Centrifugal Body Force Research Articles

Heat release and transfer of premixed propane/air flames in high g-load centrifugal force fields

Rapid combustion and propagation are crucial for energy conversion and utilization equipment, such as power plants and thrust engines. High g-load in centrifugal flow fields has been demonstrated to be able to elevate turbulent flame speed. However, more details of flame behaviors in strong centrifugal force fields still need to be investigated. This paper focuses on flame bubble behaviors and related aspects by conducting Large Eddy Simulations (LES) of high g-load centrifugal flames stabilized by a backward step in an annual combustor. A centrifugal force was produced by setting different circumference inlet velocities (0 ms/, 4 m/s, 8 m/s, 12 m/s and 16 m/s) while axial velocity was constant (12 m/s). Wall-adapting Local Eddy-viscosity (WALE) model was used as the subgrid-scale model. Flamelet Generated Manifold (FGM) model and a 31-species and 107-step propane/air reaction mechanism were used for combustion modeling. The centrifugal body force exerted on flame bubbles and cold gas parcels is found to be able to make them move oppositely in the radial direction, and thus makes the flame surface more wrinkled. This effect leads to reinforced heat exchange between hot burned gas and cold fresh mixture. The consequent results are not only that the flame propagation speed is increased and the flame zone is broadened, but also that the local heat loss is enhanced, which leads to a weaker local heat release rate and might even lead to flame extinction. Additionally, the time-averaged flame front consists of a preheating zone and a reaction zone, along with a centrifugal-force-induced heat transfer from the post-flame zone to the cold fresh mixture.

Secondary Creep Analysis of FG Rotating Cylinder with Exponential, Linear and Quadratic Volume Reinforcement.

Creep is an irreversible time-dependent deformation in which a material under constant mechanical stress and elevated temperature for a considerably prolonged period of time, starts to undergo permanent deformation. Creep deformation occurs in three stages namely, primary, secondary and tertiary. Out of these three stages, secondary or steady state creep is particularly an area of engineering interest as it has almost a constant creep rate. Creep deformation plays a significant role in understanding effective service life of an engineering component working under high temperature conditions as such components such as super-heater and re-heater tubes and headers in a boiler, jet engines operating at temperature as high as 1200 C, usually experience a failure or rupture due to creep phenomenon. Design engineers keep a close attention on working stress conditions and elevated temperature under which an engineering component is expected to work as these conditions determine the onset of creep behavior in an engineering component. By recognizing the parameters of material response to creep behavior, engineers can analyse the useful service life and hazardous working conditions for an engineering components. Recognizing the creep phenomenon as high temperature design limitation, ASME Boiler and Pressure Vessel Code have provided guidelines on maximum allowable stresses for materials to be used in creep range. One of the criteria for determination of allowable stresses is 1% creep deformation of material in 100,000 h of service. Thus, the study of creep behavior in engineering components pertaining to high stress and temperature working conditions is very important as it affects the reliability and performance of the engineering components. The aim of our study is to understand the behavior of secondary creep deformation so that an advanced reinforced functionally graded material with better creep resistance, can be designed. In this paper, a secondary creep analysis of functionally graded (FG) thick-walled rotating cylinder under internal and external pressure is conducted. The novelty of the model intends to specify secondary creep stresses and strains by employing exponential, linear and quadratic volume reinforcement for ceramic in metal matrix in radial direction. This will help us to understand the effect of volume reinforcement in FG cylinder under internal/external pressure and rotating centrifugal body force by obtaining secondary creep stresses and strains. The response of the FG cylinder with isotropic material is analyzed and the solution for stress–strain rates in radial and tangential directions are obtained in closed form. Comparison of steady state creep stresses and strains under exponential, linear and quadratic volume reinforcement profiles are discussed and presented graphically.

