Bounds on the volume fraction of 2-phase, 2-dimensional elastic bodies and on (stress, strain) pairs in composites

Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy, determinant of the stress, and determinant of the displacement gradient, which can be determined from measurements of the traction and displacement at the boundary. The bounds are sharp if in each phase certain displacement field components are constant. The inequalities we obtain also directly give bounds on the possible (average stress, average strain) pairs in a two-phase, two-dimensional, periodic or statistically homogeneous compositeComment: 16 pages, 2 figures, Submitted to Comptes Rendus Mecaniqu

On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials

The set $GU_f$ of possible effective elastic tensors of composites built from two materials with elasticity tensors \BC_1>0 and \BC_2=0 comprising the set U=\{\BC_1,\BC_2\} and mixed in proportions $f$ and $1-f$ is partly characterized. The material with tensor \BC_2=0 corresponds to a material which is void. (For technical reasons \BC_2 is actually taken to be nonzero and we take the limit \BC_2\to 0). Specifically, recalling that $GU_f$ is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases. In these cases the calculation of the minimum is reduced to a finite dimensional minimization problem that can be done numerically. Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate $p$-mode material, that is easily compliant to $p\leq 5$ independent applied strains, yet supports any stress in the orthogonal space. Thus the material can easily slip in certain directions along the walls. The region outside the walls contains "complementary Avellaneda material" which is a hierarchical laminate which minimizes the sum of complementary energies.Comment: 39 pages, 11 figure

Computational design and numerical analyses of thermal-hydraulics in a PWR-type small modular nuclear reactor

This dissertation focuses on computational design of a PWR-type small modular nuclear reactor (SMR), and analysis of coolant thermal-hydraulics during steady-state operation. Physical design of the SMR is based on the existing AP-1000 and Small Modular Reactor designs by Westinghouse Nuclear. The first paper discusses a two-stage simulation of turbulent flow in the lower plenum of the RPV. In the first stage, four time-dependent Reynolds-Averaged Navier-Stokes (RANS) based turbulence models were used to simulate turbulent flow, compare predictions and identify an appropriate turbulence model. In the second stage, the selected turbulence model was once again used to simulate flow on a refined computational mesh (wall y+ \u3c 1) and compared with time-averaged predictions of the Large Eddy Simulation (LES) model. The LES model was also able to capture a cut-off for the spatial frequency of inertial flow scales in the lower plenum. The second paper uses simulation methodology established by Westinghouse Nuclear applied to resolving turbulent flow and heat transfer in a representative volume of the reactor core, as well as flow through the complex network of internal structures in the upper core. Predicted temperature profiles were in good agreement with design targets. The third paper describes a two-stage study; the first compares predictions of RANS based models in resolving turbulent flow past the integral pressurizer, identifies the most suitable turbulence model, which is used in the second stage to simulate turbulent flow and heat transfer through both, pressurizer and steam generator units --Abstract, page iv

Characterisation of flow structures inside an engine cylinder under steady state condition

