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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗
NASA NTRS1985

Experimental and Theoretical Studies of Wetting and Multilayer Adsorption

The recent work with partially miscible binary liquid mixtures has established that the structure of the liquid-vapor interface can undergo a first-order phase transition from incomplete to complete wetting of the vapor as the temperature is raised. A discontinuity in the change of interfacial tension as a function of temperature at the phase transition has been predicted to occur in many systems and to play an important role in the growth of uniform composites from alloy melts at monotectic points. These measurements are the first to establish the order of the transition. Studies of capillary rise in SF6 in a unique interferometer have led to the first measurements of the thickness of wetting layers (or equivalently, multilayer adsorbed films) on a solid surface near a liquid-vapor critical point. Instabilities in wetting layers were observed. A theory for the instabilities is being developed and will be checked by both static and dynamic optical experiments. The effect of gravity on the apparent thickness of interfaces (as measured by ellipsometry) is under study.

Moldover, M. R.↗
DOE OSTI2021

NUMERICAL CALCULATION OF LOSSES OF TRAPPED VORTICES UNDER STRONG RF MEISSNER CURRENT AND DC SUPERHEATING FIELD IN TYPE II SUPERCONDUCTORS

Research on the vortex dynamics and enhancing of superheating field in superconductors has attracted much attention in accelerator physics community to develop next-generation high-performance accelerator cavities. However, the extreme dynamics of curvilinear elastic vortices driven by very strong currents close to the depairing limit or superheating field of a superconductor with a nanostructured surface has not been well understood. We calculated the superheating field Hsh and critical momentum kc characterizing the wavelength of the instability ?m of the Meissner state to flux penetration by solving numerically the Ginzburg?Landau equations. A bulk superconductor, superconductor with the inhomogeneous surface disorder (S-S), and multilayered surface (S-I-S) have been thoroughly investigated in this work. Our result showed that S-S and S-I-S structures can enhance the superheating field well above their clean limit. In this work extensive numerical simulation of the power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was performed. Our simulations take into account the nonlinear vortex line tension, vortex mass, Bardeen?Stephen viscous vortex drag applicable at low fields, and nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient ?(v) at high fields and pinning force. We showed that the LO decrease of ?(v) with the vortex velocity v could radically change the field dependence of the surface resistance Ri(H) caused by trapped vortices. At low frequencies Ri(H) exhibits a conventional increase with H. However, as frequency increases, the surface resistance becomes a nonmonotonic function of H which decreases with H at higher fields irrespective of the pinning distribution. Overheating can mask the descending field dependence of Ri(H) as frequency increases. Our numerical simulations also show that the LO effect can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along with the vortex when a vortex is pinned strongly to one end. Nonlinear losses of trapped vortices in thick films under high-amplitude RF fields as functions of frequency, mean free path and pinning characteristics have been calculated.

Pathirana, Walive↗
DOE OSTI2025

Property Measurements of LiF-NaF-KF Molten Salts Doped with Corrosion Products and Oxygen

Measurements of thermophysical properties of molten salts are needed for modeling and simulation activities that support the development of molten salt reactor (MSR) technologies. Properties of interest including transition temperatures, phase behavior, heat capacity, density, volumetric thermal expansion, surface tension, viscosity, thermal diffusivity, thermal conductivity, and vapor pressure are being performed at Argonne. Results of these property measurements are suitable for use in evaluating reactor performance during startup and the early operating life of the reactor. Ingressions of oxygen and moisture into the fuel salt are expected to occur at different times during the operating life of the reactor due to system leaks, maintenance, and refueling activities. The presence of these environmental contaminants induces corrosion of structural materials. The introduction of corrosion-derived species, oxygen and moisture is expected to affect the physical and chemical properties of the salt and operation of the reactor. Previous work performed at Argonne evaluated the effects of fission product dopants on the thermal properties of eutectic LiF-NaF-KF (FLiNaK). Properties of FLiNaK are commonly used to represent those of fluoride-bearing fuel salts. Metallic corrosion products such as chromium and nickel ions together with dissolved oxygen are expected to affect system redox differently than the accumulation of fission products. Work summarized in this report was performed to measure the effects of corrosion products and dissolved oxygen on the phase transitions, and specific heat capacity of FLiNaK. Thermophysical property measurements were made using four salts that were prepared by doping aliquots of a eutectic mixture of FLiNaK with surrogate corrosion products. Controlled additions of CrF 3 and NiF 2 were used as surrogates for corrosion product contamination anticipated during extended reactor operations in which fuel salt is in contact with steel reactor components. Controlled additions of UF 4 from two sources containing known amounts of UO 2 at different concentrations were used to represent oxygen contamination. The phase transitions and specific heat capacities of the four salts were measured by using differential scanning calorimetry. Measurements were made at temperatures spanning the range of 500−900 °C, which is the expected operating range of MSRs. Measured property values were compared to values measured previously with eutectic FLiNaK without dopants. Differences between property values measured for the doped and non-doped salts were compared with the uncertainties of the measurements to determine the significance of the effect of corrosion products and oxygen on salt properties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1980

