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Free laminar boundary layer flow between parallel streams of different magnetic fields and temperatures for incompressible, viscous, thermal, and electric conducting fluids
To assess the possibility of achieving extensive laminar flow on conical vehicles during hyperbolic entry, the Ames Research Center has had an ongoing program to study boundary-layer transition on ablating cones. Boundary layer transition results are presented from ballistic range experiments with models that ablated at dimensionless mass transfer rates comparable to those expected for full scale flight at speeds up to 17 km/sec. It was found possible to measure the surface recession and hence more accurately identify regions of laminar, transitional, and turbulent flow along generators of the recovered cones. Some preliminary results using this technique are presented.
Progress was made on further flow visualization of vortex-leading edge interaction, in conjunction with characterization of the unsteady pressure field. The range of scale of an elliptical leading edge, relative to the incident primary vortex, was determined. The scale of the incident vortex was characterized in terms of mean shear layer parameters. An overview of the interaction mechanism for the range of thin to thick leading-edges is given. The interaction mechanism corresponding to the case where the incident vortex is above the leading-edge is given for hydrogen bubble wires well upstream of and at the tip of the leading edge. A sample of the instantaneous pressure distribution for the case where the incident vortex dives beneath the edge is presented. The effect of scale of the incident vortex relative to that of the leading-edge was examined. The circulation and length scale of the incident vortices in the street are being characterized.
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Fluxes and exchange coefficients are derived for the transport of Sr-90, Pb-210, Bi-210, and Po-210 between the free troposphere and the marine boundary layer and between the boundary layer and the sea surface. Radionuclide concentrations previously measured near Hawaii are used in the derivations. Values obtained for the free troposphere/boundary layer exchange coefficient (expressed as a piston velocity) were 185, 228 and 203 m/d for Pb-210, Bi-210, and Sr-90, respectively. The magnitude of the local sea-surface source of Po-210 is also determined.
This paper investigates the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free stream turbulence, and (3) the potential motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2 percent. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity, measured using two single wire probes. The results show that it is possible to separate the contributions to the r.m.s. level of the velocity fluctuations, without resorting to the dubious technique of high-pass filtering. The separation could be extended to the spectral densities of the contributions, if measurements of sufficient accuracy were available. The Appendix provides a general guide for the measurement of small free stream fluctuation levels.
The radiative stability of thermally isolated coronal loops with free-flow boundary conditions by nonlinear numerical simulation are studied. A chromosphere-to-corona loop equilibrium (including the option of a deep chromosphere) is first established by following the nonlinear evolution from an initial isothermal state with rigid boundaries. The end conditions are then changed, to allow free flow and to fix the temperature, and investigate the response to nonisobaric perturbations. Within a family of loops of the same pressure, long hot loops to be stable and short cool loops to be unstable to the thermal chromospheric-expansion mode are found. The stable cases remain so, even when long chromospheric ends and/or gravity are added. In those cases which are unstable, the subsequent nonlinear evolution which exhibits swelling of the chromosphere until the entire loop becomes cool and dense are followed.
Three ice phase transitions, based on experimental and theoretical results, were incorporated into a 2D spherical convection model. These phase transitions are the exothermic Ice 1-2, the endothermic Ice 2-6, and the exothermic Ice 6-8 phase transitions. The fluid is assumed isoviscous and the anelastic liquid formulation was used. The object is an icy satellite whose physical characteristics resemble those of Ganymede or Callisto. Structural models, similar to those of Mueller and McKinnon, with different core sizes, i.e. with different degree of differentiation were studied. The shells, i.e. the mantle of the satellite, is heated both internally and from below to account for the decaying radiogenic heating and the heat flow from the solid core. The lower boundary of the mantle is rigid and isothermal, the upper boundary is isothermal. Calculations with rigid and shear stress free upper boundary are carried out in order to assess the role of the different boundary conditions. Two different Rayleigh numbers, depending on the assumed value of the viscosity, were used in the calculations and the thermal evolution of the satellite was studied. The suit of calculations presented demonstrates that phase transition cannot be ignored when the thermal evolution of a large icy satellite has to be studied. The importance of the construction of the realistic phase diagram for ice was also documented. On the other hand the degree of differentiation, simulated with the structures with different core's radius does not seem to drastically influence the overall behavior of the convective activity. Within the limits of our simulations, the post-accretional evolution seems to be independent on the degree of primordial differentiation.
Linearized Euler equations are used to simulate supersonic jet noise generation and propagation. Special attention is given to boundary treatment. The resulting solution is stable and nearly free from boundary reflections without the need for artificial dissipation, filtering, or a sponge layer. The computed solution is in good agreement with theory and observation and is much less CPU-intensive as compared to large-eddy simulations.
