Maximum intensity of rarefaction shock waves for dense gases

2009 ◽  
Vol 642 ◽  
pp. 127-146 ◽  
Author(s):  
ALBERTO GUARDONE ◽  
CALIN ZAMFIRESCU ◽  
PIERO COLONNA
Keyword(s):  
Mach Number ◽  
Shock Waves ◽  
Equations Of State ◽  
Vapour Phase ◽  
Maximum Intensity ◽  
Operating Conditions ◽  
Maximum Pressure ◽  
Pressure Jump ◽  
Shock Strength ◽  
Rarefaction Shock

Modern thermodynamic models indicate that fluids consisting of complex molecules may display non-classical gasdynamic phenomena such as rarefaction shock waves (RSWs) in the vapour phase. Since the thermodynamic region in which non-classical phenomena are physically admissible is finite in terms of pressure, density and temperature intervals, the intensity of RSWs is expected to exhibit a maximum for any given fluid. The identification of the operating conditions leading to the RSW with maximum intensity is of paramount importance for the experimental verification of the existence of non-classical phenomena in the vapour phase and for technical applications taking advantage of the peculiarities of the non-classical regime. This study investigates the conditions resulting in an RSW with maximum intensity in terms of pressure jump, wave Mach number and shock strength. The upstream state of the RSW with maximum pressure drop is found to be located along the double-sonic locus formed by the thermodynamic states associated with an RSW having both pre- and post-shock sonic conditions. Correspondingly, the maximum-Mach thermodynamic and maximum-strength loci locate the pre-shock states from which the RSW with the maximum wave Mach number and shock strength can originate. The qualitative results obtained with the simple van der Waals model are confirmed with the more complex Stryjek–Vera–Peng–Robinson, Martin–Hou and Span–Wagner equations of state for selected siloxane and perfluorocarbon fluids. Among siloxanes, which are arguably the best fluids for experiments aimed at the generation and measurement of an RSW, the state-of-the-art Span–Wagner multi-parameter equation of state predicts a maximum wave Mach number close to 1.026 for D6 (dodecamethylcyclohexasiloxane, [O-Si-(CH3)2]6). Such value is well within the capacity of the measurement system of a newly built experimental set-up aimed at the first-ever demonstration of the existence of RSWs in dense vapours.

scholarly journals Waves reflected by solid wall in the mixture of liquid with vapour bubbles

2002 ◽  
Vol 24 (3) ◽  
pp. 167-180
Author(s):  
Duong Ngoc Hai ◽  
Nguyen Van Tuan
Keyword(s):  
Shock Waves ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Solid Wall ◽  
Vapour Phase ◽  
Gas Mixtures ◽  
Industrial Processes ◽  
Shock Strength ◽  
Stationary Shock ◽  
The Waves

The liquid and gas mixtures are met in many natural and industrial processes. In the paper the results of investigation of waves reflected by solid wall of the stationary shock waves with moderate intensities or the transient pulses propagated in the mixture of liquid with vapour bubbles are presented. The effect of initial conditions, shock strength, size of the bubbles and volume fraction of vapour phase on the behaviour of the waves reflected by solid wall is studied.

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.

Assessment of the Loss Map of a Centrifugal Compressor’s External Volute

2020 ◽  
Author(s):  
Thomas Ceyrowsky ◽  
Andre Hildebrandt ◽  
Martin Heinrich ◽  
Rüdiger Schwarze
Keyword(s):  
Mach Number ◽  
Flow Rate ◽  
Numerical Approach ◽  
Operating Conditions ◽  
Circumferential Velocity ◽  
Flow Angle ◽  
Absolute Flow ◽  
Highly Sensitive ◽  
Geometrical Features ◽  
Comparison With Experimental Data

Abstract A volute’s loss coefficient is highly sensitive to Mach number, circumferential velocity and flow rate at volute inlet. In case of a backswept impeller, these parameters are coupled to each other. An increased flowrate leads to a steeper absolute flow angle at impeller exit and hence to a decrease of circumferential velocity. The absolute Mach number is also altered. Therefore, in order to investigate the effects of flowrate and flow angle separately, one would have to vary the diffuser width together with the flowrate, keeping the flow angle constant. This corresponds to coupling the volute with aerodynamically similar impellers, designed for higher and lower flowrates. Since this is elaborate, there is no adequate study available in open literature, assessing a volute’s global loss map. In this work, a new numerical approach for the prediction of a volute’s representative loss map is presented: The volute is calculated by means of steady CFD as a standalone component. The inlet boundary conditions are carefully selected by means of 1D and applied together with different diffuser widths. This allows for separate investigation of the impacts of flow angle, flow rate and Mach number. Validation against full stage CFD confirms the applicability of the standalone model. The results exhibit that minimum losses do not necessarily occur at the theoretical matching point but either when the volute is smaller or bigger, depending on the inlet flow angle. Investigations of the loss mechanisms at different operating conditions provide useful guidelines for volute design. Finally, the validity of these study’s findings for volutes with different geometrical features is examined by comparison with experimental data as well as with fullstage CFD.

Shock Wave - Film Cooling Interactions in Transonic Flows

2001 ◽  
Author(s):  
P. M. Ligrani ◽  
C. Saumweber ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Film Cooling ◽  
Cross Flow ◽  
Injection Velocity ◽  
Film Cooling Effectiveness ◽  
Mach Numbers ◽  
Density Ratios ◽  
Film Cooling Holes

Interactions between shock waves and film cooling are described as they affect magnitudes of local and spanwise-averaged adiabatic film cooling effectiveness distributions. A row of three cylindrical holes is employed. Spanwise spacing of holes is 4 diameters, and inclination angle is 30 degrees. Freestream Mach numbers of 0.8 and 1.10–1.12 are used, with coolant to freestream density ratios of 1.5–1.6. Shadowgraph images show different shock structures as the blowing ratio is changed, and as the condition employed for injection of film into the cooling holes is altered. Investigated are film plenum conditions, as well as perpendicular film injection cross-flow Mach numbers of 0.15, 0.3, and 0.6. Dramatic changes to local and spanwise-averaged adiabatic film effectiveness distributions are then observed as different shock wave structures develop in the immediate vicinity of the film-cooling holes. Variations are especially evident as the data obtained with a supersonic Mach number are compared to the data obtained with a freestream Mach number of 0.8. Local and spanwise-averaged effectiveness magnitudes are generally higher when shock waves are present when a film plenum condition (with zero cross-flow Mach number) is utilized. Effectiveness values measured with a supersonic approaching freestream and shock waves then decrease as the injection cross-flow Mach number increases. Such changes are due to altered flow separation regions in film holes, different injection velocity distributions at hole exits, and alterations of static pressures at film hole exits produced by different types of shock wave events.

Influence of Skewing of Contact Face on Performance of Wave Rotor Refrigerators and Superchargers

2013 ◽  
Author(s):  
Yuqiang Dai ◽  
Fengxia Liu ◽  
Jintao Wu ◽  
Wei Wei ◽  
Dapeng Hu ◽  
...  
Keyword(s):  
High Pressure ◽  
Mach Number ◽  
Shock Waves ◽  
Rotational Speed ◽  
Channel Width ◽  
Wave Rotor ◽  
Coriolis Forces ◽  
Local Loss ◽  
Expansion Waves ◽  
Pressure Port

As a novel generation of rotational gas wave machines, wave rotor machines such as wave rotor refrigerators (WRR) and wave rotor superchargers (WRS) are unsteady flow devices. In their passages two gas streams (with different pressure or even different phases) comes into direct contact can exchange energy due to the movement of shock waves and expansion waves. A detailed study shows that, when rotor channels open to the high pressure port gradually, the contact face in rotor channels inevitably skews, which is always accompanied with reflection of shockwaves. This causes very large energy dissipation and influences adversely on the refrigeration performance of WRR or the supercharging performance of WRS. In this work, factors such as centrifugal forces, Coriolis forces, gradual channel opening and gradual channel closing, etc, which influence the wave transportation and skewing of shock waves and contact faces are studied by means of computational fluid dynamics and experiments. The skewing of contact faces causes uneven distribution of velocity and large local loss. With rotation Mach number smaller than 0.3, the skewing of contact face can be alleviated. To reduce the adverse influence of rotation Mach number, a smaller rotor channel width or higher rotational speed is necessary. The rotation effect plays an important role for the skewing of gas discontinuities. Both the centrifugal and Coriolis forces of wave rotor cannot be ignored with the Rossby number of 1.3∼3.5. To reduce the skewing loss of contact face, a lower rotational speed seems necessary. The rotation speed of wave rotors has dialectical influences on the skewing of shock waves and contact faces. The jetting width of high pressure port is the key factor of the gradual opening of rotor channels. A feasible way to reduce skewing losses of gas waves is to optimize the ratio between high pressure port width and channel width. The validation experiments have got at least 3∼5% rise of isentropic efficiency for WRRs.

scholarly journals Modeling hydrogen solubility in hydrocarbons using extreme gradient boosting and equations of state

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohammad-Reza Mohammadi ◽  
Fahime Hadavimoghaddam ◽  
Maryam Pourmahdi ◽  
Saeid Atashrouz ◽  
Muhammad Tajammal Munir ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Equations Of State ◽  
Optimal Operation ◽  
Operating Conditions ◽  
Hydrogen Solubility ◽  
Gradient Boosting ◽  
Accurate Estimation ◽  
Support Vector ◽  
Adaptive Boosting ◽  
Extreme Gradient Boosting

AbstractDue to industrial development, designing and optimal operation of processes in chemical and petroleum processing plants require accurate estimation of the hydrogen solubility in various hydrocarbons. Equations of state (EOSs) are limited in accurately predicting hydrogen solubility, especially at high-pressure or/and high-temperature conditions, which may lead to energy waste and a potential safety hazard in plants. In this paper, five robust machine learning models including extreme gradient boosting (XGBoost), adaptive boosting support vector regression (AdaBoost-SVR), gradient boosting with categorical features support (CatBoost), light gradient boosting machine (LightGBM), and multi-layer perceptron (MLP) optimized by Levenberg–Marquardt (LM) algorithm were implemented for estimating the hydrogen solubility in hydrocarbons. To this end, a databank including 919 experimental data points of hydrogen solubility in 26 various hydrocarbons was gathered from 48 different systems in a broad range of operating temperatures (213–623 K) and pressures (0.1–25.5 MPa). The hydrocarbons are from six different families including alkane, alkene, cycloalkane, aromatic, polycyclic aromatic, and terpene. The carbon number of hydrocarbons is ranging from 4 to 46 corresponding to a molecular weight range of 58.12–647.2 g/mol. Molecular weight, critical pressure, and critical temperature of solvents along with pressure and temperature operating conditions were selected as input parameters to the models. The XGBoost model best fits all the experimental solubility data with a root mean square error (RMSE) of 0.0007 and an average absolute percent relative error (AAPRE) of 1.81%. Also, the proposed models for estimating the solubility of hydrogen in hydrocarbons were compared with five EOSs including Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Redlich–Kwong (RK), Zudkevitch–Joffe (ZJ), and perturbed-chain statistical associating fluid theory (PC-SAFT). The XGBoost model introduced in this study is a promising model that can be applied as an efficient estimator for hydrogen solubility in various hydrocarbons and is capable of being utilized in the chemical and petroleum industries.

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