scholarly journals Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 439
Author(s):  
Mikhail V. Chernyshov ◽  
Anna S. Kapralova ◽  
Stanislav A. Matveev ◽  
Karina E. Savelova
Keyword(s):  
Energy Release ◽  
Adiabatic Index ◽  
Normal Shock ◽  
Von Neumann ◽  
Reflection Transition ◽  
Real Gas Effects ◽  
Analytical Relations ◽  
Transition Criterion ◽  
Oblique Shocks ◽  
Detonation Model

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Real gas effects on the normal shock behavior near curved walls

1993 ◽  
Vol 5 (11) ◽  
pp. 2996-3003 ◽  
Author(s):  
G. H. Schnerr ◽  
P. Leidner
Keyword(s):  
Normal Shock ◽  
Real Gas ◽  
Real Gas Effects ◽  
Curved Walls

The Effect of Shock Waves on the Isentropic Efficiency of Convergent— Divergent Nozzles

1958 ◽  
Vol 62 (569) ◽  
pp. 377-382
Author(s):  
B. W. Martin ◽  
F. J. Bayley
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Back Pressure ◽  
Normal Shock ◽  
Specific Heats ◽  
Plane Normal ◽  
Design Value ◽  
Set Up ◽  
Isentropic Efficiency ◽  
Oblique Shocks

Now a Days, the phenomenon is well known of the plane normal shock waves set up in the divergent section of a convergent-divergent nozzle, and the oblique shocks which occur in the resultant jet downstream of the nozzle exit when operating under overall pressure ratios less than the design value. Stodola was among the first to demonstrate experimentally the effect on the flow within the nozzle of increasing the back pressure above the design value, and work by Schmidt, Martin) and others, has been concerned with the theoretical changes in pressure, temperature, density and Mach number across a normal shock wave whose position varies along the nozzle axis. The effect of working substance on these changes, which is taken into account by the ratio of specific heats, has also been investigated.

An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
K. Hejranfar ◽  
S. Rahmani
Keyword(s):  
Theoretical Analysis ◽  
The Body ◽  
Mathematical Function ◽  
Perfect Gas ◽  
Real Gas ◽  
One Dimensional ◽  
Wide Range ◽  
Different Types ◽  
Real Gas Effects ◽  
Analytical Relations

In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine–Hugoniot equations are applied to provide a relationship between the disturbances field of two sides of the shock. To incorporate real gas effects in the formulation, real gas relations and equilibrium air curve-fits are used in the resulting system of equations. The general formulation presented here may be simplified to derive Morkovin's formulation by the perfect gas assumption. The magnitudes of downstream disturbances field resulting from different types of upstream disturbances field (entropy wave and fast/slow acoustic waves) with the shock are expressed by appropriate analytical relations. Results for different disturbance variables are presented for a wide range of upstream Mach number considering real gas effects and compared with those of the perfect gas and some conclusions are made. The effects of the presence of body are also studied theoretically and the analytical relations for the magnitude of the pressure disturbance at the body for different types of upstream disturbances field considering real gas effects are provided and their results are presented and discussed.

scholarly journals Разрушение стационарного вихря в упругой среде за счет внешнего энергетического воздействия

2020 ◽  
Vol 90 (4) ◽  
pp. 574
Author(s):  
В.С. Сухомлинов ◽  
А.С. Мустафаев ◽  
А.А. Страхова ◽  
Н.А. Тимофеев
Keyword(s):  
Flow Pattern ◽  
Energy Release ◽  
Decay Time ◽  
Heat Conductivity ◽  
Vortex Tube ◽  
Large Diameter ◽  
Ideal Gas ◽  
Total Power ◽  
Analytical Relations ◽  
Tube Structure

The problem of the infinite vortex tube structure dynamics in an ideal gas with an explosive external supply of energy near its axis solution is considered. It was found that, neglecting viscosity and heat conductivity, the tube collapses at an arbitrarily low power of energy release, while the decay time of the vortex decreases with increasing total power of energy release. A physical flow pattern that explains the discovered patterns is constructed. Analytical relations for the practical use of explosives in the destruction of large-diameter vortices are obtained. Estimates show that the proposed method is practically feasible.

