scholarly journals Non-ideal oblique shock waves

2018 ◽  
Vol 847 ◽  
pp. 266-285 ◽  
Author(s):  
Davide Vimercati ◽  
Giulio Gori ◽  
Alberto Guardone
Keyword(s):  
Mach Number ◽  
Shock Waves ◽  
Finite Amplitude ◽  
Oblique Shock ◽  
Saturation Curve ◽  
Close Proximity ◽  
Post Shock ◽  
Shock Mach Number ◽  
Molecular Complexity ◽  
Oblique Shocks

From the analysis of the isentropic limit of weak compression shock waves, oblique shock waves in which the post-shock Mach number is larger than the pre-shock Mach number, named non-ideal oblique shocks, are admissible in substances characterized by moderate molecular complexity and in the close proximity to the liquid–vapour saturation curve. Non-ideal oblique shocks of finite amplitude are systematically analysed, clarifying the roles of the pre-shock thermodynamic state and Mach number. The necessary conditions for the occurrence of non-ideal oblique shocks of finite amplitude are singled out. In the parameter space of pre-shock thermodynamic states and Mach number, a new domain is defined which embeds the pre-shock states for which the Mach number increase can possibly take place. The present findings are confirmed by state-of-the-art thermodynamic models applied to selected commercially available fluids, including siloxanes and hydrocarbons currently used as working fluids in renewable energy systems.

Study of High Speed Turbulent Flow Over Rotating Two Stage Three Dimensional Double Wedge

2006 ◽  
Author(s):  
Khaled Alhussan
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Mach Number ◽  
Shock Waves ◽  
High Speed ◽  
Three Dimensional ◽  
Oblique Shock ◽  
Wave Interactions ◽  
Double Wedge ◽  
Slip Surfaces

In this paper some characteristics of non-steady, compressible, flow are explored, including compression and expansion wave interactions and creation. The work to be presented herein is a Computational Fluid Dynamics investigation of the complex fluid phenomena that occur inside three-dimensional region, specifically with regard to the structure of the oblique shock waves, the reflected shock waves and the interactions of the shock waves. The flow is so complex that there exist oblique shock waves, expansion fans, slip surfaces, and shock wave interactions and reflections. The flow is non-steady, turbulent, viscous, compressible, and high-speed supersonic. The work to be presented herein is a Computational Fluid Dynamics analysis of flow over a 15-degree angle double wedge for a compressible air, with spin angle of 10-degree and Mach number of 2.5. The problem to be solved involves formation of shock waves, expansion fans and slip surfaces, so that the general characteristics of supersonic flow are explored through this problem. Shock waves and slip surfaces are discontinuities in fluid mechanics problems. It is essential to evaluate the ability of numerical technique that can solve problems in which shocks and contact surfaces occur. In particular it is necessary to understand the details of developing a mesh that will allow resolution of these discontinuities. Results including contour plots of pressure, temperature, and Mach number will show that CFD is capable of predicting accurate results and is also able to capture the discontinuities in the flow, e.g., the oblique shock waves and the slip surfaces. Through this computational analysis, a better interpretation of the physical phenomenon of the three-dimensional shock waves interaction and reflection can be achieved.

Equilibrium Thermodynamic Properties Behind Strong Shocks in Helium

1968 ◽  
Vol 72 (686) ◽  
pp. 155-159
Author(s):  
M. Lalor ◽  
H. Daneshyar
Keyword(s):  
Mach Number ◽  
Partition Function ◽  
Shock Waves ◽  
Thermodynamic Properties ◽  
Strong Shock ◽  
Equilibrium Thermodynamic ◽  
Ionized Gas ◽  
Number Range ◽  
Shock Mach Number ◽  
Strong Shock Waves

Summary Tables of equilibrium thermodynamic properties of the ionized gas formed behind strong shock waves in Helium are presented, in the Mach number range 10 to 30, for initial pressures of 0-1, 0-5, 1, 5, 10, 50, 100 torr. The effect of the inclusion of the full partition function series is demonstrated in the Mach number range 20 to 30. A numerical solution has been developed such that the only experimental quantities required for its use are the shock Mach number and the pre-shock conditions.

scholarly journals Exploring the role of cosmological shock waves in the Dianoga simulations of galaxy clusters

