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A new field-theoretical crossover equation-of-state model provides a bridge between the asymptotic behavior close to a liquid-gas critical point and the expected mean field behavior farther away.
The coexistence curve of the binary fluid mixture perfluoromethylcyclohexane-isopropyl alcohol was determined by precisely measuring the refractive index both above and below its upper critical consolute point. Sixty-seven two-phase data points were obtained over a wide range of reduced temperatures, 10(exp -5) less than t less than 2.5 x 10(exp -1), to determine the location of the critical point: critical temperature=89.901 C, and critical composition = 62.2% by volume perfluoromethylcyclohexane. These data were analyzed to determine the critical exponent 8 close to the critical point, the amplitude B, and the anomaly in the diameter. The volume-fraction coexistence curve is found to be as symmetric as any composition like variable. Correction to scaling is investigated as well as the need for a crossover theory. A model is proposed that describes the asymptotic approach to zero of the effective exponent Beta, which allows an estimation of the temperature regime free of crossover effects.
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
The stability of the parallel flow of water between concentric cylinders at different temperatures is investigated for infinitesimal velocity and pressure disturbances. Primary interest is in the effect of heat transfer and the radius ratio a/b on the critical point of the neutral stability curve. The results indicate a strong dependence of the critical eigenvalues on both the heat transfer and the radius ratio. The critical Reynolds number of the nonisothermal flow appears to approach a finite value as the inner radius approaches zero (pipe flow) by showing an inflection point on the curve of critical Reynolds number vs a/b.
The large compressibility of a pure fluid near its critical point is a potential means of measuring the critical temperature. At the suggestion of Prof. Ferrell we observed electrostriction in xenon by applying a large voltage across a small, open capacitor immersed in the sample and then measuring the capacitance change caused by the subsequent increase in the xenon's local density. This scheme was attractive because the compressibility is a large, well-understood effect and because we were already familiar with low-voltage capacitance measurements. We found qualitative agreement with our initial expectations based on the fluid's compressibility. However, we also found an additional effect comparable in size to the expected electrostriction but proportional to the applied voltage. We have no explanation for this effect. Thus, given the Science Panel's recommendation against investing extensive effort in this direction, we are abandoning further development of an alternate means for measuring the critical temperature.
In the present analysis, deterministic flaw growth analysis is used to project the failure distributions from inspection data. Inspection data is reported for each critical point in the aircraft. The data will indicate either a crack of a specific size or no crack. The crack length may be either less than, equal to, or greater than critical size for that location. Non-critical length cracks are projected to failure using the crack growth characteristics for that location to find the life when it will be at critical length. Greater-than-critical length cracks are projected back to determine the life at failure, that is, when it was at critical length. The same process is used as in the case of a non-critical crack except that the projection goes the other direction. These points, along with the critical length cracks are used to determine the failure distribution. To be able to use data from different aircraft to build a common failure distribution, a consistent life variable must be used. Aircraft life varies with the severity of the usage; therefore the number of flight hours for a particular aircraft must be modified by its usage factor to obtain a normalized life which can be compared with that from other aircraft.
The modern theory of second order phase transitions is very successful in calculating the critical exponents as an asymptotic expansion in powers of epsilon = 4 - D, the deviation of D = 3, the spatial dimension of the actual physical system from that of the abstract four-dimensional reference model. This remarkable mathematical 'tour de force' leaves unanswered, however, many fundamental questions concerning the exact nature of how the fluctuations interact. I discuss here some experiments which would help to further our understanding of the equilibrium critical properties. Especially promising would be a measurement of the temperature dependence of the turbidity very close to the critical point. This has the promise of determining the small and elusive but fundamentally important anomalous dimension exponent eta. I also review various ways of measuring the critical transport coefficients and point out some cases where ground based experiments may usefully supplement flight experiments.
Boundary layer velocity and temperature profiles were measured for nitrogen near its thermodynamic critical point flowing past a horizontal flat plate. The results were compared measurements made for vertically upward flow. The boundary layer temperatures ranged from below to above the thermodynamic critical temperature. For wall temperatures below the thermodynamic critical temperature there was little variation between the velocity and temperature profiles in three orientations. In all three orientations the point of crossing into the critical temperature region is marked by a significant flattening of the velocity and temperature profiles and also a decrease in heat transfer coefficient.
The goal of the MISTE (Microgravity Scaling Theory Experiment) is to provide a stringent test of scaling theory predictions for critical behavior near a liquid-gas critical point both in the asymptomatic and crossover regions.
Boundary layer velocity and temperature profiles were measured for nitrogen near its thermodynamic critical point flowing past a horizontal flat plate. The heated surface was oriented both facing upward and downward. The results were compared to earlier work in which measurements were made for vertically upward flow. The boundary layer temperatures ranged from below to above the thermodynamic critical temperature. For wall temperatures below the thermodynamic critical temperature there was little variation between the velocity and temperature profiles in the three orientations. In all three orientations the point of crossing into the critical temperature region is marked by a significant flattening of the velocity and temperature profiles and also a decrease in heat transfer coefficient. As the heat flux and, consequently, wall temperature are further increased significant changes occur in the velocity and temperature profiles. Examination of near-critical heat transfer in these three flow orientations offers insights into the relative role of buoyancy forces in this regime.
