Kerim Yapici

Laminar Mixed-Convection Heat Transfer in a Lid-Driven Cavity with Modified Heated Wall

In this numerical study, steady laminar mixed-convection heat transfer in a two-dimensional square lid-driven cavity with a modified heated wall is investigated over a range of Richardson numbers, including 0.01, 1, and 10. The heated bottom wall of the cavity is characterized by rectangular, triangular, and sinusoidal wave shapes. The cooled top wall of the cavity is sliding with constant velocity, while the vertical walls are kept stationary and adiabatic. The governing equations are solved using a finite-volume technique. The results are presented in the form of streamlines, isotherms, and Nusselt number plots. The effects of the number of undulations and the amplitude on the flow field and heat transfer are also investigated. The predicted results demonstrate that the heat transfer enhancement is generally observed with the modification of the heated wall, while the improvement is found to be more profound for the case of rectangular wave and at low Richardson number.

Numerical method for optimizing stirrer configurations

A numerical approach for the numerical optimization of stirrer configurations is presented. The methodology is based on a parametrized grid generator, a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the Navier-Stokes equations by means of the finite-volume method for block-structured, boundary-fitted grids with multi-grid acceleration and parallelization by grid partitioning. The optimization tool is an implementation of a trust region based derivative-free method. It is designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate. An exemplary application illustrates the functionality and the properties of the proposed method.

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re > 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.

Rheological characterization of polyethylene glycol based TiO2 nanofluids

Rheological characterization of TiO2 nanoparticle dispersions in polyethylene glycol (PEG 200) is presented over 1–10 wt% particle mass fraction range in terms of shear viscosity, thixotropy and linear viscoelasticity. A stress controlled rheometer fitted by a cone-and-plate system was employed for the rheological measurements between −10°C and 40°C. The non-linear viscoelastic experiments revealed that TiO2-PEG 200 nanofluid exhibits a shear thinning behavior when particle mass fraction exceeds 1%. No appreciable change in the shear viscosity versus shear rate behavior was detected over the course of four days of dispersion storage. At high particle concentrations the dispersions had a yield stress that was determined by fitting the results through Herschel-Bukley model. Within the studied range of particle concentration, no evidence of thixotropic behavior was observed. In addition, relative viscosity measured at high shear region was found to be independent of the temperature. On the other hand, strong temperature dependency was observed at low shear region particularly at high temperatures. Storage and loss moduli of the TiO2-PEG 200 nanofluid were determined by frequency sweep measurements with applied stresses in the linear viscoelastic region. It was found that when the applied stress is lower than the corresponding yield stress TiO2-PEG 200 nanofluid showed a gel structure especially at high particle mass concentration.

Derivative free optimization methods for optimizing stirrer configurations

In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids, for allowing a flexible discretization of complex stirrer geometries. Two derivative free optimization algorithms, the DFO and CONDOR are considered, they are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. Both are designed to minimize smooth functions whose evaluations are considered to be expensive and whose derivatives are not available or not desirable to approximate. An exemplary application for a standard stirrer configuration illustrates the functionality and the properties of the proposed methods. It also gives a comparison of the two optimization algorithms.

Numerical Analysis of Viscoelastic Fluids in Steady Pressure-Driven Channel Flow

The developing steady flow of Oldroyd-B and Phan-Thien-Tanner (PTT) fluids through a two-dimensional rectangular channel is investigated computationally by means of a finite volume technique incorporating uniform collocated grids. A second-order central difference scheme is employed to handle convective terms in the momentum equation, while viscoelastic stresses are approximated by a third-order accurate quadratic upstream interpolation for convective kinematics (QUICK) scheme. Momentum interpolation method (MIM) is used to evaluate both cell face velocities and coefficients appearing in the stress equations. Coupled mass and momentum conservation equations are then solved through an iterative semi-implicit method for pressure-linked equation (SIMPLE) algorithm. The entry length over which flow becomes fully developed is determined by considering gradients of velocity, normal and shear stress components, and pressure in the axial direction. The effects of the mesh refinement, inlet boundary conditions, constitutive equation parameters, and Reynolds number on the entry length are presented. [DOI: 10.1115/1.4006696]

Benchmark results for natural and mixed convection heat transfer in a cavity

Purpose – The purpose of this paper is to numerically investigate steady, laminar natural and mixed convection heat transfer in a two-dimensional cavity by using a finite volume method with a fourth-order approximation of convective terms, with and without the presence of nanoparticles. Highly accurate benchmark results are also provided. Design/methodology/approach – A finite volume method on a non-uniform staggered grid is used for the solution of two-dimensional momentum and energy conservation equations. Diffusion terms, in the momentum and energy equations, are approximated using second-order central differences, whereas a non-uniform four-point fourth-order interpolation (FPFOI) scheme is developed for the convective terms. Coupled mass and momentum conservation equations are solved iteratively using a semi-implicit method for pressure-linked equation method. Findings – For the case of natural convection problem at high-Rayleigh numbers, grid density must be sufficiently high in order to obtain grid...

Thermal property investigation of multi walled carbon nanotubes (MWCNTs) embedded Phase Change Materials (PCMs)

In the present study the effect of different size MWCNTs, on the thermal properties such as thermal conductivity, melting/solidification temperatures and latent heats were investigated systematically. Two sizes of MWCNTs that have same diameter but two different lengths as long MWCNTs and short MWCNTs were used at various mass fractions including 1%, 3% and 5% to fabricate MWCNTs/PCM composites. The thermal conductivity, melting/solidification temperatures and latent heats of MWCNTs based composites were evaluated incorporating both particle size and mass concentrations. The experimental results demonstrated that both size and the loading content of the MWCNTs have direct effect on the thermal properties of the samples. The thermal conductivity enhancement of the short MWCNTs was realized to be lower than that of the long MWCNTs. On the other hand, latent heat was measured slightly higher for short MWCNTs than the long MWCNTs.

A comparison study on high-order bounded schemes: Flow of PTT-linear fluid in a lid-driven square cavity

In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of 1×10−5 at all studied Weissenberg (We) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, i.e. primary vortex, are captured accurately up to We = 5 by all converged schemes.

Computational analysis of hydrodynamics of shear-thinning viscoelastic fluids in a square lid-driven cavity flow

Computational results for steady laminar flow of three different shear thinning fluids lid-driven square cavity are presented. The viscoelastic nature of the fluids is represented by linear and exponential Phan-Thien Tanner (PTT) and Giesekus constitutive models. Computations are based on finite volume technique incorporating non-uniform collocated grids. The stress terms in the constitutive equations are approximated by higher-order and bounded scheme of Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection (CUBISTA). Effects of the elasticity, inertia as well as constitutive model parameters on the stress and velocity fields, size and intensity of the primary and secondary vortexes are investigated and discussed in detail. Moreover highly accurate benchmark numerical solutions are provided for each considered constitutive model.