The in-cylinder flow of internal combustion (IC) engines, formed during the intake stroke, is one of the most important factors that affect the quality of air-fuel mixture and combustion. The inducted airflow through the inlet valve is primarily influenced by the intake port design, intake valve design, valve lift and valve timing. Such parameters have a significant influence on the generation and development of in-cylinder flow motion. In most combustion systems the swirl and tumble motions are used to aid the air-fuel mixing with the subsequent decay of these bulk flow motions generating increased turbulence levels which then enhance the combustion processes in terms of rate of chemical reactions and combustion stability. Air motion formed inside the engine cylinder is three-dimensional, transient, highly turbulent and includes a wide spectrum of length and time scales. The significance of in-cylinder flow structures is mainly reflected in large eddy formation and its subsequent break down into turbulence kinetic energy. Analysis of the large scale and flow motions within an internal combustion engine are of significance for the improvement of engine performance. A first approximation of these flow structures can be obtained by steady state analysis of the in-cylinder flow with fixed valve lifts and pressure drops. Substantial advances in both experimental methods and numerical simulations provide useful research tools for better understanding of the effects of rotational air motion on engine performance. This study presents results from experimental and numerical simulations of in-cylinder flow structures under steady state conditions. Although steady state flow problem still includes complex three-dimensional geometries with high turbulence intensities and rotation separation, it is significantly less complex than the transient problem. Therefore, preliminary verifications are usually performed on steady state flow rig. For example, numerical investigation under steady state condition can be considered as a precondition for the feasibility of calculations of real engine cylinder flow. Particle Image Velocimetry (PIV) technique is used in the experimental investigations of the in-cylinder flow structures. The experiments have been conducted on an engine head of a pent-roof type (Lotus) for a number of fixed valve lifts and different inlet valve configurations at two pressure drops, 250mm and 635mm of H2O that correlate with engine speeds of 2500 and 4000 RPM respectively. From the 2-D in-cylinder flow measurements, a tumbling vortex analysis is carried out for six planes parallel to the cylinder axis. In addition, a swirl flow analysis is carried out for one horizontal plane perpendicular to the cylinder axis at half bore downstream from the cylinder head (44mm). Numerically, modelling of the in-cylinder flow is proving to be a key part of successful combustion simulation. The numerical simulations require an accurate representation of turbulence and initial conditions. This Thesis deals with numerical investigation of the in-cylinder flow structures under steady state conditions utilizing the finite-volume CFD package, STAR CCM+. Two turbulence models were examined to simulate the turbulent flow structure namely, Realizable k-ε and Reynolds Stress Turbulence Model, RSM. Three densities of generated mesh, which is polyhedral type, are examined. The three-dimensional numerical investigation has been conducted on the same engine head of a pent-roof type (Lotus) for a number of fixed valve lifts and both valves are opened configuration at two pressure drops 250mm and 635mm of H2O that is equivalent to engine speeds of 2500 and 4000 RPM respectively. The nature and modelling of the flow structure together with discussions on the influence of the pressure drop and valve lift parameters on the flow structures are presented and discussed. The experimental results show the advantage of using the planar technique (PIV) for investigating the complete flow structures developed inside the cylinder. It also highlighted areas where improvements need to be made to enhance the quality of the collected data in the vertical plane measurements. Based on the comparison between the two turbulence models, the RSM model results show larger velocity values of about 15% to 47% than those of the Realizable k-ε model for the whole regions. The computational results were validated through qualitative and quantitative comparisons with the PIV data obtained from the current investigation and published LDA data on both horizontal and vertical cross sections. The calculated correlation coefficient, which is above 0.6, indicated that a reasonable prediction accuracy for the RSM model. This verifies that the numerical simulation with the RSM model is a useful tool to analyse turbulent flows in complex engine geometries where anisotropic turbulence is created

Experiments and simulation of shaped film cooling holes fed by crossflow with rib turbulators

Most studies of turbine airfoil film cooling in laboratories have used relatively large plenums to feed flow into the coolant holes. A more realistic inlet condition for the film cooling holes is an internal crossflow channel. In this study, angled rib turbulators were installed in two geometric configurations inside the internal crossflow channel, at 45° and 135°, to assess the impact on film cooling effectiveness. Film cooling hole inlets positioned in both pre-rib and post-rib locations tested the effect of hole inlet position relative to the rib turbulators. Experiments were performed varying channel velocity ratio and jet to mainstream velocity ratio. These results were compared to the film cooling performance of previously measured shaped holes fed by a smooth internal channel, as well as RANS simulations performed for select cases. The film cooling hole discharge coefficients and channel friction factors were measured for both rib configurations. Spatially-averaged film cooling effectiveness behaves similarly to holes fed by a smooth internal crossflow channel, but hole-to-hole variation due to the obstruction by the ribs was observed.Mechanical Engineerin

Experimental and computational determination of wind loads on netted/sheeted scaffolds.

