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Papers by kadir kirkkopru

33rd Aerospace Sciences Meeting and Exhibit, Jan 9, 1995

The Eurasia Proceedings of Science Technology Engineering and Mathematics

Fused Deposition Modelling is one of the main 3D printing methods to manufacture plastic parts. T... more Fused Deposition Modelling is one of the main 3D printing methods to manufacture plastic parts. The strength of the printed part by FDM is dependent on polymer diffusion between printed layers. The polymer diffusion between two neighboring layers occur not only during the extrusion of the hot top layer, but also during the production of consecutive layers due to thermal conduction. The heat diffusion from upper layers enhances the curing of polymers, which consequently affects the strength of the part. Therefore, the history of the temperature variations - curing time and curing temperature - should be analyzed to predict the strength of the part. The goal of this study is to develop a two-dimensional transient thermal analysis solver for the investigation of time-dependent thermal changes during the printing process. This solver is developed with the use of finite difference method employed under implicit scheme. The transient temperature pattern is qualitatively compatible to the ...

Engineering Solid Mechanics, 2021

Due to complex structure of aortic valve (AV) leaflets and its strong interaction with the blood ... more Due to complex structure of aortic valve (AV) leaflets and its strong interaction with the blood flow field, realistic and accurate modeling of the valve deformations comes with many challenges. In this study, we aimed to investigate the effect of AV material properties on the valve deformations, by implementing different non-linear properties of the AV leaflets in three different material models. In the computations, we captured the dynamics between the leaflet deformations and blood flow field variations by using an iterative implicit fluid-structure interaction (FSI) approach. By comparison of the FSI simulation results of these three models, the effects of hyperelasticity and anisotropy on the valve deformations have been studied in detail. The simulation results reveal the fact that the material characteristics strongly affect the deformation characteristics of the leaflets in the systolic phase. The material anisotropy stabilizes the leaflet movements during the systolic phase...

A computational model is developed for the simulation of internal reactive fluid flow in a solid ... more A computational model is developed for the simulation of internal reactive fluid flow in a solid rocket motor with propellant burning surface regression. The model focuses on a 2D reactive flow in an end burning lab-scale motor. Chemical reaction equations with finite rate chemistry are combined with gas dynamics, and complete conservation equations of mass, momentum, energy and species are solved. Two different chemical systems, hydrogen and propane combustion processes, are studied. The regressive boundary in the combustion chamber is treated using remeshing techniques. The effect of propellant regression on gas mixture velocity and temperature distribution in the flame zone is examined. Thrust values with varying inlet temperatures are compared for both combustion models. Keywords—solid rocket motor; combustion; solid fuel regression; remeshing

Journal of Engineering Mathematics, 1991

We consider the high Reynolds number laminar flow of an incompressible fluid past a slender delta... more We consider the high Reynolds number laminar flow of an incompressible fluid past a slender delta wing at incidence. The primary separation is represented by vortex sheets emanating from the leading edges. These sheets also carry a source distribution to represent viscous displacement effects. An interactive viscous-inviscid calculation is carried out to determine the secondary-separation flow properties on the wing. Agreement between the theoretical predictions and experiment is encouraging. For example, unlike the purely inviscid calculations, there is only a small pressure recovery beyond the suction peak, as is observed in experiment. Similarly the upward and inboard movement of the vortex core due to the secondary separation is in accord with experiment, as is the position of secondary separation.

Journal of Aeronautics and Space Technologies, 2007

A multigrid scheme is applied to accelerate the convergence of numerical solution of two dimensio... more A multigrid scheme is applied to accelerate the convergence of numerical solution of two dimensional Euler equations to steady state. Cell-centered finite volume method with central differencing scheme is used for discretization. Explicit multistage time-stepping algorithm is used to advance the solution in time. Acceleration techniques including local time stepping and implicit residual smoothing are used as well. Attention is directed towards the accuracy, convergence, and computational performance of the V-cycle and W-cycle multigrid strategies together with piece-wise constant and bilinear interpolations on two grid and three grid levels. Subsonic and transonic inviscid flows past NACA 0012 airfoil are computed as test cases.