Cyclic plasticity and failure of structural components

An analytical approach for low-cycle fatigue prediction is presented. The approach combines a cyclic plasticity model with the finite element method and a damage accumulation criterion for ductile metals. The cyclic plasticity model is based on the concept of the combination of several yield surfaces. The surfaces are related to the material uniaxial stress-strain curve idealized by piecewise linear segments. The damage criterion is based on the Coffin-Manson formulae modified for the mean stress variation effect. It is extended to the multiaxial varying stress-strain field and applied for both the crack initiation and the crack growth processes. The stable slow crack growth rate is approximated by the damage accumulation gradient computed from the cracked finite element models. This procedure requires fatigue testing data of only smooth specimens under constant strain amplitudes. The present approach is illustrated by numerical examples of an aircraft wing stiffened panel subjected to compression, which causes material yielding and residual tension.

Kalev, I.↗
NASA NTRS1985

Experimental and analytical study of ceramic-coated turbine-tip shroud seals for small turbine engines

The results of an experimental and analytical evaluation of ceramic turbine tip shrouds within a small turbine engine operating environment are presented. The ceramic shrouds were subjected to 1001 cycles between idle and high power and steady-state conditions for a total of 57.8 engine hr. Posttest engine inspection revealed mud-flat surface cracking, which was attributed to microcracking under tension with crack penetration to the ceramic and bond coat interface. Sections and micrographs tend to corroborate the thesis. The engine test data provided input to a thermomechanical analysis to predict temperature and stress profiles throughout the ceramic gas-path seal. The analysis predicts cyclic thermal stresses large enough to cause the seal to fail. These stresses are, however, mitigated by inelastic behavior of the shroud materials and by the microfracturing that tensile stresses produce. Microfracturing enhances shroud longevity during early life but provides the failure mechanism during life but provides the failure mechanism during extended life when coupled with the time dependent inelastic materials effects.

Biesiadny, T. J.↗
NASA NTRS1981

Acceleration wave breakup of liquid jets with airstreams

Characteristic mean drop diameters were determined for downstream and upstream injection into nonswirling and swirling airflows. The effects of the aerodynamic and liquid surface forces on the mean drop size were obtained with a scanning radiometer. Water jet breakup was studied primarily in the acceleration wave regime with values of WeRe 10 to the 6th power and the following empirical expression was obtained: D(o)/D(m) =C (WeRe) to the 0.4, power where D(o) and D(m) are the orifice and mean drop diameters, respectively. We and Re are the Weber and Reynolds numbers defined as repectively, We = rho(a)D(o)V(r)/sigma and Re = D(o)V(r)/nu, where V(r) and rho(a) are airstream relative velocity and density, respectively, and sigma and nu are surface tension and kinematic viscosity of the liquid, respectively. The proportionally constant C was evaluated as follows: for downstream injection, C = 0.023 with nonswirling airflow, and C = 0.027 with swirling airflow. For upstream injection, the empirical expression D(o)/D(m) = 0.0045 (WeRe) to the 0.5 power was obtained with nonswirling airflow. Experimental conditions included a water flow rate of 68 liter per hour and an airflow rate per unit area range of 4.6 to 25.2 gm/sq cm sec at 293 K and atmospheric pressure.

