A Computational Study on the Leakage of Supercritical Carbon Dioxide through Labyrinth Seals

To meet future energy needs the use of alternative fuel sources are gaining popularity. The supercritical carbon dioxide Brayton cycle has been proposed as a possible cycle for next generation nuclear and concentrated solar power generation. Large density fluctuations of carbon dioxide in the supercritical region can be exploited to maintain compressor inlet conditions close to the critical point and thereby, reducing the compressor work and the back work ratio. In order to improve the efficiency of turbomachinery equipment it is important to reduce internal leakage through seals. A computational study was performed to understand the leakage through seals subject to large pressure differential using Open source CFD software OpenFOAM. FIT (Fluid Property Interpolation Tables) program is implemented in OpenFOAM to accurately model the properties of CO_(2) required to solve the governing equations. To predict flow behavior in the two phase dome HEM (Homogeneous equilibrium model) is assumed to be valid. Effects of geometrical parameters and operating conditions are isolated from each other and a parametric study was performed in two parts to understand the effects of both geometrical parameters and operating conditions. Results of the geometrical parameter study indicated that the carryover coefficient of a seal is independent of pressure drop across the seal and is only a function of geometry. A model for carryover was developed as a function of c/s (clearance to pitch ratio) and w_(cavity)/c (cavity width to clearance). It has been identified that the major non-dimensional parameter influencing the discharge through an annular orifice is w_(tooth)/c (tooth width to clearance) and a model for Cd (discharge coefficient) can be developed based on the results we obtained. Flow through labyrinth seals can be considered as a series of annular orifices and cavities. Using this analogy, leakage rate equations can be written for each tooth and the mass flow rate can be modeled as a function of the discharge coefficient under each tooth and the carryover coefficient, which accounts for the turbulent dissipation of kinetic energy in a cavity. The discharge coefficient of first tooth in a labyrinth seal is similar to that of an annular orifice, whereas, the discharge coefficient of the rest of the tooth was found to be a function of the C_(d) of the previous tooth and the carryover coefficient. To understand the effects of operating conditions, a 1-D isentropic choking model is developed for annular orifices resulting in upper and lower limit curves on a T-s diagram which show the choking phenomenon of flow through a seal. This model was applied to simulations performed on both an annular orifice and a labyrinth seal. It has been observed that the theory is, in general, valid for any labyrinth seal, but the upper and lower limit curves on a T-s diagram depend on number of constrictions. As the number of constrictions increases these two curves move farther away from the critical point. Finally, some experimental results for a plain orifice (L/D ~ 5) were used to show the capabilities of the FIT model implemented in OpenFOAM. Error analysis indicated that OpenFOAM is capable of predicting experimental data within a 10 % error with the majority of data close to a 5 % error. This validates the FIT model and HEM assumption

Comparing Monofractal and Multifractal Analysis of Corrosion Damage Evolution in Reinforcing Bars

Based on fractal theory and damage mechanics, the aim of this paper is to describe the monofractal and multifractal characteristics of corrosion morphology and develop a new approach to characterize the nonuniform corrosion degree of reinforcing bars. The relationship between fractal parameters and tensile strength of reinforcing bars are discussed. The results showed that corrosion mass loss ratio of a bar cannot accurately reflect the damage degree of the bar. The corrosion morphology of reinforcing bars exhibits both monofractal and multifractal features. The fractal dimension and the tensile strength of corroded steel bars exhibit a power function relationship, while the width of multifractal spectrum and tensile strength of corroded steel bars exhibit a linear relationship. By comparison, using width of multifractal spectrum as multifractal damage variable not only reflects the distribution of corrosion damage in reinforcing bars, but also reveals the influence of nonuniform corrosion on the mechanical properties of reinforcing bars. The present research provides a new approach for the establishment of corrosion damage constitutive models of reinforcing bars

A Model for the Ultrastructure of Bone Based on Electron Microscopy of Ion-Milled Sections

