etd@IISc Collection:http://hdl.handle.net/2005/272014-10-31T07:43:42Z2014-10-31T07:43:42ZLU-SGS Implicit Scheme For A Mesh-Less Euler SolverSingh, Manish Kumarhttp://hdl.handle.net/2005/23972014-10-10T09:47:11Z2014-10-09T18:30:00ZTitle: LU-SGS Implicit Scheme For A Mesh-Less Euler Solver
Authors: Singh, Manish Kumar
Abstract: Least Square Kinetic Upwind Method (LSKUM) belongs to the class of mesh-less method that solves compressible Euler equations of gas dynamics. LSKUM is kinetic theory based upwind scheme that operates on any cloud of points. Euler equations are derived from Boltzmann equation (of kinetic theory of gases) after taking suitable moments. The basic update scheme is formulated at Boltzmann level and mapped to Euler level by suitable moments. Mesh-less solvers need only cloud of points to solve the governing equations. For a complex configuration, with such a solver, one can generate a separate cloud of points around each component, which adequately resolves the geometric features, and then combine all the individual clouds to get one set of points on which the solver directly operates. An obvious advantage of this approach is that any incremental changes in geometry will require only regeneration of the small cloud of points where changes have occurred. Additionally blanking and de-blanking strategy along with overlay point cloud can be adapted in some applications like store separation to avoid regeneration of points. Naturally, the mesh-less solvers have advantage in tackling complex geometries and moving components over solvers that need grids. Conventionally, higher order accuracy for space derivative term is achieved by two step defect correction formula which is computationally expensive. The present solver uses low dissipation single step modified CIR (MCIR) scheme which is similar to first order LSKUM formulation and provides spatial accuracy closer to second order. The maximum time step taken to march solution in time is limited by stability criteria in case of explicit time integration procedure. Because of this, explicit scheme takes a large number of iterations to achieve convergence. The popular explicit time integration schemes like four stages Runge-Kutta (RK4) are slow in convergence due to this reason. The above problem can be overcome by using the implicit time integration procedure. The implicit schemes are unconditionally stable i.e. very large time steps can be used to accelerate the convergence. Also it offers superior robustness. The implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) scheme is very attractive due to its low numerical complexity, moderate memory requirement and unconditional stability for linear wave equation. Also this scheme is more efficient than explicit counterparts and can be implemented easily on parallel computers. It is based on the factorization of the implicit operator into three parts namely lower triangular matrix, upper triangular matrix and diagonal terms. The use of LU-SGS results in a matrix free implicit framework which is very economical as against other expensive procedures which necessarily involve matrix inversion. With implementation of the implicit LU-SGS scheme larger time steps can be used which in turn will reduce the computational time substantially. LU-SGS has been used widely for many Finite Volume Method based solvers. The split flux Jacobian formulation as proposed by Jameson is most widely used to make implicit procedure diagonally dominant. But this procedure when applied to mesh-less solvers leads to block diagonal matrix which again requires expensive inversion. In the present work LU-SGS procedure is adopted for mesh-less approach to retain diagonal dominancy and implemented in 2-D and 3-D solvers in matrix free framework.
In order to assess the efficacy of the implicit procedure, both explicit and implicit 2-D solvers are tested on NACA 0012 airfoil for various flow conditions in subsonic and transonic regime. To study the performance of the solvers on different point distributions two types of the cloud of points, one unstructured distribution (4074 points) and another structured distribution (9600 points) have been used. The computed 2-D results are validated against NASA experimental data and AGARD test case. The density residual and lift coefficient convergence history is presented in detail. The maximum speed up obtained by use of implicit procedure as compared to explicit one is close to 6 and 14 for unstructured and structured point distributions respectively. The transonic flow over ONERA M6 wing is a classic test case for CFD validation because of simple geometry and complex flow. It has sweep angle of 30° and 15.6° at leading edge and trailing edge respectively. The taper ratio and aspect ratio of the wing are 0.562 and 3.8 respectively. At M∞=0.84 and α=3.06° lambda shock appear on the upper surface of the wing. 3¬D explicit and implicit solvers are tested on ONERA M6 wing. The computed pressure coefficients are compared with experiments at section of 20%, 44%, 65%, 80%, 90% and 95% of span length. The computed results are found to match very well with experiments. The speed up obtained from implicit procedure is over 7 for ONERA M6 wing. The determination of the aerodynamic characteristics of a wing with the control surface deflection is one of the most important and challenging task in aircraft design and development. Many military aircraft use some form of the delta wing. To demonstrate the effectiveness of 3-D solver in handling control surfaces and small gaps, implicit 3-D code is used to compute flow past clipped delta wing with aileron deflection of 6° at M∞ = 0.9 and α = 1° and 3°. The leading edge backward sweep is 50.4°. The aileron is hinged from 56.5% semi-span to 82.9% of semi-span and at 80% of the local chord from leading edge. The computed results are validated with NASA experiments2014-10-09T18:30:00ZExperimental Study On The Impact Of Water Drops On Groove-Textured SurfacesKannan, Rhttp://hdl.handle.net/2005/23802014-09-08T05:52:50Z2014-09-07T18:30:00ZTitle: Experimental Study On The Impact Of Water Drops On Groove-Textured Surfaces
Authors: Kannan, R
Abstract: The interaction of a liquid drop with a solid surface is being actively studied to understand practically encountered scenarios such as the impact of fuel spray droplets onto the walls of engine combustion chamber, the formation of thermal barrier coating on the surfaces of turbine blades, the process of ink-jet printing, etc. The surface topography of solid surface is one of the major parameters influencing the dynamics of drop-surface interaction process. Understanding the precise role of surface topography features such as micro asperities and grooves on the spreading and receding processes of impacting liquid drops is crucial for the improvement in abovementioned applications. Recent developments in the fabrication of micro- and nano-structures on solid surfaces provide fabulous opportunities to investigate the role of single/multiple micro asperities and grooves on the dynamics of impacting drops.
