Three-dimensional Computational Results Research Articles

Investigation of the transition of natural convective flow of water in a differentially heated cubic enclosure

ABSTRACT The present study aims at the investigation of the transition of the natural convective flow in a water-filled differentially heated cubic enclosure. The schlieren-particle image velocimetry (PIV) system has been developed and employed for simultaneous measurement of ray-averaged velocity and temperature fields from transient schlieren images for distinct Rayleigh number (Ra) (1 × 107 ≤ Ra ≤ 5 × 108). The experimentally obtained results have been compared with three-dimensional computational results. The three-dimensional incompressible simulations are carried out for a wide range of Ra (1 × 105 ≤ Ra ≤ 5 × 108), treating the density difference using Boussinesq approximation. The results from present simulations show that the flow is found steady in the range of Ra (1 × 105 ≤ Ra ≤ 1 × 108) while the critical Ra, at which the steady flow becomes unsteady, lies between 1 × 108 and 5 × 108. The critical Ra from the experiments is found to lie between 4 × 108 and 5 × 108. Also, the three-dimensionality effect on large-scale temperature field is found to decrease as Ra increases.

A benchmark study on the axial velocity profile of wave propagation in deformable blood vessels

Wave propagation models in the time domain have been extensively used in the available literature to study the flow characteristics in blood vessels. Most of the wave propagation models have considered flat or parabolic velocity profile functions to estimate the nonlinear convection and diffusion terms present in the conservation of momentum equation. There are only a few works available on the wave propagation analysis in which the velocity profile is approximated using different polynomial functions. In this study, a computationally efficient nonlinear axisymmetric formulation is presented without a priori assumed velocity profile function across the cross section to model the blood flow. Such a formulation in terms of axial velocity (u), pressure (p), and domain radius (R) facilitates the evolution/development of axial velocity profile as the flow progresses with time. The arterial mechanical behavior is modeled using a linear elastic constitutive relation. Partial differential equations are discretized using the finite element method and the Galerkin time integration technique in space and time domains, respectively. This study finds a phase difference between the shear stress at the wall and the flow rate. The flow characteristics and the velocity profile function are found to be in good agreement with the three-dimensional computational results available in the literature. The detailed investigation of the axial velocity across the cross section reveals neither flat nor parabolic profiles, as previously assumed in the literature.

Drag and heat reduction mechanism induced by a combinational novel cavity and counterflowing jet concept in hypersonic flows

The drag and heat reduction problem of hypersonic reentry vehicles has always attracted the attention worldwide, and many novel schemes have been proposed recently. In the current study, the research progress of the combinational configuration of the forward-facing cavity and the counterflowing jet has been reviewed, and the conventional cavity configuration has been substituted by an approximate maximum thrust nozzle contour for better heat and surface pressure reduction efficiency. The Reynolds-average of Navier-Stokes (RANS) equations coupled with the SST k–ω turbulence model have been employed to calculate its surrounding flow fields. A validation metric and the grid convergence index (GCI) have been employed to conduct the turbulence model assessment and the grid independence analysis respectively. The axisymmetric assumption has been verified by three-dimensional computational results as well. The obtained results show that the SST k-ω model is more suitable for the novel drag and heat flux reduction scheme proposed in this article, and the axisymmetric assumption is approximately reasonable. After investigating the influence of jet pressure ratio, the novel combinational configuration has been verified to be more effective in heat and surface pressure reduction, and this is because the approximate maximum thrust nozzle contour contributes to better expansion and avoids total pressure loss of the jet.

Influence of non-axisymmetric terms on circumferentially averaged method in fan/compressor

The governing equations are derived by circumferentially averaging the three-dimensional (3D) Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and Navier-Stokes (N-S) throughflow model are employed to investigate the performance and flow fields of a highly loaded transonic single-stage fan ATS-2 and a four-stage fan. The results are compared with the experimental and three-dimensional computational results. It shows that the throughflow models can provide reasonable performance characteristics and N-S throughflow model gives better predictions in endwall regions. A throughflow computation in which all the non-axisymmetric terms are included has been performed at off-design condition and the radial distributions of the flow field can be well described.

Performance Measurements of a Unique Louver Particle Separator for Gas Turbine Engines

Solid particles, such as sand, ingested into gas turbine engines, reduce the coolant flow in the turbine by blocking cooling channels in the secondary flow path. One method to remove solid particles from the secondary flow path is to use an inertial particle separator because of its ability to incur minimal pressure losses in high flow rate applications. In this paper, an inertial separator is presented that is made up of an array of louvers followed by a static collector. The performance of two inertial separator configurations was measured in a unique test facility. Performance measurements included pressure loss and collection efficiency for a range of Reynolds numbers and sand sizes. To complement the measurements, both two-dimensional and three-dimensional computational results are presented for comparison. Computational predictions of pressure loss agreed with measurements at high Reynolds numbers, whereas predictions of sand collection efficiency for a sand size range 0–200μm agreed within 10% of experimental measurements over the range of Reynolds numbers. Collection efficiency values were measured to be as high as 35%, and pressure loss measurements were equivalent to less than 1% pressure loss in an engine application.

