A Generalized Approach to One-Dimensional Gas Dynamics

1962 ◽  
Vol 84 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Robert P. Benedict ◽  
William G. Steltz
Keyword(s):  
Compressible Flow ◽  
Gas Dynamics ◽  
Large Scale ◽  
Pressure Ratio ◽  
Flow Function ◽  
Flow Process ◽  
One Dimensional ◽  
Flow Maps ◽  
Shock Process ◽  
Area Variation

We present a Generalized Compressible Flow Function (Γ) which is shown to have direct application in the treatment of many simplified one-dimensional flow processes. Those particular processes treated in this paper are: (a) the familiar adiabatic flows, with or without friction, with area variations always allowed; (b) the little-discussed diabatic flows, with or without friction, with area variations allowed under certain conditions; and (c) the discontinuous normal shock process. Moreover, the Γ function is shown to have significance in a generalized flow process having an arbitrary combination of heat transfer, friction, and area variation. Development of the Γ function is given in some detail. A large scale plot of pressure ratio (p/pt) versus Γ is given along with Generalized Compressible Flow Tables for the convenience of the user. Schematic isentropic, Fanno, Rayleigh, and isothermal flow maps are presented in terms of the conventional enthalpy-entropy diagram, and again in terms of the pressure ratio —Γ diagram. Numerical examples are included to illustrate the solution of typical problems through the use of the Generalized Compressible Flow Tables.

Some Generalizations in One-Dimensional Constant Density Fluid Dynamics

1962 ◽  
Vol 84 (1) ◽  
pp. 44-48
Author(s):  
William G. Steltz ◽  
Robert P. Benedict
Keyword(s):  
Pressure Ratio ◽  
Isothermal Flow ◽  
Direct Application ◽  
Constant Density ◽  
Flow Function ◽  
Flow Process ◽  
One Dimensional ◽  
Flow Maps ◽  
Density Flow ◽  
Flow Processes

We present a Generalized Constant Density Flow Function, Γ, which is shown to have direct application in the treatment of many simplified, workless, one-dimensional flow processes. Those particular flow processes treated in this paper are: the familiar adiabatic flows, with or without friction, with area variations always allowed; and diabatic flows with or without friction, with area variations always allowed. Moreover, the Γ function is shown to have significance in a generalized flow process having an arbitrary combination of heat transfer, friction, and area and elevation variation. Development of the Γ function is given in some detail. Schematic isentropic, Fanno, Rayleigh, and isothermal flow maps are presented in terms of the conventional enthalpy—entropy diagram, and again in terms of the pressure ratio—Γ diagram. Numerical examples are included to illustrate the solution of typical problems through use of the Generalized Constant Density Flow Function.

scholarly journals EDDA: integrated simulation of debris flow erosion, deposition and property changes

2014 ◽  
Vol 7 (6) ◽  
pp. 7267-7316
Author(s):  
H. X. Chen ◽  
L. M. Zhang
Keyword(s):  
Debris Flow ◽  
Yield Stress ◽  
Water Flow ◽  
Large Scale ◽  
Limit Equilibrium ◽  
Flow Density ◽  
Catchment Scale ◽  
Flow Process ◽  
One Dimensional ◽  
Property Changes

Abstract. Debris flow material properties change during the initiation, transportation and deposition processes, which influences the runout characteristics of the debris flow. A quasi-three-dimensional depth-integrated numerical model, EDDA, is presented in this paper to simulate debris flow erosion, deposition and induced material property changes. The model considers changes in debris flow density, yield stress and dynamic viscosity during the flow process. The yield stress of debris flow mixture is determined at limit equilibrium using the Mohr–Coulomb equation, which is applicable to clear water flow, hyper-concentrated flow and fully developed debris flow. To assure numerical stability and computational efficiency at the same time, a variable time stepping algorithm is developed to solve the governing differential equations. Four numerical tests are conducted to validate the model. The first two tests involve a one-dimensional dam-break water flow and a one-dimensional debris flow with constant properties. The last two tests involve erosion and deposition, and the movement of multi-directional debris flows. The changes in debris flow mass and properties due to either erosion or deposition are shown to affect the runout characteristics significantly. The model is also applied to simulate a large-scale debris flow in Xiaojiagou Ravine to test the performance of the model in catchment-scale simulations. The results suggest that the model estimates well the volume, inundated area, and runout distance of the debris flow. The model is intended for use as a module in a real-time debris flow warning system.

A General One-Dimensional Theory of Compressible Inviscid Swirling Flows in Nozzles

1976 ◽  
Vol 27 (3) ◽  
pp. 201-216 ◽  
Author(s):  
P W Carpenter
Keyword(s):  
Compressible Flow ◽  
Mass Flux ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Swirling Flows ◽  
Radial Velocity Component ◽  
Cross Sectional ◽  
One Dimensional ◽  
Analytical Results ◽  
Impulse Function

SummaryAn approximate analytical method is presented for determining the swirling compressible flow through a nozzle. The method is developed from the techniques introduced by Carpenter and Johannesen. It is perfectly general in that the swirl distribution need not be specified a priori but the radial gradients of the stagnation enthalpy and entropy are assumed to be small. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual and smooth for the radial velocity component to be neglected at each section, i e the usual assumption of one-dimensional compressible flow theory. Analytical expressions are derived for various flow characteristics, e g mass-flux coefficient, impulse function and back-pressure ratio required for choking. The analytical results are compared to numerical results for two main classes of swirling flows. On the whole the analytical results are found to be good approximations for moderate swirl levels. The approximate numerical method is found to be reasonably successful at predicting flow reversal at the nozzle wall. The main result is that a swirl parameter is found such that, with the sole exception of the free-vortex case, the mass-flux-coefficient data for all swirling flows investigated collapse onto a single curve.

One-dimensional numerical study of compressible flow ejector

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1469-1472
Author(s):  
S. Han ◽  
J. Peddieson
Keyword(s):  
Compressible Flow ◽  
Numerical Study ◽  
One Dimensional

Altitude Effects on the Performance of Small Radial Turbomachinery: Part I — Compressor Impellers

2016 ◽  
Author(s):  
Dries Verstraete ◽  
Kjersti Lunnan
Keyword(s):  
Reynolds Number ◽  
Performance Analysis ◽  
Rotational Speed ◽  
Pressure Ratio ◽  
Unmanned Aircraft ◽  
Good Match ◽  
One Dimensional ◽  
Design Changes ◽  
Current Article ◽  
The Impact

Small unmanned aircraft are currently limited to flight ceilings below 20,000 ft due to the lack of an appropriate propulsion system. One of the most critical technological hurdles for an increased flight ceiling of small platforms is the impact of reduced Reynolds number conditions at altitude on the performance of small radial turbomachinery. The current article investigates the influence of Reynolds number on the efficiency and pressure ratio of two small centrifugal compressor impellers using a one-dimensional meanline performance analysis code. The results show that the efficiency and pressure ratio of the 60 mm baseline compressor at the design rotational speed drops with 6–9% from sea-level to 70,000 ft. The impact on the smaller 20 mm compressor is slightly more pronounced and amounts to 6–10%. Off-design changes at low rotational speeds are significantly higher and can amount to up to 15%. Whereas existing correlations show a good match for the efficiency drop at the design rotational speed, they fail to predict efficiency changes with rotational speed. A modified version is therefore proposed.

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