Numerical Simulation of Inviscid Transonic Flow Through Nozzles With Fluctuating Back Pressure

1989 ◽  
Vol 111 (2) ◽  
pp. 169-180 ◽  
Author(s):  
A. Bo¨lcs ◽  
T. H. Fransson ◽  
M. F. Platzer
Keyword(s):  
Steady State ◽  
Two Dimensions ◽  
Back Pressure ◽  
Nozzle Geometry ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Transonic Flows ◽  
One Dimensional ◽  
Flux Vector Splitting ◽  
Shock Position

The study presents a numerical method, based on the flux vector splitting approach, to the problem of unsteady one-dimensional and two-dimensional inviscid transonic flows, with emphasis on the numerical determination of the shock position, through nozzles with time-varying back pressure. The model is first validated by comparison with exact (one dimension) and numerical (two dimensions) steady-state solutions. It is thereafter applied to the problem of time-fluctuating back pressure in quasi-one-dimensional and two-dimensional nozzles. The one-dimensional results are validated by comparison with a small perturbation analytical unsteady solution, whereafter a few sample cases are presented with the objective of understanding fundamental aspects of unsteady transonic flows. It is concluded that both the amplitude and frequency of the imposed fluctuating exit pressure are important parameters for the location of the unsteady shock. It is also shown that the average unsteady shock position is not necessarily identical with the steady-state position, and that the unsteady shock may, under certain circumstances, propagate upstream into the subsonic flow domain. The pressure jump over the shock, as well as the unsteady post-shock pressure, is different for identical shock positions during the cycle of fluctuation, which implies that an unsteady shock movement, imposed by oscillating back pressure, may introduce a significant unsteady lift and moment. This may be of importance for flutter predictions. It is also noted that, although the sonic velocity is obtained in the throat of steady-state, quasi-one-dimensional flow, this is not necessarily true for the unsteady solution. During part of the period with fluctuating back pressure, the flow velocity may be subsonic at the throat and still reach a supersonic value later in the nozzle. This phenomenon depends on the frequency and amplitude of the imposed fluctuation, as well as on the nozzle geometry.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

An Instrument for One- or Two-Dimensional Tracking

1965 ◽  
Vol 21 (1) ◽  
pp. 307-312
Author(s):  
William C. Roehrig
Keyword(s):  
Low Cost ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Error Signal ◽  
One Dimensional ◽  
Constant Torque ◽  
Sinusoidal Motion ◽  
The Cross ◽  
Target Path

A rugged electro-mechanical tracking apparatus of simple, low-cost construction is described. The apparatus can be used for one-dimensional tracking by connecting only the longitudinal motor, thus forcing the target to move back and forth in either simple sinusoidal motion or according to the sum of two or three sinusoids. The relative phases of the three sinusoids can be rapidly altered, as can the amplitudes (within limits) of each of the sinusoids. The frequency of the sinusoids can be changed either independently or conjointly. By also connecting the cross-feed motor, an essentially unpredictable target path in two dimensions is obtained, and this path can be rapidly altered by changing cams, and/or frequency, amplitude, and phase of the sinusoids. Movement of the cursor is by low, constant torque lathe-type controls. The distance the cursor moves per each rotation of the controls, can be altered for either or both of the controls. A continuous error signal is generated which is directly proportional to the distance the cursor is off target in any direction.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

Steady-State Bifurcation for a Biological Depletion Model

2016 ◽  
Vol 26 (04) ◽  
pp. 1650066 ◽  
Author(s):  
Yan’e Wang ◽  
Jianhua Wu ◽  
Yunfeng Jia
Keyword(s):  
Steady State ◽  
Bifurcation Theory ◽  
Steady States ◽  
Two Dimensional ◽  
Implicit Function ◽  
Flux Boundary Condition ◽  
One Dimensional ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Theoretical Results

A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.