Ingebo, R. D.↗
NASA NTRS1992

Finite-element analyses and fracture simulation in thin-sheet aluminum alloy

A two-dimensional, elastic-plastic finite-element analysis was used with a critical crack-tip-opening angle (CTOA) fracture criterion to model stable crack growth in thin-sheet 2024-T3 aluminum alloy under monotonic loading after precracking at different cyclic stress levels. Tests were conducted on three types of specimens: middle-crack, three-hole-crack and blunt-notch tensile specimens. An experiment technique was developed to measure CTOA during crack growth initiation and stable tearing using a high-resolution video camera and recorder. Crack front shapes were also measured during initiation and stable tearing using a fatigue marker-load technique. Three-dimensional elastic-plastic finite-element analyses of these crack shapes for stationary cracks were conducted to study the crack-front opening displacements. Predicted load against crack extension on middle-crack tension specimens agreed well with test results even for large-scale plastic deformations. The analyses were able to predict the effects of specimen size and precracking stress history on stable tearing. Predicted load against load-line displacements agreed well with test results up to maximum load bu the analyses tended to overpredict displacements as crack grew beyond the maximum load under displacement-controlled conditions. During the initiation phase, the measured CTOA values were high but decreased and remained nearly constant after a small amount of stable tearing. The constant value of CTOA agree well with the calculated value from the finite-element analysis. The larger CTOA values measured at the sheet surface during the initiation phase may be associated with the crack tunneling observed in the tests. Three-dimensional analyses for nonstraight crack fronts predicted much higher displacements near the free surface than in the interior.

Newman, J. C., Jr.↗
NASA NTRS1999

Viscosity Measurement of Highly Viscous Liquids Using Drop Coalescence in Low Gravity

The method of drop coalescence is being investigated for use as a method for determining the viscosity of highly viscous undercooled liquids. Low gravity environment is necessary in this case to minimize the undesirable effects of body forces and liquid motion in levitated drops. Also, the low gravity environment will allow for investigating large liquid volumes which can lead to much higher accuracy for the viscosity calculations than possible under 1 - g conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the Navier-Stokes equations as well as on data from experiments conducted in near zero gravity environment. In the analytical aspect of the method two liquid volumes are brought into contact which will coalesce under the action of surface tension alone. The free surface geometry development as well as its velocity during coalescence which are obtained from numerical computations are compared with an analogous experimental model. The viscosity in the numerical computations is then adjusted to bring into agreement of the experimental results with the calculations. The true liquid viscosity is the one which brings the experiment closest to the calculations. Results are presented for method validation experiments performed recently on board the NASA/KC-135 aircraft. The numerical solution for this validation case was produced using the Boundary Element Method. In these tests the viscosity of a highly viscous liquid, in this case glycerine at room temperature, was determined to high degree of accuracy using the liquid coalescence method. These experiments gave very encouraging results which will be discussed together with plans for implementing the method in a shuttle flight experiment.

Antar, Basil N.↗
NASA NTRS2020

Asymmetric Surface Brightness Structure of Caustic Crossing Arc in SDSS J1226+2152: A Case for Dark Matter Substructure

We study the highly magnified arc SGAS J122651.3+215220 caused by a star-forming galaxy at z s = 2.93 crossing the lensing caustic cast by the galaxy cluster SDSS J1226+2152 (z l = 0.43), using Hubble Space Telescope observations. We report in the arc several asymmetric surface brightness features whose angular separations are a fraction of an arcsecond from the lensing critical curve and appear to be highly but unequally magnified image pairs of underlying compact sources, with one brightest pair having clear asymmetry consistently across four filters. One explanation of unequal magnification is microlensing by intracluster stars, which induces independent flux variations in the images of individual or groups of source stars in the lensed galaxy. For a second possibility, intracluster dark matter subhaloes invisible to telescopes effectively perturb lensing magnifications near the critical curve and give rise to persistently unequal image pairs. Our modelling suggests, at least for the most prominent identified image pair, that the microlensing hypothesis is in tension with the absence of notable asymmetry variation over a six-year baseline, while subhaloes of ∼10 6 –10 8 \Mꙩ anticipated from structure formation with cold dark matter typically produce stationary and sizable asymmetries. We judge that observations at additional times and more precise lens models are necessary to stringently constrain temporal variability and robustly distinguish between the two explanations. The arc under this study is a scheduled target of a Director’s Discretionary Early Release Science program of the James Webb Space Telescope, which will provide deep images and a high-resolution view with integral field spectroscopy.