Numerical investigation of high-pressure turbine blade tip flows: analysis of aerodynamics

The current contribution reports on the validation and analysis of three-dimensional computational results of the flow around four distinct high-pressure turbine blade tip geometries (TG1, 2, 3, and 4 hereinafter), taking into account the effect of the entire internal cooling setup inside the blade, at design exit Mach number: M = 0.8, and high exit Reynolds number: Re C = 900 000. Three of the four geometries represent different tip design solutions – TG1: full squealer rim; TG2: single squealer on the suction side; TG3: partial suction and pressure side squealer, and one (TG4) models TG1 in worn condition. This article provides a comparison between the different geometries from the aerodynamic point of view, analyses the losses, and evaluates the distinct design solutions. An assessment of the effect of the uneven rubbing of the blade tip was performed as well. TG1 was found to be the top performer followed by TG3 and TG2. According to the investigations, the effect of rubbing increased the kinetic loss coefficient by 10–15 per cent.

SIMULATING THE FLUID DYNAMICS OF NATURAL AND PROSTHETIC HEART VALVES USING THE IMMERSED BOUNDARY METHOD

The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a model of a natural aortic valve and a model of a chorded prosthetic mitral valve. Each valve is mounted in a semi-rigid flow chamber. In the case of the mitral valve, the flow chamber is a circular pipe, and in the case of the aortic valve, the flow chamber is a model of the aortic root. The model valves and flow chambers are immersed in a viscous incompressible fluid, and realistic fluid boundary conditions are prescribed at the upstream and downstream ends of the chambers. To connect the immersed boundary models to the boundaries of the fluid domain, we introduce a novel modification of the standard immersed boundary scheme. In particular, near the outer boundaries of the fluid domain, we modify the construction of the regularized delta function which mediates fluid-structure coupling in the immersed boundary method, whereas in the interior of the fluid domain, we employ a standard four-point delta function which is frequently used with the immersed boundary method. The standard delta function is used wherever possible, and the modified delta function continuously transitions to the standard delta function away from the outer boundaries of the fluid domain. Three-dimensional computational results are presented to demonstrate the capabilities of our immersed boundary approach to simulating the fluid dynamics of heart valves.

Three-Dimensional Computations of the Motion of a Newtonian Drop Rising through Immiscible Quiescent Shear-Thinning Liquids

Three-dimensional direct numerical simulations of the motion of a Newtonian drop rising in Carreau–Yasuda model fluids were carried out by a coupled level-set/volume-of-fluid (CLSVOF) method. Our numerical approach simulated faithfully the physical shear-thinning properties and 3D-nonlinear dynamics that are observed in experiments. Three-dimensional computational results showed that the local change in viscosity around a drop greatly depended on the drop shape and the shear-thinning properties of the quiescent liquid. We quantitatively considered the drop rise motion based on the modified dimensionless numbers (ReM and MM) and the effective viscosity.

A computational study of local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens

In this paper, the local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens are investigated by finite element analyses. Based on the experimental observations of kinked crack growth mechanisms in lap-shear specimens under cyclic loading conditions, three-dimensional and two-dimensional plane-strain finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Semi-elliptical cracks with various kink depths are assumed in the three-dimensional finite element analysis. The local stress intensity factor solutions at the critical locations or at the maximum depths of the kinked cracks are obtained. The computational local stress intensity factor solutions at the critical locations of the kinked cracks of finite depths are expressed in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The three-dimensional finite element computational results show that the critical local mode I stress intensity factor solution increases and then decreases as the kink depth increases. When the kink depth approaches to 0, the critical local mode I stress intensity factor solution appears to approach to that for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The two-dimensional plane-strain computational results indicate that the critical local mode I stress intensity factor solution increases monotonically and increases substantially more than that based on the three-dimensional computational results as the kink depth increases. The local stress intensity factor solutions of the kinked cracks of finite depths are also presented in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.

