A model for closing the inviscid form of the average-passage equation system

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented

Improved Approximation Algorithms for Stochastic Matching

In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive profit, and each node is assigned a positive integer called timeout. We know whether an edge exists or not only after probing it. On this random graph we are executing a process, which one-by-one probes the edges and gradually constructs a matching. The process is constrained in two ways: once an edge is taken it cannot be removed from the matching, and the timeout of node $v$ upper-bounds the number of edges incident to $v$ that can be probed. The goal is to maximize the expected profit of the constructed matching. For this problem Bansal et al. (Algorithmica 2012) provided a $3$-approximation algorithm for bipartite graphs, and a $4$-approximation for general graphs. In this work we improve the approximation factors to $2.845$ and $3.709$, respectively. We also consider an online version of the bipartite case, where one side of the partition arrives node by node, and each time a node $b$ arrives we have to decide which edges incident to $b$ we want to probe, and in which order. Here we present a $4.07$-approximation, improving on the $7.92$-approximation of Bansal et al. The main technical ingredient in our result is a novel way of probing edges according to a random but non-uniform permutation. Patching this method with an algorithm that works best for large probability edges (plus some additional ideas) leads to our improved approximation factors

Semidirect computations for transonic flow

A semidirect method, driven by a Poisson solver, was developed for inviscid transonic flow computations. It is an extension of a recently introduced algorithm for solving subsonic rotational flows. Shocks are captured by implementing a form of artificial compressibility. Nonisentropic cases are computed using a shock tracking procedure coupled with the Rankine-Hugoniot relationships. Results are presented for both subsonic and transonic flows. For the test geometry, an unstaggered cascade of 20 percent thick circular arc airfoils at zero angle of attack, shocks are crisply resolved in supercritical situations and the algorithm converges rapidly. In addition, the convergence rate appears to be nearly independent of the entropy and vorticity production at the shock

Three red giants with substellar-mass companions

We present three giant stars from the ongoing Penn State-Toru\'n Planet Search with the Hobby-Eberly Telescope, which exhibit radial velocity variations that point to a presence of planetary --mass companions around them. BD+49 828 is a $M=1.52 \pm 0.22$ $M_{\odot}$ K0 giant with a $m sini$=$1.6^{+0.4}_{-0.2}$ $M_{J}$ minimum mass companion in $a=4.2^{+0.32}_{-0.2}$ AU ($2590^{+300}_{-180}$d), $e=0.35^{+0.24}_{-0.10}$ orbit. HD 95127, a log$L$/$L_{\odot}$=$2.28 \pm 0.38$, $R = 20\pm 9$ $R_{\odot}$, $M=1.20 \pm 0.22$ $M_{\odot}$ K0 giant has a $m sini$=$5.01^{+0.61}_{-0.44}$ $M_{J}$ minimum mass companion in $a=1.28^{+0.01}_{-0.01}$ AU ($482^{+5}_{-5}$d), $e=0.11^{+0.15}_{-0.06}$ orbit. Finally, HD 216536, is a $M=1.36 \pm 0.38$ $M_{\odot}$ K0 giant with a $m sin i=1.47^{+0.20}_{-0.12}$ $M_{J}$ minimum mass companion in $a=0.609^{+0.002}_{-0.002}$ AU ($148.6^{+0.7}_{-0.7}$d), $e=0.38^{+0.12}_{-0.10}$ orbit. Both, HD 95127 b and HD 216536 b in their compact orbits, are very close to the engulfment zone and hence prone to ingestion in the near future. BD+49 828 b is among the longest period planets detected with the radial velocity technique until now and it will remain unaffected by stellar evolution up to a very late stage of its host. We discuss general properties of planetary systems around evolved stars and planet survivability using existing data on exoplanets in more detail.Comment: 47 pages, 11 figures. Accepted by Ap

TAPAS - Tracking Advanced Planetary Systems with HARPS-N. II. Super Li-rich giant HD 107028