Characterization of disturbance propagation in weak shock-wave reflections

1994 ◽  
Vol 277 ◽  
pp. 331-345 ◽  
Author(s):  
Akihiro Sasoh ◽  
Kazuyoshi Takayama
Keyword(s):  
Mach Reflection ◽  
Weak Shock ◽  
Propagation Speed ◽  
Pressure Increase ◽  
Mach Stem ◽  
Local Curvature ◽  
Von Neumann ◽  
Disturbance Propagation ◽  
Transition Criterion ◽  
Trajectory Angle

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection, the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by χ1 = χs where χ1 is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by χg—θw (χg is the angle of glancing incidence, and θw is the apex angle of the wedge) and χs is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0° to 30°, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.

Evaluation of the Cycle Averaged Performances of a Pulsed Detonation Engine Based on Thermodynamic Cycle Computations

2016 ◽  
Author(s):  
Cleopatra Florentina Cuciumita ◽  
Tudor Cuciuc ◽  
Ionut Porumbel
Keyword(s):  
Pressure Ratio ◽  
Numerical Data ◽  
Thermodynamic Cycle ◽  
Thermodynamic Efficiency ◽  
Specific Work ◽  
Numerical Application ◽  
Von Neumann ◽  
Pulsed Detonation ◽  
Detonation Engine ◽  
Detonation Model

The paper presents a numerical algorithm for the theoretical calculation of the thermodynamic cycle of a pulsed detonation based engine, based on the Zeldovich – von Neumann – Doring detonation model, together with the algorithm employed to perform them, and a numerical application. The results are compared to numerical data obtained for the Chapman – Jouguet detonation thermodynamic parameters using the NASA – Glenn Chemical Equilibrium Program CEA2. As a reference, the thermodynamic cycle of a Brayton engine operating under the same conditions of compressor pressure ratio and fuel mass flow rate is computed and included in the paper. It is found that the CEA2 detonation model predicts a very low engine thermodynamic efficiency, while the ZND model yields a higher efficiency of the detonation based engine with respect to the Brayton cycle engine. The specific work of the detonation engine is higher than the Brayton engine, but the power remains lower.

NUMERICAL SIMULATIONS OF INVISCID AIRFLOWS IN RAMJET INLETS

2009 ◽  
Vol 33 (2) ◽  
pp. 271-296 ◽  
Author(s):  
M. Akbarzadeh ◽  
M. J. Kermani
Keyword(s):  
Numerical Simulations ◽  
Heat Rate ◽  
Artificial Viscosity ◽  
Back Pressure ◽  
Normal Shock ◽  
Nozzle Throat ◽  
Flux Limiter ◽  
Fluent Software ◽  
Oblique Shocks ◽  
Good Agreement

The performances of three different ramjet inlets and an entire ramjet are numerically studied in this paper. The fluid is assumed to be inviscid. Inlet 1 is a SCRAMJET inlet and is chosen from the literature. Inlets 2 and 3 are instead designed based on the Oswatitsch principle. Inlets 2 and 3 produce a series of oblique shocks merging at the engine cowl lip followed by a terminating normal shock just downstream of the inlet throat. In ramjet, the combustion is modeled using a non-uniform volumetric heat source distributed in the combustor area. The position of the terminating normal shock in Inlets 2 and 3 is controlled via the inlet’s back pressure. Instead, in ramjet it is bounded by the amount of heat rate added in combustor and the exhaust nozzle throat area. For the numerical simulations, the Roe (1981) and MacCormack (1969) schemes are used. To prevent the spurious numerical oscillations in high resolution computations by Roe scheme the van Albada flux limiter (1982) is used, while in MacCormack scheme artificial viscosity terms are added to damp the oscillations. To double check the accuracy of the computations, the Fluent software package has also been used. Comparisons show very good agreement.

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

Von Neumann, Morgenstern, and the Creation of Game Theory

2010 ◽  
Author(s):  
Robert Leonard
Keyword(s):  
Game Theory ◽  
Von Neumann ◽  
The Creation
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