This thesis describes an investigation into the wind loading on access scaffolds erected around a cubical building, clad by impermeable sheeting or permeable debris netting. The subject was investigated experimentally by tests in a wind-tunnel and theoretically using computational fluid dynamics techniques. The results were verified from the wind tunnel tests and computational analyses on the Silsoe Experimental Building (SEB) using data from the full-scale tests made in 1993-94 at Silsoe, U.K. The lower portion of the Atmospheric Boundary Layer exhibits different flow properties to the upper elevations. A procedure is presented for modelling the atmospheric surface layer flow properties in a boundary-layer wind-tunnel at useful model scales. The full-scale data available from the cubical 6m x 6m x 6m SEB was used to validate the results presented in this study. A model scale of 1:30 were used both for experiments in a wind-tunnel and in the computational analyses undertaken in the study. Pressure data obtained from the wind-tunnel experiments on the SEB model were compared to full-scale data with good agreement. These data were also compared with various computational fluid dynamics techniques available commercially and the conclusions drawn on the use of the different techniques. The wind-tunnel simulations on an SEB model and on a sheet/elevated sheet clad scaffold models were undertaken based on a duplication of the turbulence intensities and small-scale turbulence of the incidence flow. It is very difficult to achieve equality of Reynolds number in the wind-tunnel as it is very difficult to achieve exactly the same integral scales of turbulence. Two different types of terrain and inflow boundary conditions were simulated in the wind-tunnel for the models and results are reported here. Large suctions (separation of flows) occur near the leading edges and roof corners. The modelling of these phenomena in the wind-tunnel remains a problem. Because of the limited space near the corners and leading edges, it is difficult to make reliable measurements by introducing probes in these areas. This difficulty can be overcome by modelling the flow with Large Eddy Simulation (LES) numerical techniques. However, the disparity between the large and small scales, especially under extreme wind conditions, makes it extremely difficult to resolve the entire range of dynamic scales. The pressure force on bare pole access scaffolds are further influenced by the presence of the building façade which induces a shielding effect. A 2-D model of bare pole scaffolds surrounding the SEB using CFD techniques was successfully achieved whereas a 3-D model could not be produced because of the limitations of the meshing-software GAMBIT available to the author. Cladding increases the wind loads on scaffold structures above the pressure force on bare pole access scaffolds. To determine the wind forces on net/sheet clad scaffolds the Silsoe Experimental Building was used as a base model and simulated scaffolds erected around it. Although, sheeting/netting exhibits aero-elastic behaviour under wind load, an assumption was made to treat the cladding (sheeting/netting) surrounding the scaffold as being made of static solid thin plates. Models were tested in a wind-tunnel and the same assumptions were used in the computational fluid dynamics analyses. For the sheet clad scaffolds, two models were made, one with sheeting touching the ground and the other with an elevated sheet surrounding the building. These models were tested in a wind-tunnel to determine the pressure coefficients on the outer and inner faces of the sheeting. The permeability of the two types of net were successfully obtained from wind-tunnel tests. The simulated data from the wind-tunnel tests were used as input for different computational techniques with good agreement. A new procedure was developed to extend the computational model to net clad scaffolds (both elevated and touching the ground) with the netting simulated as porous media. The author presents new results of the pressure coefficients on sheeted scaffolds obtained using CFD and wind-tunnel techniques and also CFD results on netted scaffold structures. This thesis is the result of research undertaken to assess various methods available for the numerical simulation of turbulent fluid flow using the Fluent Software Package and to see their applicability in computational wind engineering. Investigations have concentrated on analysing the accuracy and numerical stability of a number of different turbulence models including both widely available models and state of the art techniques. Furthermore, Large Eddy Simulations using the dynamic kinetic energy sub-grid-scale model have been completed on some models, in order to account for the four dimensional nature of turbulent flow and to show the best correlation between wind-tunnel, full-scale and sheeted scaffolds. The author has detailed and tested all the above techniques and gives recommendations on the appropriate turbulence model to be used for successful computational wind engineering. Finally the author has given recommendations on the wind pressures to be used in analysing the scaffold structures

A Robust Conjugate Heat Transfer Methodology with Novel Turbulence Modeling Applied to Internally-Cooled Gas Turbine Airfoils