Two Dimensional Ultrasonic Beam Distortion in the Breast: In Vivo Measurements and Effects

1992 ◽  
Vol 14 (4) ◽  
pp. 398-414 ◽  
Author(s):  
P. D. Freiburger ◽  
D. C. Sullivan ◽  
B. H. LeBlanc ◽  
S. W. Smith ◽  
G. E. Trahey
Keyword(s):  
Two Dimensions ◽  
System Response ◽  
Two Dimensional ◽  
Time Data ◽  
Phase Aberration ◽  
One Dimensional ◽  
Function Generation ◽  
Spread Function ◽  
Generation Computer

Two dimensional arrival time data was obtained for the propagation of ultrasound across the breasts of 7 female volunteers. These profiles were extracted through the use of cross-correlation measurements and a simulated annealing process that maintained phase closure while aligning the data. The phase aberration measured in two dimensions had a larger magnitude than previously reported phase aberration measured in one dimension in the breast A point spread function generation computer program was used to demonstrate the system response degrading effects of the measured phase aberration and the usefulness of current one dimensional phase aberration correction techniques. The results indicate that two dimensional correction algorithms are necessary to restore the system performance losses due to phase aberration.

scholarly journals Investment in time preference and long-run distribution

2019 ◽  
Vol 71 (2) ◽  
pp. 171-190
Author(s):  
Takashi Hayashi
Keyword(s):  
Steady State ◽  
Time Preference ◽  
Dimensional Space ◽  
Physical Capital ◽  
Two Dimensional ◽  
Lower Side ◽  
One Dimensional ◽  
Dynamic General Equilibrium Model ◽  
Long Run ◽  
Opt Out

AbstractThis paper presents a simple dynamic general equilibrium model in which each household can make a costly investment in patience capital at each time. We show that the interior long-run steady state is unstable, in the sense that per household, there is a one-dimensional curve lying in the two-dimensional space of its patience capital and physical capital amounts, and convergence happens only when its initial pair falls exactly on the curve. Households with the initial vectors falling in the upper side of the curve invest more in patience capital, which leads themselves to save more, and hence, the consumption level grows in the long run. Households with the initial vectors falling in the lower side opt out from investing in patience capital, leading to a decay of patience level, which leads themselves to save less and hence they perish in the long run. We also show a possibility that there is an expanding swing between the two classes.

Two-Dimensional Thin-Layer Chromatography on Two-Layer Plates of Amino Acids

1970 ◽  
Vol 16 (8) ◽  
pp. 662-666 ◽  
Author(s):  
F Kraffczyk ◽  
R Helger ◽  
H Lang
Keyword(s):  
Amino Acids ◽  
Thin Layer ◽  
Thin Layer Chromatography ◽  
Two Dimensions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Acid Cation ◽  
Solvent Systems ◽  
Strong Acids ◽  
Layer Chromatography

Abstract Separation of the amino acids in urine by use of thin-layer chromatography (TLC) has hitherto required that the specimen be first desalted and then chromatographed in two dimensions with at least two pairs of developing solvent systems. We wished to simplify both steps. The customary method of desalting on a column is replaced by desalting on a plate that supports a strongly acid cation-exchanger and a cellulose layer. This method, originally developed for one-dimensional TLC, is used here for two-dimensional TLC. Urine is applied to the ion-exchange layer and strong acids and neutral substances are removed with water. The amino acids are then chromatographed into the cellulose layer, and are separated there two dimensionally with a newly devised pair of developing solutions. This pair of solvents separates nearly all of the amino acids in urine.

A Comparison of Diffusion Flame Stability in One and Two Spatial Dimensions Near Cold, Inert Surfaces

2001 ◽  
Author(s):  
Robert Vance ◽  
Indrek S. Wichman
Keyword(s):  
Two Dimensions ◽  
Low Flow ◽  
Dimensional System ◽  
Flame Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Cellular Flames ◽  
The One ◽  
Inert Surfaces

Abstract A linear stability analysis is performed on two simplified models representing a one-dimensional flame between oxidizer and fuel reservoirs and a two-dimensional “edge-flame” between the same reservoirs but above a cold, inert wall. Comparison of the eigenvalue spectra for both models is performed to discern the validity of extending the results from the one-dimensional problem to the two-dimensional problem. Of primary interest is the influence on flame stability of thermal-diffusive imbalances, i.e. non-unity Lewis numbers. Flame oscillations are observed when Le > 1, and cellular flames are witnessed when Le < 1. It is found that when Le > 1 the characteristics of flame behavior are consistent between the two models. Furthermore, when Le < 1, the models are found to be in good agreement with respect to the magnitude of the critical wave numbers. Results from the coarse mesh analysis of the two-dimensional system are presented and compared to the one-dimensional eigenvalue spectra. Additionally, an examination of low reactant convection is undertaken. It is concluded that for low flow rates the behavior in one and two dimensions are similar qualitatively and quantitatively.

