Numerical investigation of vortical evolution in a backward-facing step expansion flow

A numerical investigation of laminar flow over a backward-facing step is presented for the Reynolds number in the range of 50Re2500. The objective of this numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the expansion flow structure. We proceed with the analysis by verifying the computer code through the Pearson vortex problem. We then perform a parametric study by varying the Reynolds number, with the aim of determining whether or not there exists a critical Reynolds number, above which reattachment length on the channel floor decreases. We also concentrate on subjects that have been little explored in the flow, examples of which are the onset of a single vortex in the primary eddy and how the recirculating bubble containing flow reversals is torn into smaller eddies. Eddy distortion, leading to mobile saddle points, and the merging of eddies are also discussed in this study.     

Parametric optimization of a four-link close-chain manipulator with active and passive actuators

We investigate the problem of optimization of motion laws and design parameters of a four-link manipulator with a closed-chain kinematic structure. The manipulator performs cyclic transfer operations in a horizontal plane under the action of active and passive (springs and dampers) actuators. As a minimization criterion, we take a quadratic (with respect to control moments of forces) functional. An algorithm is proposed for constructing a suboptimal solution of the formulated problem based on parametrization of the generalized coordinates of the manipulator with a family of given functions and on the use of numerical procedures of mathematical programming.     

Numerical study of turbulent diesel flow in a pipe with sudden expansion

Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel flow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k–ε, the RNG k–ε and the two-scale k–ε models. The performance of the models is investigated with regard to the non-equilibrium parameter η and the mean strain of the flow, S. Velocity and turbulence kinetic energy predictions of the different models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The effect of more accurate near-wall modeling to the two-equation models is also investigated. The results of the study demonstrate the superiority of the second-moment closure in predicting the flow characteristics over the entire domain. From the two-equation models the RNG derived k–ε model also gave very good predictions, especially when non-equilibrium wall-functions were implemented. As far as η and S are concerned, only the closures with greater physical consistency, such as the two-scale k–ε model, give satisfactory results.     

Numerical investigation of blood flow. Part II: In capillaries

In order to understand the normal and pathologic behavior of the human vascular system, detailed knowledge of blood flow and the response of blood vessels is required. In fact the ability to predict the flow hydrodynamics at any site in the vessels can lead to a better understanding of the behavior of blood flow. Simulation can play an important role in understanding the hemodynamic forces. The objective of the present attempt was to simulate the behavior of blood flow in microvessels using computational fluid dynamics (CFD). Numerical analysis is performed using a commercially available CFD package Fluent 6.2 which is based on the finite volume method. A continuum approach is proposed in which fluid structure interaction has been taken into account. Based on limitations imposed by computational resources, a more simplified model based on volume of fluid (VOF) approach is suggested to simulate movements of RBCs in capillaries and also to predict RBCs’ deformation. Three-dimensional incompressible laminar flow fields are obtained by solving continuity and Navier–Stokes equations computationally. It was found that multiphase CFD simulations may give further insight into the dynamic characteristics of blood flow under complex flow conditions.     

Nonself-similar flow with a shock wave reflected from the center of symmetry and new self-similar solutions with two reflected shocks

In some problems concerning cylindrically and spherically symmetric unsteady ideal (inviscid and nonheat-conducting) gas flows at the axis and center of symmetry (hereafter, at the center of symmetry), the gas density vanishes and the speed of sound becomes infinite starting at some time. This situation occurs in the problem of a shock wave reflecting from the center of symmetry. For an ideal gas with constant heat capacities and their ratio γ (adiabatic exponent), the solution of this problem near the reflection point is self-similar with a self-similarity exponent determined in the course of the solution construction. Assuming that γ on the reflected shock wave decreases, if this decrease exceeds a threshold value, the flow changes substantially. Assuming that the type of the solution remains unchanged for such γ, self-similarity is preserved if a piston starts expanding from the center of symmetry at the reflection time preceded by a finite-intensity reflected shock wave propagating at the speed of sound. To answer some questions arising in this formulation, specifically, to find the solution in the absence of the piston, the evolution of a close-to-self-similar solution calculated by the method of characteristics is traced. The required modification of the method of characteristics and the results obtained with it are described. The numerical results reveal a number of unexpected features. As a result, new self-similar solutions are constructed in which two (rather than one) shock waves reflect from the center of symmetry in the absence of the piston.     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

Numerical computation of wavelet expansion: W error estimate

We consider the numerical procedure introduced in [1] in order to compute the expansion of a function f with respect to a compactly supported wavelet basis, for which we give an error estimate in the W^3,p norm. We also prove an interpolation estimate in the H³ norm.     

