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Improved understanding of solid surface energy and its role in the overall mechanical properties is of great interest due to the emerging manufacturing techniques of nanostructures, coatings, and synthetic/biological bilayer-polymer hybrids. Continuum numerical modeling of surface stresses efficiently incorporates a zero-thickness membrane bonded to a bulk, intrinsically accounting for surface tension and surface elasticity. Compressive surface stresses are not possible in a purely membrane formulation, ignoring the surface flexural resistance. The extension of material surfaces to account for flexural resistance, i.e., the Steigmann–Ogden model, requires spatial derivatives of second order, posing significant challenges to standard discretization techniques. Hence, the effect of surface curvature resistance on the overall mechanical behavior of complex geometries remains elusive. Here, we develop a three-dimensional computational formulation of curvature-dependent surface energetics at finite strains using surface-enriched isogeometric analysis. Coupled with a hyperelastic bulk, bending-resistance of material surfaces furnishes a new physical length scale, i.e., the elastobending length. We quantify the effect of elastobending deformations for several numerical examples involving soft materials with thin coatings and liquid-shell surfaces, capturing budding-like behavior observed at cell membranes. Our results demonstrate a stiffer overall mechanical behavior when material surfaces resist bending deformations and illustrate how curvature effects lead to complex budding deformations at non-zero initial curvature states. The proposed methodology provides a robust computational foundation to help improve our understanding and mechanical characterization of soft solids, nanostructures, and biological membranes at small scales.

Improved understanding of solid surface energy and its role in the overall mechanical properties is of great interest due to the emerging manufacturing techniques of nanostructures, coatings, and synthetic/biological bilayer-polymer hybrids. Continuum numerical modeling of surface stresses efficiently incorporates a zero-thickness membrane bonded to a bulk, intrinsically accounting for surface tension and surface elasticity. Compressive surface stresses are not possible in a purely membrane formulation, ignoring the surface flexural resistance. The extension of material surfaces to account for flexural resistance, i.e., the Steigmann–Ogden model, requires spatial derivatives of second order, posing significant challenges to standard discretization techniques. Hence, the effect of surface curvature resistance on the overall mechanical behavior of complex geometries remains elusive. Here, we develop a three-dimensional computational formulation of curvature-dependent surface energetics at finite strains using surface-enriched isogeometric analysis. Coupled with a hyperelastic bulk, bending-resistance of material surfaces furnishes a new physical length scale, i.e., the elastobending length. We quantify the effect of elastobending deformations for several numerical examples involving soft materials with thin coatings and liquid-shell surfaces, capturing budding-like behavior observed at cell membranes. Our results demonstrate a stiffer overall mechanical behavior when material surfaces resist bending deformations and illustrate how curvature effects lead to complex budding deformations at non-zero initial curvature states. The proposed methodology provides a robust computational foundation to help improve our understanding and mechanical characterization of soft solids, nanostructures, and biological membranes at small scales.

Two sets of experiments were performed on a simulated turbine nozzle guide vane. First, adiabatic and overall effectiveness measurements were taken in the showerhead region of the vane using adiabatic and matched Biot vane models, respectively. Measurements of overall effectiveness in the showerhead region are not found in the literature, and are a useful baseline for validating the results of computational fluid dynamics (CFD) simulations. Overall effectiveness is useful because it shows the results of combining film cooling, internal convection, and surface conduction to provide a more complete picture of vane cooling than adiabatic effectiveness. An impingement plate was utilized to generate internal jet cooling. Momentum flux ratios were matched between the models and ranged from I*SH = 0.76 to 6.70, based on showerhead upstream approach velocity. The second set of experiments used a different model to examine the effects of surface curvature on adiabatic effectiveness. Results in open literature are found by varying the radius of curvature of a fixed setup, so the current approach was novel in that it looked at adiabatic effectiveness at locations of various curvature around the same vane. Blowing ratios from M = 0.4 to M = 1.6 were tested at a density ratio of DR = 1.20 for two locations on the suction side of the vane. Results were presented in terms of laterally averaged adiabatic effectiveness and contour plots of adiabatic effectiveness, and were compared to literature.

Two sets of experiments were performed on a simulated turbine nozzle guide vane. First, adiabatic and overall effectiveness measurements were taken in the showerhead region of the vane using adiabatic and matched Biot vane models, respectively. Measurements of overall effectiveness in the showerhead region are not found in the literature, and are a useful baseline for validating the results of computational fluid dynamics (CFD) simulations. Overall effectiveness is useful because it shows the results of combining film cooling, internal convection, and surface conduction to provide a more complete picture of vane cooling than adiabatic effectiveness. An impingement plate was utilized to generate internal jet cooling. Momentum flux ratios were matched between the models and ranged from I*SH = 0.76 to 6.70, based on showerhead upstream approach velocity. The second set of experiments used a different model to examine the effects of surface curvature on adiabatic effectiveness. Results in open literature are found by varying the radius of curvature of a fixed setup, so the current approach was novel in that it looked at adiabatic effectiveness at locations of various curvature around the same vane. Blowing ratios from M = 0.4 to M = 1.6 were tested at a density ratio of DR = 1.20 for two locations on the suction side of the vane. Results were presented in terms of laterally averaged adiabatic effectiveness and contour plots of adiabatic effectiveness, and were compared to literature.

