Notes on gas–dynamic design of supersonic flying vehicles

It is shown that the lift–to–drag ratio of a thin delta wing is significantly lower than the lift–to–drag ratio of an infinitely long swept plate with an identical lift force. The effect of sweep on a finite wing may be used by excluding disturbances from the leading edge of the wing via introducing a hardened stream surface (wedge) and increasing the wing length. A three–shock waverider is proposed for choosing the optimal parameters. The sharp wedge may be avoided by replacing planar shock waves by a cylindrical shock wave upstream of the blunted wedge. If the leading edge of the wedge is not parallel to the rib that is a source of the expansion wave, a plate with zero wave drag, generating a lift force, may be obtained behind this rib. The system of regularly intersecting shock waves may be applied to design a forward–swept wing.     

Using S-statistic for investigating the effect of temperature on hydrodynamics of gas–solid fluidization

The influence of temperature on fluidization was investigated by a statistical chaotic attractor comparison test known as S-statistic. After calibration of the variables used in this method, the S-test was applied to the radioactive particle tracking (RPT) data obtained from a lab-scale fluidized bed. Experiments were performed with sand as fluidized particles and in temperatures from ambient up to 600 °C with superficial gas velocities of 0.29, 0.38 and 0.52 m/s. Considering the behavior of bubbles and comparing with frequency domain analysis, it was concluded that S-statistic is a reliable method for characterization of fluidization process behavior at different temperatures.     

Review on vertical gas–liquid slug flow

Vertical slug flow is characterized by the rise of long bullet-shaped gas bubbles with a diameter almost matching that of the tube - Taylor bubbles. Liquid slugs separate consecutive Taylor bubbles, which may interact and coalesce if the distance between them is small. Slug flow has numerous industrial applications, being also observed on physiological and geological systems. In spite of the contribution of the development of non-intrusive experimental techniques to a deeper understanding of slug flow features, the complexity of this flow pattern requires the combined use of numerical approaches to overcome some of the optical problems reported in experimental methods, and other limitations related to the flow aperiodic behavior.The need to systematize the large amount of data published on the subject and to understand the limitations of the techniques employed constitutes the motivation for this review. In the present work, literature on vertical gas–liquid slug flow, with Newtonian fluids, from 1943 to 2015, covering theoretical, experimental and numerical approaches, is reviewed. Focus is given to single and trains of Taylor bubbles rising through stagnant and co-current liquids.It should be emphasized, however, that further research still needs to be conducted in some particular areas, namely the hydrodynamics of the liquid film surrounding the Taylor bubbles, the interaction between consecutive bubbles, and a more detailed approach to the flow of Taylor bubbles through co-current liquids.     

On the use of the stratified momentum balance for the deduction of shear stress in horizontal gas–liquid pipe flow

The use of the stratified flow momentum balance for the deduction of interfacial and liquid wall shear stresses from experimental measurements is examined. A systematic error analysis is applied to the governing equations using the principle of maximum uncertainty. A series of air–water experiments were conducted in 50 and 80 mm diameter pipes, in which gas pressure drop, liquid height and gas wall shear stress were measured. A framework for the correlation of the deduced shear stresses is proposed from the experimental measurements. The uncertainty analysis is used to show that the definition of mean liquid height does not significantly influence the overall results. The development of empirical equations based on such methods may lead to total uncertainties of up to 40%, irrespective of accuracy of the experimental data or the appropriateness of the correlating technique. Comparisons with state-of-the-art correlations for the liquid wall and interfacial friction factor data showed even larger discrepancies between measurement and prediction.     

On the accuracy of gas flow rate measurements in gas–liquid pipe flows by cross-correlating dual wire-mesh sensor signals

This article presents an assessment of the accuracy of gas flow rate measurement in gas–liquid pipe flows by cross-correlating dual wire-mesh sensor signals. The differences between the estimated and the actual gas superficial velocities in different flow regimes were analyzed. It was demonstrated that this gas flow rate measurement method is susceptible to significant systematic errors, some of which are inherent to the use of cross-correlation and others which are specific to wire-mesh sensors. It was concluded that this method would be accurate only for flow conditions within narrow ranges.     

Prediction of the entrained liquid fraction in vertical annular gas–liquid two-phase flow

The study considers the prediction of the entrained liquid fraction in adiabatic gas–liquid annular two-phase flow in vertical pipes. Nine empirical correlations have been tested against an experimental data bank drawn together in this study containing 1504 points for 8 different gas–liquid combinations and 19 different tube diameters from 5.00 mm to 57.1 mm. The correlation of Sawant, Ishii and Mishima and the one of Oliemans, Pots and Trompé were found to best reproduce the available data. A new correlating approach, derived from both physical intuition and dimensional analysis and capable of providing further physical insight into the liquid film atomization process, was proposed and worked better than any of the existing methods. This new correlation is based on the core flow Weber number that is also a controlling dimensionless group in determining the wall shear stress and associated frictional pressure gradient of annular flows.     

Numerical study of the spontaneous nucleation of self-rotational moist gas in a converging–diverging nozzle

Spontaneous nucleation is the primary way of droplet formation in the supersonic gas separation technology, and the converging–diverging nozzle is the condensation and separation unit of supersonic gas separation devices. A three-dimensional geometrical model for the generation of self-rotational transonic gas flow is set up, based on which, the spontaneous nucleation of self-rotational transonic moist gas in the converging–diverging nozzle is carried out using an Eulerian multi-fluid model. The simulated results of the main flow and nucleation parameters indicate that the spontaneous nucleation can occur in the diverging part of the nozzle. However, different from the nucleation flow without self-rotation, the distributions of these parameters are unsymmetrical about the nozzle axis due to the irregular flow form caused by the self-rotation of gas flow. The nucleation region is located on the position where gas flows with intense rotation and the self-rotation impacts much on the nucleation process. Stronger rotation delays the onset of spontaneous nucleation and yields lower nucleation rate and narrow nucleation region. In addition, influences of other factors such as inlet total pressure p ₀, inlet total temperature T ₀, the nozzle-expanding ratio ? and the inlet relative humidity ф ₀ on the nucleation of self-rotational moist gas flow in the nozzle are also discussed.     

