Chemical amplification at the wave head of a finite amplitude gasdynamic disturbance

1977 ◽  
Vol 81 (2) ◽  
pp. 257-264 ◽  
Author(s):  
J. F. Clarke
Keyword(s):  
Shock Wave ◽  
Sound Speed ◽  
Method Of Characteristics ◽  
Ignition Time ◽  
Finite Amplitude ◽  
General State ◽  
Expansion Waves ◽  
Shock Wave Formation ◽  
Reactive Mixture ◽  
Background State

Consider a background state which consists of a spatially uniform chemically reactive mixture in a general state of disequilibrium. The analytical method of characteristics is used to show that a plane finite amplitude disturbance propagates through this system at the frozen sound speed and, if the degree of disequilibrium is sufficient, is amplified by the chemical reaction. Some comments are made about the time to shock-wave formation and its relation to the homogeneous explosion ignition time, and also about expansion waves, which are found to have a tendency towards fixed-strength ‘quenching waves’, their strength being proportional to the extent of the ambient disequilibrium.

Shock Tube Simulation of the Transient Surge Phase Inside an Axial Compressor

2018 ◽  
Author(s):  
Paul Xiubao Huang ◽  
Robert S. Mazzawy
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
High Speed ◽  
Transient Flow ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Dynamic Effect ◽  
Initiation Site ◽  
Flow Reversal ◽  
Expansion Waves

This paper is a continuing work from one author on the same topic of the transient aerodynamics during compressor stall/surge using a shock tube analogy by Huang [1, 2]. As observed by Mazzawy [3] for the high-speed high-pressure (HSHP) ratio compressors of the modern aero-engines, surge is an event characterized with the stoppage and reversal of engine flow within a matter of milliseconds. This large flow transient is accomplished through a pair of internally generated shock waves and expansion waves of high strength. The final results are often dramatic with a loud bang followed by the spewing out of flames from both the engine intake and exhaust, potentially damaging to the engine structure [3]. It has been demonstrated in the previous investigations by Marshall [4] and Huang [2] that the transient flow reversal phase of a surge cycle can be approximated by the shock tube analogy in understanding its generation mechanism and correlating the shock wave strength as a function of the pre-surge compressor pressure ratio. Kurkov [5] and Evans [8] used a guillotine analogy to estimate the inlet overpressure associated with the sudden flow stoppage associated with surge. This paper will expand the progressive surge model established by the shock tube analogy in [2] by including the dynamic effect of airflow stoppage using an “integrated-flow” sequential guillotine/shock tube model. It further investigates the surge formation (characterized by flow reversal) and propagation patterns (characterized by surge shock and expansion waves) after its generation at different locations inside a compressor. Calculations are conducted for a 12-stage compressor using this model under various surge onset stages and compared with previous experimental data [3]. The results demonstrate that the “integrated-flow” model closely replicates the fast moving surge shock wave overpressure from the stall initiation site to the compressor inlet.

scholarly journals FORMATION OF SINGULARITY AND SMOOTH WAVE PROPAGATION FOR THE NON-ISENTROPIC COMPRESSIBLE EULER EQUATIONS

2011 ◽  
Vol 08 (04) ◽  
pp. 671-690 ◽  
Author(s):  
GENG CHEN
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Initial Data ◽  
Differential Equations ◽  
Euler Equations ◽  
Hyperbolic Systems ◽  
Ideal Gas ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Shock Wave Formation

We define the notion of compressive and rarefactive waves and derive the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize Lax's singularity (shock wave) formation results (established in 1964 for hyperbolic systems with two variables) to the 3 × 3 compressible Euler equations for a polytropic ideal gas. Our results are valid globally without restriction on the size of the variation of initial data.

scholarly journals The production of waves by the sudden release of a spherical distribution of compressed air in the atmosphere

1941 ◽  
Vol 178 (973) ◽  
pp. 153-170 ◽  
Keyword(s):  
Shock Wave ◽  
Sound Wave ◽  
Complete Solution ◽  
Spherical Wave ◽  
Three Dimensional ◽  
Wave Theory ◽  
Initial Distribution ◽  
Finite Amplitude ◽  
Compressed Air ◽  
Compressible Medium

An attempt has been made to develop a method for dealing with solutions of problems connected with the production of waves by spherical concentrations of compressed air. Starting from the general equations for three-dimensional spherically symmetrical flow in a homogeneous compressible medium having constant entropy everywhere, a process has been devised to apply step-by-step calculations over small intervals of time to investigate the general features of such a motion. A complete solution has been worked out in one particular case for a not very intense initial distribution of pressure, and various indirect checks have indicated that the results are reasonably accurate. These results show m any features of definite interest. As distinct from plane or spherical sound wave theory, it is found that a train of waves passes away from the centre of disturbance, the amplitudes and wave lengths falling off from wave to wave. Furthermore, as distinct from finite amplitude plane wave theory which shows that any wave must eventually become a shock wave, the waves obtained in the finite amplitude spherical wave case show no indication of becoming shock waves, and indeed show towards the closing stages of the calculation a similarity to sound wave propagation. The method is applicable to any spherically symmetrical motion up to such a time as the formation of a shock wave takes place and then fails owing to the assumption of constant entropy.

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