Lithium rich giant stars are rare objects. For some of them, Li enrichment exceeds abundance of this element found in solar system meteorites, suggesting that these stars have gone through a Li enhancement process. We identified a Li rich giant HD 107028 with A(Li) > 3.3 in a sample of evolved stars observed within the PennState Torun Planet Search. In this work we study different enhancement scenarios and we try to identify the one responsible for Li enrichment for HD 107028. We collected high resolution spectra with three different instruments, covering different spectral ranges. We determine stellar parameters and abundances of selected elements with both equivalent width measurements and analysis, and spectral synthesis. We also collected multi epoch high precision radial velocities in an attempt to detect a companion. Collected data show that HD 107028 is a star at the base of Red Giant Branch. Except for high Li abundance, we have not identified any other anomalies in its chemical composition, and there is no indication of a low mass or stellar companion. We exclude Li production at the Luminosity Function Bump on RGB, as the effective temperature and luminosity suggest that the evolutionary state is much earlier than RGB Bump. We also cannot confirm the Li enhancement by contamination, as we do not observe any anomalies that are associated with this scenario. After evaluating various scenarios of Li enhancement we conclude that the Li-overabundance of HD 107028 originates from Main Sequence evolution, and may be caused by diffusion process.Comment: Accepted for publication in A&

Supersonic unstalled flutter

Flutter analyses were developed to predict the onset of supersonic unstalled flutter of a cascade of two-dimensional airfoils. The first of these analyzes the onset of supersonic flutter at low levels of aerodynamic loading (i.e., backpressure), while the second examines the occurrence of supersonic flutter at moderate levels of aerodynamic loading. Both of these analyses are based on the linearized unsteady inviscid equations of gas dynamics to model the flow field surrounding the cascade. These analyses are utilized in a parametric study to show the effects of cascade geometry, inlet Mach number, and backpressure on the onset of single and multi degree of freedom unstalled supersonic flutter. Several of the results are correlated against experimental qualitative observation to validate the models

Tracking Advanced Planetary Systems (TAPAS) with HARPS-N. III. HD 5583 and BD+15 2375 - two cool giants with warm companions

Evolved stars are crucial pieces to understand the dependency of the planet formation mechanism on the stellar mass and to explore deeper the mechanism involved in star-planet interactions. Over the past ten years, we have monitored about 1000 evolved stars for radial velocity variations in search for low-mass companions under the Penn State - Torun Centre for Astronomy Planet Search program with the Hobby-Eberly Telescope. Selected prospective candidates that required higher RV precision measurements have been followed with HARPS-N at the 3.6 m Telescopio Nazionale Galileo under the TAPAS project. We aim to detect planetary systems around evolved stars to be able to build sound statistics on the frequency and intrinsic nature of these systems, and to deliver in-depth studies of selected planetary systems with evidence of star-planet interaction processes. For HD 5583 we obtained 14 epochs of precise RV measurements collected over 2313 days with the Hobby-Eberly Telescope (HET), and 22 epochs of ultra-precise HARPS-N data collected over 976 days. For BD+15 2375 we collected 24 epochs of HET data over 3286 days and 25 epochs of HARPS-S data over 902 days. We report the discovery of two planetary mass objects orbiting two evolved Red Giant stars: HD~5583 has a m sin i = 5.78 M$_{J}$ companion at 0.529~AU in a nearly circular orbit (e=0.076), the closest companion to a giant star detected with the RV technique, and BD+15~2735 that with a m sin i= 1.06 M$_{J}$ holds the record of the lightest planet found so far orbiting an evolved star (in a circular e=0.001, 0.576~AU orbit). These are the third and fourth planets found within the TAPAS project, a HARPS-N monitoring of evolved planetary systems identified with the Hobby-Eberly Telescope.Comment: 9 pages, 6 figures. Accepted by Astronomy and Astrophysic

Turbomachinery

The discipline research in turbomachinery, which is directed toward building the tools needed to understand such a complex flow phenomenon, is based on the fact that flow in turbomachinery is fundamentally unsteady or time dependent. Success in building a reliable inventory of analytic and experimental tools will depend on how the time and time-averages are treated, as well as on who the space and space-averages are treated. The raw tools at disposal (both experimentally and computational) are truly powerful and their numbers are growing at a staggering pace. As a result of this power, a case can be made that a situation exists where information is outstripping understanding. The challenge is to develop a set of computational and experimental tools which genuinely increase understanding of the fluid flow and heat transfer in a turbomachine. Viewgraphs outline a philosophy based on working on a stairstep hierarchy of mathematical and experimental complexity to build a system of tools, which enable one to aggressively design the turbomachinery of the next century. Examples of the types of computational and experimental tools under current development at Lewis, with progress to date, are examined. The examples include work in both the time-resolved and time-averaged domains. Finally, an attempt is made to identify the proper place for Lewis in this continuum of research

A numerical simulation of the inviscid flow through a counter-rotating propeller

The results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration are presented. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown