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.

An Analytical Approach for Gas Turbine Parameter Corrections

2008 ◽  
Author(s):  
Vasileios E. Kyritsis ◽  
Pericles Pilidis
Keyword(s):  
Mach Number ◽  
Mass Flow ◽  
Pressure Ratio ◽  
Mathematical Formulation ◽  
Flow Speed ◽  
Correction Factors ◽  
Specific Heats ◽  
Isentropic Exponent ◽  
Scaling Parameters ◽  
Mach Numbers

Turbomachinery component behavior depends on dimensionless parameters, such as inlet and circumferential Mach numbers and the ratio of specific heats. Regarding mass flow and speed, their dimensionless scaling parameters are usually used instead based on Mach number similarity. A given dimensionless aerodynamic operating point is defined by certain values of axial and circumferential Mach numbers. To such a point and for a certain value of isentropic exponent, a given dimensionless enthalpy variation corresponds as the work parameter. When turbo-machinery performance sizes, such as the work parameter and efficiency, are plotted against mass flow and speed to form a characteristic, the absence of the isentropic exponent as an additional dimension causes inaccuracies. The extent of the inaccuracies firstly depends on the scaling groups used for mass low, speed and work, that is whether they include the gas property parameters, such as the isentropic exponent and the gas constant. The aforementioned shows that for rigorous calculations correction factors have to be applied, especially when quasi-dimensionless groups are used and/or pressure ratio is used as the work parameter. Typically, the corrections for mass flow and speed may take the form of multipliers, which consist of ratios of the isentropic exponent and/or the gas constant between the examined condition and the reference one. Alternatively, for the case of mass flow the exponents of temperature and pressure can deviate from their theoretical values of 0.5 and 1.0 respectively. Scope of the current work is the mathematical formulation of such exponents for a variety of scaling groups regarding mass flow, speed and work. The correction factors are a strong function of the operating condition, temperature and gas composition, which fully define gas properties. Among the findings of the current study, evidence is provided that the practically one-to-one relationship considered between dimensionless mass flow and inlet Mach number holds for low Mach number values. This is particularly true, since its sensitivity to variations of the isentropic exponent gets increasingly larger with Mach number. Additionally, for a given dimensionless enthalpy change, the exchange rate of pressure ratio against variations of the isentropic exponent is much more increased for an expansion rather than a compression. The latter justifies the use of dimensionless enthalpy drop in turbine characteristics.

The Effect of Variable Solar Wind Conditions on the Bow Shock Structure and its Ability to Generate Energetic Ions

2020 ◽  
Author(s):  
Harald Kucharek ◽  
Matthew Young ◽  
Noe Lugaz ◽  
Charles Farrugia ◽  
Steven Schwartz ◽  
...  
Keyword(s):  
Solar Wind ◽  
Plasma Heating ◽  
Bow Shock ◽  
Interplanetary Shocks ◽  
Plasma Parameters ◽  
Energetic Ions ◽  
Suprathermal Ions ◽  
Upstream Solar Wind ◽  
The Magnetic Field ◽  
Bulk Plasma

<p>Turbulent fluctuations in the magnetic field and in the bulk plasma parameters of the solar wind have important effects on the propagation and evolution of energetic particles throughout the heliosphere and on the coupling of the solar wind to the Earth's magnetosphere. At the shock the solar wind kinetic energy is converted into downstream plasma heating, ion reflection and acceleration. Changes in upstream plasma conditions can result in changes in the dynamics of the shock, its structure, and the suprathermal ion population it generates. These upstream variations can be due to transients, interplanetary shocks, and other discontinuities. They can also result from nonlinear interactions, causing an intermittent energy dissipation and leading to possible currents sheet structures. A number of these events can be found in observations from STEREO (for interplanetary traveling shocks) and CLUSTER/MMS (for the Earth’s bow shock) in the magnetosheath. </p><p>We performed 3D-hybrid simulations to study the effects of spatially confined disturbances, such as density enhancements, depletions, and current layers/sheets and studied the shock dynamics, and the energetic particle release at various distances from the bow shock. The results of these simulations are then discussed in terms of multi-spacecraft observations in the magnetosheath at various scales.  The results show that shock reformation is highly impacted by density depressions/enhancements and so is the generation of waves and suprathermal ions. Also, upstream solar wind variations can alter the shock properties considerably at the various virtual spacecraft in the simulations.</p>

ABOUT CONSTRUCTION OF FLAT BODIES WITH INCREASED CRITICAL MACH NUMBER

2016 ◽  
Vol 47 (6) ◽  
pp. 563-579
Author(s):  
Sergey Alexandrovich Takovitskii
Keyword(s):  
Mach Number ◽  
Critical Mach Number

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.

