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Theory describes behavior of eccentric and angularly-misalined incompressible-fluid shaft seals. Direct and cross-coupled stiffness and damping coefficients expressed in terms of degree of eccentricity and coefficients of concentric system.
Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.
Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the Space Shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modelling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.
The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.
Fuel injection and turbulent mixing at supercritical pressures determines ignition and combustion in numerous engineering applications. Flow evolution under such conditions is characterized by strong non-linear coupling between dynamics, transport coefficients, and thermodynamics. Experimental studies observe that the jets injected at supercritical pressures exhibit significantly different dynamics from the jets at subcritical conditions, owing to the lack of distinct liquid and gas phases in supercritical state. Thus, the averaged flow quantities such as the potential core length, jet spatial growth rate and velocity decay profiles differ in the two conditions, resulting in different mixed-fluid distributions. In this study, turbulent jet direct numerical simulations (DNS) are performed to examine the variations in flow statistics between injection of Nitrogen (N₂) in Nitrogen (N₂) at both subcritical (perfect-gas) and supercritical conditions. In all cases, isothermal round jets at Reynolds number (Re_{D}), based on jet diameter (D) and jet orifice velocity (U₀), of 5000 are considered. For mixing analyses, a passive scalar transported with the flow is examined.
A predictive, self-consistent integrated model of the tokamak edge plasma and neutral system has been developed and validated against experimental data from DIII-D, spanning from the divertor target and scrape-off layer to the top of the pedestal. The model uses the SOLPS-ITER fluid boundary plasma and neutral code to constrain the EPED prediction of the pedestal height and width by taking the separatrix temperature and density calculated from SOLPS as inputs to EPED. An empirical proxy function based on data from a subset of these discharges is then used to infer the ratio of density at the pedestal top to that at the separatrix based on the electron temperature at the divertor target. This allows the density at the top of the pedestal to be provided to EPED as well, so that knowledge of this quantity is no longer required a priori, while SOLPS radial transport coefficients are needed instead. The gas puff rate provided to SOLPS is then a primary model input for this forward model coupling (along with radial transport coefficients, which are kept fixed through each scan in this study). Comparisons with measurements from DIII-D density scans through a range of target conditions find significant pedestal pressure degradation as the density is increased towards detachment in three different divertor configurations, consistent with the experimental data in these ballooning-limited pedestal regimes.
Radiationless K-LL transition probabilities have been calculated nonrelativistically in j-j coupling and in intermediate coupling, without and with configuration interaction, for elements with atomic numbers from 13 to 47. The system is treated as a coupled two-hole configuration. The single-particle radial wave functions required in the calculation of radial matrix elements, and in the calculation of mixing coefficients in the intermediate-coupling scheme, were obtained from Green's atomic independent-particle model. Comparison with previous theoretical work and with experimental data is made. The effects of intermediate coupling, configuration interaction, and relativity are noted.
Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.
Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results of this study are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.
The dissociation and recombination of H2 over the temperature range 1000-5000 K are calculated in a nonempirical manner. The computation procedure involves the calculation of the state-to-state energy transfer rate coefficients, the solution of the 349 coupled equations which form the master equation, and the determination of the phenomenological rate coefficients. The nonempirical results presented here are in good agreement with experimental data at 1000 and 3000 K.
Dropwise condensation of steam on hydrophobic substrates has a 10X higher heat transfer coefficient compared to filmwise condensation. To promote dropwise condensation, low surface energy hydrophobic coatings (polymers) are typically utilized. The low intrinsic thermal conductivity (k < 1 W/(m · K)) of polymers, coupled with high heat transfer coefficient of dropwise condensation (100 kW/(m 2 · K)), necessitates that the coating be thin (< 1µm) in order to avoid reducing the overall heat exchanger conductance. However, thin polymeric films easily degrade. The two opposing requirements result in the need for optimization between the durability (thick coating) and the heat transfer (thin coating). To enable high thermal conductivity in thicker coatings, we develop metal-polymer structured surfaces. By using porous structures as inter-connected heat-conducting backbones that are filled with hydrophobic materials, we enable tuning of the coating effective thermal conductivity and surface energy. Three metal structures were studied; micro/nanowires, inverse opals, and sintered spheres. Heat transfer performance was calculated using three-dimensional finite element method simulations with two distinct boundary conditions; convection at the walls and isothermal walls. Interestingly, the overall conductance shows up to 40% difference depending on the boundary condition used in calculating the composite coating effective thermal conductivity. We use our model to predict the heat transfer performance as a function of metal fraction by volume and by surface area for condensation. By coupling our thermal simulations with a previously verified analytical model for predicting wetting behavior on heterogeneous surfaces, we propose a regime map to predict dropwise-to-filmwise transition. Furthermore, our work not only forms a starting point for the development of durable dropwise condensing surfaces, it identifies important considerations needed for computing effective thermal conductivity of composites.