The sensitivity of recrystallization kinetics in metals to the heterogeneity of microstructure and deformation history is a widely accepted experimental fact. However, most of the available recrystallization models employ either a mean field approach or use grain-averaged parameters, and thus neglecting the mesoscopic heterogeneity induced by prior deformation. Here in the present study, we investigate the impact of deformation-induced dislocation (subgrain) structure on the kinetics of recrystallization in metals using the phase-field approach. The primary focus here is upon the role of dislocation cell boundaries. The free energy formulation of the phase-field model accounts for the heterogeneity of the microstructure by assigning localized energy to the resulting dislocation microstructure realizations generated from experimental data. These microstructure realizations are created using the universal scaling laws for the spacing and the misorientation angles of both the geometrically necessary and incidental dislocation boundaries. The resulting free energy is used into an Allen-Cahn based model of recrystallization kinetics, which are solved using the finite element method. The solutions thus obtained shed light on the critical role of the spatial heterogeneity of deformation in the non-smooth growth of recrystallization nuclei and on the final grain structure. The results showed that, in agreement with experiment, the morphology of recrystallization front exhibits protrusions and retrusions. By resolving the subgrain structure, the presented algorithm paves the way for developing predictive kinetic models that fully account for the deformed state of recrystallizing metals.
The axisymmetric linearized Euler equations are used to simulate noise amplification and radiation from a supersonic jet. The effect of heating on the noise field of the jet is studied and compared to experimental results. Special attention was given to boundary treatment, and the resulting solution is stable and nearly free from boundary reflections.
Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).
In this paper an investigation of the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure is described. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free-stream turbulence, and (3) the irrotational motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2%. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity fluctuations, measured using two single-wire probes. The results show that it is possible to separate the contributions to the rms level of the velocity fluctuations without resorting to the dubious technique of high-pass filtering. This separation could be extended to the spectral densities of the contributions if measurements of sufficient accuracy were available.
In modal testing and finite element model correlation, analysts desire modal results using free-free or rigid boundary conditions to ease comparisons of test versus analytical data. It is often expensive both in cost and schedule to build and test with boundary conditions that replicate the free-free or rigid boundaries. Static test fixtures for load testing are often large, heavy, and unyielding, but do not provide adequate boundaries for modal tests because they are dynamically too flexible and often contain natural frequencies within the test article frequency range of interest. The dynamic coupling between the test article and test fixture complicates the model updating process because significant effort needs to be spent on modeling the test fixture and boundary conditions in addition to the test article. If the modal results could be corrected for fixture coupling, then setups used for other structural testing could be adequate for modal testing and would allow significant schedule and cost savings by eliminating a unique setup for only modal testing. To simplify future modal tests, this paper reports on a fixed base correction method that was investigated during modal testing of a full-scale, half-span, flexible wing cantilevered from a static test fixture. The results of this fixed base correction approach look very promising. The method aided in producing similar wing modal characteristics for two different physical boundary configurations of a dynamically active test fixture.
In modal testing and finite element model correlation, analysts desire modal results using free-free or rigid boundary conditions to ease comparisons of test versus analytical data. It is often expensive both in cost and schedule to build and test with boundary conditions that replicate the free-free or rigid boundaries. Static test fixtures for load testing are often large, heavy, and unyielding, but do not provide adequate boundaries for modal tests because they are dynamically too flexible and often contain natural frequencies within the frequency range of interest of the test article. Dynamic coupling between the test article and test fixture complicates the model updating process because significant effort is required to model the test fixture and boundary conditions in addition to the test article. If there were a way to correct the modal results for fixture coupling, then setups used for other structural testing could be adequate for modal testing. In the case described in this paper, a partial static loads testing setup was used, which allowed significant schedule and cost savings by eliminating a unique setup for a modal test. A fixed base correction technique was investigated during modal testing of a flexible wing cantilevered from part of a static test fixture. The technique was successfully used to measure the wing modes de-coupled from the dynamically active test fixture. The technique is promising for future aircraft applications, but more research is needed.
In modal testing and finite element model correlation, analysts desire modal results using free-free or rigid boundary conditions to ease comparisons of test versus analytical data. It is often expensive both in cost and schedule to build and test with boundary conditions that replicate the free-free or rigid boundaries. Static test fixtures for load testing are often large, heavy, and unyielding, and not provide adequate boundaries for modal tests because they are dynamically too flexible and often contain natural frequencies within the test article frequency range of interest. The dynamic coupling between the test article and test fixture complicates the model updating process because significant effort needs to be spent on modeling the test fixture and boundary conditions in addition to the test article. If the modal results could be corrected for fixture coupling, then setups used for other structural testing could be adequate for modal testing and would allow significant schedule and cost savings by eliminating a unique setup for only modal testing. To simplify future modal tests, this report describes a Fixed Base Correction method that was investigated during modal testing of a full-scale, half-span, flexible wing cantilevered from a static test fixture. The results of this Fixed Base Correction approach look very promising. The method aided in producing similar wing modal characteristics for two different physical boundary configurations of a dynamically active test fixture.
Laminar boundary-layer heat transfer and shear stress predictions from similarity solutions, emphasizing large free-stream velocity gradients and highly cooled walls