In this contribution, an assessment of compressible Reynolds Averaged Navier Stokes equations (RANS) and Large Eddy Simulation (LES) is presented using transonic organic vapor flow past a NACA4412 airfoil as a case study. The NACA4412 represents a canonical geometry, which, in case of air, has been well investigated numerically and experimentally. The results of the real gas simulations are compared with those of air simulations. For the real gas, the organic vapor Novec 649 ® is chosen as a representative fluid. The thermodynamic behavior of Novec 649 ® is modeled with the Peng-Robinson equation of state. Different inlet Mach numbers are applied, namely, a sub-critical, the critical, and a super-critical Mach number. It turns out, that the critical Mach number of the NACA4412 airfoil increases when Novec 649 ® is used as working fluid. Furthermore, it is shown that real gas flow simulations cause additional difficulties for the computational fluid dynamics (CFD) analysis. Although the speed of sound of Novec 649 ® is lower than the speed of sound of air, a finer grid resolution is required for the real gas simulations due to its high density. Based on an extensive simulation study, an assessment of different numerical modelling strategies and methods is given.

The present paper theoretically treats weakly nonlinear propagation of plane progressive waves in an initially quiescent compressible liquid containing a tremendously large number of spherical gas bubbles, focusing on the derivation of an amplitude evolution equation (i.e., nonlinear wave equation). We emphasize the following points: (i) the compressibility of the liquid phase, which has long been neglected, is considered; (ii) the wave propagates with a large phase velocity exceeding the speed of sound in pure water; (iii) bubbles are not created or annihilated. From the method of multiple scales with an appropriate scaling of three nondimensional parameters, we can derive an attenuated nonlinear Schrödinger (NLS) equation, where the phase velocity is larger than the speed of sound in a pure liquid.

This paper first applies flux vector type splitting method based on numerical speed of sound for computing incompressible single and multi-fluid flows. Here, a preconditioning matrix based on Chorin’s artificial compressibility concept is used to modify the incompressible multi-fluid Navier-Stokes Equations to be hyperbolic and density or volume fraction independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratio and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially non-oscillatory (ENO) type primitive variable extrapolations coupling with an ENO-MUSCL type volume fraction recompressed reconstruction within a mesh cell is used to maintain the preservation of sharp interface evolutions in multi-fluid flow simulation. Benchmark tests including a solid rotation test of a notched 2D cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, the Rayleigh-Taylor instability and the cavitated flow problems are chosen to validate the current incompressible multi-fluid methodology.

A simple semi-empirical method is presented for calculating the speed of sound and attenuation factor for an unknown medium enclosed in a pipe. This method is based on the calculation of four-pole matrix parameters. It can be used in connection with transient or steady state excitation. The material presented is limited by the fact that no ideal measurement process exists. This limitation is significant when gathering attenuation factor and speed of sound data over a wide frequency range. However, the results, which are easily obtainable, are more than sufficient in solving daily engineering problems.