The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute entropic order parameters in weakly coupled gauge theories. To perform this computation, the natural route of evaluating expectation values of physical (smeared) non-local operators is prevented by known difficulties in constructing suitable smeared Wilson loops. We circumvent this problem by studying the smeared non-local class operators in the enlarged non-gauge invariant Hilbert space. This provides a generic approach for smeared operators in gauge theories and explicit formulas at weak coupling. In this approach, the Wilson and ’t Hooft loops are labeled by the full weight and co-weight lattices respectively. We study generic Lie groups and discuss couplings with matter fields. Smeared magnetic operators, as opposed to the usual infinitely thin ones, have expectation values that approach one at weak coupling. The corresponding entropic order parameter saturates to its maximum topological value, except for an exponentially small correction, which we compute. On the other hand, smeared ’t Hooft loops and their entropic disorder parameter are exponentially small. We verify that both behaviors match the certainty relation for the relative entropies. In particular, we find upper and lower bounds (that differ by a factor of 2) for the exact coefficient of the linear perimeter law for thin loops at weak coupling. This coefficient is unphysical/non-universal for line operators. We end with some comments regarding the RG flows of entropic parameters through perturbative beta functions.
A test program developed for dynamic testing of straight and convergent-tapered seals, with the capability of separately determining both direct and cross-coupled stiffness, damping, and added mass coefficients is described. The test apparatus causes the seal journal to execute small-eccentricity centered circular orbits within its bearings. Dynamic measurements are made and recorded of the seal-displacement-vector components, and of the pressure field. The pressure field is integrated to yield seal reaction force components. The displacement and force vector components are analyzed via a generalized Newton-Raphson procedure to yield the desired seal dynamic coefficients. Representative test data are provided and discussed.
HPOTP and HPFTP vibration test results have exhibited transient and steady characteristics which may be due to impeller leakage path (ILP) related forces. For example, an axial shift in the rotor could suddenly change the ILP clearances and lengths yielding dynamic coefficient and subsequent vibration changes. ILP models are more complicated than conventional-single component-annular seal models due to their radial flow component (coriolis and centrifugal acceleration), complex geometry (axial/radial clearance coupling), internal boundary (transition) flow conditions between mechanical components along the ILP and longer length, requiring moment as well as force coefficients. Flow coupling between mechanical components results from mass and energy conservation applied at their interfaces. Typical components along the ILP include an inlet seal, curved shroud, and an exit seal, which may be a stepped labyrinth type. Von Pragenau (MSFC) has modeled labyrinth seals as a series of plain annular seals for leakage and dynamic coefficient prediction. These multi-tooth components increase the total number of 'flow coupled' components in the ILP. Childs developed an analysis for an ILP consisting of a single, constant clearance shroud with an exit seal represented by a lumped flow-loss coefficient. This same geometry was later extended to include compressible flow. The objective of the current work is to: supply ILP leakage-force impedance-dynamic coefficient modeling software to MSFC engineers, base on incompressible/compressible bulk flow theory; design the software to model a generic geometry ILP described by a series of components lying along an arbitrarily directed path; validate the software by comparison to available test data, CFD and bulk models; and develop a hybrid CFD-bulk flow model of an ILP to improve modeling accuracy within practical run time constraints.
A method is presented for formulating stiffness terms and thermal coefficients of stiffened, fiber-reinforced composite panels. The method is robust enough to handle panels with general cross sectional shapes, including those which are unsymmetric and/or unbalanced. Nonlinear, temperature and load dependent constitutive material data of each laminate are used to 'build-up' the stiffened panel membrane, bending, and membrane-bending coupling stiffness terms and thermal coefficients. New thermal coefficients are introduced to quantify panel response from through-the-thickness temperature gradients. A technique of implementing this capability with a single plane of shell finite elements using the MSC/NASTRAN analysis program (FEA) is revealed that provides accurate solutions of entire airframes or engines with coarsely meshed models. An example of a composite, hat-stiffened panel is included to demonstrate errors that occur when an unsymmetric panel is symmetrically formulated as traditionally done. The erroneous results and the correct ones produced from this method are compared to analysis from discretely meshed three-dimensional FEA.
