions in order to demonstrate the prediction capability of the numerical scheme. The acoustic field resulting from the interaction of the incident, reflected, and diffracted fields has been predicted very well in both the shadow and the illuminated zones. The scheme has also been applied to compute the diffraction of plane waves as well as that of a monopole acoustic field by a GA(W)-1 airfoil. I. Introduction W HEN sound waves impinge upon large rigid obstacles in their path, the resultant aeroacoustic field comprises of the incident waves, the reflected waves, and the diffracted waves. The diffraction of sound waves in the shadow zone plays a key role in assessing the acoustic shielding capability of aerodynamic bodies and forms a problem of fundamental importance in the field of aeroacoustics . The various fluctuating quantities that describe the aeroacoustic field are governed by the Euler equations which are, of course, nonlinear. Even if the governing equations are linearized, it is extremely difficult to obtain analytical solutions in the cases of the realistic twodimensional obstacles such as airfoils without some unacceptable drastic simplifications. The difficulty can be essentially attributed to the complexities associated with the treatment of the boundary conditions. These difficulties pertaining to the analytical solutions have been appreciated by many investigators14 and have led to the emergence of a new field of computational aeroacoustics (CAA). Progress in the methods of CAA has now advanced because of the considerable advances in the fields of computational fluid dynamics (CFD) and computer technology. The aim of both CFD and CAA is to find solutions to the practical problems numerically, but the main differences between the two lie in the nature of the problems one deals with and in the type of the information one wishes to obtain. CFD treats steady as well as unsteady problems, whereas all the CAA problems are, by definition, unsteady. In current CFD problems, interests are focused primarily on the flowfield in the immediate vicinity of an aerodynamic body, and the objectives are to determine aerodynamic quantities such as pressure distributions, skin friction, lift and drag, etc. On the other hand, in CAA problems, attention is directed to both the near-field acoustic vibrations and the far-field noise radiation away from the body, and the objectives are to find the directivity and the spectral characteristics of the acoustic field. Therefore, while the well-established techniques of CFD can be utilized in order to develop the

An adaptive finite volume method for the simulation of time-dependent, viscous flow is presented. The Navier–Stokes equations are discretized by central schemes on unstructured grids and solved by an explicit Runge–Kutta method. The essential topics of the present study are a new concept for a local Runge–Kutta time-stepping scheme, called multisequence Runge–Kutta, which reduces the severe stability restriction in unsteady problems, a common grid generation and adaptation procedure and the application of dynamic grids for capturing moving flow structures. Results are presented for laminar, separated flow around an aerofoil with a flap.

The new generation of power plants based on innovative thermodynamic cycles operating with unconventional working fluids, such as CO2 close to its thermodynamic critical point or organic fluids close to their vapour saturation line, is an attractive option for high efficiency conversion of sustainable energy sources in the low and medium power output range. One of the most challenging tasks is to make this technology competitive by realizing highly efficient turbomachinery components. The main difficulty stems from the strongly non-ideal fluid dynamic behaviour of such fluids, which largely deviates from that of fluids commonly employed in standard applications. As a consequence, special design is needed, as available methods for turbomachinery of steam or gas turbine power plants cannot be used. The scarce knowledge on both the numerical modeling of non-ideal fluid flows and on their performance in turbomachinery applications makes research crucial. Computational fluid dynamics (CFD) is a powerful tool to investigate the physics of non-ideal flows and to assist the design of unconventional machines. This thesis presents original research in the field of non-ideal fluid dynamics on three complementary aspects, namely numerical methods, applications, and theory, aiming at (i) developing new numerical schemes for the accurate and efficient CFD simulation of non-ideal compressible flows; (ii) investigating the performance of turbomachinery operating with unconventional fluids; (iii) studying the hydrodynamic stability of variable property fluid flows. The core of the report consists of five self-contained chapters, each addressing a specific problem, which are grouped into three parts according to their area of contribution. In the first part, novel implicit schemes for the spatial discretization of the Navier--Stokes equations in the framework of the finite-volume method are introduced (Chapter 2). The look-up table approach is extensively analyzed and proposed as an accurate and efficient alternative to the direct solution of the equation of state model for fluid property evaluation. In order to address the proper handling of sub-domains interfaces needed in unsteady turbomachinery simulations, a new flux-conserving treatment of non-conformal mesh blocks interfaces is proposed in Chapter 3. In the second part, the focus shifts to the investigation of non-ideal fluid flows in turbomachines. Chapter 4 reports the CFD computation of the performance map of a 20 mm diameter radial compressor operating with supercritical CO2 designed for a power of 50 kW and a rotational speed of 75 krpm. Results obtained by means of Reynolds-averaged Navier--Stokes (RANS) simulations are compared to experimental measurements of isentropic efficiency and specific enthalpy rise, showing a reasonable agreement and providing a validation for the numerical schemes introduced in Chapter 2. Chapter 5 investigates the unsteady operation of a supersonic turbine for organic Rankine cycle applications using unsteady RANS simulations. The evolution of shock waves and viscous wakes and their interaction are described in details and related to the fluctuations of blade loads, which can be of the same order of magnitude of their time-averaged values, demonstrating the primary importance of performing unsteady simulations when studying such non-conventional machines. A third part concludes the thesis presenting an analytical study of the hydrodynamic stability of a thermally-stratified channel flow with temperature dependent properties. The classical linear stability analysis framework is extended to include the effect of variable transport properties. Various distributions of thermal conductivity and specific heat across the channel height are considered in order to assess under which conditions variable properties contribute to the stabilization or destabilization of the flow. The presented results have practical implications in the study of the transition to turbulence of wall bounded flows of unconventional fluids and in devising flow control strategies.

Computational Fluid Dynamics (CFD) has become an indispensable tool for analyzing and understanding complex flow phenomena in various engineering fields.While its applications in urban flow and building aerodynamics are well-established, CFD also plays a critical role in the automotive industry, particularly for aerodynamic analysis and vehicle design optimization.In this study, a comprehensive CFD investigation of wind flow around an automobile was conducted usingOpenFOAM, an open-source CFD platform, to evaluate aerodynamic behavior and flow characteristics under different conditions.The methodology involved the development of a detailed numerical model representing the car geometry and its surrounding domain, followed by the specification of appropriate boundary conditions and the solution of the governing Navier-Stokes equations using OpenFOAM.Simulations were performed for a range of wind speeds, incident flow directions, and car configurations to capture diverse aerodynamic scenarios.The resulting data provided valuable insights into the pressure distribution, wake formation, and local turbulence structures around the vehicle.To further assess the reliability of OpenFOAM for automotive CFD applications, its results were compared with those obtained from Fluent, the commercial finite volume (FV) solver commonly used at Volvo Car Corporation (VCC).The comparison focused on key aerodynamic parameters such as drag and lift coefficients for a generic vehicle model using incompressible, steady-state Reynolds-Averaged Navier-Stokes (RANS) simulations.Additionally, incompressible Large Eddy Simulations (LES) were conducted for a generic Sports Utility Vehicle (SUV) to capture transient flow behavior and refine the understanding of turbulent wake dynamics.The findings demonstrate that OpenFOAM is a robust and capable tool for automotive aerodynamic analysis, offering comparable accuracy to commercial solvers while providing the advantages of open-source flexibility and customization.The results contribute to a deeper understanding of vehicle aerodynamics and can inform future efforts in optimizing car design, improving fuel efficiency, and reducing carbon emissions.Future work will focus on experimental validation and the integration of additional factors such as thermal effects, surface roughness, and pollutant dispersion to enhance model fidelity and broaden application potential.