Computation of large-scale statistics in decaying isotropic turbulence

We have performed large-eddy simulations of decaying isotropic turbulence to test the prediction of self-similar decay of the energy spectrum and to compute the decay exponents of the kinetic energy. In general, good agreement between the simulation results and the assumption of self-similarity were obtained. However, the statistics of the simulations were insufficient to compute the value of gamma which corrects the decay exponent when the spectrum follows a k(exp 4) wave number behavior near k = 0. To obtain good statistics, it was found necessary to average over a large ensemble of turbulent flows

An Energy Use and Emissions Inventory

Maintaining a 400-acre campus which supports the education of 3000 students requires energy. Data were gathered from across campus as part of a faculty research project and in conjunction with an undergraduate course. The project was initiated in order to develop an energy usage and emissions inventory for the University while at the same offering students exposure to the process. Inventory inputs included stationary consumption (burning of natural gas to supply heat), electricity purchased, campus vehicle usage (gasoline consumption), commuter vehicle usage (faculty and staff only), and transportation and distribution (T&D) expenses. Whereas the student population has increased by only 8% since 2000, the dollar amount budgeted for energy expenses on campus has risen by 50% over the same time period. Emissions from the various energy inputs were analyzed. In 2007, electricity purchased from the local utility company accounted for 74% of the campus energy usage. Since the university does not have direct control over which fuel is being used to provide this needed electricity and since Congress is currently debating “Cap and Trade” legislation, it behooves the university to take a serious look at its energy conservation practices. Recommendations to the university administration include the following: (1) line-item the energy cost to students as a part of their bills, (2) increase the rate of replacing older equipment with high-efficiency units, (3) develop a plan for becoming carbon-neutral by a specified date in the future, and (4) sponsor a project which integrates environmental, business, engineering, and technical writing majors to produce a “Green Guide” for the campus

Similarity states of homogeneous stably-stratified turbulence at infinite Froude number

We present evidence of similarity states which may develop inhomogeneous stably-stratified flows if a dimensionless group in addition to the Reynolds number, the so-called Froude number, is sufficiently large. Here, we define the Froude number as the ratio of the internal wave time-scale to the turbulence time-scale. We examine three different similarity states which may develop depending on the initial conditions of the velocity and density fields. Theoretical arguments and results of large-eddy simulations will be presented. We will conclude this report with some speculative thoughts on similarity states which may develop in stably-stratified turbulence at arbitrary Froude number as well as our future research plans in this area

Cutting Away from the Power Grid

One of the course objectives for the junior-level Thermodynamics course being taught to our mechanical engineering (ME) majors is “students will analyze engineering systems to evaluate their thermodynamic designs”. The Rankine Cycle and its application to power plants were studied intensely. Students were provided with the results of the campus Energy Usage and Emissions Inventory. Some key data which they noted was (1) 74% of the campus energy usage was electricity purchased from the local distributor (2007), (2) roughly 90% of the campus energy usage over the past 10 years was attributed to either purchased electricity or purchased natural gas, and (3) while the student body has grown a modest 8% over the past 10 years, the dollar amount of the energy purchased by Cedarville University has risen 50% over that same 10- year period. Students were then placed onto teams and assigned one of six alternative energy sources (wind, natural gas, fuel cell, solar, biodiesel, or nuclear) for which they developed a Partial Replacement of Campus Electricity plan. Student teams were required to identify Cedarville’s electricity supplier’s energy source, its cost of purchasing the electricity, and the carbon output resulting from the electricity purchased by the university. Their task was to locate an existing commercial power generating unit which could generate at least 15% of Cedarville’s current electricity demands, compute the capital expenditure to purchase and install the unit, and perform a lifecycle analysis in order to compute total cost to the university over a 30-year period for implementing their plan. Though Congress has yet to finalize “Cap-and-Trade” legislation, students were also asked to compute the cost savings to the university for a “carbon credit” of $50 per tonne of CO2 saved. The student teams then developed conclusions as to the viability of their proposals. They freely expressed their feelings about the relative importance of “carbon neutrality” versus their personal educational expenses

Theoretical study of turbulent channel flow: Bulk properties, pressure fluctuations, and propagation of electromagnetic waves

In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr--Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O--S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend stongly on the structure of the turbulence spectrun at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel

Human adaptation to adaptive machines converges to game-theoretic equilibria

Adaptive machines have the potential to assist or interfere with human behavior in a range of contexts, from cognitive decision-making to physical device assistance. Therefore it is critical to understand how machine learning algorithms can influence human actions, particularly in situations where machine goals are misaligned with those of people. Since humans continually adapt to their environment using a combination of explicit and implicit strategies, when the environment contains an adaptive machine, the human and machine play a game. Game theory is an established framework for modeling interactions between two or more decision-makers that has been applied extensively in economic markets and machine algorithms. However, existing approaches make assumptions about, rather than empirically test, how adaptation by individual humans is affected by interaction with an adaptive machine. Here we tested learning algorithms for machines playing general-sum games with human subjects. Our algorithms enable the machine to select the outcome of the co-adaptive interaction from a constellation of game-theoretic equilibria in action and policy spaces. Importantly, the machine learning algorithms work directly from observations of human actions without solving an inverse problem to estimate the human's utility function as in prior work. Surprisingly, one algorithm can steer the human-machine interaction to the machine's optimum, effectively controlling the human's actions even while the human responds optimally to their perceived cost landscape. Our results show that game theory can be used to predict and design outcomes of co-adaptive interactions between intelligent humans and machines

Investigation of the asymptotic state of rotating turbulence using large-eddy simulation

Study of turbulent flows in rotating reference frames has long been an area of considerable scientific and engineering interest. Because of its importance, the subject of turbulence in rotating reference frames has motivated over the years a large number of theoretical, experimental, and computational studies. The bulk of these previous works has served to demonstrate that the effect of system rotation on turbulence is subtle and remains exceedingly difficult to predict. A rotating flow of particular interest in many studies, including the present work, is examination of the effect of solid-body rotation on an initially isotropic turbulent flow. One of the principal reasons for the interest in this flow is that it represents the most basic turbulent flow whose structure is altered by system rotation but without the complicating effects introduced by mean strains or flow inhomogeneities. The assumption of statistical homogeneity considerably simplifies analysis and computation. The principal objective of the present study has been to examine the asymptotic state of solid-body rotation applied to an initially isotropic, high Reynolds number turbulent flow. Of particular interest has been to determine the degree of two-dimensionalization and the existence of asymptotic self-similar states in homogeneous rotating turbulence