Wake Flow of Single and Multiple Yawed Cylinders

An experimental and computational study is performed of the wake flow behind a single yawed cylinder and a pair of parallel yawed cylinders placed in tandem. The experiments are performed for a yawed cylinder and a pair of yawed cylinders towed in a tank. Laser-induced fluorescence is used for flow visualization and particle-image velocimetry is used for quantitative velocity and vorticity measurement. Computations are performed using a second-order accurate block-structured finite-volume method with periodic boundary conditions along the cylinder axis. Results are applied to assess the applicability of a quasi-two-dimensional approximation, which assumes that the flow field is the same for any slice of the flow over the cylinder cross section. For a single cylinder, it is found that the cylinder wake vortices approach a quasi-two-dimensional state away from the cylinder upstream end for all cases examined (in which the cylinder yaw angle covers the range 0⩽ϕ⩽60°). Within the upstream region, the vortex orientation is found to be influenced by the tank side-wall boundary condition relative to the cylinder. For the case of two parallel yawed cylinders, vortices shed from the upstream cylinder are found to remain nearly quasi-two-dimensional as they are advected back and reach within about a cylinder diameter from the face of the downstream cylinder. As the vortices advect closer to the cylinder, the vortex cores become highly deformed and wrap around the downstream cylinder face. Three-dimensional perturbations of the upstream vortices are amplified as the vortices impact upon the downstream cylinder, such that during the final stages of vortex impact the quasi-two-dimensional nature of the flow breaks down and the vorticity field for the impacting vortices acquire significant three-dimensional perturbations. Quasi-two-dimensional and fully three-dimensional computational results are compared to assess the accuracy of the quasi-two-dimensional approximation in prediction of drag and lift coefficients of the cylinders.

Modeling and Numerical Prediction of Flow Boiling in a Thin Geometry

An analysis capability to examine the two-phase bubbly flow in high pressure boiling systems has been developed. The models have been adapted from the literature for a narrow high aspect ratio geometry using the measurements obtained in a companion paper. Three-dimensional computational results have been compared with cross-section averaged and line-averaged void fractions measured with a gamma densitometer, and local void fraction measured with a hot-film anemometer. These comparisons have been made over a wide range of flow inlet conditions, wall heating and system pressure. Comparisons are found to be good when the flow is bubbly, but at high void fractions, where the flow is churn-turbulent or annular, the two-field modeling approach does not perform adequately. This result emphasizes the need for multiple field modeling.

Numerical investigation on the Aeroelastic instability of bluff cylinders

We numerically investigate the aeroelastic instability of an elongated rectangular cylinder. Through the comparison between three-dimensional computational results for the fixed and the forced-oscillating rectangular cylinders, it is confirmed the flow structure around the oscillating cylinder becomes two-dimensional in the spanwise direction. Then, on the basis of the two-dimensional simulations, we discuss the aeroelastic characteristics on the free oscillation of a rectangular cylinder in uniform flows.

Fatigue life estimation in resistance spot welds: initiation and early growth phase: Sheppard, S.D. and Strange, M. Fatigue Fract. Eng. Mater. Struct. June 1992 15, (6), 531–549

In this paper, the local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens are investigated by finite element analyses. Based on the experimental observations of kinked crack growth mechanisms in lap-shear specimens under cyclic loading conditions, three-dimensional and two-dimensional plane-strain finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Semi-elliptical cracks with various kink depths are assumed in the three-dimensional finite element analysis. The local stress intensity factor solutions at the critical locations or at the maximum depths of the kinked cracks are obtained. The computational local stress intensity factor solutions at the critical locations of the kinked cracks of finite depths are expressed in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The three-dimensional finite element computational results show that the critical local mode I stress intensity factor solution increases and then decreases as the kink depth increases. When the kink depth approaches to 0, the critical local mode I stress intensity factor solution appears to approach to that for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The two-dimensional plane-strain computational results indicate that the critical local mode I stress intensity factor solution increases monotonically and increases substantially more than that based on the three-dimensional computational results as the kink depth increases. The local stress intensity factor solutions of the kinked cracks of finite depths are also presented in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.

Turbulent compressible convection in a deep atmosphere. IV - Results of three-dimensional computations

The behavior of turbulent convection in deep atmospheres is studied by numerically solving the three-dimensional Navier Stokes equations. It is found that the mean vertical velocity is an important link between the buoyancy work and the heat flux. In regions with efficient convection, the total flux is composed of the enthalpy flux and the flux of kinetic energy. The characteristics of these components of the total flux are examined. It is shown that the production of kinetic energy depends on the local variables and the flux. However, the dissipation of kinetic energy is nonlocal. A substantial amount of kinetic energy is carried away from the location of production to be dissipated in lower regions.

Elastic-plastic fracture mechanics analysis of an SENB specimen

This paper describes the elastic-plastic analysis of a Single Edge Notched Bend (SENB) specimen, a specimen commonly used for the determination of the fracture toughness of a material. First, a two-dimensional convergence study is described to investigate the influence of mesh size on the global response of the specimen and the fracture mechanics parameters J and COD. Then a three-dimensional analysis is compared with experimental results. The three-dimensional computational results show a good agreement with the experiments, except for the load region where the global deformations were dominated by the Lueders zone in the material stress-strain curve.