Numerical investigation of interactions of multiple spherical shock waves between themselves and with the underlying surface

Within the investigation of various aspects of asteroid and comet danger and, in particular, the explosion of several fragments of meteoroids in the atmosphere above the Earth surface, the toy problem about four point explosions in the case of their special arrangement above the underlying surface is numerically solved. Complex interactions of primary and secondary shock waves between themselves, with the hard surface, and with tangential discontinuities are examined. The structure of flow inside gas regions disturbed by the explosions—the occurrence of eddy structures in them and the influence of reflected shocks waves on them—are investigated. The tendency of the external wave fronts of each explosion to form a unified front and the tendency of their internal hot domains to merge into a joined configuration (where the second process proceeds a little later than the first one) is revealed. This unified front and joined configuration are qualitatively identical to the external internal structure for the solitary explosion. The specially arranged explosions are chosen because the effects of multiple diffraction, interference, and, the main thing, cumulation of spherical waves are manifested more clearly in this caseTwo variants with different altitude of the explosions above the surface are calculated.     

Modified projective synchronization of chaotic systems with disturbances via active sliding mode control

We apply the active sliding mode control technique to realize the modified projective synchronization of the chaotic systems. The disturbances are considered both in the drive system and the response system. The sufficient conditions for the modified projective synchronization both the non-identical and identical chaotic systems are presented. The corresponding numerical simulations are provided to illuminate the effectiveness of the proposed active sliding mode controllers.     

Use of active control for elimination of flow separation with estimation of energy costs

Problems were posed and solved concerning the aerodynamic computation of the flow past an airfoil with an active boundary layer control device used to prevent flow separation. A moving wall, suction, or tangential blowing in the boundary layer was used as a flow control device. The turbulent boundary layer was computed by directly solving the boundary layer equations using an implicit difference scheme with adaptive grid generation and the determination of the computational domain size. A software code was developed, and numerical simulations were performed taking into account the energy costs related to the flow control device. The numerical results showed that the active flow control devices can be used to prevent flow separation.     

Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling

This present study consists of a numerical investigation of transient heat transfer in channel flow of an electrically conducting variable viscosity Boussinesq fluid in the presence of a magnetic field and thermal radiation. The temperature dependent nature of viscosity is assumed to follow an exponentially model and the system exchanges heat with the ambient following Newton’s law of cooling. The governing nonlinear equations of momentum and energy transport are solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that combined effect of thermal radiation, magnetic field, viscosity variation and convective cooling have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Valuation of variable annuities with guaranteed minimum withdrawal and death benefits via stochastic control optimization

In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behavior solved as an optimal stochastic control problem. This product simultaneously deals with financial risk, mortality risk and human behavior. We assume that market is complete in financial risk and mortality risk is completely diversified by selling enough policies and thus the annuity price can be expressed as appropriate expectation. The computing engine employed to solve the optimal stochastic control problem is based on a robust and efficient Gauss–Hermite quadrature method with cubic spline. We present results for three different types of death benefit and show that, under the optimal policyholder behavior, adding the premium for the death benefit on top of the GMWB can be problematic for contracts with long maturities if the continuous fee structure is kept, which is ordinarily assumed for a GMWB contract. In fact for some long maturities it can be shown that the fee cannot be charged as any proportion of the account value — there is no solution to match the initial premium with the fair annuity price. On the other hand, the extra fee due to adding the death benefit can be charged upfront or in periodic installment of fixed amount, and it is cheaper than buying a separate life insurance.     

Optimal control of an M/G/1 queuing system with removable server via diffusion approximation

In this paper, applying the technique of diffusion approximation to an M/G/1 queuing system with removable server, we provide a robust approximation model for determining an optimal operating policy of the system. The following costs are incurred to the system: costs per hour for keeping the server on or off, fixed costs for turning the server on or off, and a holding cost per customer per hour. The expected discounted cost is used as a criterion for optimality. Using a couple of independent diffusion processes approximating the number of customers in the system, we derive approximation formulae of the expected discounted cost that do not depend on the service time distribution but its first two moments. Some new results on the characterization of the optimal operating policy are provided from these results. Moreover, in order to examine the accuracy of the approximation, they are numerically compared with the exact results.     