Multiferroic composites consisting of a single-phase multiferroic [0.6(PbZr 0.53 Ti 0.47 O 3 )-0.4(PbFe 0.5 Ta 0.5 )O 3 ] as a matrix and a magnetostrictive phase (Co 0.6 Zn 0.4 Fe 1.7 Mn 0.3 O 4 ) dispersed in the matrix are fabricated via hybrid synthesis technique. The structure and surface morphology studies using x-ray diffraction and field emission scanning electron microscopy techniques indicate the formation of 3-0 type particulate composites. Coexistence of soft-magnetic behavior and ferroelectric characteristics are confirmed for composites from magnetization vs magnetic field (M–H) and polarization vs electric field (P–E) measurements, respectively. Magneto-dielectric (MD) measurement shows significant changes in the dielectric properties with the application of a magnetic field, indicating the existence of strong MD behavior. The biquadratic nature of magneto-electric (ME) coupling is described by the Landau free energy equation arising from the strain transfer at the interfaces between the constituent phases. The direct magneto-electric voltage coefficient measurement also confirms very strong coupling between ferroelectricity and magnetism and supports the strain-mediated magneto-electric effect in composites. The Φ = 0.3 composite exhibits the maximum ME coefficient of 20.72 mV/cm Oe with M S = 24.62 emu/g, H C = 59.66 Oe, and piezoelectric coefficient value d 33 = 19 pC/N. In conclusion, the strong magneto-electric effect along with low dielectric loss at room temperature in these composites suggests their suitability for multifunctional magneto-electric device applications such as magnetic sensors, etc.
Preliminary sizing of an oscillating surge wave energy converter (OSWEC) is an iterative process that relies on knowledge of the relevant hydrodynamic coefficients for a given geometry. Often, the complex definition of the device geometry requires coefficients to be obtained through experiments or numerical boundary element solvers such as WAMIT. These techniques demand significant user and computational effort, therefore inhibiting the fine scale parametrization of object dimensions. In this study, a theoretical model, originally presented in Michele et al. (2016), is developed and demonstrated to efficiently optimize the power production for an OSWEC device (subjected to certain environmental conditions) with variations in device widths, heights, and distances from the seabed. Assuming negligible device thickness, the OSWEC motions are modelled as a bottom-raised two-dimensional flap in regular waves using potential flow theory formulated in elliptical coordinates. The solutions to this diffraction-radiation problem are obtained using Mathieu functions with appropriate boundary conditions. The resulting potentials are then used to derive frequency-dependent expressions for the added mass and radiation damping coefficients, along with wave excitation magnitude in surge, pitch, and coupled surge-pitch motions. Good agreement in hydrodynamic coefficient curves is shown between the theoretical model and the numerical results obtained from the boundary element-based program WAMIT. The theoretical model is then employed to maximize the time-averaged output power while maintaining or reducing the hinge reaction force, with variations in device dimensions, wave frequency and amplitude.
Preliminary sizing of an oscillating surge wave energy converter (OSWEC) is an iterative process that relies on knowledge of the relevant hydrodynamic coefficients for a given geometry. Often, the complex definition of the device geometry requires coefficients to be obtained through experiments or numerical boundary element solvers such as WAMIT. These techniques demand significant user and computational effort, therefore inhibiting the fine scale parametrization of object dimensions. In this study, a theoretical model, originally presented in Michele et al. (2016), is developed and demonstrated to efficiently optimize the power production for an OSWEC device (subjected to certain environmental conditions) with variations in device widths, heights, and distances from the seabed. Assuming negligible device thickness, the OSWEC motions are modelled as a bottom-raised two-dimensional flap in regular waves using potential flow theory formulated in elliptical coordinates. The solutions to this diffraction-radiation problem are obtained using Mathieu functions with appropriate boundary conditions. The resulting potentials are then used to derive frequency-dependent expressions for the added mass and radiation damping coefficients, along with wave excitation magnitude in surge, pitch, and coupled surge-pitch motions. Good agreement in hydrodynamic coefficient curves is shown between the theoretical model and the numerical results obtained from the boundary element-based program WAMIT. The theoretical model is then employed to maximize the time-averaged output power while maintaining or reducing the hinge reaction force, with variations in device dimensions, wave frequency and amplitude.