Stationary Square Research Articles

Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations.

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

Numerical flow and experimental heat transfer of S-shaped two-pass square channel with cooling applications to gas turbine blade

This study experimentally detected the endwall Nusselt numbers (Nu) distributions, Fanning friction factors (f) and thermal performance factors (TPF) for a stationary S-shaped two-pass square channel with the associated turbulent flow fields analyzed by ANSYS Fluent code to disclose the flow mechanisms responsive to the measured thermal performances. The full-field Nu distributions over the endwalls of present S-shaped inlet/outlet legs and 180° sharp bend at Reynolds numbers (Re) of 5000, 7500, 10,000, 12,500, 15,000, 20,000 and 30,000 were measured using the steady-state infrared thermography method; while the validated RNG k-ε turbulence model was adopted to reveal the fields of time-mean fluid velocity, turbulent kinetic energy and cross-plane secondary flow. Acting by sectional vortices induced along the inlet/outlet S-pathways and 180° sharp bend, the core-to-wall momentum/heat exchanges are boosted to elevate both Nu and f values. Accompanying with the f augmentations from 10.19–8.27 times of Balssius f∞ levels, the area-averaged Nusselt numbers (Nu‾A) over the entire S-shaped endwall were elevated to 3.21–3.09 times of Dittus-Boelter Nusselt number (Nu∞) values at 5000⩽Re⩽30,000, resulting in the TPF between 1.4 and 1.44. To assist relevant engineering applications, two sets of empirical correlations evaluating the regionally averaged endwall Nusselt numbers and f factors are devised.

Using a fully-Lagrangian meshless method for the study of aerosol dispersion and deposition

ABSTRACTSmoothed Particle Hydrodynamics was employed in the present two-dimensional simulations, thus the algorithms implemented for both continuous and dispersed phase share a common Lagrangian stencil. The results were benchmarked against those produced in earlier investigations of particle deposition resulting from the flow around a stationary square obstacle. The proposed numerical procedure also facilitates the investigation of the fundamental physics governing the transport of resuspended particles in the wake of a moving operator, e.g., inside cleanroom facilities. Aiming to illustrate this capability, the dispersion of neutrally suspended particles behind an impulsively-started plate has been numerically simulated. Two distinct particle dispersion patterns, characterized by different Reynolds numbers, have been obtained for this problem. Altogether the results have demonstrated the accuracy of the method and associated advantages for multiphase flow studies, especially in cases involving moving bo...

Isotropic covariance matrix polynomials on spheres

ABSTRACTThis article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization to examine the validity of a matrix function whose entries are polynomials of degrees up to 4, we obtain a necessary and sufficient condition for the polynomial matrix to be an isotropic covariance matrix function on the sphere.

Modelling of fluid–structure interaction with multiphase viscous flows using an immersed-body method

An immersed-body method is developed here to model fluid–structure interaction for multiphase viscous flows. It does this by coupling a finite element multiphase fluid model and a combined finite–discrete element solid model. A coupling term containing the fluid stresses is introduced within a thin shell mesh surrounding the solid surface. The thin shell mesh acts as a numerical delta function in order to help apply the solid–fluid boundary conditions. When used with an advanced interface capturing method, the immersed-body method has the capability to solve problems with fluid–solid interfaces in the presence of multiphase fluid–fluid interfaces. Importantly, the solid–fluid coupling terms are treated implicitly to enable larger time steps to be used. This two-way coupling method has been validated by three numerical test cases: a free falling cylinder in a fluid at rest, elastic membrane and a collapsing column of water moving an initially stationary solid square. A fourth simulation example is of a water–air interface with a floating solid square being moved around by complex hydrodynamic flows including wave breaking. The results show that the immersed-body method is an effective approach for two-way solid–fluid coupling in multiphase viscous flows.

Constrained large-eddy simulation of turbulent flow and heat transfer in a stationary ribbed duct

Purpose– The knowledge about the heat transfer and flow field in the ribbed internal passage is particularly important in industrial and engineering applications. The purpose of this paper is to identify and analyze the performance of the constrained large-eddy simulation (CLES) method in predicting the fully developed turbulent flow and heat transfer in a stationary periodic square duct with two-side ribbed walls.Design/methodology/approach– The rib height-to-duct hydraulic diameter ratio is 0.1 and the rib pitch-to-height ratio is 9. The bulk Reynolds number is set to 30,000, and the bulk Mach number of the flow is chosen as 0.1 in order to keep the flow almost incompressible. The CLES calculated results are thoroughly assessed in comparison with the detached-eddy simulation (DES) and traditional large-eddy simulation (LES) methods in the light of the experimentally measured data.Findings– It is manifested that the CLES approach can predict both aerodynamic and thermodynamic quantities more accurately than the DES and traditional LES methods.Originality/value– This is the first time for the CLES method to be applied to simulation of heat and fluid flow in this widely used geometry.

