etd@IISc Collection:http://hdl.handle.net/2005/272016-05-30T17:02:40Z2016-05-30T17:02:40ZDetermination Of Isopectral Rotating And Non-Rotating BeamsKambampati, Sandilyahttp://hdl.handle.net/2005/25232016-04-27T07:07:09Z2016-04-26T18:30:00ZTitle: Determination Of Isopectral Rotating And Non-Rotating Beams
Authors: Kambampati, Sandilya
Abstract: In this work, rotating beams which are isospectral to non-rotating beams are studied. A rotating beam is isospectral to a non-rotating beam if both the beams have the same spectral properties i.e; both the beams have the same set of natural frequencies under a given boundary condition. The Barcilon-Gottlieb transformation is extended, so that it converts the fourth order governing equation of a rotating beam (uniform or non-uniform), to a canonical fourth order eigenvalue equation. If the coefficients in this canonical equation match with the coefficients of the non-rotating beam (non-uniform or uniform) equation, then the rotating and non-rotating beams are isospectral to each other. The conditions on matching the coefficients lead to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of isospectral rotating and non-rotating beams. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. The mass and stiffness functions for the isospectral rotating and non-rotating beams are obtained. We use these mass and stiffness functions in a finite element analysis to verify numerically the isospectral property of the rotating and non-rotating beams. Finally, the example of beams having a rectangular cross section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the isospectral rotating beams.2016-04-26T18:30:00ZA Residual Based h-Adaptive Strategy Employing A Zero Mean Polynomial ReconstructionPatel, Sumit Kumarhttp://hdl.handle.net/2005/25152016-04-18T07:42:56Z2016-04-17T18:30:00ZTitle: A Residual Based h-Adaptive Strategy Employing A Zero Mean Polynomial Reconstruction
Authors: Patel, Sumit Kumar
Abstract: This thesis deals with the development of a new adaptive algorithm for three-dimensional fluid flows based on a residual error estimator. The residual, known as the R –parameter has been successfully extended to three dimensions using a novel approach for arbitrary grid topologies. The computation of the residual error estimator in three dimensions is based on a least-squares based reconstruction and the order of accuracy of the latter is critical in obtaining a consistent estimate of the error. The R –parameter can become inconsistent on three–dimensional meshes depending on the grid quality. A Zero Mean Polynomial(ZMP) which is k–exact, and which preserves the mean has been used in this thesis to overcome the problem. It is demonstrated that the ZMP approach leads to a more accurate estimation of solution derivatives as opposed to the conventional polynomial based least-squares method. The ZMP approach is employed to compute the R –parameter which is the n used to derive the criteria for refinement and derefinement. Studies on three different complex test problems involving inviscid, laminar and turbulent flows demonstrate that the new adaptive algorithm is capable of detecting the sources of error efficiently and lead to accurate results independent of the grid topology.2016-04-17T18:30:00ZDynamics Of Water Drops Impacting Onto The Junction Of Dual-Textured Substrates Comprising Hydrophobic And Hydrophilic PortionsVaikuntanathan, Visakhhttp://hdl.handle.net/2005/24122014-11-24T09:13:06Z2014-11-23T18:30:00ZTitle: Dynamics Of Water Drops Impacting Onto The Junction Of Dual-Textured Substrates Comprising Hydrophobic And Hydrophilic Portions
Authors: Vaikuntanathan, Visakh
Abstract: The research topic of liquid drop interaction with solid surfaces is being actively pursued to gain in-depth understanding of several practical cases such as the impingement of fuel spray droplets on surfaces like combustion chamber walls and piston top of an I.C. engine, heat transfer via spray impingement, ink-jet printing, etc. In most of the cases, the physical and flow properties of the liquid drop/spray may be fixed whereas it may be possible to tune the physical and chemical properties of the solid surface thereby enabling to control the interaction process. The present work belongs to the study of liquid drop-solid surface interaction process with special focus on the physical characteristics of solid surface. The thesis reports an experimental study of the dynamics of millimetric water drops impacted onto the junction of dual-textured substrates made of stainless steel. The dual-textured substrates consisted of hydrophobic (textured) and hydrophilic (smooth) portions. The entire textured portion comprised of parallel groove-like structures separated by solid posts/pillars. Two dual-textured substrates, which differ only in the geometry of their textured portions, were employed. Surface topography features of the dual-textured substrates were characterized using scanning electron microscopy (SEM) and optical surface profilometer. The wetting behavior of the textured and smooth portions of the substrates, quantified in terms of the equilibrium, advancing, and receding contact angles adopted by a water drop on the surface portions, was characterized experimentally through the methods of sessile drop formation, captive needle volume addition, and drop evaporation under ambient conditions. Free-falling water drops were impacted from a height onto the junction between the hydrophobic (textured) and hydrophilic (smooth) portions of the dual-textured substrates. A set of twelve different impact experiments were conducted on each of the target substrates with drop impact velocity (Uo) ranging from 0.37 to 1.50 m/sec. The dynamics of drop impact were captured using a high speed camera with frame rate ranging from 3000 to 10000 frames per second. From the captured frames, the temporal variations of the impacting drop parameters were measured