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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Boundary perturbation method for free boundary problem in convectively cooled continuous casting

Novel mathematical techniques are here used to treat general boundary conditions in convectively cooled continuous ingot casting problems, applying a constant convective heat transfer coefficient at the ingot sides (so that the temperature distribution along the sides is unknown). The problem is first inverted to treat the physical coordinates as dependent variables of temperature and heat flow, mapping the ingot into a region that is nearly rectangular. A boundary perturbation method is then used to obtain an analytical solution in this near-rectangular region. Solidification interface shapes depend on two dimensionless parameters: one is a function of the casting velocity, while the other is dependent on the convective heat transfer coefficient at the cooled wall.

Siegel, R.↗
NASA NTRS1993

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗
NASA NTRS1991

Second order modeling of boundary-free turbulent shear flows

A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.

Shih, T.-H.↗
NASA NTRS1991

Second order modeling of boundary-free turbulent shear flows

A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.

Shih, T.-H.↗
NASA NTRS1986

Free boundary shape of a convectively cooled solidified region

The two-dimensional steady-state shape of a solidified region, such as a frost layer, was determined analytically for formation on a plate that is convectively cooled. The nonuniform shape of the layer is produced by exposure to a spatially nonuniform distribution of radiant energy. For high convective cooling the cooled wall approaches a uniform temperature, and an exact solution is obtained for the free boundary shape. For a lesser amount of convective cooling, the variation in temperature along the cooled boundary is treated by a boundary perturbation method. Some illustrative examples are given that show the effects of nonuniform heating and the magnitude of convective heat transfer at the cooled wall. Only one boundary condition is approximated by the perturbation solution; all of the other boundary conditions are satisfied exactly. The calculated results given here were found to satisfy the approximate boundary condition within a very small error.

Siegel, R.↗
NASA NTRS1986

Temperature and velocity profiles in sooting free boundary layer flames

Temperature and velocity profiles are presented for cyclohexane, n-heptane, and iso-octane free, laminar, boundary layer, sooting, diffusion flames. Temperatures are measured with 3 mil Pt/Pt-13 percent Rh thermocouples. Corrected gas temperatures are derived by performing an energy balance of convection to and radiation from the thermocouple bead incorporating the variation of air conductivity and platinum emissivity with temperature. Velocities are measured using laser doppler velocimetry techniques. Profiles are compared with previously reported analytic temperature and velocity fields. Comparison of theoretical and experimental temperature profiles suggests improvement in the analytical treatment is needed, which accounts more accurately for the local soot radiation. The velocity profiles are in good agreement, with the departure of the theory from observation partially due to the small fluctuations inherent in these free flows.

Ang, J. A.↗
NASA NTRS1992

Lumley's energy cascade dissipation rate model for boundary-free turbulent shear flows

True dissipation occurs mainly at the highest wavenumbers where the eddy sizes are comparatively small. These high wavenumbers receive their energy through the spectral cascade of energy starting with the largest eddies spilling energy into the smaller eddies, passing through each wavenumber until it is dissipated at the microscopic scale. However, a small percentage of the energy does not spill continuously through the cascade but is instantly passed to the higher wavenumbers. Consequently, the smallest eddies receive a certain amount of energy almost immediately. As the spectral energy cascade continues, the highest wavenumber needs a certain time to receive all the energy which has been transferred from the largest eddies. As such, there is a time delay, of the order of tau, between the generation of energy by the largest eddies and the eventual dissipation of this energy. For equilibrium turbulence at high Reynolds numbers, there is a wide range where energy is neither produced by the large eddies nor dissipated by viscosity, but is conserved and passed from wavenumber to higher wavenumbers. The rate at which energy cascades from one wavenumber to another is proportional to the energy contained within that wavenumber. This rate is constant and has been used in the past as a dissipation rate of turbulent kinetic energy. However, this is true only in steady, equilibrium turbulence. Most dissipation models contend that the production of dissipation is proportional to the production of energy and that the destruction of dissipation is proportional to the destruction of energy. In essence, these models state that the change in the dissipation rate is proportional to the change in the kinetic energy. This assumption is obviously incorrect for the case where there is no production of turbulent energy, yet energy continues to cascade from large to small eddies. If the time lag between the onset on the energy cascade to the destruction of energy at the microscale can be modeled, then there will be a better representation of the dissipation process. Development of an energy cascade time scale equation is discussed.

Duncan, B. S.↗
NASA NTRS1981

Large-eddy simulation of the shear-free turbulent boundary layer

The shear-free turbulent boundary layer is calculated by the large-eddy simulation technique. The filtered Navier-Stokes equations are used; the method of integration employs Fourier expansions in the homogeneous directions and finite differences in the cross-stream direction. Results indicate that the simulation is capable of predicting the primary Reynolds-number effects.

Biringen, S.↗
NASA NTRS2018

Lebedev Scheme for Ultrasound Simulation in Composites

The growing use of composite materials for aerospace applications has resulted in a need for quantitative nondestructive evaluation (NDE) methods appropriate for characterizing damage in composite components. NDE simulation tools, such as ultrasound models, can aid in enabling optimized inspection methods and establishing confidence in inspection capabilities. In this paper, a mathematical approach using the Lebedev Finite Difference (LFD) method is presented for ultrasonic wave simulation in composites. Boundary condition equations for implementing stress-free boundaries (necessary for simulation of NDE scenarios) are also presented. Quantitative comparisons between LFD guided wave ultrasound simulation results, experimental guided wave data, and dispersion curves are described. Additionally, stability tests are performed to establish the LFD code behavior in the presence of stress-free boundaries and low-symmetry anisotropy. Results show that LFD is an appropriate approach for simulating ultrasound in anisotropic composite materials and that the method is stable in the presence of low-symmetry anisotropy and stress-free boundaries. Studies presented in this paper include guided wave simulation in hexagonal, monoclinic, triclinic and layered composite laminates.

Guided wave↗