Development of a Spray-Coated Tactile Sensor – Prototype and Modeling of 2D Sensor on Cylindrical Surface –

2019 ◽  
Vol 31 (6) ◽  
pp. 882-893
Author(s):  
Kouki Sato ◽  
Luis Canete ◽  
Takayuki Takahashi ◽  
◽  
Keyword(s):  
Equivalent Circuit ◽  
Cylindrical Surface ◽  
Delay Time ◽  
Tactile Sensor ◽  
Two Dimensions ◽  
One Dimension ◽  
Two Dimensional ◽  
One Dimensional ◽  
Contact Position ◽  
Spray Gun

The objective of this study is to extend the application of the spray-coated tactile sensor, ScoTacS, which is being developed by the authors and can be constructed simply by “coating” with a spray gun, from one dimension to two dimensions, and further to configure it into various shapes such as a ring. This sensor is constructed by coating three layers-conductive, piezoelectric, and resistive films-in sequence. It is based on a unique principle by which the contact position is detected from the delay time, i.e., the time difference between the arrivals of peaks in the output signals. As the delay time varies with the contact position, it can be used to estimate the contact position. In this paper, after analyzing the characteristics of one-dimensional sensors, such as linear and ring sensors, we present the equivalent circuit models and experimental results of a two-dimensional sensor fully coated on a cylinder.

A Numerical Study of High Temperature and High Velocity Gaseous Hydrogen Flow in a Cooling Channel of a Nuclear Thermal Rocket Core

2014 ◽  
Author(s):  
K. M. Akyuzlu
Keyword(s):  
Steady State ◽  
Gaseous Hydrogen ◽  
Hydrodynamic Characteristics ◽  
Two Dimensional ◽  
Cooling Channel ◽  
Fuel Cladding ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hydrogen Flow ◽  
Cooling Channels

Two mathematical models (a one-dimensional and a two-dimensional) were adopted to study, numerically, the thermal hydrodynamic characteristics of flow inside the cooling channels of a Nuclear Thermal Rocket (NTR) engine. In the present study, only a single one of the cooling channels of the reactor core is simulated. The one-dimensional model adopted here assumes the flow in this cooling channel to be steady, compressible, turbulent, and subsonic. The physics based mathematical model of the flow in the channel consists of conservation of mass, momentum, and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The working fluid (gaseous hydrogen) is assumed to be compressible through a simple ideal gas relation. The physical and transport properties of the hydrogen is assumed be temperature dependent. The governing equations of the compressible flow in cooling channels are discretized using the second order accurate MacCormack finite difference scheme. Convergence and grid independence studies were done to determine the optimum computational cell mesh size and computational time increment needed for the present simulations. The steady state results of the proposed model were compared to the predictions by a commercial CFD package (Fluent.) The two-dimensional CFD solution was obtained in two domains: the coolant (gaseous hydrogen) and the ZrC fuel cladding. The wall heat flux which varied along the channel length (as described by the nuclear variation in the nuclear power generation) was given as an input. Numerical experiments were carried out to simulate the thermal and hydrodynamic characteristics of the flow inside a single cooling channel of the reactor for a typical NERVA type NTR engine where the inlet mass flow rate was given as an input. The time dependent heat generation and its distribution due to the nuclear reaction taking place in the fuel matrix surrounding the cooling channel. Numerical simulations of flow and heat transfer through the cooling channels were generated for steady state gaseous hydrogen flow. The temperature, pressure, density, and velocity distributions of the hydrogen gas inside the coolant channel are then predicted by both one-dimensional and two-dimensional model codes. The steady state predictions of both models were compared to the existing results and it is concluded that both models successfully predict the steady state fluid temperature and pressure distributions experienced in the NTR cooling channels. The two dimensional model also predicts, successfully, the temperature distribution inside the nuclear fuel cladding.

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