using a MATLAB-assisted program. A systematic analysis of experimental data revealed the existence of four distinct regimes of drop dynamics on the dual-textured substrate: (a) early inertia driven drop spreading, (b) primary drop receding, (c) secondary spreading on the hydrophilic portion, and (d) final equilibrium regimes. It is shown that the drop impact dynamics during the early inertia driven impact regime remains unaffected by the dual-texture feature of the substrate. A larger retraction speed of impacting drop liquid observed on the hydrophobic portion of the substrate makes the drop liquid on the higher wettability/hydrophilic portion to advance further (secondary drop spreading). The net horizontal drop velocity towards the hydrophilic portion of the dual-textured substrate decreases with increasing drop impact velocity. The available experimental results suggest that the movement of bulk drop liquid away from the impact point during drop impact on the dual-textured substrate is larger for the impact of low inertia drops. A semi-empirical model, based on the balance of the wettability gradient, contact angle hysteresis, and viscous forces acting on impacted drop liquid on the substrate, is formulated to predict the movement of bulk drop liquid away from the impact point (ξ). A satisfactory comparison between the model predictions and the experimental measurements is reported for the variation of ξ with Uo.2014-11-23T18:30:00ZEnergy Separation And Lox Separation Studies In Vortex TubesBehera, Upendrahttp://hdl.handle.net/2005/24132014-11-24T09:55:39Z2014-11-23T18:30:00ZTitle: Energy Separation And Lox Separation Studies In Vortex Tubes
Authors: Behera, Upendra
Abstract: Vortex Tube (VT) is a simple device having no moving mechanical parts, in which compressed gas at high pressure is injected through one or more tangential nozzles into a vortex chamber resulting in the separation of the inlet flow into two low pressure streams. One of the streams is the peripheral flow that is warmer than the inlet stream while the other is the central (core) flow that is colder than the inlet stream. This separation of the inlet flow into high and low temperature streams is known as temperature or energy separation. It is suggested by many investigators that compressed air of few atmospheres pressure and at room temperature can produce temperatures as high as +200ºC at the hot end (peripheral flow exit) and as low as -50ºC at the cold end (core flow exit) of the VT. Though VTs have large potential for simple heating and cooling applications, the mechanism of energy separation is not clear so far. Based on their studies, many investigators have suggested various theories, different from each other, but having specific lacunas and is an unresolved issue. Also, till date, experimental and industrial designs of the VTs are based purely on empirical correlations.
Apart from heating and cooling applications, VTs can also be used for separation of binary gas mixtures and separation of oxygen from two-phase precooled air stream. The conceptual futuristic cryogenic launch vehicle designs are being attempted with in-flight liquid oxygen (LOX) collection system that significantly improves the pay load fraction. Vortex tube technology is one of the few promising technologies for futuristic in-flight LOX separation based launch vehicles. This technology has significant advantages over its counterparts as it is a simple, compact and light weight, and most importantly have no moving parts and unaffected by gravity and orientation.
In order that VTs become an acceptable technology for in-flight LOX separation system, it is necessary to achieve minimum oxygen purity of 90% with more than 60% yield (separation efficiency) for the oxygen enriched stream in the VT. A survey of the available open literature has shown very little reported details, in particular, on achieving the required specifications for in-flight LOX separation systems. Till date, the highest LOX purity of 60% with 40% separation efficiency has been reported with VT technology. In view of the above mentioned facts, the work carried out has been focused on to: • Optimize the critical parameters of the VT to achieve maximum energy separation by CFD and experimental studies. • Understand the flow behaviour in the VT by estimating the velocity, temperature and pressure profiles at various locations in the VT and validation of secondary circulation flow and its effect on the performance of energy separation in VT. • Estimation of the energy transfer between the core and the peripheral layers of fluid flow in VT by analytical and CFD methods to propose the most appropriate mechanism of energy separation in VT. • Design and development of a dedicated experimental setup for both energy separation and LOX separation studies in VTs. • Design and fabrication of straight and conical VTs and experimental programme on energy separation and LOX separation. • Development of the VT air separation technology to achieve the required specifications of in-flight LOX separation system for futuristic launch vehicles. With these specific objectives and motivations, the total work was carried out with the following planned and sequential steps: • The first step was the CFD modeling of the VT with the available CFD software (Star-CD) and obtain the energy separation phenomena for a 12mm diameter VT. After gaining sufficient confidence level, optimization of the critical parameters like the air injection nozzle profile, number of nozzles, cold end orifice diameter dc, length to diameter (L/D) ratio, hot gas fraction etc of the VT was carried out through CFD and experimental studies. • The studies show that 6 convergent nozzles perform better in comparison to other configurations like circular helical, rectangular helical, 2 convergent and 6 straight nozzles. The studies also show that cold end orifice diameter (dc) plays an important