Stochastic representations of isotropic vector random fields on spheres

ABSTRACTA stochastic representation is derived for a vector random field that is stationary, isotropic, and mean square continuous on a sphere or unit circle. The established stochastic representation is an infinite series involving the sequence of ultraspherical or Gegenbauer's polynomials, looks like a mimic of the series representation of the covariance matrix function of the isotropic vector random field, but differs from the spectral representation in terms of the ordinary spherical harmonics. It is also shown in this paper that some isotropic and continuous covariance matrix functions on the real line or , if they are compactly supported, can be adopted as covariance matrix functions on the unit circle or .

Effect of Income Inequality on Health Indicators in Nigeria (1980-2014)

The rising profile of income inequality and the challenges it poses on the health of the entire citizenry in Nigeria over the pass years has brought about an increase in mortality rate and low life expectancy. Thus, this study examined the effect of income inequality, per capita income, education level and savings level on health indicators proxied by mortality and life expectancy rate in Nigeria using stationary, co-integration test and dynamic ordinary least square (DOLS) method. The study used time series data from International Monetary Fund World Economic Outlook which spanned from 1980-2014. The unit root test applied to the variables showed that the variables were stationary in the short run and co-integration test confirmed a long run relationship between the variables. Furthermore, the study showed that income inequality has an inverse effect on mortality rate. However, direct relationship existed between income inequality and life expectancy rate in the model. Finally, per capita income, education level and saving level employed as control variables have positive effect on health indicators in Nigeria. The study therefore concluded that health indicators are highly influenced by income inequality, per capita income, education level and savings level in Nigeria.

On the immersed boundary method: Finite element versus finite volume approach

Two immersed boundary methods (IBM) for the simulation of fluid flow problems with complex geometries are introduced: a direct-forcing immersed finite element method (IFEM) and a direct-forcing immersed finite volume method (IFVM).In the IFEM a projection approach is presented for the coupled system of time-dependent incompressible Navier–Stokes equations (NSEs) in conjunction with the IBM for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body-fitted mesh. Dirichlet boundary constraints are satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface/volume mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the NSEs as a Lagrange multiplier in a fashion very similar to the effect that pressure has on the momentum equations to satisfy the divergence-free constraint. The IFEM approach presented shows third order accuracy in space and second order accuracy in time when the simulation results for the Taylor–Green decaying vortex are compared to the analytical solution.For the IFVM presented, a ghost-cell approach with sharp interface scheme is used to enforce the boundary condition at the fluid/solid interface. The interpolation procedure at the immersed boundary preserves the overall second order accuracy of the base solver. The developed ghost-cell method is applied on a staggered configuration with the Semi-Implicit Method for Pressure-Linked Equations Revised algorithm. Second order accuracy in space and first order accuracy in time are obtained when the Taylor–Green decaying vortex test case computed with the IFVM is compared to the analytical solution.Computations were performed using the IFEM and IFVM approaches for the two-dimensional flow over a backward-facing step, two-dimensional flow past a stationary circular cylinder, three-dimensional flow past a sphere and two-dimensional oscillating circular cylinder in a stationary square domain. The numerical results obtained with the discussed IFEM and IFVM were compared against other IBMs available in literature and simulations performed with the commercial computational fluid dynamics code STAR-CCM+/V7.04.006. The benchmark test cases showed that the numerical results obtained with the implemented immersed boundary methods are in good agreement with the predictions from STAR-CCM+ and the numerical data from the other IBMs. The immersed boundary method based on finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.

Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is to study ground-based response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, interaction of the spinning rotor and the flexible housing is manifested theoretically, numerically, and experimentally. In the theoretical analysis, we show that the interaction primarily appears in coupled rotor–bearing–housing modes whose response is dominated by the housing. Specifically, let a housing-dominant mode have natural frequency ω(H) and the spin speed of the rotor to be ω3. In rotor-based coordinates, response of the spinning rotor for the housing-dominant mode will possess frequency splits ω(H)±ω3. In ground-based coordinates, response of the spinning rotor will possess alternative frequency splits ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3, where k is an integer determined by the cyclic symmetry of the rotor and the housing-dominant mode of interest. In the numerical analysis, we study a benchmark model consisting of a spinning slotted disk mounted on a stationary square plate via two ball bearings. The numerical model successfully confirms the frequency splits both in the rotor-based and ground-based coordinates. In the experimental analysis, we conduct vibration testing on a rotor–bearing–housing system that mimics the numerical benchmark model. Test results reveal two housing-dominant modes. As the rotor spins at various speed, measured waterfall plots confirm that the housing-dominant modes split according to ω(H)-(k+1)ω3 and ω(H)-(k-1)ω3 as predicted.

Experimental investigation of flow field behind two tandem square cylinders with oscillating upstream cylinder

In this paper, the fluid flow around two identical square cylinders arranged in tandem has been discussed. The upstream cylinder is oscillated in the transverse direction while the downstream cylinder is held stationary. The experiments are conducted at a Reynolds number of 295. Both the influences of spacing between two cylinders, as well as the effect of oscillation, of the upstream cylinder are investigated using Particle image velocimetry, hotwire anemometry and flow visualization techniques. The spacing ratios are varied from 1.5 to 5 while the upstream cylinder is oscillated in harmonics of the vortex shedding frequency of a stationary cylinder at the fixed amplitude. It is observed that there is a strong effect of spacing between the cylinders on vortex shedding mechanism and flow structures. When two cylinders are in tandem there is a critical distance below which vortex shedding of the upstream cylinder is suppressed. Three distinct flow regimes are captured and the detailed investigation of the intricate flow field is done both spatial and temporal domain. The vortex shedding frequency of a single stationary square cylinder is measured with hotwire anemometer and this frequency is being used to oscillate the upstream cylinder with its sub-harmonic, harmonic and super-harmonic frequency ratios. The effect of forcing frequency on flow interference, wake oscillation frequencies, aerodynamic forces and turbulence statistics have been studied for these spacing ratios. Flow fields are investigated in terms of the time-averaged drag coefficient, stream traces, vorticity contours, turbulence statistics and the time-dependent flow field is captured using flow visualization, vorticity contours, and Strouhal number.

Flow past two tandem square cylinders vibrating transversely in phase

Numerical investigations have been carried out to study the wake characteristics of flow past two tandem square cylinders vibrating in phase. Both the cylinders vibrate in a transverse direction, i.e., perpendicular to the incoming flow with the same frequency and amplitude. The frequency of vibration of the cylinders and the inter-cylinder spacing are varied for fixed values of the Reynolds number (Re = 100) and the amplitude ratio ( = 0.4). The synchronous or lock-in regime for the oscillatory wake of the vibrating cylinders has been identified by varying the frequency of the vibration from = 0.4 to 1.6 ( being the frequency of vortex shedding behind a stationary square cylinder). The characteristics of lift and drag and the mechanism of vortex shedding are studied by varying the excitation frequency within the lock-in range for each value of inter-cylinder spacing. The complex interaction of flow between the cylinders gives rise to a variety of characteristically different shedding patterns in their wake. For values of inter-cylinder spacing equal to 2D and 3D, periodic, as well as quasi-periodic, lock-in behaviors are observed in the synchronous range.

Covariance Matrix Functions of Isotropic Vector Random Fields

An isotropic scalar or vector random field is a second-order random field in (d ⩾ 2), whose covariance function or direct/cross covariance functions are isotropic. While isotropic scalar random fields have been well developed and widely used in various sciences and industries, the theory of isotropic vector random fields needs to be investigated for applications. The objective of this article is to study properties of covariance matrix functions associated with vector random fields in which are stationary, isotropic, and mean square continuous, and derives the characterizations of the covariance matrix function of the Gaussian or second-order elliptically contoured vector random field in . In particular, integral or spectral representations for isotropic and continuous covariance matrix functions are derived.

Wake-Induced Vibrations of a Circular Cylinder behind a Stationary Square Cylinder Using a Semi-Implicit Characteristic-Based Split Scheme

This study develops a semi-implicit characteristic-based-split (SI-CBS) finite-element algorithm under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. The authors present a modified linear spring analogy algorithm for successful updating of the grid deformation. They verify the computational code against two benchmark problems. One is the VIV of an elastically mounted cylinder with transverse oscillation at R=150. The other is the transversely wake-induced vibration (WIV) of a circular cylinder by a stationary one. The authors conduct a two-dimensional (2D) numerical investigation on the problem of laminar flow over a two-cylinder system, which consists of a front stationary square cylinder and a rear two-degree-of-freedom (2-DOF) circular cylinder in a tandem arrangement. They find that the Reynolds number and reduced velocities play key roles in the WIVs of the circular cylinder. In addition to the wake patterns 2S, 2P, and P+S, the authors observe a steady-state wake pattern. They observe performances of dual-resonance, which means synchronization in both the in-line and transverse directions. For the X-Y trajectories of the circular cylinder, they obtain figures in the shape of an egg, a figure-8, and a point.

Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers

We perform a detailed numerical analysis of square-wave (SW) polarization switching in two semiconductor lasers with time-delayed, orthogonal mutual coupling. An in-depth mapping of the dynamics in the two-parameter plane coupling strength versus frequency detuning shows that stable SWs occur in narrow parameter regions that are localized close to the boundary of stability of the pure-mode solution. In this steady state, the two coupled lasers emit orthogonal polarizations. We also show that there are various types of SW forms and that stable switching does not need the inclusion of noise or nonlinear gain in the model. As these narrow regions of deterministic and stable SWs occur for quite different combinations of parameters, they could potentially explain the waveforms that have been observed experimentally. However, on the other hand, these regions are narrow enough to be in fact considered as experimentally unreachable. Therefore, our results indicate that further experimental statistical studies are needed in order to distinguish deterministic and stationary square waveforms from long transients because of noise.

A Finite Element Analysis of Flow Around a Square Cylinder with Cross Flow Oscillations at two Angles of Attack

AbstractIn this article a two dimensional incompressible viscous flow past a square cylinder oscillating in cross flow with zero and 45 degree angles of attack is numerically studied by a Characteristics Based Splitter (CBS) finite element method. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for the body motion in the flow field. First, the accuracy of the numerical code is tested by comparing the numerical results obtained for the flow over the stationary square cylinder at the three different Reynolds numbers (Re = 100, 200, and 300) with the experimental data available. Then, the numerical results for the square cylinder undergoing transverse oscillations in the two angles of attack at different values of frequency and amplitude are investigated to determine the lock-on region. The results indicate physical similarity between circular and square cylinders concerning lock-on regions. Also the effect of lock-on phenomenon on the flow field pattern and time-averaged drag coefficient is investigated.

Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number

Vortex-induced vibrations (VIV) of a square cylinder at a Reynolds number of 100 and a low mass ratio of 3 are studied numerically by solving the Navier-Stokes equations using the finite element method. The equation of motion of the square cylinder is solved to simulate the vibration and the Arbitrary Lagrangian Eulerian scheme is employed to model the interaction between the vibrating cylinder and the fluid flow. The numerical model is validated against the published results of flow past a stationary square cylinder and the results of VIV of a circular cylinder at low Reynolds numbers. The effect of flow approaching angle (α) on the response of the square cylinder is investigated. It is found that α affects not only the vibration amplitude but also the lock-in regime. Among the three values of α (α = 0°, 45°, and 22.5°) that are studied, the smallest vibration amplitude and the narrowest lock-in regime occur at α = 0°. It is discovered that the vibration locks in with the natural frequency in two regimes of reduced velocity for α = 22.5°. Single loop vibration trajectories are observed in the lock-in regime at α = 22.5° and 45°, which is distinctively different from VIV of a circular cylinder. As a result, the vibration frequency in the in-line direction is the same as that in the cross-flow direction.

Isotropic Variogram Matrix Functions on Spheres

This paper is concerned with vector random fields on spheres with second-order increments, which are intrinsically stationary and mean square continuous and have isotropic variogram matrix functions. A characterization of the continuous and isotropic variogram matrix function on a sphere is derived, in terms of an infinite sum of the products of positive definite matrices and ultraspherical polynomials. It is valid for Gaussian or elliptically contoured vector random fields, but may not be valid for other non-Gaussian vector random fields on spheres such as a χ 2, log-Gaussian, or skew-Gaussian vector random field. Some parametric variogram matrix models are derived on spheres via different constructional approaches. A simulation study is conducted to illustrate the implementation of the proposed model in estimation and cokriging, whose performance is compared with that using the linear model of coregionalization.

CFD Prediction of Heat and Fluid Flow through U-Bends using High Reynolds-number EVM and DSM Models

The cooling system of gas turbine blades understanding and improvement is increasing desires for computational techniques which can accurately model the flow field and heat transfer characteristics of blade cooling passage designs under realistic operating conditions. The present study discusses the comparisons between modeling and measuring gas turbine blade-cooling applications of the flow development and heat transfer in a stationary square cross-sectioned U-bend of strong curvature of Rc/D = 0.65. A turbulence model of the differential stress model (DSM) is used in combination with three different wall treatments such as a standard form of the wall function (SWF), an analytical wall function (AWF) and a numerical wall function (NWF). The combination of DSM with the numerical wall function (DSM/NWF) has improved markedly the Nusselt number predictions along the outer wall after the bend exit, but did not show any other distinctive predictive advantages over the other DSM models.

Stationary and Isotropic Vector Random Fields on Spheres

This paper presents the characterization of the covariance matrix function of a Gaussian or second-order elliptically contoured vector random field on the sphere which is stationary, isotropic, and mean square continuous. This characterization involves an infinite sum of the products of positive definite matrices and Gegenbauer’s polynomials, and may not be available for other non-Gaussian vector random fields on spheres such as a χ2 or log-Gaussian vector random field. We also offer two simple but efficient constructing approaches, and derive some parametric covariance matrix structures on spheres.