Journal of Aeronautics and Space Technologies, 2005

Cell-centered finite volume method with multistage time-stepping is successfully applied to two-d... more Cell-centered finite volume method with multistage time-stepping is successfully applied to two-dimensional mass-weighted, time-averaged Navier-Stokes equations for the computation of viscous flows. In the cellcentered scheme, flow quantities are associated with the center of a cell. Convective fluxes at the cell faces are evaluated by means of upwind Roe Flux Differencing Scheme (Roe FDS) with Monotone Upwind Schemes for Scalar Conservation Laws (MUSCL) approach. Green?s theorem is employed for evaluation of gradients in computation of viscous fluxes. Five stage hybrid time-stepping scheme is implemented for integration to steady state. Convergence is accelerated by utilizing local time stepping and residual smoothing. The accuracy of the present Navier-Stokes solver is verified by comparing flat-plate laminar boundary-layer solutions with theoretical solutions of Blasius and by comparing laminar airfoil solutions with those available in literature. Convergence down to machine zero...

Unsteady flow in a semi-closed axisymmetric cylindrical channel with steady sidewall mass injecti... more Unsteady flow in a semi-closed axisymmetric cylindrical channel with steady sidewall mass injection that simulates a model of a solid propellant rocket combustion chamber is studied computationally. Planar pressure disturbances prescribed on the open exit plane are the source of the acoustic disturbances in the system. Amplitudes of the oscillatory pressure disturbances are chosen accordingly for different flow Mach numbers, so that nonlinear processes affect the evolution of the unsteady flow. Investigations with the unsteady vortical part of the velocity extracted from the total velocity field show that unsteady vorticity larger than that in the steady flow conditions is generated at the injecting sidewall of the cylinder and that this unsteady vorticity eventually fills the entire chamber.

Solid propellant rocket boosters (SPRB) are used extensively in aerospace activities when a stron... more Solid propellant rocket boosters (SPRB) are used extensively in aerospace activities when a strong thrust is needed as in the case of lifting off the satellites for space activities. Flow structures occurring within the SPRB's have drawn the attention of the researchers either experimentally, or as it happens increasingly today, computationally. The flow field inside the combustion chamber experiences different processes since the characteristic velocity throughout the chamber is on the order of Ma O(10 exp-2), whereas the exit velocity is supersonic. Time dependent behavior of various processes, turbulence, combustion, as well as with the compressibility effects add intricacy into the simulation processes. Today, major study field for the SPRBs is the flow stability problem inside the combustion chamber, and its interaction with combustion and turbulence. This study is the first part of an ongoing research held in the Faculty of Mechanical Engineering at Istanbul Technical Univ...

Physics of Fluids A: Fluid Dynamics, 1989

The induction zone characteristics of a planar subsonic high-speed reactive flow downstream of a ... more The induction zone characteristics of a planar subsonic high-speed reactive flow downstream of a specific origin are investigated theoretically for the global irreversible reaction F + Ox yields nuP. The equation of state for the reacting gas mixture is more general than that for a constant molecular weight gas. Perturbation methods based on the limit of high activation energy are used to construct the general parameter-dependent analytical solutions. The dependence of the ignition delay distance on the kinetic, stoichiometric, and flow parameters is discussed in detail. Significantly, it is shown that the reaction with a mole decrement (nu = 1) yields the minimum, and a mole increment (nu = 3) yields the maximum ignition delay distance when the chemical heat addition and the origin values of parameters are fixed. The physics and length scales found from the perturbation analysis are used as a guide in generating supporting numerical solutions.

Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B, 2011

... Cagri NART, Oktay YILMAZ and Kadir KIRKKOPRU Faculty of Mechanical Engineering Istanbul Techn... more ... Cagri NART, Oktay YILMAZ and Kadir KIRKKOPRU Faculty of Mechanical Engineering Istanbul Technical University Istanbul, Turkey ABSTRACT Coextrusion heads are widely used to producemulti-layered products such as pipes and vessels in plastics industry. ...

Euler equations are solved by means of three efficient and robust finite volume schemes, namely, ... more Euler equations are solved by means of three efficient and robust finite volume schemes, namely, central scheme of Jameson-Schmidt-Turkel (JST) and upwind schemes of Roe's Approximate Riemann Solver and Convective Upwind Split Pressure (CUSP) Scheme. Cell-centered discretization technique is employed. Multistage time- stepping algorithm is used to advance the solution in time. Acceleration techniques including local time stepping and implicit residual smoothing are applied for faster convergence to steady state. The flux at the cell faces is computed using MUSCL approach in upwind schemes and simple averaging procedure in JST scheme. MUSCL is enhanced by employing Van Albada limiter to suppress oscillations in regions of sharp gradients. Attention is directed towards the accuracy, convergence, and computational performance of the schemes. All schemes yield good convergence rates for a wide range of flow speeds.

Journal of Propulsion and Power, 1996

Journal of Fluid Mechanics, 2000

A mathematical model is formulated to describe the initiation and evolution of intense unsteady v... more A mathematical model is formulated to describe the initiation and evolution of intense unsteady vorticity in a low Mach number (M), weakly viscous internal flow sustained by mass addition through the sidewall of a long, narrow cylinder. An O(M) axial acoustic velocity disturbance, generated by a prescribed harmonic transient endwall velocity, interacts with the basically inviscid rotational steady injected flow to generate time-dependent vorticity at the sidewall. The steady radial velocity component convects the vorticity into the flow. The axial velocity associated with the vorticity field varies across the cylinder radius and in particular has an instantaneous oscillatory spatial distribution with a characteristic wavelength O(M) smaller than the radius. Weak viscous effects cause the vorticity to diffuse on the small radial length scale as it is convected from the wall toward the axis. The magnitude of the transient vorticity field is larger by O(M−1) than that in the steady flo...

Fibers and Polymers, 2014

ABSTRACT Several restrictions which are related to extruder machinery and nature of process mater... more ABSTRACT Several restrictions which are related to extruder machinery and nature of process material exist in the design of plastic extrusion dies. To this respect, it is very important to consider design criteria and limitations in order to operate extrusion dies at desired production rate and temperature. In the current study, flow field characteristics through a conical spiral mandrel die are analysed in detail by 3D Computational Fluid Dynamics (CFD) simulations. The effects of operating conditions such as production rate and temperature on pressure drop through the spiral mandrel die and the occurence of melt fracture are investigated. The temperature dependent viscosity versus shear rate data for grade QB79P (CarmelTech) polypropylene (PP) melt under study are measured by use of rotational and capillary rheometers. Stress terms in the momentum equations are modeled by Generalized Newtonian Fluid (GNF) Model. For this, Bird-Carreau Model is employed as the viscosity model for the polymer melt. 3D CFD analyses provide comprehensive data and understanding with regard to flow behaviour through complex extrusion dies.

SIAM Journal on Applied Mathematics, 1991

ABSTRACT The author presents a study of the structure of a subsonic high speed reaction zone down... more ABSTRACT The author presents a study of the structure of a subsonic high speed reaction zone downstream of a specific origin is investigated theoretically for the global reaction F+O P. The molecular weights of the reactants are arbitrary and the reaction is not mole-preserving in general. As a result, the equation of state for the reacting mixture is more general than that for a perfect gas. The chemical heat addition is significant relative to the initial enthalpy of the flow. Perturbation methods based on the limits of high activation energy are used to construct solutions. The structure of the entire deflagration is determined by a fundamental balance of convection, reaction and compressibility effects except in a very thin zone adjacent to the origin where transport effects are important. A convecting thermal explosion is observed in a subsequent ignition zone where the ignition delay distance is dependent on the initial stoichiometry of the flow. As a result of the non-mole preserving reaction, the flow velocity decreases with increasing temperature when the chemical heat release parameter is less than a special value dependent on the stoichiometry of the flow. In a downstream region characterized by a strong interaction between large heat release and flow compressibility, the flow velocity reaches a maximum and then declines while the final temperature increase occurs if the chemical heat release parameter is greater than this special value. Additionally, it is found that the flow cannot evolve to the Chapman-Jouguet condition where the final local Mach number is unity and the reactant concentration is zero.

