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NASA NTRS1977

Concepts and methods for describing critical phenomena in fluids

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.

Sengers, J. V.↗

NASA NTRS1978

Two-scale-factor universality near the critical point of fluids

Thermodynamic data from interferometric density profile studies and light-scattering experiments near the critical isochore of Xe, CO2 and SF6 provide a basis for examining the hypothesized two-scale-factor universality for the correlation function of fluids near the gas-liquid critical point. For the investigation, three-scale-factor universality is assumed, with Ising-like critical exponent values obtained through the renormalization group technique. The two thermodynamic scale factors are found from the density profiles, while the scale factor for the correlation length is obtained from the light-scattering data.

Sengers, J. V.↗

NASA NTRS1984

The rheology of icy satellites

High-temperature creep in orthoenstatite under conditions of controlled oxygen fugacity was studied. It was found that creep was conttrolled by the extremely thin layer of SiO2 which wetted the grain boundaries. Slight reduction of the (Mg, Fe)SiO3 enstatite during hot pressing produced microscopic particles of Fe and the thin film of intergranular SiO2. This result highlights another complication in determining the flow properties of iron bearing silicates which constitute the bulk of terrestrial planets and moons. The Phenomenon may be important in the ductile formation of any extraterrestrial body which is formed in a reducing environment. The rheology of dirty ice was studied. This involves micromechanical modeling of hardening phenomena due to contamination by a cosmic distribution of silicate particles. The larger particles are modeled by suspension theory. In order to handle the distribution of particles sizes, the hardening is readed as a critical phenomenon, and real space renormalization group techniques are used. Smaller particles interact directly with the dislocations. The particulate hardening effect was studied in metals. The magnitude of such hardening in ice and the defect chemistry of ice are studied to assess the effects of chemical contamination by methane, ammonia, or other likely contaminants.

Sammis, C. G.↗

NASA NTRS1985

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

Chapman, G. T.↗

NASA NTRS1985

Diffusion and localization of a particle in a periodic potential coupled to a dissipative environment

The phase diagram of a Hamiltonian which describes a particle moving in a periodic potential and coupled to an external heat bath has been analyzed in detail. By renormalization-group methods, it is proved that this system exhibits an unusual transition between diffusive behavior and a self-trapped phase. The dynamics along the transition line is shown to be integrable and the order parameter, the mobility, is computed exactly.

Guinea, F.↗

NASA NTRS1985

Critical Transport Phenomena in Fluid Helium Under Low Gravity

The feasibility of carrying out measurements of certain critical transport properties of pure fluid under conditions of low gravity was studied. These properties are the thermal conductivity, kappa, the shear viscosity zeta and the diffusive relaxation time tau, which are predicted to diverge (tend to infinity) as the liquid-vapor critical point is approached. However, in this critical region, the Earth's gravity effect becomes very important. As the critical point is approached, the gravity effects increasingly distort the results. The reason for this is that the compressibility of the fluid also diverges and under the influence of gravity causes a vertical density gradient in the fluid, which is significant even when very thin fluid layers (typically 1 mm high) are being used. The result is that the temperature dependence of kappa, zeta, and tau tends to flatten off as T sub c is approached instead of continuing to increase, and therefore the predictions from the renormalization group and mode coupling theories cannot be subjected to a satisfactory test.

Meyer, H.↗

NASA NTRS1984

High accuracy heat capacity measurements through the lambda transition of helium with very high temperature resolution

A measurement of the heat capacity singularity of helium at the lambda transition was performed with the aim of improving tests of the Renormalization Group (RG) predictions for the static thermodynamic behavior near the singularity. The goal was to approach as closely as possible to the lambda-point while making heat capacity measurements of high accuracy. To do this, a new temperature sensor capable of unprecedented resolution near the lambda-point, and two thermal control systems were used. A short description of the theoretical background and motivation is given. The initial apparatus and results are also described.

Fairbanks, W. M.↗

NASA NTRS1986

Universal amplitude ratios and the interfacial tension near consolute points of binary liquid mixtures

The interfacial tension of the binary liquid mixtures triethylamine/heavy water, triethylamine/water, and cyclohexane/methanol near their consolute temperatures is determined experimentally by measuring the densities of the phases and the capillary lengths. The results are presented in tables and graphs and compared with published data obtained by other methods and with theoretical predictions. The findings are shown to be in good agreement with previous experiments, confirming the discrepancy between temperature-independent universal amplitude ratios calculated from such data and those predicted by renormalization-group calculations or Monte Carlo simulations of Ising models.