The thesis deals with an experimental work on the impact of water drops on stainless steel surfaces comprising unidirectional parallel grooves. A group of six target grooved surfaces covering a wide range of surface wettability were considered. The target surfaces were prepared using the techniques of photolithography, electro discharge machining, and laser machining. Scanning electron microscope and optical surface profilometer were used to characterize the groove texture geometrical parameters of the target grooved surfaces. The experiments of drop impact were carried out in an experimental apparatus consisting of a liquid drop generator, a substrate table, and a digital video imaging system. Free-falling distilled water drops released from a certain height were allowed to impact normally on the target surfaces. The image sequences of drop impact dynamics were constructed from the images captured using the digital video imaging system. Majority of the drop impact experiments were captured using a high speed video camera operating with frame speed ranging from 3000 to 10000 fps. For the target grooved surfaces, the impact dynamics was analyzed for the impacting drop liquid oriented both in the direction perpendicular to the grooves ( ) and in the direction parallel to the grooves (||) via independent test runs. The captured digital frames were used to deduce the temporal variation of impacting drop parameters such as drop contact diameter, drop contact angle, and drop height at the center of impacting drop with the aid of image processing software.
The impacting drops were characterized in terms of Weber number, We expressed in terms of drop impact velocity and drop diameter measured just before the start of impact process. The study covered We ranging from 1.8 to 170. In general, the groove texture on the solid surface influences the drop impact process for all We examined in the study. The effect is more pronounced for the receding of impacting drops. For high We drops, the groove texture enhances the perturbations seen at the periphery of spreading lamella. The study showed quantitatively that the drop impact process on a target grooved surface comprising unidirectional parallel grooves develops a non-axisymmetric drop flow on the grooved surface exhibiting different spreading and receding processes of impacting drop liquid in the directions perpendicular ( ) and parallel (||) to the grooves. The maximum spreading diameter reached immediately after the completion of early inertia-dominated spreading in is less than that obtained in || due to the loss of drop kinetic energy caused by the pinned motion of drop liquid in . The non- axisymmetric drop flow on the target grooved surface develops a difference between the frequencies of contact angle oscillation of impacting drop liquid in and ||. The frequency difference in contact angle oscillation causes the beating phenomenon in the temporal variation of the contact angle anisotropy, Δθ and drop height at the center of impacting drop, Z. For a given target grooved surface, the experimental measurements suggested that the beat frequency is almost independent of We. The temporal variation of Δθ and Z do not show the traces of beating phenomenon for the impact of high We drops. Owing to the non-axisymmetric drop flow, the final equilibrium drop shape is eccentric for the impact of low We drops and approaches a circular shape for the impact of high We drops. The role of groove texture geometrical parameters is seen in the drop impact process via the surface wettability especially for the impact of low We drops. Larger surface roughness factor makes the target grooved surface to exhibit hydrophobic characteristics.2014-09-07T18:30:00ZA Synergetic Micromechanics Model For Fiber Reinforced CompositesPadhee, Srikant Sekharhttp://hdl.handle.net/2005/23812014-09-08T07:09:25Z2014-09-07T18:30:00ZTitle: A Synergetic Micromechanics Model For Fiber Reinforced Composites
Authors: Padhee, Srikant Sekhar
Abstract: Composite materials show heterogeneity at different length scales. hence concurrent multiscale analysis is the only reliable method to analyze them. But unfortunately there is no concurrent multi-scale strategy that is efficient, and accurate while addressing all kinds of problems. This lack of reliability is partly because there is no micro-mechanical model which inherently keeps all relevent global information with it. This thesis tries to fill this gap. The
presented micro-mechanical model not only homogenizes the micro-structure but also keeps the global information with it. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis which results in loss of information and accuracy. In the present approach also, the RVE has been extracted
from the continuum but with the major difference that all the macro/meso-scopic parameters are accounted for. Five macro/meso-scopic one dimensional parameters have been defined which completely define the effect of continuum. 11 for one dimensional stretch, _1 for torsion, __ (_ = 2, 3) for bending and _33 for uniform pressurization due to the presence
of the continuum. Further, the above macro/meso-scopic parameters are proven, by the asymptotic, theory to be constant at a cross section but vary, in general, over the length of the fiber. Hence, the analysis is valid for any location and is not restricted to any local domain.