Acomputational study is performed for the simulation of reactive fluid flow in a solid rocket mot... more Acomputational study is performed for the simulation of reactive fluid flow in a solid rocket motor chamber with pressure dependent propellant burning surface regression. The model geometry consists of a 2D end burning lab-scale motor. Complete conservation equations of mass, momentum, energy and species are solved with finite rate chemistry. The pressure dependent regressive boundary in the combustion chamber is treated by use of remeshing techniques. Hydrogen and propane combustion processes are examined. Time dependent pressure and burning rate variations are illustrated comprehensively. Temperature and species mass fraction variations are given within the flame zone. Temperature, velocity and density distributions are compared for both constant burning rate and pressure dependent burning rate simulations.

A computer code, implementing a novel Dual Time Stepping (DTS) algorithm, is developed in order t... more A computer code, implementing a novel Dual Time Stepping (DTS) algorithm, is developed in order to simulate two-dimensional unsteady cold flow in Solid Rocket Motors (SRM) involving variable internal geometry. Simulation of unsteady flow at all-speeds is essential, since flow speed of combustion gases through an SRM ranges from incompressible limit to supersonic speeds and internal geometry of the SRM varies in time due to regression of combusting propellant surface. In this respect, present code solves compressible form of time dependent conservation laws, written in Arbitrary Lagrangian-Eulerian (ALE) form, on deforming grids at low Mach numbers (M 1) as well as at supersonic speeds. The present code exploits low Mach number preconditioning technique to modify compressible form of Navier-Stokes equations for simulation of all-speed flows. Time dependent Navier-Stokes equations are written in ALE form in order to solve flow problems involving moving boundaries. Time dependent pre...

Journal of Applied Fluid Mechanics

The aortic valve is located at left ventricular outlet and is exposed to the highest pressure in ... more The aortic valve is located at left ventricular outlet and is exposed to the highest pressure in the cardiovascular system. Problems associated with the valve leaflet movement can cause complications for the heart. Specifically, aortic stenosis (AS) arises when aortic leaflets do not efficiently open. In the present study, Lagrangian Coherent Structures (LCSs) were utilized by processing a variety of Computational Fluid Dynamics (CFD) models velocity vector data further to identify the characteristics of AS jets. Particularly, effective orifice areas (EOA) for different cases were accurately identified from unstable manifolds of finite time Lyapunov exponent (FTLE) fields. Calcified leaflets were modeled by setting the leaflet's Young modulus to 10 MPa and 20 MPa for moderately and severely calcified leaflets respectively while a healthy leaflet's Young modulus was assigned to be 2 MPa. Increase in calcification degree of the leaflet caused destruction of the vortex structures near the fibrosa layer of the leaflet indicating a malfunctioning for the movement mechanism of the leaflet. Furthermore, when we analyzed stable manifolds, we identified a blockage region at the flow upstream due to the stagnant blood here. Compared to a healthy case, for the calcified valve, this blockage region was enlarged, implying an increase in AS jet velocity and wall shear stress on leaflets. As a conclusion, results from the present study indicate that aortic leaflet malfunctioning could be accurately evaluated when LCS technique was employed by post processing velocity vector data from CFD. Such precise analysis is not possible using the Eulerian CFD approach or a Doppler echocardiography since these methods are based on only analyzing instantaneous flow quantities and they overlook fluid flow characteristics of highly unsteady flows.