Shock compression of a perfect gas

1956 ◽  
Vol 1 (4) ◽  
pp. 399-408 ◽  
Author(s):  
Cerda Evans ◽  
Foster Evans
Keyword(s):  
Shock Compression ◽  
Entropy Change ◽  
Rigid Wall ◽  
Adiabatic Process ◽  
Perfect Gas ◽  
Compression Process ◽  
Specific Heats ◽  
Initial Shock ◽  
The One ◽  
Shock Reflections

The compression of a perfect gas between a uniformaly moving piston and a rigid wall is discussed in the one-dimensional case. If the piston moves with a finite speed, it will initiate a shock in the gas which will reflect successively from rigid wall and piston and cause the compression process to deviate from a reversible adiabatic process. Expressions are derived for the relative changes in pressure and density at each shock reflection. Then values of density and pressure after any number of shock reflections are computed relative to their initial values, and, in terms of these, the corresponding values of temperature and entropy, as well as shock speeds, are determined. The limiting value of the entropy change, as the number of reflections goes to infinity, is obtained as a function of the ratio of specific heats of the gas and the strength of the initial shock. Hence it is possible to estimate an upper limit to the deviation of the shock compression process from a reversible adiabatic process. Some illustrative numerical examples are given.

scholarly journals On the measurement of the ratio of the specific heats using small volumes of gas.—The ratios of the specific heat of air and of hydrogen at atmospheric pressure and a temperatures between 20°C. and —183°C

1925 ◽  
Vol 107 (743) ◽  
pp. 510-543 ◽  
Keyword(s):  
Systematic Error ◽  
Low Temperatures ◽  
Room Temperature ◽  
Expansion Chamber ◽  
Small Vessels ◽  
Specific Heats ◽  
Large Expansion ◽  
Before And After ◽  
The One ◽  
Chamber Capacity

Introduction .—In nearly all the previous determinations of the ratio of the specific heats of gases, from measurements of the pressures and temperature before and after an adiabatic expansion, large expansion chambers of fror 50 to 130 litres capacity have been used. Professor Callendar first suggests the use of smaller vessels, and in 1914, Mercer (‘Proc. Phys. Soc.,’ vol. 26 p. 155) made some measurements with several gases, but at room temperature only, using volumes of about 300 and 2000 c. c. respectively. He obtained values which indicated that small vessels could be used, and that, with proper corrections, a considerable degree of accuracy might be obtained. The one other experimenter who has used a small expansion chamber, capacity about 1 litre, is M. C. Shields (‘Phys. Rev.,’ 1917), who measured this ratio for air and for hydrogen at room temperature, about 18° C., and its value for hydroger at — 190° C. The chief advantage gained by the use of large expansion chambers is that no correction, or at the most, a very small one, has to be made for any systematic error due to the size of the containing vessels, but it is clear that, in the determinations of the ratio of the specific heats of gases at low temperatures, the use of small vessels becomes a practical necessity in order that uniform and steady temperature conditions may be obtained. Owing, however, to the presence of a systematic error depending upon the dimensions of the expansion chamber, the magnitude of which had not been definitely settled by experiment, the following work was undertaken with the object of investigating the method more fully, especially with regard to it? applicability to the determination of this ratio at low temperatures.

Unsteady transonic flows in two-dimensional channels

1972 ◽  
Vol 52 (3) ◽  
pp. 437-449 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Inviscid Flow ◽  
Time Varying ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Flow Disturbance ◽  
Specific Heats ◽  
Isentropic Flow ◽  
Perturbation Potential ◽  
Temporal Flow ◽  
Nozzle Flows

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

scholarly journals XVI. On the specific heats of gases at constant volume.—Part II. Carbon dioxide

1894 ◽  
Vol 185 ◽  
pp. 943-959 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Specific Heat ◽  
Constant Volume ◽  
Specific Heats ◽  
Extended Range ◽  
Absolute Density ◽  
Lower Temperature ◽  
The One ◽  
Range Observation ◽  
Linear Nature

The present paper is occupied with an experimental investigation into the variation of the specific heat at constant volume of carbon dioxide attending change of absolute density. The investigation is in continuation of a previous one, in which Carbon Dioxide, Air, and Hydrogen were the subjects of a similar enquiry over low ranges of density. It appeared to me desirable to extend the observations more especially in the case of carbon dioxide, because of the extended knowledge we already possess of its isothermals, and the fact that its critical temperature is within convenient reach. Other physical properties of the gas have also received much attention of recent years. It is also readily procured in a nearly pure state. The observations recorded in this paper extend, in the one direction, to densities, such that liquid is present at the lower temperature; and in the other, to a junction with the highest densities of the former paper. A plotting of the new observations is in satisfactory agreement with the record of the old. It reveals, however, the fact that the linear nature of the variation of the specific heat with density, deduced from the former results, is not truly applicable over the new, much more extended range observation. For convenience the chart at the end of this paper embraces the former results, and the present paper is extended to include the entire results on the variation of specific heat with density where the range of temperature, obtaining at each experiment, is approximately the same: that from air temperature to 100° C.