Computational fluid dynamics and heat transfer (CFD) has become a viable, physics-based analysis tool for complex flow and/or heat transfer problems in recent years due, in large part, to rapid advances in computing power. CFD based on the Reynolds-averaged Navier-Stokes (RANS) equations is starting to enter the mainstream design environment in certain industries where rapid and reliable predictive capability is necessary. One such application is the gas turbine industry, where thermal management of airfoils at extremely high temperatures is one of the most critical components in engine design for reliability. The problem is complicated by the need for advanced airfoil cooling techniques, which typically includes internal convection cooling. Current turbine aerothermal design practice involves separate simulations or empirical correlations for the airfoil external aerodynamics and heat transfer, the internal heat transfer, and conduction in the metal part. This approach is time-consuming and quite inefficient when design iterations are required, and accuracy is lost in the decoupling of the heat transfer modes. The physically-realistic approach is a single CFD simulation in which the convective heat transfer (fluid zones) and heat diffusion in the solid are fully coupled. This is known as the conjugate heat transfer (CHT) method, and it is ideally suited to the rigors of design. An obstacle to the adoption of the CHT method is difficulty in the accurate prediction of heat transfer coefficients on both external and internal surfaces, which is usually attributed to performance of the turbulence models used to close the RANS equations. The present study develops a comprehensive, \u27best-practice\u27 RANS-based conjugate heat transfer methodology for application to the aerothermal problem of an internally-cooled gas turbine airfoil at realistic operating conditions. With the design environment in mind, attention is given to high-quality mesh generation, efficient solution initialization, and solution-based adaption for grid-independence. Matching the conditions of the only experimental test case available in the literature, the simulations consist of a linear cascade of C3X vanes cooled by air flowing radially through ten smooth-walled cooling channels. Initially, popular \u27off-the-shelf\u27 k-e turbulence models are employed. Predictions for vane external surface temperature distribution at the midspan generally agree well with experimental data. The only exception is along a portion of the suction (convex) surface of the airfoil, where the predicted temperature is significantly greater than measured. This indicates an overprediction in the local heat transfer coefficient, and it corresponds to the region of strong curvature of the surface. In an effort to correct the excessive heat transfer coefficients predicted on the vane suction surface, a new eddy-viscosity-based turbulence model is developed to include correct sensitivity to the effects of streamline curvature (and, by analogy, system rotation). The novel feature of the model is the elimination of second derivatives in the formulation of the eddy-viscosity, making it much more robust than other curvature-sensitive models when implemented in general-purpose solvers with unstructured meshes. A new dynamic two-layer near-wall treatment is included for integration of the flow to the wall. The new model is proven to exhibit physically-accurate results in several fundamental test cases. When the C3X vane conjugate heat transfer simulation is revisited with the new model, the heat transfer coefficients in the region of strong convex curvature are correctly attenuated, and the wall temperature predictions are much closer to measurements. Cooling channels in many hot-section turbine airfoils have ribs machined on their walls to augment heat transfer, and they make multiple passes through the airfoil, meaning sharp turns are present. In order to extend the CHT methodology to these more complex internal cooling configurations, work is also conducted on the prediction of heat transfer in ribbed channels and in channel 180-deg-turns. In the two ribbed-channel cases studied, the use of steady simulations with popular turbulence models result in a significant underprediction of Nusselt numbers on the ribbed walls. Predictions improve significantly with unsteady (time-accurate) RANS simulations using another new in-house turbulence model, which is designed to promote and sustain small-scale unsteady motions. The results clearly show the importance of capturing the unsteady shear layer breakup into roller vortices aft of the ribs. In a simulation of a channel of square cross-section making a sharp 180-deg-turn, the new curvature-sensitive turbulence model gives Nusselt number predictions that are superior to existing k-e models. With the added capability to handle complex internal cooling configurations, the conjugate heat transfer methodology becomes a versatile gas turbine aerothermal design tool

Detailed Understanding of Flow, Heat Transfer, and Pressure Drop Behavior in a Square Channel With 45 Deg Ribs