Three major problems have been addressed:
• Homogenization and analysis of RVE without any defects
• Homogenization and analysis of RVE with fiber-matrix de-bonding
• Homogenization and analysis of RVE with radial matrix cracking.
Variational Asymptotic Method (VAM) has been used to solve the above mentioned problems
analytically. The results have been compared against standard results in the literature and
against 3D FEA.
At the end, results for “Radial deformation due to torsion” problem will be presented
which was solved “accidentally.”2014-09-07T18:30:00ZModeling And Computation Of Turbulent Nonreacting And Reacting SpraysDe, Santanuhttp://hdl.handle.net/2005/23792014-09-05T06:51:23Z2014-09-04T18:30:00ZTitle: Modeling And Computation Of Turbulent Nonreacting And Reacting Sprays
Authors: De, Santanu
Abstract: Numerical modeling of several turbulent nonreacting and reacting spray jets is carried out using a fully stochastic separated flow (FSSF) approach. As is widely used, the carrier-phase is considered in an Eulerian framework, while the dispersed phase is tracked in a Lagrangian framework following the stochastic separated flow (SSF) model. Various interactions between the two phases are taken into account by means of two-way coupling. Spray evaporation is described using a thermal model with an infinite conductivity in the liquid phase. The gas-phase turbulence terms are closed using the k-� model. In the classical SSF (CSSF) approach the effects of turbulent velocity fluctuations of the gas-phase are modeled stochastically to obtain instantaneous gas-phase velocity, which subsequently is used to estimate droplet dispersion and interphase transport rates. However, in the CSSF model, no such effort is made to model the effects of the fluctuations in the gas-phase reactive scalars, namely temperature and species mass fractions. Instead, the mean value of these scalars is used while solving for the droplet governing equations and estimating various interphase source terms. Also, in flamelet model and conditional moment closure (CMC) applications of turbulent sprays, the mixture fraction is defined using conventional definition, which is no longer a conserved quantity due to associated phase change.
Therefore, in this thesis a novel mixture fraction based FSSF approach is used to stochastically model the fluctuating temperature and composition of the gas phase. These gas-phase reactive scalars are then used to refine the estimates of the heat and mass transfer rates between the droplets and the surrounding gas-phase. It is assumed that the fluctuations in the gas-phase reactive scalars are inherently associated with the fluctuation of a single conserved scalar, namely instantaneous mixture fraction. Instantaneous value of the gas-phase reactive scalars seen by individual droplets is then estimated from the instantaneous gas-phase mixture fraction, which is obtained as the Weiner process by randomly sampling a known beta-function probability density function (PDF) of the local mixture fraction field. Finally, Favre mean value of the gas-phase scalars are recovered as appropriate moments of the PDF. The present definition of the mixture fraction based on its instantaneous value facilitate exact calculation of the source terms in the transport equation for variance of the mixture fraction, whereas conventional definition leads to terms which require further modeling and simplifications. The present FSSF model also accounts for the possibility of existence of an envelope flame between the droplet and the bulk gas-phase, which greatly increases the heat and mass transfer rates to the droplet. The present model allows us to treat the occurrence of envelope flame separately which is otherwise neglected in the conventional spray combustion models.
The FSSF model is implemented into a numerical code, and different well-defined nonreacting and reacting turbulent spray jets are investigated. For the reacting spray jets, single-step irreversible reaction with infinitely fast chemistry is assumed in the body of the flow. In such cases special care must be taken with modeling the upstream boundary condition. This is because the flow from the spray jet nozzle is unreacted and yet it becomes well reacted shortly downstream. Numerical results are compared against experimental measurements as well as with predictions using the CSSF approach. Numerical results from the FSSF and CSSF model are almost identical for the nonreacting spray jets, where the fluctuations in the gas-phase scalars are relatively low. For the reacting sprays, significant differences are found between the results of the FSSF and CSSF models for the reacting spray jets, where the fluctuations in the reactive scalars are high. The FSSF model reasonably predicts many features of the jet spray flames, such as flame length, gas-phase temperature, and spray droplet velocity/diameter distribution; results appear to be close to the experimental measurements.
Finally, the combustion characteristics of the reacting spray jets are studied following classical group combustion theory. It shows that these spray jets have external group combustion mode near the nozzle-exit. Transition to internal group combustion takes place at different downstream locations based on the droplet loading and equivalence ratio at the nozzle-exit, whereas single droplet combustion regime is observed near the tip of the visible flame. Another alternate approach to study the combustion behavior of a cloud is proposed based on fraction of droplets having i) no envelope flame, ii) envelope flame, iii) extinguished envelope flame due to high slip velocity, iv) extinguished envelope flame due to droplet diameter being too small, v) both iii) and iv) above. Based on these, different group combustion behavior of the reacting spray jets are interpreted.2014-09-04T18:30:00Z