Liang Dai↗
NASA NTRS2010

Using Cassini UVIS Data to Constrain Enceladus' Libration State

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, stall amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production along the tiger stripes as produced by tidal shear heating and a previous study has explored possible libration states that provided better matches to Cassini CIRS observations of heat along the tiger stripes. Cassini UVIS stellar occultations provided measurements of the column density of the Enceladus plume at two different points in Enceladus' orbit and find comparable column density values. This column density may be a reflection of the amount of the tiger stripe rifts in tension and able to vent volatiles and a physical libration will also affect the fraction of tiger stripe in tension at different points in the orbit. We have modeled the expected fraction of tiger stripes in tension under different libration conditions. Without libration the amount of tiger stripe rifts in tension at both paints in the orbit would not be comparable and therefore may not allow comparable amounts of volatiles to escape. However, we identify libration conditions that do allow comparable amounts of the tiger stripes to be in tension at each point in the orbit, which might lead to comparable column densities. The librations identified coincide with possible librations states identified in the earlier study, which used Cassini CIRS observations.

Hurford, Terry A.↗
DOE OSTI2023

Interaction of extended dislocations with nanovoid clusters

Voids of nanoscale dimensions in irradiated metals can act as obstacles to dislocation motion and cause strengthening. In this work, nanovoid strengthening and the influences of void size, void spacing and material properties, such as stacking fault energies, on dislocation bypass mechanisms are investigated using Phase Field Dislocation Dynamics, a three-dimensional mesoscale model that predicts the minimum energy pathway taken by discrete dislocations. A broad range of face centered cubic metals (copper, nickel, silver, rhodium, and platinum) and nanovoid sizes and spacings are treated, altogether spanning void size–to–dislocation stacking fault width ratios from less than unity to ten. Material γ-surfaces, calculated from ab initio methods, are input directly into the formulation. The analysis reveals that the critical bypass stress scales linearly with the linear void fraction, effective isotropic shear modulus, and ratio of the intrinsic to unstable stacking fault energies. With only a few exceptions, the critical stress is controlled by the stress required for the leading partial to impinge the voids (to move within range of the attractive image stress field of the void). When the void diameter is nearly an order of magnitude greater than the stacking fault width, the mechanism determining critical strength shifts to the stress for the dislocation to breakaway after partially cutting the void. Furthermore, this situation corresponds to that treated by line tension models and is realized here for Pt, with a sub-nanometer stacking fault width.

36 MATERIALS SCIENCE↗
NASA NTRS2001

Effects of Electrons, Protons, and Ultraviolet Radiation on Thermophysical Properties of Polymeric Films

The response of coated thin polymer films to ultraviolet (UV), electron and proton radiation simultaneously has been evaluated, with selected measurements in situ. Exposure was intended to simulate the electron and proton radiation environment near the Earth-Sun Lagrangian points (LI and L2) for five years and approximately 1000 equivalent solar hours (ESH) UV. These orbital environments are relevant to several potential missions such as the Next Generation Space Telescope and Geomagnetic Storm Warning, both of which may use thin film based structures for a sunshade and solar sail, respectively. The thin film candidates (12.5 micrometers thick) consisted of commercially available materials (Kapton(R) E, HN, Upilex(R) S, CP-1, CP-2, TOR-RC, and TOR-LMBP) that were metalized on one side with vapor deposited aluminum. All of the films are aromatic polyimides, with the exception of TORLMBP, which is a copoly(arylene ether benzimidazole). The films were exposed as second surface mirrors and the effects of the exposure on solar absorptance, thermal emittance, and tensile properties were determined. The in situ changes in solar absorptance from Kapton(R) and Upilex(R) were less than 0. 1, whereas the solar absorptance of TOR and CP films increased by more than 0.3 without saturating. The thermal emittance measurements also showed that the Kapton(R) and Upilex(R) materials increased only 1-2%, but the remaining materials increased 5-8%. Based on tensile property measurements made in air following the test, the failure stress of every type of polymer film decreased as a result of irradiation. The polymers most stable in reflectance, namely Upilex(R) and Kapton(R), were also the strongest in tension before irradiation, and they retained the greatest percentage of tensile strength. The films less stable in reflectance were also weaker in tension, and lost more tensile strength as a result of irradiation. The apparent failure strain (as a percent of original gage length) of every type of polymer film except TOR-RC, decreased as a result of irradiation.

