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Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗

Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992

The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Liou, William W.↗

Uncertainty reasoning in expert systems

Intelligent control is a very successful way to transform the expert's knowledge of the type 'if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible' into an actual control. To apply this transformation, one must choose appropriate methods for reasoning with uncertainty, i.e., one must: (1) choose the representation for words like 'small', 'big'; (2) choose operations corresponding to 'and' and 'or'; (3) choose a method that transforms the resulting uncertain control recommendations into a precise control strategy. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From a mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. In this project, a new mathematical formalism (based on group theory) is developed that allows us to solve the problem of optimal choice and thus: (1) explain why the existing choices are really the best (in some situations); (2) explain a rather mysterious fact that fuzzy control (i.e., control based on the experts' knowledge) is often better than the control by these same experts; and (3) give choice recommendations for the cases when traditional choices do not work.

Kreinovich, Vladik↗

Research activities at the Center for Modeling of Turbulence and Transition

The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.

Shih, Tsan-Hsing↗

Center for modeling of turbulence and transition: Research briefs, 1993

This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from June 1992 to July 1993. It is also an annual report to the Institute for Computational Mechanics in Propulsion located at Ohio Aerospace Institute and NASA Lewis Research Center. The main objectives of the research activities at CMOTT are to develop, validate, and implement turbulence and transition models for flows of interest in propulsion systems. Currently, our research covers eddy viscosity one- and two-equation models, Reynolds-stress algebraic equation models, Reynolds-stress transport equation models, nonequilibrium multiple-scale models, bypass transition models, joint scalar probability density function models, and Renormalization Group Theory and Direct Interaction Approximation methods. Some numerical simulations (LES and DNS) have also been carried out to support the development of turbulence modeling. Last year was CMOTT's third year in operation. During this period, in addition to the above mentioned research, CMOTT has also hosted the following programs: an eighteen-hour short course on 'Turbulence--Fundamentals and Computational Modeling (Part I)' given by CMOTT at the NASA Lewis Research Center; a productive summer visitor research program that has generated many encouraging results; collaborative programs with industry customers to help improve their turbulent flow calculations for propulsion system designs; a biweekly CMOTT seminar series with speakers from within and without the NASA Lewis Research Center including foreign speakers. In addition, CMOTT members have been actively involved in the national and international turbulence research activities. The current CMOTT roster and organization are listed in Appendix A. Listed in Appendix B are the abstracts of the biweekly CMOTT seminar. Appendix C lists the papers contributed by CMOTT members.

Liou, William W.↗

Dynamic stall of an oscillating wing. Part 1: Evaluation of turbulence models

Unsteady flowfields of a two-dimensional oscillating wing are calculated using an implicit, finite-difference, Navier-Stokes numerical scheme using five widely used turbulence models. The objective of this study is to identify an appropriate turbulence model for accurate simulation of three-dimensional dynamic stall. Three unsteady flow conditions corresponding to attached flow, light-stall, and deep-stall of an oscillating wing experiment were chosen as test cases for computations. Results of unsteady airload hysteresis curves, harmonics of unsteady pressures, and instantaneous flow pictures are presented. Comparison of unsteady airloads with experiment show that all models are deficient in some sense and not a single model predicts all airloads consistently and in agreement with experiment for all flow conditions. For the attached flow condition, the Renormalization Group Theory (RNG), the Johnoson-King (J-K), and the Spalart-Allmaras (S-A) models have better performance. The Baldwin-Lomax (B-L) and the Baldwin-Barth (B-B) models fair poorly. At the light-stall condition, the results for the RNG, the J-K, and S-A models are in agreement with experiment for the upstroke but they all over predict the separation shown by the experiment and therefore have bigger hysteresis loops than experimental results. The B-B model results are also in good agreement for upstroke but have poor lift hysteresis for downstroke. It has superior drag and pitching-moment predictions. For deep-stall conditions, the airloads for the RNG, the B -B, and the S-A models have fair agreement with experiment, but the B-B model performed better at the extreme deep-stall condition. Overall, the RNG model provides significant improvement over the B-L model in all flow regimes with no additional computational cost. The Baldwin-Barth model is the most expensive of the models considered here, costing about 2.5 times that of the Baldwin-Lomax model. Finally, a brief discussion of the effects of grid density, time-step size, and numerical dissipation on the unsteady solutions are also presented.

Srinivasan, G. R.↗

Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil

Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.

