Nozzles for Supersonic Flow Without Shock Fronts

1944 ◽  
Vol 11 (2) ◽  
pp. A93-A100
Author(s):  
Ascher H. Shapiro
Keyword(s):  
Cross Section ◽  
Compressible Fluids ◽  
Three Dimensions ◽  
Infinite Length ◽  
Constant Cross Section ◽  
Nozzle Design ◽  
Wave Fronts ◽  
A Value ◽  
Parallel Stream ◽  
Shock Fronts

Abstract Flow patterns for compressible fluids at supersonic velocities are discussed, and it is shown that shock fronts form when neighboring Mach lines (envelopes of wave fronts originating from point disturbances) intersect. A criterion for divergence of Mach lines is developed for cases in which the passage is symmetrical in two or three dimensions and has a straight axis. This criterion is used as the basis for designing supersonic nozzles and diffusers. The analysis indicates that only a nozzle of infinite length can discharge a parallel stream into a tube of constant cross section without the formation of shock fronts. Methods are presented for designing nozzles of finite length, with the intensity of shock fronts reduced to as small a value as possible, and it is shown that nozzles of reasonable length may be designed so that shock fronts are insignificant. Experimental observations indicate that the proposed method of nozzle design is a practical one. With regard to supersonic diffusers having a straight axis, it is shown that shock fronts cannot be avoided, even though the diffuser is of infinite length. However, the methods of this paper may be used as an aid in determining the best diffuser design.

FLOW OF GAS THROUGH A TUBE OF CONSTANT CROSS-SECTION WITH HEAT EXCHANGE THROUGH THE TUBE WALLS

1945 ◽  
Vol 23a (1) ◽  
pp. 1-11 ◽  
Author(s):  
B. Szczeniowski
Keyword(s):  
Heat Exchange ◽  
Cross Section ◽  
Stream Velocity ◽  
Constant Cross Section ◽  
Velocity Of Sound ◽  
Heat Conductance ◽  
A Value ◽  
Maximum Value ◽  
Theoretical Investigations ◽  
Present View

The influence of the exchange of heat between a gas flowing through a tube and the outside atmosphere on the pressure in the gas stream is usually overlooked. Theoretical investigations show, however, that this influence is marked in the case of large stream velocities, approximating the velocity of sound. In addition, the theory permits us to state that the heat exchange is possible only when the stream velocity is maintained beyond certain limits. For stream velocities within these limits, heat exchange is not possible.The conclusion is reached that the velocity of flow in the tube, if the tube is heated or cooled, shows a natural and permanent tendency to reach the velocity of sound, after which the heat exchange is no longer possible.Finally, this theoretical investigation shows that the present view that the heat conductance coefficient increases continually with the stream velocity is wrong. This coefficient will be equal to zero when the stream velocity reaches the velocity of sound. This means that it will reach a certain maximum value corresponding to a value of stream velocity which is not exactly known but which will be less than that of sound.

scholarly journals Karakteristik Aerodinamika Pontoon Pesawat NXXX Versi Amfibi

2021 ◽  
Vol 12 (2) ◽  
pp. 475-485
Author(s):  
Andreas Maulana Irsabudi ◽  
◽  
Gaguk Jatisukamto ◽  
Hary Sutjahjono
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Cross Section ◽  
Step Height ◽  
Constant Cross Section ◽  
A Value ◽  
Computational Fluid Dynamics Cfd

Seaplanes are aircraft that can take off and landing on water. A seaplane’s requirement is its need to take off and landing on watery conditions which is equipped with a pontoon. Pontoon of a seaplane needs to be evaluated in terms of aerodynamics characteristics when a seaplane flies. The purpose of this study is to determine the correlation of various geometric combinations of deadrise angle, step height, and constant cross-section length with the values of coefficient of drag (CD), coefficient of lift (CL) and coefficient of moment (CM). The methodology was carried out by simulating Computational Fluid Dynamics (CFD) using OpenFOAM software. The results of this study could be concluded that deadrise angle affected coefficient of drag (CD), coefficient of lift (CL) and coefficient of moment (CM) with each value of 0.0055, 0.0044, -0.0036, while step height didn’t influence significantly on coefficient of drag (CD) and didn’t affect coefficient of lift (CL) and coefficient of moment (CM). Constant cross-section length didn’t affect significantly on coefficient of drag (CD) and coefficient of lift (CL) but increasing constant cross-section length increased coefficient of moment (CM) with a value of -0.0039.

Effects of openings on the seismic behavior and performance level of concrete shear walls

2019 ◽  
Author(s):  
Hossein Alimohammadi ◽  
Mostafa Dalvi Esfahani ◽  
Mohammadali Lotfollahi Yaghin
Keyword(s):  
Static Analysis ◽  
Cross Section ◽  
Seismic Behavior ◽  
Shear Walls ◽  
Shear Wall ◽  
Constant Cross Section ◽  
Added Resistance ◽  
Different Shapes ◽  
And Performance ◽  
Abaqus Software

In this study, the seismic behavior of the concrete shear wall considering the opening with different shapes and constant cross-section has been studied, and for this purpose, several shear walls are placed under the increasingly non-linear static analysis (Pushover). These case studies modeled in 3D Abaqus Software, and the results of the ductility coefficient, hardness, energy absorption, added resistance, the final shape, and the final resistance are compared to shear walls without opening.