Russell, Dennis A.↗
DOE OSTI2021

Burst characteristics of advanced accident-tolerant FeCrAl cladding under temperature transient testing

Here assessment of burst characteristics of accident-tolerant fuel (ATF) claddings is essential to evaluate the safety margins of nuclear reactors, and better understanding can enable accelerated licensing for reactor concepts that include the new materials. Therefore, this study investigated the burst behavior of an ATF candidate of C26M, which is an iron–chromium–aluminum alloy (FeCrAl) under transient testing like the simulated loss-of-coolant accident (LOCA) conditions, except the water-quenching phase, in light-water reactors (LWRs). The effect of LOCA specimen length was assessed in terms of post-burst tube parameters. No critical length effect was determined on the burst pressure, burst location, and burst size measurements. Burst temperature showed larger variation likely due to its measurement approach used in this study. The post-test diametral strain was identified as the critical parameter to reduce the specimen length as compared to tube burst length or width. Postmortem optical metrology and digital image correlation were employed to determine the local strain-state during the simulated LOCA, which showed the loading path was close to equibiaxial conditions in regions away from the burst location, rather than internally pressurized conditions (or “plane-strain” tension). Pst-test microstructural characterizations of the FeCrAl revealed that ductile damage was present at the edge of the outer radial surface while the rest of the material was ruptured via cleavage at LOCA burst temperatures. Furthermore, internal grain boundary cracks were observed at locations away from the tube burst region. This behavior was considered to occur during the cooling down period of the simulated LOCA test. Overall, this study aimed to provide essential data for fuel performance code development by considering micromechanics of the deformation and failure.

36 MATERIALS SCIENCE↗
NASA NTRS1982

Accomplishments of the NASA Johnson Space Center portion of the soil moisture project in fiscal year 1981

The NASA/JSC ground scatterometer system was used in a row structure and row direction effects experiment to understand these effects on radar remote sensing of soil moisture. Also, a modification of the scatterometer system was begun and is continuing, to allow cross-polarization experiments to be conducted in fiscal years 1982 and 1983. Preprocessing of the 1978 agricultural soil moisture experiment (ASME) data was completed. Preparations for analysis of the ASME data is fiscal year 1982 were completed. A radar image simulation procedure developed by the University of Kansas is being improved. Profile soil moisture model outputs were compared quantitatively for the same soil and climate conditions. A new model was developed and tested to predict the soil moisture characteristic (water tension versus volumetric soil moisture content) from particle-size distribution and bulk density data. Relationships between surface-zone soil moisture, surface flux, and subsurface moisture conditions are being studied as well as the ways in which measured soil moisture (as obtained from remote sensing) can be used for agricultural applications.

Paris, J. F.↗
NASA NTRS1984

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

Newman, J. C., Jr.↗
NASA NTRS1971

Investigation of flaw geometry and loading effects on plane strain fracture in metallic structures

The effects on fracture and flaw growth of weld-induced residual stresses, combined bending and tension stresses, and stress fields adjacent to circular holes in 2219-T87 aluminum and 5AI-2.5Sn(ELI) titanium alloys were evaluated. Static fracture tests were conducted in liquid nitrogen; fatigue tests were performed in room air, liquid nitrogen, and liquid hydrogen. Evaluation of results was based on linear elastic fracture mechanics concepts and was directed to improving existing methods of estimating minimum fracture strength and fatigue lives for pressurized structure in spacecraft and booster systems. Effects of specimen design in plane-strain fracture toughness testing were investigated. Four different specimen types were tested in room air, liquid nitrogen and liquid hydrogen environments using the aluminum and titanium alloys. Interferometry and holograph were used to measure crack-opening displacements in surface-flawed plexiglass test specimens. Comparisons were made between stress intensities calculated using displacement measurements, and approximate analytical solutions.

Hall, L. R.↗
NASA NTRS1992

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Dijkstra, Henk A.↗