Srinivasan, G. R.↗

Measurements of Tc (Q,P): Depression of the Superfluid Transition Temperature by a Heat Current Along the Lambda Line

We report experimental measurements of Tc (Q,P) for heat currents (Q) between I1and 100 micro W/sq cm and pressure (P) between SVP and 15 bar. The measurements were performed in a normal gravity environment, using the low-gravity simulator facility at JPL without the magnet being energized. The sample pressure was controlled to 0.1 micro bar using a hot volume, and a Straty-Adams capacitive pressure gauge. The total volume of helium in the sample cell and the hot volume was held constant using a pneumatic low temperature valve. A melting curve thermometer (MCT) measured the transition temperature (Tc) with a resolution of about 10 nK through a sidewall probe of the thermal conductivity sample cell. We employed the same measurement technique and procedure described by DAS. Preliminary results indicate that Tc (Q,P) depends very little on the pressure in the pressure range between SVP and 15 bar with a variation in the amplitude of Tc(Q,P) of less than about 5% observable in this pressure range. According to the Renormalization-group theory calculation by Haussmann and Dohm, the amplitude of Tc (Q,P) has a leading pressure-dependence term proportional to xi(sub 0) (sup (1/nu)), where xi(sub 0) is the correlation-length amplitude and nu is the correlation-length exponent. Thus, a small pressure dependence of the amplitude of Tc (Q,P) is expected since xi(sub 0) is very weakly dependent on pressure between SVP and 15 bar, consistent with our measurements.

Liu, Yuan-Ming↗

Helium-4 Experiments near T-lambda in a Low-Gravity Simulator

We report our studies of gravity cancellation in a liquid helium sample cell along the lambda-line using a low-gravity simulator facility. The simulator consists of a superconducting magnet capable of producing B(delta-B/delta-z) = 22squareT)/cm. We have verified experimentally that the simulator can cancel gravity to about 0.01g in a cylindrical sample volume of 0.5 cm in diameter and 0.5 cm in height. This allows us to approach more closely the superfluid transition without entering the normal-superfluid two phase region induced by gravity. We also present the measurements of T-c(Q,P): depression of the superfluid transition temperature by a heat current(Q) along the lambda-line (P). The results are consistent with the Renormalization-group theory calculation. Measurements of thermal expansion coefficient in a heat current will also be discussed. The work has been carried out by JPL, California Institute of Technology under contract to NASA.

Liu, Yuanming↗

Measurement of the Specific Heat Using a Gravity Cancellation Approach

The specific heat at constant volume C(sob V) of a simple fluid diverges near its liquid-vapor critical point. However, gravity-induced density stratification due to the divergence of isothermal susceptibility hinders the direct comparison of the experimental data with the predictions of renormalization group theory. In the past, a microgravity environment has been considered essential to eliminate the density stratification. We propose to perform specific heat measurements of He-3 on the ground using a method to cancel the density stratification. A He-3 fluid layer will be heated from below, using the thermal expansion of the fluid to cancel the hydrostatic compression. A 6% density stratification at a reduced temperature of 10(exp -5) can be cancelled to better than 0.1% with a steady 1.7 micro K temperature difference across a 0.05 cm thick fluid layer. A conventional AC calorimetry technique will be used to determine the heat capacity. The minimized bulk density stratification with a relaxation time 6500 sec at a reduced temperature of 10(exp -5) will stay unchanged during 1 Hz AC heating. The smear of the specific heat divergence due to the temperature difference across the cell is about 0.1% at a reduced temperature of 10(exp -6). The combination of using High Resolution Thermometry with a 0.5 n K temperature resolution in the AC technique and the cancellation of the density stratification will enable C(sub V) to be measured down to a reduced temperature of 10(exp -6) with less than a 1% systematic error.

Zhong, Fang↗

A Study in HRT Resolution: Seeking Maximum Sensitivity Among Variations in Sensing Element Material

The EXACT (Experiments Along Coexistence near Tricriticality) project endeavors to perform the most rigorous test to date of Renormalization Group theory. In most cases, the theory gives only approximate solutions, but it offers exact predictions in the case of the He-3-He-4 tricritical point. Currently, the project is focused on maximizing the performance of the low-temperature system's HRT (high resolution thermometer) near the tricritical point. The HRT uses a PdMn sensing element, the qualities of which change based on its Mn concentration and whether or not it is annealed. All sensing element combinations will be catalogued, and through the data, the optimum configuration will be reported.

Morales, Jeremy M.↗

The Goal of the IAU/IAG Joint Working Group on the Theory of Earth Rotation

In 2012 the International Association of Geodesy (IAG) and the International Astronomical Union (IAU) initiated a process to establish a Joint Working Group (JWG) on theory of Earth rotation with the purpose of promoting the development of improved theories of the Earth rotation which reach the accuracy required to meet the needs of the near future as recommended by, e.g. GGOS, the Global Geodetic Observing System of the IAG. The JWG was approved by both organizations in April 2013 with the chairs being the two authors of this paper. Its structure comprises three Sub Working Groups (SWGs) addressing Precession/Nutation, Polar Motion and UT1, the Numerical Solutions and Validation, respectively. The SWGs should work in parallel for the sake of efficiency, but should keep consistency as an overall goal. This paper offers a view of the objectives and scope of the JWG and reports about its initial activities and plans.

Ferrandiz, J. M.↗

Dynamical theory of dense groups of galaxies

It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups.

Mamon, Gary A.↗

On time changes in a digraph.

Probabilistic model for analyzing changes through time in binary dyadic relation on finite set of points

PROBABILITY THEORY↗