Internal Duct Cooling (IDC) with rib turbulators is one of the common cooling techniques applied inside the turbine airfoils. It is very important for the gas turbine industry to design and develop an optimized cooling channel that maximizes the amount of heat removed, while simultaneously minimizing the pressure drop for a target overall cooling effectiveness. Angled ribs perform superior to the transverse ribs due to additional secondary flow associated with them. However, they result in a highly non-homogenous heat transfer distribution, which is a manifestation of the complex, turbulent flow field inside the channel. It is very important to comprehend the secondary flow physics to characterize the heat transfer distribution in such angled ribbed channels. Additionally, due to the manufacturing constraint, the gas turbine industry encounters a challenge to make ribs edge sharp and results in ribs with rounded edges. The one of the main objectives of the present study is to provide a fundamental understanding of the flow physics on the heat transfer and pressure drop behavior in 45° ribbed channels both with sharp and rounded-edge ribs. It is found that the secondary flow has a significant effect on the heat transfer behavior for both types of ribs. There is a great need of high-fidelity PIV flow field data in the inter-rib space for an angled ribbed channel which can be used for CFD validation, especially for LES. The current study provides benchmarking flow field data in the inter-rib space in a square channel with 45° ribs using stereoscopic PIV technique. Besides the experiments, numerical studies were also conducted by using LES and different RANS models. The LES results show an excellent prediction capability for aerothermal behavior in such channels. However, the prediction capability of RANS models is found to be inconsistent for different rib configurations and flow conditions

Development of Novel Passive Control Techniques for More Uniform Temperature at Combustor Exit and Hybrid Les/Rans Modeling

Gas turbines have become an important, widespread, and reliable device in the field of power generation. For any gas turbine system, the combustor is an integral part responsible for the combustion of the fuel. A number of studies have shown that the flow field exiting a combustor is highly non-uniform in pressure, velocity and, most importantly, temperature. Hot streaks amongst other non-uniformities cause varying thermal stresses on turbine blades and put pressure on the blade materials. In particular, these non-uniformities can have detrimental effects on the performance of the engine and cause a reduction in the expected life of critical components such as the turbine vanes. Due to the importance and severity of the problem, a large portion of the total combustor development effort is devoted to achieving better temperature uniformity. The present work is another attempt to develop novel passive control techniques to enhance mixing in a facility simulating the dilution zone of a typical gas turbine combustor and produce more uniform temperature at the combustor exit. Extensive experimentation was conducted to compare the proposed dilution techniques - staggered dilution holes, staggered dilution holes with streamlined body and staggered dilution holes with guide vanes at various orientations (0°, 30°, 60° and 90°). A weighted parameter was defined called `uniformity factor (\u27χ^\u27 ) to compare how close the mixture fraction is to the equilibrium value. For the majority of the flow conditions tested, the 30° guide vanes gave the most uniform temperature flow with just about 2% higher pressure loss as compared to the staggered dilution holes geometry. The fact that the use of 30° guide vanes can provide the turbine blade with 15% more uniform temperature flow than the staggered dilution holes design with merely 2% more pressure drop, has a very important implementation in order to reduce the damage of the turbine blades due to non-uniform temperature flow and extend its life-span. This would result in an overall reduction in the maintenance cost of the gas turbine systems which is quite significant. Furthermore, it was found that the introduction of the streamlined body not only improved the mixing in some cases but also helped decrease the pressure drop from inlet to exit of the experimental set-up. This is expected to increase the overall system efficiency and decrease the operating cost of a gas turbine system. Additionally, numerical modeling was used for various parametric studies to explore the effect of jet-to-mainstream momentum flux ratio on the exit temperature uniformity, variation of the cooling rate within the dilution zone, exergy analysis, etc. The other significant part of this work comprised of development of an Algebraic Stress Model (ASM) in order to estimate the turbulence via Reynolds stresses prediction. The ASM model developed is validated for a simple two-dimensional turbulent flow over a flat plate and a complex three dimensional flow around Ahmed body. The developed model is capable of predicting Reynolds stresses for a variety of flow regimes. Based on these validation it can be concluded that adopting a hybrid approach which combines the advantages of the ASM model with other turbulence models can be sought after for a more in-depth analysis of the flow structures and turbulent quantities both near-wall and away from the boundary for any fluid flow problem. The accurate prediction of the turbulent quantities plays a significant role in not just the fluid motion/transfer phenomenon rather it governs the heat exchange process as well especially in regions close to the wall