Thermo-elastic creep analysis and life assessment of rotating thick pressurized cylindrical shells using third-order shear deformation theory

In the present study, time-dependent thermo-elastic creep behavior and life assessment of rotating thick-walled cylindrical shells made of 304L austenitic stainless steel (304L SS) are investigated based on the third-order shear deformation theory (TSDT). Loading is composed of a uniform internal pressure, distributed temperature field, and a centrifugal body force due to rotating speed. Norton’s law is utilized as the material creep constitutive model. Using the minimum total potential energy principle, a system of differential equations in terms of displacement and boundary conditions are derived. Then, the governing equations are solved with an analytical approach, which leads to an accurate solution. Subsequently, an iterative procedure is also proposed to determine the stresses and deformations at different creep times. Larson-Miller Parameter (LMP) and Robinson's linear life fraction damage rule are employed for assessing the creep damages and the remaining life of cylindrical shells. To the best of the researcher’s knowledge, in the previous studies, there is no study carried out into third-order shear deformation theory for thermo-elastic creep analysis of cylinders. To validate the accuracy of the suggested method based on TSDT, a comparison among analytical results and those of the finite element method (FEM) is performed and very good agreement is found. The results indicate that the present analysis is accurate and computationally efficient.

Centrifugal buoyancy in a rotating fluid layer next to and distant from the rotation axis

An analytical investigation of the stability and onset of natural convection in a rotating fluid layer subject to a centrifugal body force and placed an arbitrary offset distance from the axis of rotation is presented. Linear stability as well as weak nonlinear analyses is performed to demonstrate the effect of centrifugal buoyancy. In the limit of an infinite distance from the center of rotation, the results are identical to the natural convection resulting from heating a fluid layer from below subject to the gravitational body force. The results provide the stability map for all non-negative values of the parameter controlling the offset distance from the axis of rotation. A clear break of symmetry results from the centrifugal buoyancy if the offset distance from the axis of rotation is not too large. The weak nonlinear solutions produce amplitudes for the convection velocity and temperature via the solution of a Landau amplitude equation. The latter are being used in evaluating the Nusselt number representing the average heat transfer coefficient in dimensionless form. No oscillatory convection is possible when the Coriolis effect is small and negligible.

Numerical modeling of segmented flow in coiled flow inverter: Hydrodynamics and mass transfer studies

A novel CFD modeling approach was developed to investigate the hydrodynamics and mass transfer in a gas–liquid slug flowing through microscale coil and coiled flow inverter channels. One straight slug model was formulated by adding a virtual centrifugal body force. The model was validated in terms of the helicity and secondary flow magnitude. The secondary flow magnitude was shown to be a power function of the Dean number, and a new correlation was proposed. The mass transfer across the interface was compared to that obtained in previous studies. The new model described the temporal and spatial distribution of species in the slug reasonably well. The volumetric mass transfer coefficient kLa in the coil was found to be 1.5 times higher than that in the straight channel, and the enhancement in kLa reached a maximum at a modified Dean number of 1.2.

Thermo-Mechanical Analysis for an Axisymmetric Functionally Graded Rotating Disc under Linear and Quadratic Thermal Loading

The study presents thermo-mechanical analysis of functionally graded (FG) rotating disc whose material properties, namely, Young’s modulus, density and coefficient of thermal expansion in radial direction are tailored from inner to outer radius using power law form. The disc is considered to be under the influence of internal pressure, centrifugal body force and thermal loading of the form linear as well as quadratic. Response of FG disc under linear and quadratic temperature profile subjected to internal pressure as well as centrifugal body force is analysed. An exact solution for stress in radial and tangential directions, under mechanical and thermal loading is presented. Numerical solutions for stresses under internal pressure with uniform thermal loading are obtained using finite element method and its comparison with analytical results is presented graphically. Results for radial displacement, radial stress and tangential stress are depicted graphically and their interpretation has been discussed.

Laminar spread of a circular liquid jet impinging axially on a rotating disc

The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number,$Ro$. The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by$Ro$. Its numerical solutions are discussed for a wide range of values of$Ro$. The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases$Ro\gg 1$and$Ro\ll 1$. The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.