Aeroelastic Problems in connection with High-Speed Flight

1956 ◽  
Vol 60 (547) ◽  
pp. 459-475 ◽  
Author(s):  
E. G. Broadbent
Keyword(s):  
Mach Number ◽  
High Speed ◽  
The Other ◽  
Control Surface ◽  
The Past ◽  
Other Hand ◽  
Aerodynamic Derivatives ◽  
Mach Numbers ◽  
The One

SummaryA review is given of developments in the field of aeroelasticity during the past ten years. The effect of steadily increasing Mach number has been two-fold: on the one hand the aerodynamic derivatives have changed, and in some cases brought new problems, and on the other hand the design for higher Mach numbers has led to thinner aerofoils and more slender fuselages for which the required stiffness is more difficult to provide. Both these aspects are discussed, and various methods of attack on the problems are considered. The relative merits of stiffness, damping and massbalance for the prevention of control surface flutter are discussed. A brief mention is made of the recent problems of damage from jet efflux and of the possible aeroelastic effects of kinetic heating.

scholarly journals Critical Mach Numbers of Flow around Two-Dimensional and Axisymmetric Bodies

Aerodynamics ◽  
2021 ◽  
Author(s):  
Vladimir Frolov
Keyword(s):  
Mach Number ◽  
Cross Section ◽  
Flow Simulation ◽  
The Body ◽  
Two Dimensional ◽  
Critical Mach Number ◽  
Method Of Integral Relations ◽  
Viscosity Factor ◽  
Mach Numbers ◽  
Axisymmetric Bodies

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

scholarly journals Self-Consistent Cathode–Plasma Coupling and Role of the Fluid Flow Approach in Torch Modeling

2021 ◽  
Author(s):  
Margarita Baeva ◽  
Tao Zhu ◽  
Thorben Kewitz ◽  
Holger Testrich ◽  
Rüdiger Foest
Keyword(s):  
Mach Number ◽  
Gas Flow ◽  
Stokes Equations ◽  
Cathode Plasma ◽  
Plasma Parameters ◽  
Plasma Properties ◽  
Flow Rates ◽  
High Mach Number ◽  
Self Consistent ◽  
High Mach

AbstractA two-dimensional and stationary magnetohydrodynamic model of a plasma spray torch operated with argon is developed to predict the plasma properties in a steady operating mode. The model couples a submodel of a refractory cathode and its non-equilibrium boundary layer to a submodel of the plasma in local thermodynamic equilibrium in a self-consistent manner. The Navier–Stokes equations for a laminar and compressible flow are solved in terms of low and high Mach number numerical approaches. The results show that the Mach number can reach values close to one. Simulations are performed for electric currents of 600 A and 800 A, and gas flow rates of 40, 60, and 80 NLPM. The plasma parameters obtained by the two approaches differ, and the differences become more pronounced for higher currents and gas flow rates. The arc voltage, the electric power, and the thermal efficiency from both the low and high Mach number models of the plasma agree well with experimental findings for a current of 600 A and a flow rate of 40 NLPM. For higher currents and gas flow rates, the results of the low and high Mach number models gradually differ and underline the greater appropriateness of the high Mach number model.

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.

Experiments with a Pitot Rake at M = l·60

1963 ◽  
Vol 67 (636) ◽  
pp. 793-795 ◽  
Author(s):  
V. G. Quincey ◽  
J. Callinan
Keyword(s):  
Mach Number ◽  
Tube Diameter ◽  
Rectangular Slab ◽  
The One

SummaryTests at a Mach number of 1·60 show clear evidence of interference on the end tubes of a Pitot rake whose adjacent tubes touch. This effect is increased when the rake is made into a solid rectangular slab by the addition of fillets between the tubes. By making the gap between the tubes equal to one tube diameter the interference is almost eliminated.The magnitude of the interference on the end tubes is considerably affected by the ratio of the Pitot orifice to the tube diameter; of the three values of this ratio tested the one close to unity (i.e. a sharp-edged Pitot) was found to have the least interference.

Sign in / Sign up

Export Citation Format

Share Document