The predictions of theoretical models for a critical-point phase transistion in fluids, namely the classical equation with third-degree critical isotherm, that with fifth-degree critical isotherm, and the lattice gas, are reviewed. The renormalization group theory of critical phenomena and the hypothesis of universality of critical behavior supported by this theory are discussed as well as the nature of gravity effects and how they affect cricital-region experimentation in fluids. The behavior of the thermodynamic properties and the correlation function is formulated in terms of scaling laws. The predictions of these scaling laws and of the hypothesis of universality of critical behavior are compared with experimental data for one-component fluids and it is indicated how the methods can be extended to describe critical phenomena in fluid mixtures.
The Comet Nucleus Sample Return (CNSR) mission, one of the four cornerstones of the ESA scientific program, is one of the most complex space ventures within the next century, both from technological and deep space exploration point of view. In the Rosetta scenario the sample acquisition phase represents the most critical point for the global mission's success. The proposed paper illustrates the main results obtained in the context of the CNSR-SAS ongoing activity. The main areas covered are related to: (1) sample properties characterization (comet soil model, physical/chemical properties, reference material for testing); (2) concepts identification for coring, shovelling, harpooning and anchoring; (3) preferred concept (trade off among concepts, identification of the preferred configuration); and (4) proposed development activity for gaining the necessary confidence before finalizing the CNSR mission. Particular emphasis will be given to the robotic and flexibility aspects of the identified sample acquisition systems (SAS) configuration, intended as a means for the overall system performance enhancement.
We first report on our current progress in the area of explicit methods for tangent curve computation. The basic idea of this method is to decompose the domain into a collection of triangles (or tetrahedra) and assume linear variation of the vector field over each cell. With this assumption, the equations which define a tangent curve become a system of linear, constant coefficient ODE's which can be solved explicitly. There are five different representation of the solution depending on the eigenvalues of the Jacobian. The analysis of these five cases is somewhat similar to the phase plane analysis often associate with critical point classification within the context of topological methods, but it is not exactly the same. There are some critical differences. Moving from one cell to the next as a tangent curve is tracked, requires the computation of the exit point which is an intersection of the solution of the constant coefficient ODE and the edge of a triangle. There are two possible approaches to this root computation problem. We can express the tangent curve into parametric form and substitute into an implicit form for the edge or we can express the edge in parametric form and substitute in an implicit form of the tangent curve. Normally the solution of a system of ODE's is given in parametric form and so the first approach is the most accessible and straightforward. The second approach requires the 'implicitization' of these parametric curves. The implicitization of parametric curves can often be rather difficult, but in this case we have been successful and have been able to develop algorithms and subsequent computer programs for both approaches. We will give these details along with some comparisons in a forthcoming research paper on this topic.
The thermal conductivity of a fluid exhibits a pronounced anomalous increase in a large range of densities and temperatures around the gas-liquid critical point. In this paper we discuss an attempt to estimate the thermal conductivity in the critical region of fluids from a knowledge of the equilibrium properties and the regular behavior of the transport properties outside the critical region.
Near the liquid-vapor critical point, density stratification supports internal gravity waves which affect 1-g viscosity measurements in the CVX (Critical Viscosity of Xenon) experiment. Two internal-wave modes were seen in the horizontal viscometer. The frequencies of the two modes had different temperature dependences: with decreasing temperature, the higher frequency increased monotonically from 0.7 to 2.8 Hz, but the lower frequency varied non-monotonically, with a maximum of 1.0 Hz at 20 mK above the critical temperature. The measured frequencies agree with independently calculated frequencies to within 15%.
Experiments investigating the stability characteristics of a single-phase free convection loop are reported. Results of the study confirm the contention made by previous workers that instabilities near the thermodynamic critical point can occur for ordinary fluids as well as those with unusual behavior in the near-critical region. Such a claim runs counter to traditional beliefs, but it is supported by the observation of such instabilities for water at atmospheric pressure and moderate temperatures in the present work.
This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.
The dynamic responses of liquid-fuel droplet vaporization and combustion to ambient pressure oscillations are examined. The analysis is based on the complete sets of conservation equations for both gas and liquid phases, and accommodates detailed treatments of finite-rate chemical kinetics and variable properties. With a full account of thermodynamic phase equilibrium at the droplet surface, the model enables a systematic examination of the effects of ambient flow conditions on the droplet behavior. The responses of hydrocarbon fuel droplets in both sub- and super-critical environments are investigated. Results indicate that the droplet gasification and burning mechanisms depend greatly on the ambient pressure. In particular, a rapid enlargement of the vaporization and combustion responses occurs when the droplet surface reaches its critical point, mainly due to the strong variations of latent heat of vaporization and thermophysical properties at the critical state.