Dual-Solution and Choked Flow Treatment in a Streamline Curvature Throughflow Solver

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Prashant Tiwari ◽  
Alex Stein ◽  
Yu-Liang Lin
Keyword(s):  
Supersonic Flow ◽  
Dual Solution ◽  
Gradient Term ◽  
Transonic Flows ◽  
Choked Flow ◽  
Streamline Curvature ◽  
Short Period ◽  
Curvature Gradient ◽  
Suitable Technique ◽  
Flow Treatment

In most turbomachinery design systems, streamline curvature based throughflow calculations make the backbone of aero design process. The fast, reliable, and easy to understand solution is especially useful in performing several multistage design iterations in a short period of time. Although the streamline curvature based technique enjoys many benefits for subsonic applications, there are some challenges for transonic and supersonic flow applications, which is the focus of this paper. In this work, it is concluded that three key improvements are required to handle transonic flows in a streamline curvature throughflow solver. These are (1) the ability to overcome dual sub and supersonic solutions and guide the solver towards a supersonic flow solution where applicable; (2) a suitable technique to calculate the streamline curvature gradient term, which can avoid singularity at sonic meridional Mach number and high gradient values in transonic flows; and (3) a suitable technique to handle choked flow in the turbomachinery flowpath. Solution procedures for “dual-solution” and choked flow treatment are new and developed as part of this work. However, a procedure for calculating streamline curvature gradient is leveraged from earlier work done by Denton (1978, “Throughflow Calculations for Transonic Axial Flow Turbines,” Trans. ASME, 100, pp. 212–218) and Came (1995, “Streamline Curvature Throughflow Analysis,” VDI-Ber., 1185, p. 291). Implementation of these improvements is performed in a streamline curvature based throughflow solver. Numerical improvements presented here have been tested for a range of compressor and turbine cases (both subsonic and supersonic). It is shown that the numerical improvements presented in this paper resulted in an enhanced version of the streamline curvature throughflow solver. The new code produces consistent solutions for subsonic applications with no sacrifice in the accuracy of the solver. However, considerable robustness improvements are achieved for transonic turbine cases.

Dual-Solution and Choked Flow Treatment in a Streamline Curvature Throughflow Solver

2011 ◽  
Author(s):  
Prashant Tiwari ◽  
Alex Stein ◽  
Yu-Liang Lin
Keyword(s):  
Supersonic Flow ◽  
Dual Solution ◽  
Gradient Term ◽  
Transonic Flows ◽  
Choked Flow ◽  
Streamline Curvature ◽  
Short Period ◽  
Curvature Gradient ◽  
Suitable Technique ◽  
Flow Treatment

In most turbomachinery design systems streamline curvature based throughflow calculations makes the backbone of aero design process. The fast, reliable and easy to understand solution is especially useful in performing several multistage design iterations in a short period of time. Although the streamline curvature based technique enjoys many benefits for subsonic applications there are some challenges for transonic and supersonic flow applications, which is the focus of this paper. In this work it is concluded that three key improvements are required to handle transonic flows in a streamline curvature throughflow solver. These are: 1) ability to overcome dual sub- and supersonic solution and guide the solver towards supersonic flow solution where applicable; 2) suitable technique to calculate the streamline curvature gradient term which can avoid singularity at sonic meridional Mach number and high gradient values in transonic flows; 3) suitable technique to handle choked flow in the turbomachinery flowpath. Solution procedures for “dual-solution” and choked flow treatment are new and developed as part of this work. However, procedure for calculating streamline curvature gradient is leveraged from earlier work done by Denton [1] and Came [2]. Implementation of these improvements is performed in a streamline curvature based throughflow solver. Numerical improvements presented here have been tested for a range of compressor and turbine cases (both subsonic and supersonic). It is shown that the numerical improvements presented in this paper resulted in an enhanced version of streamline curvature throughflow solver. The new code produces consistent solution for subsonic applications with no sacrifice in accuracy of the solver. However, considerable robustness improvements are achieved for transonic turbine cases.

scholarly journals Developed liquid film passing a trailing edge under the action of gravity and capillarity

2018 ◽  
Vol 850 ◽  
pp. 924-953 ◽  
Author(s):  
B. Scheichl ◽  
R. I. Bowles ◽  
G. Pasias
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Asymptotic Structure ◽  
General Sense ◽  
Trailing Edge ◽  
Choked Flow ◽  
Edge Singularity ◽  
Streamline Curvature ◽  
Free Interaction ◽  
Weak Disturbances