Vibration and Buckling Analysis of a Rotating Annular Plate Subjected to a Compressive Centrifugal Body Force

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

Axisymmetric Vibration of Rotating Annular Plate with Variable Thickness Subjected to Tensile Centrifugal Body Force

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

Convective heat transfer in axisymmetric enclosures of different configurations under the conditions of their axial rotation and external heating

The phenomenon of the intensification of convective heat transfer through air cavities under the conditions of their axial rotation and external heating based on the rise of centrifugal body forces in differently heated air medium has been substantiated theoretically and confirmed experimentally. The criterion dependencies for convection coefficients of axisymmetric cylindrical and conical closed air cavities subjected to external heating and axial rotation have been obtained using the results of the physical and numerical experiments. Both single-layer cylindrical cavities and two-layer ones with perforating internal orifices have been considered.

A novel analytical-numerical solution for nonlinear time-dependent electro-thermo-mechanical creep behavior of rotating disk made of piezoelectric polymer

A new analytical-numerical method has been developed for electro-thermo-mechanical transient creep response of rotating disk made of nonlinear piezoelectric polymer. The viscoelastic properties are stress, temperature and time dependent. The disk has been placed in an axisymmetric distributed temperature field and is subjected to a centrifugal body force with free-free, free-fixed and fixed-free boundary conditions. The Burgers’ viscoelastic creep model for long time prediction has been employed. Using the potential-displacement equation, charge equation of electrostatics, strain-displacement equations, stress-strain relations and equilibrium equation, the constitutive differential equation in terms of displacement is obtained. The non-homogeneous part of which contains creep strains. An analytical solution for radial displacement in terms of creep strains has been performed. Then the stresses, strains and electric potentials are also derived in terms of creep-strains. Prandtl-Reuss relations and the material creep model are employed to obtain history of displacement, stresses, strains and electric potential. It is concluded that the displacement is increasing with time while effective stresses are decreasing. A significant redistribution occurs for the electric potential which is due to stress redistribution during the lifetime of the disk. The results are validated with ABAQUS software. The analytical-numerical method can be used to predict the history of displacement and stresses in all structures made of nonlinear viscoelastic material.

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.

Exact Solutions for Stresses, Strains, and Displacements of a Rotating Annular Plate with Variable Thickness Subjected to a Centrifugal Body Force

AbstractThe author has discovered several errors that are not typographical in a famous governing differential equation and its general solution. The purpose of the current study is to reveal the errors, correct them, and present some numerical results.

Long-term durability of tri-axial woven CFRP tube structure extended along the spin axis of spinning platforms for the SCOPE mission

This study investigates the strength and long-term durability of a spin-axis extensible rigid antenna element, made of tri-axial woven carbon fiber-reinforced polymer (CFRP), for a spinning spacecraft. Due to a slight deviation between the spin axis and antenna-extended axis with the spin, the antenna is subjected to centrifugal body force; the centrifugal force enhances the antenna deflection. A relationship between centrifugal force and antenna deflection is derived from beam theory. As the apparent material modulus decreases with time, the deflection increases simultaneously. The time dependence of mechanical properties of the tri-axial woven CFRP is hence examined by a creep test. The time-dependent failure criterion of the antenna is then examined using a flexural durability test. Based on the beam theory and experimental results, we examine the long-term reliability of applying the tri-axial woven CFRP to extensible rigid antenna for the spinning spacecraft, especially for SCOPE mission; it is verified that the current design tolerance for the mission assures certain durability for long-term usage.

Onset of centrifugal filtration convection: departure from thermal equilibrium

This paper deals with convective instability in a fluid-saturated, rotating porous layer subject to alternating direction of the centrifugal body force, when the layer fails to exhibit thermal equilibrium. The Darcy model is used to describe the flow, and a two-field model is used to take care of the energy exchange. The normal mode approach of the linear theory and the energy approach of the nonlinear theory are used to find the stability characteristics. Unconditional and sharp nonlinear thresholds are found. The study brings out the failure of the linear theory in describing the instability in most parts of the parameter space of interest where possible subcritical instabilities may arise. The stability boundaries are presented graphically and it is found that the inter-phase heat transfer coefficient has a significant effect in the thermal non-equilibrium regime.