This study performed detailed measurements on and around scaled up conducting and adiabatic airfoils with and without film cooling. The conducting vane was a matched Bi airfoil, which accurately scaled the convective heat transfer and conduction through the solid, in order to produce non-dimensional surface temperatures and thermal boundary layers that were representative of an actual engine. Measurements made on all vane models included surface temperature measurements and thermal profiles above the walls. Separate measurements on non-film cooled and film cooled conducting models allowed for the individual contributions of the internal convective cooling and external film cooling to the overall cooling scheme to be quantified. Surface temperature and thermal field measurements above the wall were also performed on a film cooled adiabatic model. For the conducting model with internal cooling only, strong streamwise temperature variations were seen. The surface temperature variations were highly dependent on the local external and internal heat transfer coefficients. Spanwise temperature variations also existed, but were modest in comparison to streamwise variations. Comparing the thermal fields above the film cooled adiabatic and conducting walls allowed for the assumption that the conducting wall would not significantly affect the thermal field in the film cooling jet to be tested. Near the edge of the film cooling jet the developing thermal boundary layer had a clear effect on the overlying gas temperature, suggesting that the common assumption that the adiabatic wall temperature is the appropriate driving temperature for heat transfer to a film cooled wall was invalid. On the jet centerline thermal boundary layer effects were less influential, due to the development of a new, thin boundary layer. This suggested that the adiabatic wall temperature as driving temperature for heat transfer was a reasonable assumption on the jet centerline for most cases tested. As film cooling momentum flux ratio increase, thermal boundary layer effects became more influential on the jet centerline. Additionally, the high resolution surface temperature measurements and thermal field measurements above the wall presented in the current study represent a significant improvement in the data available for validation of computational simulations of conducting turbine airfoils.

This study performed detailed measurements on and around scaled up conducting and adiabatic airfoils with and without film cooling. The conducting vane was a matched Bi airfoil, which accurately scaled the convective heat transfer and conduction through the solid, in order to produce non-dimensional surface temperatures and thermal boundary layers that were representative of an actual engine. Measurements made on all vane models included surface temperature measurements and thermal profiles above the walls. Separate measurements on non-film cooled and film cooled conducting models allowed for the individual contributions of the internal convective cooling and external film cooling to the overall cooling scheme to be quantified. Surface temperature and thermal field measurements above the wall were also performed on a film cooled adiabatic model. For the conducting model with internal cooling only, strong streamwise temperature variations were seen. The surface temperature variations were highly dependent on the local external and internal heat transfer coefficients. Spanwise temperature variations also existed, but were modest in comparison to streamwise variations. Comparing the thermal fields above the film cooled adiabatic and conducting walls allowed for the assumption that the conducting wall would not significantly affect the thermal field in the film cooling jet to be tested. Near the edge of the film cooling jet the developing thermal boundary layer had a clear effect on the overlying gas temperature, suggesting that the common assumption that the adiabatic wall temperature is the appropriate driving temperature for heat transfer to a film cooled wall was invalid. On the jet centerline thermal boundary layer effects were less influential, due to the development of a new, thin boundary layer. This suggested that the adiabatic wall temperature as driving temperature for heat transfer was a reasonable assumption on the jet centerline for most cases tested. As film cooling momentum flux ratio increase, thermal boundary layer effects became more influential on the jet centerline. Additionally, the high resolution surface temperature measurements and thermal field measurements above the wall presented in the current study represent a significant improvement in the data available for validation of computational simulations of conducting turbine airfoils.

This thesis presents a new system that reconstructs the 3D representation of dental casts. To maintain the integrity of the 3D representation, a standard model is built to cover the blind spots that the camera cannot reach. The standard model is obtained by scanning a real human mouth model with a laser scanner. Then the model is simplified by an algorithm which is based on iterative contraction of vertex pairs. The simplified standard model uses a local parametrization method to obtain the curvature information. The system uses a digital camera and a square tube mirror in front of the camera to capture multi-view images. The mirror is made of stainless steel in order to avoid double reflections. The reflected areas of the image are considered as images taken by the virtual cameras. Only one camera calibration is needed since the virtual cameras have the same intrinsic parameters as the real camera. Depth is computed by a simple and accurate geometry based method once the corresponding points are identified. Correspondences are selected using a feature point based stereo matching process, including fast normalized cross-correlation and simulated annealing.