Condensation in a Variable Acceleration Field and the Condensing Thermosyphon

1965 ◽  
Vol 87 (4) ◽  
pp. 355-360 ◽  
Author(s):  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Radial Distance ◽  
Constant Cross Section ◽  
Linear Variation ◽  
Temperature Differential ◽  
Acceleration Field ◽  
Nusselt Numbers ◽  
Increasing Temperature ◽  
Limiting Values

The general problem of condensation in a variable acceleration field was investigated analytically. The case of the linear variation, which occurs in a constant cross section, rotating thermosyphon, was treated in detail. The results show that the condensate thickness and Nusselt numbers approach limiting values as the radial distance increases. The effects of the temperature differential and the Prandtl number are similar to those in other condensation problems; i.e., the heat transfer increases slightly with increasing temperature differential if Pr > 1, but it decreases with increasing temperature differential if Pr ≪ 1.

Turbulent buoyant convection from a source in a confined region

1969 ◽  
Vol 37 (1) ◽  
pp. 51-80 ◽  
Author(s):  
W. D. Baines ◽  
J. S. Turner
Keyword(s):  
Point Source ◽  
Cross Section ◽  
Laboratory Experiments ◽  
Region Of Interest ◽  
Constant Cross Section ◽  
General Shape ◽  
Turbulent Environment ◽  
Starting Conditions ◽  
Upward Velocity ◽  
Local Mean

This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.

The interaction of kinks and elastic waves

1962 ◽  
Vol 266 (1325) ◽  
pp. 222-246 ◽  
Keyword(s):  
Energy Density ◽  
Cross Section ◽  
Elastic Waves ◽  
String Model ◽  
Zero Point ◽  
Radiation Reaction ◽  
Point Energy ◽  
A Value ◽  
Ordinary Point ◽  
Isotropic Elastic Medium

A kink on a dislocation in an isotropic elastic medium is treated as a 'point defect’ with a certain mass, constrained to move along a line and subject to a radiation reaction. A value for the mass is obtained from the well know n stretched-string model, and the radiation reaction is found by calculating the rate at which an oscillating kink radiates energy into the medium . It is found that the kink has a scattering cross-section for elastic waves which i§ proportional to the square of its width. For long waves the cross-section is independent of frequency, in contrast to the case of ordinary point defects. A kink moving through an isotropic flux of elastic waves experiences a retarding force proportional to the product of its velocity and the energy density of the waves. In connexion with a similar result for the retarding force on a dislocation moving rigidly it has been suggested that the expression for the energy density should include the zero-point energy. A formal quantum -mechanical calculation shows that this is not so in the case of a kink.

Hg(63P1)-sensitized decomposition of HNCO vapor and HNCO–H2 mixtures; the reaction of hydrogen atoms with HNCO

1968 ◽  
Vol 46 (4) ◽  
pp. 527-530 ◽  
Author(s):  
N. J. Friswell ◽  
R. A. Back
Keyword(s):  
Quantum Yield ◽  
Cross Section ◽  
Initial Step ◽  
Primary Process ◽  
Hydrogen Atoms ◽  
Direct Photolysis ◽  
A Value ◽  
The Cross

The Hg(63P1)-sensitized decomposition of HNCO vapor has been briefly studied at 26 °C with HNCO pressures from about 3 to 30 Torr. The products detected were the same as in the direct photolysis, CO, N2, and H2. The quantum yield of CO was appreciably less than unity, compared with a value of 1.5 in the direct photolysis under similar conditions. From this and other observations it is tentatively concluded that a single primary process occurs:[Formula: see text]From a study of the mercury-photosensitized reactions in mixtures of HNCO with H2, it was concluded that hydrogen atoms react with HNCO to form CO but not N2. The initial step is probably addition to form NH2CO. From the competition between reaction [1] and the corresponding quenching by H2, the cross section for reaction [1] was estimated to be 2.3 times that of hydrogen.

Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

scholarly journals Calculation of acoustic flow-rate measurements error with the help of Fermat’s principle

2018 ◽  
Vol 211 ◽  
pp. 04007
Author(s):  
Alexander Petrov ◽  
Semyon Shkundin
Keyword(s):  
Control Systems ◽  
Cross Section ◽  
Flow Rate ◽  
Three Dimensional ◽  
Air Flow Rate ◽  
Velocity Measurements ◽  
Three Dimensional Flow ◽  
Automatic Control Systems ◽  
A Value ◽  
Flow Changes

The establishment of dispatching and automatic control systems for mine ventilation is impossible without the availability of perfect air flow rate sensors. Existing anemometers (tachometer, heat) do not meet these requirements. The error of average in cross section velocity measurements with such sensors reaches 15-20, sometimes 30%. The reason - the speed measured at one point is interpreted as the average over the cross section. The reliability of the sensors is small, because they are exposed to the damaging effect of a dusty atmosphere. Stationary installed anemometers clutter cross section, which is not always allowed. Fermat’s variational principle is used for derivation of the formula for the time of propagation of a sonic signal between two set points A and B in a steady three-dimensional flow of a fluid or gas. It is shown that the fluid flow changes the time of signal reception by a value proportional to the flow rate independently of the velocity profile. The time difference in the reception of the signals from point B to point A and vice versa is proportional with a high accuracy to the flow rate. It is shown that the relative error of the formula does not exceed the square of the largest Mach number. This makes it possible to measure the flow rate of a fluid or gas with an arbitrary steady subsonic velocity field

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