scholarly journals I. On the ratio of the specific heats of the paraffins, and their monohalogen derivatives

1894 ◽  
Vol 185 ◽  
pp. 1-36 ◽  
Keyword(s):  
Thermal Properties ◽  
Kinetic Theory ◽  
Kinetic Theory Of Gases ◽  
Perfect Gas ◽  
Specific Heats ◽  
Different Gases

The experiments to be described in the present paper were undertaken in the hope of obtaining data which would throw light on one of the most obscure points of the kinetic theory of gases, namely, the distribution of energy in the molecule. The properties of gases on which the kinetic theory gained its reputation were the constancy of the product of pressure and volume, and the uniformity of the coefficient of expansion. For the explanation of these in the ease of the hypothetical perfect gas no knowledge of the special constitution of the molecule is required, but for most other properties, and especially thermal properties, the kinetic theory fails to explain the facts from want of information concerning the dynamical peculiarities of the molecules of different gases.

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.

Validation of a 3D RANS Solver With a State Equation of Thermally Perfect and Calorically Imperfect Gas on a Multi-Stage Low-Pressure Steam Turbine Flow

2005 ◽  
Vol 127 (1) ◽  
pp. 83-93 ◽  
Author(s):  
Piotr Lampart ◽  
Andrey Rusanov ◽  
Sergey Yershov ◽  
Stanislaw Marcinkowski ◽  
Andrzej Gardzilewicz
Keyword(s):  
Steam Turbine ◽  
Low Pressure ◽  
State Equation ◽  
Linear Functions ◽  
Perfect Gas ◽  
Specific Heats ◽  
Flow Parameters ◽  
Imperfect Gas ◽  
Multi Stage ◽  
Pressure Steam

A state equation of thermally perfect and calorically imperfect gas is implemented in a 3D RANS solver for turbomachinery flow applications. The specific heats are assumed as linear functions of temperature. The model is validated on a five-stage low-pressure steam turbine. The computational results exhibit the process of expansion in the turbine. The computed and measured distributions of flow parameters in axial gaps downstream of subsequent turbine stages are found to agree reasonably well. It is also shown that the obtained numerical solution gives considerable improvement over the solution based on the thermally and calorically perfect gas model.

scholarly journals VI. The specific heats of metals and the relation of specific heat to atomic weight.—Part III

1904 ◽  
Vol 203 (359-371) ◽  
pp. 139-149 ◽  
Keyword(s):  
Specific Heat ◽  
Atomic Weight ◽  
The Other ◽  
Influence Of Temperature ◽  
Specific Heats ◽  
Weight Part ◽  
Chemical Combination ◽  
Influence Of Temperature On ◽  
The Mean ◽  
The One

The law of Neumann assumes that when an atom enters into chemical combination it retains the same capacity for heat as when in the uncombined or elemental state. This generalisation is, however, based on the values observed for the mean specific heats of elements and their compounds between 0° and 100° C. Attention was directed in Part II. of this investigation to the great differences found in the influence of temperature on the specific heats of various metals, such as aluminium on the one hand, and silver or platinum on the other. The experiments now about to be described were undertaken with the object of ascertaining to what extent these differences persist in the compounds of such elements.

A parametric survey of the first critical Mach number for a fast MHD shock

1984 ◽  
Vol 32 (3) ◽  
pp. 429-441 ◽  
Author(s):  
J. P. Edmiston ◽  
C. F. Kennel
Keyword(s):  
Mach Number ◽  
Flow Speed ◽  
Interplanetary Shocks ◽  
Plasma Parameters ◽  
Energetic Ions ◽  
Critical Mach Number ◽  
Specific Heats ◽  
Solar Wind Parameters ◽  
The One ◽  
Downstream Flow

The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.

Unified geometric and analytical treatment of magneto– gasdynamic shocks. Part 2. The shock polars

1973 ◽  
Vol 10 (3) ◽  
pp. 397-423 ◽  
Author(s):  
Lee A. Bertram
Keyword(s):  
Particle Velocity ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Analytical Treatment ◽  
Classification Schemes ◽  
One Dimensional ◽  
The One ◽  
Shock Solution ◽  
Special Case ◽  
Alfven Velocity

Previously derived shock solutions for a perfectly conducting perfect gas are used to compute shock polars for the one-dimensional unsteady and two- dimensional non-aligned shock representations. A new special-case shock solution, having a downstream particle velocity relative to the shock equal to upstream Alfvén velocity, is obtained, in addition to exhaustive analytical classification schemes for the shock polars. Eight classes of one-dimensional polars and twelve classes of two-dimensional polars are identified.

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