Moldover, M. R.↗

NASA NTRS1987

High-resolution thermal-conductivity measurements near the lambda point of helium

Measurements of the thermal conductivity of helium in the region from 6 x 10 to the -8th to 6 x 10 to the -4th K above the lambda point at the vapor pressure are reported. Within 5 x 10 to the -6th K of the transition conductivity values are found significantly lower than expected on the basis of theoretical extrapolations from previous experiments. When the parameter Rk is calculated, a maximum about 2 x 10 to the -6th K above the transition is found, in disagreement with the predictions of the two-loop dynamic renormalization-group theory. The uncertainties in the results in this region are discussed in detail.

Lipa, J. A.↗

NASA NTRS1989

High accuracy thermal conductivity measurements near the lambda transition of helium with very high temperature resolution

Over the past few years extensive thermal conductivity measurements near the lambda point of helium were made. The original goal of measuring the thermal conductivity with a resolution of t = T/T sub lambda -1 of 3 x 10(-8) was reached, but with somewhat less accuracy than was hoped. Subtle effects in the apparatus near the transition were observed which reduced the ability to interpret the results. Nevertheless, for resolution of t is greater than or equal to 10(-7) reliable data was obtained, extending previous measurements by more than an order of magnitude. Deviations from theoretical predictions were observed for t is less than or equal to 3 x 10(-6) leading to the question of the validity of the present renormalization group analysis of transport properties, at least for the case of helium. This anomaly led to closer examination of the boundary effects in the measurements. During the experiments a totally unexpected effect in the very dilute He-3 - He-4 mixtures was observed which led to the explanation of the anomalous results. The concentration dependence of the thermal conductivity near T sub lambda in the superfluid phase was found to deviate strongly from the predictions. The results gave an independent verification of this behavior and caused reanalysis of the Khalatnikov theory of hydrodynamics of the mixtures. An alternative solution was found which is in better agreement with the experiment.

Fairbank, William M.↗

NASA NTRS1988

Turbulent viscosity

A model for fully developed turbulence is proposed whose predictions compare favorably with those of the direct interaction approximation (DIA) model and whose main equations are easy to handle. Four different expressions for the turbulent viscosity are derived which contain no free parameters. Two of the expressions are given in terms of properties of the turbulent fluid itself; the other two are given in terms of the instability that generated the turbulence and of the properties of the mean flow. The numerical coefficients entering these relations are evaluated and found to be in good agreement with previous theoretical estimates based on Kraichnan's DIA, the renormalization group method, and turbulence modeling. In the case of shear in the mean flow, the Shakura-Sunyaev alpha parameter is shown to be less than 0.01. The four expressions can be generalized to include the effect of rotation and/or magnetic fields.

Canuto, V. M.↗

NASA NTRS1990

Absence of first-order unbinding transitions of fluid and polymerized membranes

Unbinding transitions of fluid and polymerized membranes are studied by renormalization-group (RG) methods. Two different RG schemes are used and found to give rather consistent results. The fixed-point structure of both RG's exhibits a complex behavior as a function of the decay exponent tau for the fluctuation-induced interaction of the membranes. For tau greater than tau(S2) interacting membranes can undergo first-order transitions even in the strong-fluctuation regime. These estimates for tau(S2) imply, however, that both fluid and polymerized membranes unbind in a continuous way in the absence of lateral tension.

Grotehans, Stefan↗

NASA NTRS1990

Charged polymers in high dimensions

A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

Kantor, Yacov↗

NASA NTRS1991

An analysis of RNG based turbulence models for homogeneous shear flow

In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG based calculation of C(sub epsilon1). It is shown that with the new value of C(sub epsilon1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.

Speziale, Charles G.↗

NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗

NASA NTRS1991

An algebraic RNG-based turbulence model for three-dimensional turbomachinery flows

An algebraic eddy viscosity turbulence model based on Renormalization Group (RNG) theory for complex three-dimensional turbomachinery flows is presented. Modifications are made to the baseline RNG model for wakes and separated flows. The model has several advantages over popular algebraic models most notably its lack of empirically determined coefficients. The model is used to compute the mean flow in a low speed axial compressor rotor. The agreement with blade boundary layer and radial flow experimental data is very good and shows improvement over the Baldwin-Lomax model. The development of the tip leakage vortex is also well predicted. The computed wake decay also compares favorably with recent experimental data.

Kirtley, K. R.↗

NASA NTRS1991

Nonlinear Reynolds stress model for turbulent shear flows

A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

Barton, J. Michael↗

NASA NTRS1991

An analysis of RNG-based turbulence models for homogeneous shear flow

In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon 1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG-based calculation of C(sub epsilon 1). It is shown that with the new value of C(sub epsilon 1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.

Speziale, Charles G.↗