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

Models of comets with strongly variable nongravitational effects

1999 ◽  
Vol 173 ◽  
pp. 381-387
Author(s):  
M. Królikowska ◽  
G. Sitarski ◽  
S. Szutowicz
Keyword(s):  
Cometary Nucleus ◽  
Spin Axis ◽  
Reactive Force ◽  
Orbital Elements ◽  
Cometary Nuclei ◽  
Short Period ◽  
Basic Parameters ◽  
Polar Radius ◽  
Cometary Activity ◽  
Nongravitational Effects

AbstractThe nongravitational motion of five “erratic” short-period comets is studied on the basis of published astrometric observations. We present the precession models which successfully link all the observed apparitions of the comets: 21P/Giacobini-Zinner, 31P/Schwassmann-Wachmann 2, 32P/Comas Solá, 37P/Forbes, and 43P/Wolf-Harrington. We used the Sekanina's forced precession model of the rotating cometary nucleus to include the nongravitational terms into equations of the comet's motion. Values of six basic parameters (four connected with the rotating comet nucleus and two describing the precession of spin-axis of the nucleus) have been determined along the orbital elements from positional observations of the comets. The solutions were derived with additional assumptions which introduce instantaneous changes of modulus of reactive force,Aand of maximum of cometary activity with respect to perihelion time. The present precession models impose some contraints on sizes and rotational periods of cometary nuclei. According to our solutions the nucleus of 21P/Giacobini-Zinner with oblateness along the spin-axis of about 0.32 (equatorial to polar radius of 1.46) is the most oblate among five investigated comets.

Covering of cometary nucleus by refractory crust and its evolution into asteroid-like body

1999 ◽  
Vol 173 ◽  
pp. 365-370
Author(s):  
Kh.I. Ibadinov
Keyword(s):  
Laboratory Experiments ◽  
Cometary Nucleus ◽  
Sublimation Rate ◽  
Cometary Nuclei ◽  
Short Period Comet ◽  
Short Period ◽  
Brightness Decrease ◽  
Crust Thickness ◽  
Ice Sublimation ◽  
Period Comet

AbstractFrom the established dependence of the brightness decrease of a short-period comet dependence on the perihelion distance of its orbit it follows that part of the surface of these cometary nuclei gradually covers by a refractory crust. The results of cometary nucleus simulation show that at constant insolation energy the crust thickness is proportional to the square root of the insolation time and the ice sublimation rate is inversely proportional to the crust thickness. From laboratory experiments resulted the thermal regime, the gas productivity of the nucleus, covering of the nucleus by the crust, and the tempo of evolution of a short-period comet into the asteroid-like body studied.

From the Oort cloud to Halley-type comets

1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
Author(s):  
J.A. Fernández ◽  
T. Gallardo
Keyword(s):  
Total Population ◽  
Complex Function ◽  
Dynamical Evolution ◽  
Oort Cloud ◽  
Capture Process ◽  
Influx Rate ◽  
Short Period ◽  
Dynamical Properties ◽  
Orbital Periods ◽  
Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods < 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq <2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods < 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Some comments about observations and image processing of comet 29P/Schwassmann-Wachmann 1

1999 ◽  
Vol 173 ◽  
pp. 243-248
Author(s):  
D. Kubáček ◽  
A. Galád ◽  
A. Pravda
Keyword(s):  
Image Processing ◽  
Large Scale ◽  
Harvard College ◽  
Oak Ridge ◽  
Large Scale Structures ◽  
Short Period Comet ◽  
Short Period ◽  
Scale Structures ◽  
Harvard College Observatory ◽  
Period Comet

AbstractUnusual short-period comet 29P/Schwassmann-Wachmann 1 inspired many observers to explain its unpredictable outbursts. In this paper large scale structures and features from the inner part of the coma in time periods around outbursts are studied. CCD images were taken at Whipple Observatory, Mt. Hopkins, in 1989 and at Astronomical Observatory, Modra, from 1995 to 1998. Photographic plates of the comet were taken at Harvard College Observatory, Oak Ridge, from 1974 to 1982. The latter were digitized at first to apply the same techniques of image processing for optimizing the visibility of features in the coma during outbursts. Outbursts and coma structures show various shapes.

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