scholarly journals Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

2016 ◽  
Vol 800 ◽  
pp. 278-306 ◽  
Author(s):  
Alberto Guardone ◽  
Davide Vimercati
Keyword(s):  
Shock Waves ◽  
Exact Solutions ◽  
Single Phase ◽  
Ambient Pressure ◽  
Vapour Phase ◽  
Saturation Curve ◽  
Sonic Point ◽  
Isentropic Flow ◽  
Flow Features ◽  
Nozzle Flows

Steady nozzle flows of Bethe–Zel’dovich–Thompson fluids – substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid–vapour saturation curve – are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging–diverging nozzle are determined within the quasi-one-dimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states.

scholarly journals Some nozzle flows found by the hodograph method

1959 ◽  
Vol 1 (1) ◽  
pp. 80-94 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Exact Solutions ◽  
Two Dimensions ◽  
Nozzle Design ◽  
Perfect Gas ◽  
Field Equations ◽  
Rigid Boundary ◽  
Hodograph Method ◽  
Isentropic Flow ◽  
Fixed Boundaries ◽  
Nozzle Flows

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

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.

scholarly journals Толстые слои alpha-Ga-=SUB=-2-=/SUB=-O-=SUB=-3-=/SUB=- на сапфировых подложках, полученные методом хлоридной эпитаксии

2019 ◽  
Vol 53 (6) ◽  
pp. 789
Author(s):  
А.И. Печников ◽  
С.И. Степанов ◽  
А.В. Чикиряка ◽  
М.П. Щеглов ◽  
М.А. Одноблюдов ◽  
...  
Keyword(s):  
Single Phase ◽  
Film Growth ◽  
Vapour Phase ◽  
Wide Bandgap ◽  
Structural And Optical Properties ◽  
Vapour Phase Epitaxy ◽  
Record Value ◽  
Epitaxial Film Growth ◽  
Thick Layers

This paper reports on epitaxial film growth and characterization of α-Ga2O3, a novel wide bandgap semiconducting material. The films were deposited by halide vapour phase epitaxy on basal plane sapphire substrates. The films were from 0.5 μm to over 10 μm in thickness, the latter being the record value by now. Structural and optical properties of the specimens were studied. All specimens were structurally uniform, single phase, and had a corundum-like r3c structure similar to that of sapphire substrate. It was found that the full width at half maximum for the (0006) α-Ga2O3 reflection varies with layer thickness and approaches 240 arcsec for the thickest layer. Both thin and thick layers were transparent in the visible and UV spectral range up to the absorption edge at 5.2 eV.

scholarly journals Fuel spray vapour distribution correlations for a high pressure diesel fuel spray cases for different injector nozzle geometries.

2017 ◽  
Author(s):  
Darlington Njere ◽  
Nwabueze Emekwuru
Keyword(s):  
High Pressure ◽  
Liquid Phase ◽  
Diesel Fuel ◽  
Ambient Pressure ◽  
Vapour Phase ◽  
Fuel Spray ◽  
Combustion Chambers ◽  
Complete Combustion ◽  
Fuel Injectors ◽  
Fuel Vapour

The evolution of diesel fuel injection technology, to facilitate strong correlations of in-cylinder spray propagation with injection conditions and injector geometry, is crucial in facing emission challenges. More observations of spray propagation are, therefore, required to provide valuable information on how to ensure that all the injected fuel has maximum contact with the available air, to promote complete combustion and reduce emissions. In this study, high pressure diesel fuel sprays are injected into a constant-volume chamber at injection and ambient pressure values typical of current diesel engines. For these types of sprays the maximum fuel liquid phase penetration is different and reached sooner than the maximum fuel vapour phase penetration. Thus, the vapour fuel could reach the combustion chamber wall and could be convected and deflected by swirling air. In hot combustion chambers this impingement can be acceptable but this might be less so in larger combustion chambers with cold walls. The fuel-ambient mixture in vapourized fuel spray jets is essential to the efficient performance of these engines. For this work, the fuel vapour penetration values are presented for fuel injectors of different k-factors. The results indicate that the geometry of fuel injectors based on the k-factors appear to affect the vapour phase penetration more than the liquid phase penetration. This is a consequence of the effects of the injector types on the exit velocity of the fuel droplets.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4951

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).

Single phase (112¯2) AlN grown on (101¯0) sapphire by metalorganic vapour phase epitaxy

2015 ◽  
Vol 414 ◽  
pp. 94-99 ◽  
Author(s):  
Duc V. Dinh ◽  
M. Conroy ◽  
V.Z. Zubialevich ◽  
N. Petkov ◽  
J.D. Holmes ◽  
...  
Keyword(s):  
Single Phase ◽  
Vapour Phase ◽  
Vapour Phase Epitaxy ◽  
Metalorganic Vapour Phase Epitaxy

On the stability of stationary shock waves in nozzle flows with homogeneous condensation

2001 ◽  
Vol 13 (9) ◽  
pp. 2706-2719 ◽  
Author(s):  
C. F. Delale ◽  
G. Lamanna ◽  
M. E. H. van Dongen
Keyword(s):  
Shock Waves ◽  
Stationary Shock ◽  
Homogeneous Condensation ◽  
The Stability ◽  
Nozzle Flows
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