Inclusion of flexibility benefits in discounted cash flow analyses for investment evaluation: A simulation/optimization model

It has been argued that conventional discounted cash flow (DCF) techniques, which are commonly used for investment justification, are inadequate and may even be inappropriate for the justification of advanced manufacturing systems whose strategic value comes from such attributes as flexibility. The problem lies in the proper estimation of the value of flexibility in financial or cash flow terms, so that the DCF techniques, which are otherwise conceptually sound, become relevant. This involves an assessment of the value of the flexibility of the manufacturing system in dealing with the uncertainties in its operating environment. We propose a simulation-optimization methodology for this assessment in cash flow terms and use it in a DCF framework. We use simulation to generate the environmental parameters in each period of an appropriate evaluation horizon. We develop a mathematical programming model to determine the distribution of the possible net revenues of the system in each period by capturing the combined effect of the different types of flexibilities that the manufacturing system may possess. We illustrate the application of our methodology using numerical examples and discuss how it can be used to assess the value of flexibility in cash flow terms. We show that our approach facilitates the justification of capital investment in advanced manufacturing systems which tend to get undervalued under the traditional DCF approaches. It would also help managers address such important questions as “how much incremental investment should we be willing to make now for the additional flexibility features?” and “does the expected present value of the future benefits of added flexibility justify the incremental capital investment now?” In essence, our paper addresses the question as to appropriate techniques or approaches for justifying proposed strategic investment decisions.     

Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids

Steady, mixed convection laminar boundary layer flow of incompressible nanofluid along the vertical plate with temperature dependent heat source/sink has been investigated numerically. The resulting non-linear governing equations (obtained with the Boussinesq approximation) are solved, using a robust, extensively validated, variational finite element method (FEM) for both spherical and cylindrical shaped nanoparticles with volume fraction ranging up to 4%, with associated boundary conditions and the effect of the parameters governing the problem are discussed. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are taken into consideration. The results show that the average Nusselt number is found to decrease for Ag, Cu, CuO, Al₂O₃, and TiO₂. The present study is of immediate interest in next-generation solar film collectors, heat exchangers technology, materials processing exploiting vertical surfaces, geothermal energy storage and all those processes which are highly affected with heat enhancement concept.     

Numerical analysis of a Picard multilevel stabilization of mixed finite volume method for the 2D/3D incompressible flow with large data

In this article, we develop a branch of nonsingular solutions of a Picard multilevel stabilization of mixed finite volume method for the 2D/3D stationary Navier‐Stokes equations without relying on the unique solution condition. The method presented consists of capturing almost all information of initial problem (the nonlinear problems) on the coarsest mesh and then performs one Picard defect correction (the linear problems) on each subsequent mesh based on previous information thus only solving one large linear systems. What is more, the method presented can results in a better coefficient matrix in the model presented with small viscosity. Theoretical results show that the method presented is derived with the convergence rate of the same order as the corresponding finite volume method/finite element method solving the stationary Navier‐Stokes equations on a fine mesh. Therefore, the method presented is definitely more efficient than the standard finite volume method/finite element method. Finally, numerical experiments clearly show the efficiency of the method presented for solving the stationary Navier‐Stokes equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 34: 30–50, 2018     

Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis

In this paper, heat and mass transfer analysis for boundary layer stagnation-point flow over a stretching sheet in a porous medium saturated by a nanofluid with internal heat generation/absorption and suction/blowing is investigated. The governing partial differential equation and auxiliary conditions are converted to ordinary differential equations with the corresponding auxiliary conditions via Lie group analysis. The boundary layer temperature, concentration and nanoparticle volume fraction profiles are then determined numerically. The influences of various relevant parameters, namely, thermophoresis parameter Nt, Brownian motion parameter Nb, Lewis number Le, suction/injection parameter S, permeability parameter k₁, source/sink parameter λ and Prandtl parameter Pr on temperature and concentration as well as wall heat flux and wall mass flux are discussed. Comparison with published results is presented.