The Polytropic Approach in Modelling Compressible Flows Through Constant Cross-Section Pipes

2021 ◽  
Author(s):  
Alessandro Ferrari ◽  
Oscar Vento ◽  
Tantan Zhang
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Compressible Flows ◽  
Analytical Formula ◽  
Local Maximum ◽  
Wall Friction ◽  
Numerical Code ◽  
Maximum Temperature ◽  
Constant Cross Section ◽  
Polytropic Exponent

Abstract A compressible flow with wall friction has been predicted in a constant cross-section duct by means of a barotropic modelling approach, and new analytical formulas have been proposed that also allow any possible heat transfer to the walls to be taken into account. A comparison between the distributions of the steady-state flow properties, pertaining to the new formulas, and to those of a classic Fanno analysis has been performed. In order to better understand the limits of the polytropic approach in nearly chocked flow applications, a numerical code, which adopts a variable polytropic coefficient along the duct, has been developed. The steady-state numerical distributions along the pipe, obtained for either a viscous adiabatic or an inviscid diabatic flow by means of this approach, coincide with those of the Fanno and Rayleigh models for Mach numbers up to 1. A constant polytropic exponent can be adopted for a Fanno flow that is far from choking conditions, while it cannot be adopted for the simulation of a Rayleigh flow, even when the flow is not close to choking conditions. Finally, under the assumption of diabatic flows with wall friction, the polytropic approach, with a constant polytropic exponent, is shown to be able to accurately approximate cases in which no local maximum is present for the temperature along the duct. The Mach number value at the location where the local maximum temperature possibly occurs has been obtained by means of a new analytical formula.

scholarly journals Steady-state flow of a shear-thinning liquid in an unbounded pipeline system

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Giovanni P. Galdi ◽  
Carlo R. Grisanti
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Existence And Uniqueness ◽  
Shear Thinning ◽  
Pipeline System ◽  
Constant Cross Section ◽  
Steady State Flow ◽  
Compactness Property ◽  
Newtonian Liquids ◽  
Steady State Solutions

AbstractWe show existence and uniqueness of steady-state solutions to the equations of generalized Newtonian liquids of shear-thinning type in an unbounded region that includes semi-infinite cylinders of constant cross-section (pipeline system). This result is established under the assumption that the datum (flow-rate) is sufficiently small. The main feature of our approach is the proof of a “global compactness” property of the sequence of approximating solutions.

scholarly journals Estimation of the Maximum Temperature in a Radially Constricted Gas Discharge Between Electrodes

1961 ◽  
Vol 14 (1) ◽  
pp. 129
Author(s):  
PW Seymour
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Free Boundary ◽  
Cross Section ◽  
Discharge Tube ◽  
Boundary Surface ◽  
Gas Discharge ◽  
Maximum Temperature ◽  
Main Question ◽  
The Cross

A steady-state deuterium discharge between two electrodes is considered and the free boundary surface of the plasma is assumed thermally insulated when pinched away from the walls of the discharge tube. Cooling is therefore by heat conduction to the electrodes, compared to which bremsstrahlung loss is shown to be negligible if the discharge is not too long. The main question examined is how much the maximum temperature T m can be raised by constricting the cross section of the discharge near the centre.

Prediction of Tire Tread Wear with FEM Steady State Rolling Contact Simulation

2003 ◽  
Vol 31 (3) ◽  
pp. 189-202 ◽  
Author(s):  
D. Zheng
Keyword(s):  
Weight Loss ◽  
Steady State ◽  
Cross Section ◽  
Rolling Contact ◽  
Dynamic Simulations ◽  
Element Analysis ◽  
Vehicle Acceleration ◽  
Steady State Rolling ◽  
Driving Conditions ◽  
Rate Profile

Abstract A procedure based on steady state rolling contact Finite Element Analysis (FEM) has been developed to predict tire cross section tread wear profile under specified vehicle driving conditions. This procedure not only considers the tire construction effects, it also includes the effects of materials, vehicle setup, test course, and driver's driving style. In this algorithm, the vehicle driving conditions are represented by the vehicle acceleration histogram. Vehicle dynamic simulations are done to transform the acceleration histogram into tire loading condition distributions for each tire position. Tire weight loss rates for different vehicle accelerations are generated based on a steady state rolling contact simulation algorithm. Combining the weight loss rate and the vehicle acceleration histogram, nine typical tire loading conditions are chosen with different weight factors to represent tire usage conditions. It is discovered that the tire tread wear rate profile is changing continuously as the tire is worn. Simulation of a new tire alone cannot be used to predict the tire cross-section tread wear profile. For this reason, an incremental tread wear simulation procedure is performed to predict the tire cross section tread wear profile. Compared with actual tire cross-section tread wear profiles, good results are obtained from the simulations.

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.

scholarly journals Transient Current Density in a Pair of Long Parallel Conductors

2021 ◽  
Vol 11 (15) ◽  
pp. 6920
Author(s):  
Oldřich Coufal
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Current Density ◽  
Circular Cross Section ◽  
Transient Current ◽  
Constant Current ◽  
Voltage Source ◽  
Sinusoidal Voltage ◽  
Steady State Current ◽  
Maximum Current

Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

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.

Drawing of Tubes

1980 ◽  
Vol 47 (4) ◽  
pp. 736-740 ◽  
Author(s):  
D. Durban
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Radial Flow ◽  
Material Behavior ◽  
Wall Friction ◽  
Flow Rule ◽  
Flow Conditions ◽  
Steady State Flow ◽  
Linear Hardening ◽  
Von Mises

The process of the tube drawing between two rough conical walls is analyzed within the framework of continuum plasticity. Material behavior is modeled as rigid/linear-hardening along with the von-Mises flow rule. Assuming a radial flow pattern and steady state flow conditions it becomes possible to obtain an exact solution for the stresses and velocity. Useful relations are derived for practical cases where the nonuniformity induced by wall friction is small. A few restrictions on the validity of the results are discussed.

Sign in / Sign up

Export Citation Format

Share Document