role on energy separation and bring out the existence of secondary circulation flow with improper design of cold end orifice diameter. Through our studies, the effect of cold end diameter on the secondary circulation flow has been evaluated for the first time. Also, the mechanism of energy transfer in VT based on heat pump mechanism enabled by secondary circulation flow as suggested by some investigators has been evaluated in our studies. The studies show that cold end orifice diameter dc = 7mm is optimum for 12mm diameter VT, which matches fairly with the correlations given by other investigators. The studies confirms that CFD modeling carried out in this work is capable of selecting the correct dc value for a VT, without resorting to the empirical correlations as a design guide or a laborious experimental programme. • Through the CFD and experimental studies on different length to diameter (L/D) ratios and hot gas fractions, maximum hot gas temperature of 391K was obtained for L/D = 30 with hot gas fraction of 12-15 % and minimum cold gas temperature of 267K for L/D = 35 was obtained for cold gas fraction ≈ 60% (lowest cold gas fraction possible with the present experimental system). • CFD analysis has been carried out to investigate the variation of static and total temperatures, static and total pressures as well as the velocity components of the particles as it progresses in the flow field, starting from the entry through the nozzles to the exit of the VT by tracking the particles to understand the flow phenomenon and energy transfer mechanism inside the VT. The studies indicate that the mechanism of energy transfer from the core flow to the peripheral flow in VT is predominantly occurs by the tangential shear work. Thus the investigations reported in the thesis have given a clear understanding of the contributing mechanism for energy separation in VT, which has been an unresolved issue for long time. The net energy transfer between the core and the peripheral fluid has been calculated analytically and compared with the values obtained by CFD model for VTs of L/D ratios equal to 10 and 30. The net energy transfer by analytical and CFD model for VT with L/D = 10 is 159.87W and 154.2W respectively whereas the net energy transfer by analytical and CFD model for VT with L/D = 30 is 199.87W and 192.3W respectively. The results show that CFD results are in very good agreement with the analytical results and CFD can be used as a tool for optimization of the critical parameters and to analyze the flow parameters and heat transfer analysis for VTs. Also, the net energy transfer between the core and peripheral fluids calculated analytically matches very well with that of the net energy transfer by CFD analysis, without considering the effect of acoustic streaming. Thus acoustic streaming may not be the mechanism of energy separation in VT as suggested by some investigators. • By optimizing the critical parameters of the 12mm diameter straight VT through CFD and experimental studies, LOX separation studies have been carried out using both straight and conical VTs of dc = 7mm and of different L/D ratios for high LOX purity and separation efficiency. It is observed that conical (3º divergence) VTs perform better as compared to straight VTs for LOX separation whereas straight VTs perform better for energy separation. The better performance of conical VT as compared to straight VTs can be attributed to its increased surface area for condensation-evaporation phenomenon of oxygen and nitrogen molecules. Experimental studies have been conducted to evaluate the influence of the inlet pressure and the inlet temperature (liquid fraction) on LOX purity. Studies indicate that for achieving high LOX purity for the studied experimental system, the inlet pressure is to be in the range of 6-6.5bar and there exists a very narrow band of inlet temperature zone in which high LOX purity can be achieved. Experimental studies on VTs show that VT can be optimized suitably either for high LOX purity with low separation efficiency or low LOX purity with high separation efficiency by adjusting the hot end mass fraction accordingly. It is also observed that it is not possible to obtain both high purity and high separation efficiency simultaneously with the single VT. Staging approach has to be adapted to achieve higher LOX purity with higher separation efficiency. By staging the VTs, the enriched air stream (hot end outlet flow) from the first stage of VTs is introduced to the inlet of the second stage of VTs. Experimental studies have been conducted to evaluate the design parameters on staging of VTs. LOX purity of 48% with 89% separation efficiency has been achieved for conical first stage VT of L/D = 25. LOX purity of about 94% with separation efficiency of 84% has been achieved for 50% oxygen content at the inlet of the second stage VT. Similarly, LOX purity of 96% with separation efficiency of 73.5% has been achieved for 60% oxygen content at the inlet of the VT. This is the highest LOX purity and separation efficiency reported so far indicating that, conical VT of optimized diameter, L/D ratio and orifice diameter can yield the hot end flow very close to the target value of futuristic in-flight LOX separation based launch vehicles.
The present investigation has focused the optimization of the critical parameters of VTs through CFD and experimental studies. It has also given an insight to the mechanism of energy transfer between the core and peripheral flow in VT by evaluating two of the existing theories on mechanism of energy transfer in VT. The studies also highlighted the fact that custom designed and precision fabricated VTs can be very useful for obtaining maximum / minimum temperatures of fluid flow as well as LOX separation with high purity and high separation efficiency needed for futuristic in-flight LOX separation based space launch vehicles.2014-11-23T18:30:00Z