2021 ◽  
Author(s):  
S Planelles ◽  
S Borgani ◽  
V Quilis ◽  
G Murante ◽  
V Biffi ◽  
...  
Keyword(s):  
Mach Number ◽  
Shock Waves ◽  
Galaxy Clusters ◽  
Cluster Mass ◽  
Mach Number Distribution ◽  
Disturbed Systems ◽  
Shock Mach Number ◽  
Formation And Evolution ◽  
Massive Clusters

Abstract Cosmological shock waves are ubiquitous to cosmic structure formation and evolution. As a consequence, they play a major role in the energy distribution and thermalization of the intergalactic medium (IGM). We analyse the Mach number distribution in the Dianoga simulations of galaxy clusters performed with the SPH code GADGET-3. The simulations include the effects of radiative cooling, star formation, metal enrichment, supernova and active galactic nuclei feedback. A grid-based shock-finding algorithm is applied in post-processing to the outputs of the simulations. This procedure allows us to explore in detail the distribution of shocked cells and their strengths as a function of cluster mass, redshift and baryonic physics. We also pay special attention to the connection between shock waves and the cool-core/non-cool core (CC/NCC) state and the global dynamical status of the simulated clusters. In terms of general shock statistics, we obtain a broad agreement with previous works, with weak (low-Mach number) shocks filling most of the volume and processing most of the total thermal energy flux. As a function of cluster mass, we find that massive clusters seem more efficient in thermalising the IGM and tend to show larger external accretion shocks than less massive systems. We do not find any relevant difference between CC and NCC clusters. However, we find a mild dependence of the radial distribution of the shock Mach number on the cluster dynamical state, with disturbed systems showing stronger shocks than regular ones throughout the cluster volume.

Observations on oblique shock waves in gaseous detonations

1963 ◽  
Vol 17 (1) ◽  
pp. 21-32 ◽  
Author(s):  
D. H. Edwards ◽  
T. G. Jones ◽  
B. Price
Keyword(s):  
Boundary Layer ◽  
Shock Waves ◽  
Pressure Difference ◽  
Detonation Front ◽  
Supersonic Nozzle ◽  
Circular Cross Section ◽  
Oblique Shock ◽  
Detonation Waves ◽  
Wall Boundary Layer ◽  
Oblique Shocks

An account is given of photographic and pressure observations made on the oblique shock waves occurring in the wake of self-sustaining detonation waves in hydrogen-oxygen mixtures initially at atmospheric pressure. Four explosion tubes were employed, of which three are of circular cross-section with internal diameters of 10, 5 and 1·6 cm and the fourth is a square-section tube of side 1·5 in.On the assumption that the oblique shocks are sufficiently weak to be regarded as Mach waves, the flow Mach number relative to the detonation front is determined; these are found to be substantially higher than the values predicted by deal one-dimensional theory. The measured flow Mach numbers in the rarefaction are then used to calculate the pressure distribution in this region on the basis of the supersonic nozzle model due to Fay (1959, 1962). The predictions of this model are found to disagree with with the observed static pressure profiles. Moreover, the pressure following the initial peak persists at a higher value than the theoretical for distances of the order of 5–10 cm behind the front. This phenomenon implies that the wall boundary-layer pressure remains higher than the C-J value and it is suggested that the pressure difference across the boundary layer can account for the formation of the oblique waves.The supersonic features of the flow can be accounted for by the turbulent-structure hypothesis of White (1961). Some validation of this hypothesis is provided here by the observation of the absence of the oblique shocks in overdriven detonation waves caused by the diminished effects of turbulence. This observation is consistent with the view that the oblique shocks are generated by the pressure difference across the boundary layer near the front as this difference would also be diminished in an over-driven wave.

An Iteration Process for the Solution of the Prandtl-Meyer Expansion

1961 ◽  
Vol 65 (605) ◽  
pp. 357-359 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Shock Waves ◽  
Present Note ◽  
Iteration Process ◽  
Oblique Shock ◽  
Expansion Fan ◽  
Iteration Methods ◽  
Oblique Shocks

In the Journal of the Royal Aeronautical Society, November 1959, the writer described an iteration process for the solution of the equations for plane oblique shock waves. Iteration methods avoid the difficulty of reading a solution from a chart; or, given a chart, provide a means of checking such a reading and, usually, of improving the accuracy to any desired degree.As with plane oblique shocks, it is usual to use a chart to obtain the solution of a problem involving a Prandtl-Meyer expansion fan. The present note proposes an iteration process to avoid the use of a Prandtl-Meyer chart; or, given such a chart, offers the possibility of improvement in the accuracy of the solution obtained by reading from it, the limit being set by the accuracy of the trigonometric tables used.

Interaction of Liquid Droplets With Planar Shock Waves

1990 ◽  
Vol 112 (4) ◽  
pp. 481-486 ◽  
Author(s):  
T. Yoshida ◽  
K. Takayama
Keyword(s):  
Mach Number ◽  
Shock Waves ◽  
Reynolds Numbers ◽  
Liquid Droplets ◽  
Double Exposure ◽  
Cross Sectional ◽  
Planar Shock ◽  
Shock Mach Number ◽  
Holographic Interferogram ◽  
Double Exposure Holographic Interferometry

Interactions and breakup processes of 1.50-mm-diameter ethyl alcohol droplets and 5.14-mm-diameter water bubbles with planar shock waves were observed using double-exposure holographic interferometry. Experiments were conducted in a 60 mm × 150 mm cross-sectional shock tube for shock Mach number 1.56 in air. The Weber numbers of droplets and liquid bubbles were 5.6 × 103 and 2.9 × 103, respectively, while the corresonding Reynolds numbers were 4.2 × 10 and 1.5 × 105. It is shown that the resulting holographic interferogram can eliminate the effect of the mists produced by the breakup of the droplets and clearly show the structure of a disintegrating droplet and its wake. This observation was impossible by conventional optical flow visualization. It is demonstrated that the time variation of the diameter of a breaking droplet measured by conventional optical techniques has been overestimated by up to 35 percent.

scholarly journals Admissibility region for rarefaction shock waves in dense gases

2008 ◽  
Vol 599 ◽  
pp. 363-381 ◽  
Author(s):  
CALIN ZAMFIRESCU ◽  
ALBERTO GUARDONE ◽  
PIERO COLONNA
Keyword(s):  
Shock Waves ◽  
Mechanical Stability ◽  
Practical Importance ◽  
Second Law Of Thermodynamics ◽  
Vapour Phase ◽  
Industrial Applications ◽  
Saturation Curve ◽  
Post Shock ◽  
Definition Of ◽  
Rarefaction Shock

In the vapour phase and close to the liquid–vapour saturation curve, fluids made of complex molecules are expected to exhibit a thermodynamic region in which the fundamental derivative of gasdynamic Γ is negative. In this region, non-classical gasdynamic phenomena such as rarefaction shock waves are physically admissible, namely they obey the second law of thermodynamics and fulfil the speed-orienting condition for mechanical stability. Previous studies have demonstrated that the thermodynamic states for which rarefaction shock waves are admissible are however not limited to the Γ<0 region. In this paper, the conditions for admissibility of rarefaction shocks are investigated. This results in the definition of a new thermodynamic region – the rarefaction shocks region – which embeds the Γ<0 region. The rarefaction shocks region is bounded by the saturation curve and by the locus of the states connecting double-sonic rarefaction shocks, i.e. shock waves in which both the pre-shock and post-shock states are sonic. Only one double-sonic shock is shown to be admissible along a given isentrope, therefore the double-sonic states can be connected by a single curve in the volume–pressure plane. This curve is named the double sonic locus. The influence of molecular complexity on the shape and size of the rarefaction shocks region is also illustrated by using the van der Waals model; these results are confirmed by very accurate multi-parameter thermodynamic models applied to siloxane fluids and are therefore of practical importance in experiments aimed at proving the existence of rarefaction shock waves in the single-phase vapour region as well as in future industrial applications operating in the non-classical regime.

Further results on the over-all density ratios of shock waves in carbon dioxide

1963 ◽  
Vol 17 (2) ◽  
pp. 267-270 ◽  
Author(s):  
H. K. Zienkiewicz ◽  
N. H. Johannesen ◽  
J. H. Gerrard
Keyword(s):  
Carbon Dioxide ◽  
Mach Number ◽  
Shock Waves ◽  
Density Ratio ◽  
Shock Mach Number ◽  
Density Ratios

Previous results on the over-all density ratio of shock waves in CO2, confirming experimentally the theoretical equilibrium value, have been extended to a shock Mach number of 7·3. The discrepancy between our results and earlier Princeton results approaches 18% at a Mach number of 7. Possible reasons for this are discussed, with particular reference to the interferometer technique, but no explanation has been found.

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