Paper 34: Effects of Variable Specific Heats and Gas Composition on Unsteady Flow Calculations

1969 ◽  
Vol 184 (7) ◽  
pp. 101-107 ◽  
Author(s):  
R. S. Benson ◽  
A. Wild ◽  
D. Woollatt
Keyword(s):  
Pipe Wall ◽  
Exhaust System ◽  
New Method ◽  
Gas Composition ◽  
Perfect Gas ◽  
Engine Exhaust ◽  
One Dimensional ◽  
Specific Heats ◽  
Flow Problems ◽  
Longitudinal Variations

A numerical method has been developed for the solution of one-dimensional non-steady flow problems including the effects of friction, gradual area change, heat transfer between the gas and the pipe wall, longitudinal variations, and discontinuities in gas composition and entropy. The fluid considered obeys the perfect gas equation of state, but the specific heats may vary with temperature. The method is not intended for use when shocks are present, but will give an approximate solution if shocks occur. The accuracy of the new method has been checked against existing methods for more simple cases, and although the new method has been found to be slightly superior it is more complicated, much slower, and the boundary conditions are more difficult to develop. For this reason, it is suggested that the new method be used to check on the adequacy of the existing simpler methods for each new application. The methods have been compared for the case of a typical diesel engine exhaust system and it has been found that the earlier methods are adequate for all practical purposes.

The Application of Unsteady Gas-Dynamic Theories to the Exhaust System of Turbocharged Two-Stroke Engines

1966 ◽  
Vol 88 (1) ◽  
pp. 31-39 ◽  
Author(s):  
D. Woollatt
Keyword(s):  
Numerical Calculation ◽  
Unsteady Flow ◽  
Digital Computer ◽  
Exhaust System ◽  
One Dimensional ◽  
Flow Problems ◽  
Gas Dynamic ◽  
Crank Angle ◽  
Measured Pressure ◽  
Development Engineer

The paper reviews the methods available for solution of unsteady-flow problems and describes an approximate method which is suitable for numerical calculation on a digital computer. Results of calculations made by this method assuming homentropic, one-dimensional flow are compared with measured pressure versus crank-angle diagrams in the exhaust system of turbocharged two-stroke engines. It is considered that the results achieved are sufficiently accurate to be of use to the design or development engineer.

One-dimensional adiabatic flow of equilibrium gas–particle mixtures in long vertical ducts with friction

1989 ◽  
Vol 203 ◽  
pp. 251-272 ◽  
Author(s):  
Guido Buresti ◽  
Claudio Casarosa
Keyword(s):  
Equilibrium Mixture ◽  
Adiabatic Heating ◽  
Explosive Eruptions ◽  
Perfect Gas ◽  
Typical Application ◽  
One Dimensional ◽  
Adiabatic Flow ◽  
Flow Parameters ◽  
Constant Area ◽  
Inlet Conditions

The equations of the steady, adiabatic, one-dimensional flow of an equilibrium mixture of a perfect gas and incompressible particles, in constant-area ducts with friction, are derived taking into account the effects of gravity and of the finite volume of the particles. As is the case for a pure gas, the mixture is shown to be subject to the phenomenon of choking, and the possibility of an adiabatic heating of the mixture in a subsonic expansion is also theoretically predicted for certain flow inlet conditions. The model may be used to approximately describe the conditions existing in portions of volcanic conduits during the Plinian phases of explosive eruptions. Some results of the numerical integration of the equations for a typical application of this type are briefly discussed, thus showing the potential of the model for carrying out rapid analyses of the influence of the main geometrical and flow parameters describing the problem. A non-volcanological application is also analysed to illustrate the possibility of the adiabatic heating of the mixture.

The determination of arc temperatures from shock velocities

1957 ◽  
Vol 240 (1220) ◽  
pp. 54-66 ◽  
Keyword(s):  
Shock Wave ◽  
Strong Shock ◽  
Weak Shock ◽  
Wave Theory ◽  
New Method ◽  
Shock Propagation ◽  
Plane Shock ◽  
Gas Temperature ◽  
Specific Heats ◽  
Arc Discharges

The measurement of the high gas temperatures associated with arc discharges requires special techniques. One such method, developed by Suits (1935), depends on the measure­ment of the velocity of a sound wave passing through an arc column, although in fact Suits measured the velocity of a very weak shock wave. The new method described in the present paper is one in which temperatures are determined from the measurement of the velocity of a relatively strong shock wave propagated through an arc. The new method has the merit of consistently producing accurately measurable records and of increasing the accuracy of the temperature determination. The shock velocities are measured by means of a rotating mirror camera. Within the arc, the shock propagation is observable by virtue of the increased arc brightness produced by the shock. In the non-luminous regions surrounding the arc, the shock propagation is displayed by means of a Schlieren system. The interpretation of the measurements depends upon a one-dimensional analysis given in this paper which is similar to that of Chisnell (1955) and which describes the interaction of a plane shock with a con­tinuously varying temperature distribution. In our analysis account is taken also of the continuous variation in specific heats and molecular weight which are of importance under high gas temperature conditions. In practice plane wave theory cannot adequately describe the shock propagation, since attenuation occurs both in the free gas and in the arc column. The effects of this attenuation on the temperature determinations may be accounted for by the use of an experimentally determined attenuation relationship given in the paper. The finally developed method yields temperature values to an accuracy of ± 2%. Experiments are described for carbon and tungsten arcs in air and nitrogen for currents up to 55 amperes and pressures up to 3 atmospheres. The values obtained range from 6200 to 7700° K and are in good agreement with values determined by other techniques.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems

1995 ◽  
Vol 117 (4) ◽  
pp. 683-690 ◽  
Author(s):  
Peter E. Raad ◽  
Shea Chen ◽  
David B. Johnson
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Pressure Field ◽  
Flow Simulation ◽  
New Method ◽  
Computational Domain ◽  
Critical Feature ◽  
Flow Problems ◽  
Macro Cell ◽  
Marker And Cell Method

A new method of calculating the pressure field in the simulation of two-dimensional, unsteady, incompressible, free surface fluid flow by use of a marker and cell method is presented. A critical feature of the new method is the introduction of a finer mesh of cells in addition to the regular mesh of finite volume cells. The smaller (micro) cells are used only near the free surface, while the regular (macro) cells are used throughout the computational domain. The movement of the free surface is accomplished by the use of massless surface markers, while the discrete representation of the free surface for the purpose of the application of pressure boundary conditions is accomplished by the use of micro cells. In order to exploit the advantages offered by micro cells, a new general equation governing the pressure field is derived. Micro cells also enable the identification and treatment of multiple points on the free surface in a single surface macro cell as well as of points on the free surface that are located in a macro cell that has no empty neighbors. Both of these situations are likely to occur repeatedly in a free surface fluid flow simulation, but neither situation has been explicitly taken into account in previous marker and cell methods. Numerical simulation results obtained both with and without the use of micro cells are compared with each other and with theoretical solutions to demonstrate the capabilities and validity of the new method.

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