Semi-analytical solution for electromagnetothermoelastic creep response of functionally graded piezoelectric rotating disk

Time-dependent electromagnetothermoelastic creep response of rotating disk made of functionally graded piezoelectric materials (FGPM) is studied. The disk is placed in a uniform magnetic and a distributed temperature field and is subjected to an induced electric potential and a centrifugal body force. The material thermal, mechanical, magnetic and electric properties are represented by power-law distributions in radial direction. The creep constitutive model is Norton's law in which the creep parameters are also power functions of radius. Using equations of equilibrium, strain-displacement and stress–strain relations in conjunction with the potential-displacement equation a non-homogeneous differential equation containing time-dependent creep strains for displacement is derived. A semi-analytical solution followed by a numerical procedure has been developed to obtain history of stresses, strains, electric potential and creep-strain rates by using Prandtl–Reuss relations. History of electric potential, Radial, circumferential and effective stresses and strains as well as the creep stress rates and effective creep strain rate histories are presented. It has been found that tensile radial stress distribution decreases during the life of the FGPM rotating disk which is associated with major electric potential redistributions which can be used as a sensor for condition monitoring of the FGPM rotating disk.

Sharp nonlinear stability for centrifugal filtration convection in magnetizable media

A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection.

Newtonian pizza: spinning a viscous sheet

We study the axisymmetric stretching of a thin sheet of viscous fluid driven by a centrifugal body force. Time-dependent simulations show that the sheet radiusR(t) tends to infinity in finite time. As timetapproaches the critical timet*, the sheet becomes partitioned into a very thin central region and a relatively thick rim. A net momentum and mass balance in the rim leads to a prediction for the sheet radius near the singularity that agrees with the numerical simulations. By asymptotically matching the dynamics of the sheet with the rim, we find that the thicknesshin the central region is described by a similarity solution of the second kind, withh∝ (t* −t)αwhere the exponent α satisfies a nonlinear eigenvalue problem. Finally, for non-zero surface tension, we find that the exponent increases rapidly to infinity at a critical value of the rotational Bond numberB= 1/4. ForB> 1/4, surface tension defeats the centrifugal force, causing the sheet to retract rather than to stretch, with the limiting behaviour described by a similarity solution of the first kind.

Global stability of centrifugal filtration convection

A nonlinear stability analysis is performed to study the onset of convection in a fluid saturated porous layer subject to alternating direction of the centrifugal body force. By introducing a suitable energy functional, the analysis is carried out for the Darcy and the Brinkman models of flow through porous media. The nonlinear result is unconditional and its sharpest limit is determined and is compared with the corresponding linear limit. The failure of linear theory in describing the instability is established in a certain region of the parameter space where possible subcritical instabilities may arise. The stability boundaries are discussed graphically for various values of the Darcy number and comparison is made with the available known results.

Optimization of material distribution in functionally graded structures with stress constraints

AbstractThis work describes a topology optimization framework to design the material distribution of functionally graded structures considering mechanical stress constraints. The problem of interest consists in minimizing the volumetric density of a material phase subjected to a global stress constraint. Due to the existence of microstructure, the micro‐level stress is considered, which is computed by means of a mechanical concentration factor using a p‐norm of the Von Mises stress criterium (applied to the micro‐level stress). Because a 0–1 (void–solid) material distribution is not being sought, the singularity phenomenon of stress constraint does not occur as long as the material at any point of the medium does not vanish and it varies smoothly between material 1 and material 2. To design a smoothly graded material distribution, a material model based on a non‐linear interpolation of the Hashin–Strikhman upper and lower bounds is considered. Consistently with the framework adopted here in, the so‐called ‘continuous approximation of material distribution’ approach is employed, which considers a continuous distribution of the design variable inside the finite element. As examples, the designs of functionally graded disks subjected to centrifugal body force are presented. The method generates smooth material distributions, which are able to satisfy the stress constraint. Copyright © 2006 John Wiley & Sons, Ltd.