Influence of the operation pressure on slug length in near horizontal gas–liquid pipe flow

Slug flow is commonly observed in gas production offshore fields. At high operation pressure only short hydrodynamic slugs are observed. However, as the offshore fields become older, the operation pressure becomes lower and long slugs may form. At near atmospheric pressures the long slugs may reach a size of 500 pipe diameters or more. Such slugs can cause serious operational failures due to the strong fluctuating pressure. Identifying the operation pressure conditions at which the long slugs appear, may reduce or prevent these negative effects.     

Description of liquid–gas phase transition in the frame of continuum mechanics

A new method of describing the liquid–gas phase transition is presented. It is assumed that the phase transition is characterized by a significant change of the particle density distribution as a result of energy supply at the boiling point that leads to structural changes but not to heating. Structural changes are described by an additional state characteristics of the system—the distribution density of the particles which is presented by an independent balance equation. The mathematical treatment is based on a special form of the internal energy and a source term in the particle balance equation. The presented method allows to model continua which have different specific heat capacities in liquid and in gas state.     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

Effect of a falling gas–liquid absorption film temperature on entropy generation

In this paper, an analytical study about the effect of a falling gas–liquid absorption film temperature on entropy generation is carried out. Entropy generation formulations due to viscous effects and mass transfer are derived. Results in terms of viscous, mass transfer and total irreversibilities are graphically presented and discussed.     

Investigating the effects of shear rate on the collapse time in a gas–liquid system by lattice Boltzmann

In order to evaluate the effects of shear rate on the time of collapse process in a two-phase; one component system, a free energy lattice Boltzmann model is developed. Considering a system consists of two droplets in the surrounding vapor it is observed that, for various physical and geometrical conditions, imposing shear flow has similar effects on the collapse time. Actually, for each case there is an optimum shear rate of collapse that is corresponded to highest collapse rate and smallest time. In all test cases, for shear rates smaller than the optimum value, increasing the shear rate raise collapse rate and reduce its time. But for higher shear rates, increasing the shear rate has reverse effect and decreases the collapse rate. The results also show that, higher droplet radius ratio, viscosity ratio, surface tension and interface thickness lead to a higher optimum shear rate of collapse while higher density ratio of liquid and vapor decreases that.     

Orientation of cylindrical particles in gas–solid circulating fluidized bed

The orientation of cylindrical particles in a gas–solid circulating fluidized bed was investigated by establishing a three-dimensional Euler–Lagrange model on the basis of rigid kinetics, impact kinetics and gas–solid two-phase flow theory. The resulting simulation indicated that the model could well illustrate the orientation of cylindrical particles in a riser during fluidization. The influences of bed structure and operation parameters on orientation of cylindrical particles were then studied and compared with related experimental results. The simulation results showed that the majority of cylindrical particles move with small nutation angles in the riser, the orientation of cylindrical particles is affected more obviously by their positions than by their slenderness and local gas velocities. The simulation results well agree with experiments, thus validating the proposed model and computation.     

Dynamics of annular gas–liquid two-phase swirling jets

The dynamics of annular gas–liquid two-phase swirling jets have been examined by means of direct numerical simulation and proper orthogonal decomposition. An Eulerian approach with mixed-fluid treatment, combined with an adapted volume of fluid and a continuum surface force model, was used to describe the two-phase flow system. The unsteady, compressible, three-dimensional Navier–Stokes equations have been solved by using highly accurate numerical methods. Two computational cases have been performed to examine the effects of liquid-to-gas density ratio on the flow development. It was found that the higher density ratio case is more vortical with larger spatial distribution of the liquid, in agreement with linear theories. Proper orthogonal decomposition analysis revealed that more modes are of importance at the higher density ratio, indicating a more unstable flow field. In the lower density ratio case, both a central and a geometrical recirculation zone are captured while only one central recirculation zone is evident at the higher density ratio. The results also indicate the formation of a precessing vortex core at the high density ratio, indicating that the precessing vortex core development is dependent on the liquid-to-gas density ratio of the two-phase flow, apart from the swirl number alone.     

Squeeze-flow and vane rheometry of a gas–liquid foam

The rheology and slip of a dry shaving foam are investigated using squeeze-flow and rotating-vane methods. Constant-force squeeze flow between planar surfaces is used to study the effect of surface roughness on slip and to obtain the yield stress. Non-slip vane measurements are used to obtain the linear shear viscosity and elasticity at small strains, and the yield stress and strain at large strains. Data are compared with the small-strain Maxwell and Kelvin–Voigt linear-viscoelastic models. An apparent dependence of the yield stress and elasticity on the rotational speed of the vane is shown to result from time-dependent rheological parameters as the foam ages. The effect of viscosity in the pre-yield region may give an erroneous identification of yield.     

Dynamics of a cylindrical shell with elastic bottom filled with a gas–liquid mixture and subject to two-frequency excitation

The paper reports experimental data on the nonlinear dynamic deformation of the elastic bottom of a cylindrical shell and the formation of bubbles and their clusters under two-frequency excitation     

X-ray measurements on the influence of optical probes on gas–solid fluidized beds

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