The relationship between the mineral component of bone and associated collagen has been a matter of continued dispute. We use transmission electron microscopy (TEM) of cryogenically ion milled sections of fully-mineralized cortical bone to study the spatial and topological relationship between mineral and collagen. We observe that hydroxyapatite (HA) occurs largely as elongated plate-like structures which are external to and oriented parallel to the collagen fibrils. Dark field images suggest that the structures (“mineral structures”) are polycrystalline. They are approximately 5 nm thick, 70 nm wide and several hundred nm long. Using energy-dispersive X-ray analysis we show that approximately 70% of the HA occurs as mineral structures external to the fibrils. The remainder is found constrained to the gap zones. Comparative studies of other species suggest that this structural motif is ubiquitous in all vertebrates

The Influence of Mineralization on Intratrabecular Stress and Strain Distribution in Developing Trabecular Bone

The load-transfer pathway in trabecular bone is largely determined by its architecture. However, the influence of variations in mineralization is not known. The goal of this study was to examine the influence of inhomogeneously distributed degrees of mineralization (DMB) on intratrabecular stresses and strains. Cubic mandibular condylar bone specimens from fetal and newborn pigs were used. Finite element models were constructed, in which the element tissue moduli were scaled to the local DMB. Disregarding the observed distribution of mineralization was associated with an overestimation of average equivalent strain and underestimation of von Mises equivalent stress. From the surface of trabecular elements towards their core the strain decreased irrespective of tissue stiffness distribution. This indicates that the trabecular elements were bent during the compression experiment. Inhomogeneously distributed tissue stiffness resulted in a low stress at the surface that increased towards the core. In contrast, disregarding this tissue stiffness distribution resulted in high stress at the surface which decreased towards the core. It was concluded that the increased DMB, together with concurring alterations in architecture, during development leads to a structure which is able to resist increasing loads without an increase in average deformation, which may lead to damage

Heat transfer and fluid flow characteristics of supercritical carbon dioxide flow

The goal of this dissertation is to enhance the fundamental understanding of heat transfer phenomenon of sCO2 especially near the critical point and to investigate the thermal-hydraulic characteristics of printed circuit heat exchangers used in supercritical CO2 power cycles. To achieve these goals an experimental test facility was constructed to investigate the heat transfer and pressure drop characteristics of supercritical CO2 (sCO2) flow inside circular tubes and prototypic printed circuit heat exchangers. To achieve the first goal of the dissertation, the test facility was used to investigate the effect of variable fluid properties on the sCO2 flow inside heated circular tubes. Two circular tube test sections with inner diameters of 10.9 and 7.9 mm were selected for investigation. Wall temperatures and heat transfer coefficients were measured for a wide range of operating conditions by varying the fluid inlet temperature, mass flux, heat flux and system pressure. Three different test section orientations - horizontal, upward and downward flows were tested to investigate the effect of buoyancy on the heat transfer. Separate set of correlations are proposed for the horizontal, upward and downward flow test data. To achieve the second goal of the dissertation, the thermal-hydraulic characteristics of two discontinuous fin printed circuit heat exchangers (PCHEs) with offset rectangular and offset NACA0020 airfoil fin patterns were evaluated experimentally. The pressure drops and the heat transfer coefficients for both the PCHEs were measured over a wide range of conditions with Reynolds numbers in the range of 2,700-38,000 and Prandtl numbers in the range of 0.8-25. Based on the experimental data, friction factor and Nusselt number correlations were developed for both the PCHE test sections. Using the developed correlations, the impact of the tested discontinuous fin printed circuit heat exchangers (PCHEs) on the performance and the capital cost of supercritical CO2 Brayton cycle was investigated. A simulation model was developed for supercritical CO2 Brayton cycle and optimal flow regimes for several PCHEs were identified. The offset rectangular fin PCHE offered highest cycle efficiency and lowest capital cost (on $/KWe basis) followed by S-shaped fin, zigzag channel and the offset NACA0020 airfoil fin PCHEs.Ph.D