Negative pressure is one of the metastable states of liquids at which it can be extended up to a certain limit without a gap of continuity. There are numerous experimental studies where a negative pressure up to 40 MPa has been obtained at laboratory conditions. However, these results of the experimental works were not practically implemented, as real liquids both in the nature and the technological processes contain impurities. Under certain kinetic and hydrodynamic conditions the waves of negative pressure in real liquids (crude oil, water, and water-based solutions) were observed. The wave of negative pressure is a turned soliton wave with one negative hump. It is a conservative wave, which maintains its shape and dimensions, and travels long distances with the speed of sound. An advanced technology of generation of the negative pressure wave in real systems allowed creating completely new energy saving technology. This technology based on negative pressure phenomenon has been already used for increasing oil production efficiency during various oil well operations, cleaning of oil well bore, and pipelines from various accumulations. It is shown that a new technology has a lot of potentials for bottom-hole cleaning operations, oil recovery enhancement, pipeline transportation, gas-lift operation etc. Negative pressure is known to be one of the metastable states at which liquids can be extended up to a certain limit. Theoretic evaluations show that in pure liquids negative pressure may reach large values while the liquid may stand significant extending efforts. For instance, the maximum negative pressure that may be sustained by ideally pure water is estimated as −10 9 N/m 2 . It means that an imaginable rope of completely pure water with the diameter of 0.01m can sustain a huge extending effort more than 10 5 N. It is evident that the real experimental values of negative pressure are much less than the corresponding theoretic estimations. It is connected with the impossibility of obtaining ideally pure liquids without any “weak places” (gas bubbles, admixture, etc) and with the circumstance that in experience, the rupture often happens not in the liquid volume but on the surface touching the walls of the vessels weakened by the existence of thin films, embryos, etc. There are numerous results of the experimental work of static and dynamic character, where negative pressure has appeared in one or another degree [1]. In laboratory conditions, negative pressure apparently was first revealed in the experiences made by F. M. Donny (1843), who used degassed sulfuric acid and obtained negative pressure only −0.012 MPa. Among the further attempts of receiving bigger negative pressure, it is worth mentioning the experiences made by O.Reynolds, M.Bertelot and J.Meyer. Basing upon a centrifugal method and using mercury, L.J.Briggs obtained the record value of negative pressure (−42.5 MPa). But as a matter of fact, beginning from the first experiences by F. M. Donny, the main condition in the investigations for the appearance of negative pressure has been the homogeneous character of the liquid and high degree of the purity the liquid-vessel system. Significant values of negative pressure has been obtained under those conditions, however these results of a great scientific importance have no effective applications in practice as real liquids in Nature and technological processes are heterogeneous multicomponent systems. A long-term experimental work has been done to generate negative negative pressure in real liquid systems and investigate influence of this state on thermohydrodynamical characteristics of natural and technological processes [2,3]. Basing on the idea that negative pressure can be created due to the sudden character of extending efforts a direct wave of the negative pressure in real liquids (water, oil, solutions etc.) have been obtained experimentally. For impulsive entering into metastable (overheated) zone in a phase diagram “liquid-vapor” the pressure should drop so fast that the existing centers of evaporation (bubbles, embryos, admixtures etc.) would not be able to manifest themselves for this period. In these terms purity of the liquid is not decisive, and herewith there might exist states of an overheated liquid with the manifestation of negative pressure. It was determined that wave of the negative pressure resembling overturned soliton wave with one but negative peak propagates with speed of sound. The typical variation of the pressure in the petroleum stream in pipe is given in Figure 1. Reversed wave of the negative pressure was not recorded during the experiments. Evidently this is associated with considerable structural changes in the liquid after the passing of the direct wave. The arising negative pressure though being a short-term, results in a considerable overheating of the fluid system and leads to spontaneous evaporation and gas-emanation with the further cavitation regime. It was determined that after passing of the negative pressure wave hydraulic resistance in the system becomes much less, and significant increase of permeability of the porous medium and intensification of the filtration process take place. On the base of the investigations it was made a conclusion that any discharge in the hydraulic systems when the drop of the pressure requires much less time that relaxation of the pressure in the system inevitably results in the arising of rarefaction wave, in particular, the negative pressure wave [4]. The larger is the hydraulic system and the higher is the depression of the pressure, the more intensively the negative pressure wave may manifest itself. In certain terms waves of the positive pressure may be reflected from free surfaces, different obstacles, from contact surfaces between phases in the form of the reverse wave of the negative pressure. On this base there were presented numerous theoretical and experimental works on the simulation of the process, investigation of impact of the negative pressure on certain physical features of real systems [5]. The negative pressure wave may lead to very hard complications: showings of oil and gas leading sometimes to dreadful open fountains, borehole wall collapse, column crushing, gryphon appearance [6]. Analysis of numerous facts of complications, troubles in wells as water-oil-gas showings, crushing of columns, collapses, gryphon formation demonstrates that they arise usually as a result of round-trip operations in drilling of wells and their capital repairs. The negative pressure wave may be initiated by a sudden pulling of pipes or drilling equipment, as well as their sudden braking, quick opening of a valve at the well exit, etc, resulting in metastable extension of the working fluid agent. Though impulse negative pressure manifests itself as a significant dynamic factor, its structural consequences are more dangerous for an oil well. Moving along a well the negative pressure wave results in the spontaneous boiling of the water in the drilling fluid, and as a result of considerable reduction of its specific weight the hydrostatic column is “switched-off’ for some seconds and this may be sufficient for oil and gas showings of the well to be appeared accompanied often by crushing of columns and collapsing of wells due to great destroying energy manifestation. Negative pressure waves may be considered also as one of the dominant factors in geophysical processes, especially, in evolution and appearance of volcanic eruptions and earthquakes [7,8]. Extreme dynamic processes in the underground medium as a matter of fact can be considered as a synergetic manifestation of the negative pressure together with other thermohydrodynamical factors. The waves of negative pressure in the underground environment may be initiated by tectonic dislocations and faults as a result of different dynamic processes, dramatic decrease of pressure during the displacement of fluids and rocks. They may arise also in the form of a reverse waves as a result of reflection of ordinary seismic waves from different underground surfaces. On the basis of received results the method of artificial creation of negative pressure waves has been created [4]. The essence of the method is that negative pressure waves can be generated by means of discharge in hydraulic systems (pipes, wells, etc) when the drop of the pressure takes place during the characteristic time much less than that of pressure relaxation in the system. The greater is the volume of hydraulic system and the higher is the depression of the pressure, the more intensively the negative pressure wave may manifest itself. This method was taken as a basis of elaboration of principally new technologies and installations to increase effectiveness and efficiency of some oil recovery processes. It has been worked out and widely tested in field conditions new technologies on using of the negative pressure phenomenon for cleaning of oil producing hydraulic systems/well bore, pipeline/from various accumulations and increasing of effectiveness of oil producing at different well operation methods. The technology provides generation negative pressure waves in the well using the special mechanisms that leads to the shock depression impact upon the oil stratum, and as a result, to considerable growth in the oil influx, bottom-hole cleaning, accompanied by essential saving both reservoir and lifting energies, elimination and prevention of sandy bridging, paraffin, silt, water, etc. accumulations. For implementations of these technologies corresponding installations have been elaborated, in part, equipments for cleaning out of oil holes from sand plugs, increasing of efficiency and effectiveness of gas-lift well operations and bottom-hole pumping. In cleaning out of oil-holes from sand plugs the most operative and effective liquidation of different sand plugs irrespective of their rheological character is provided, associated with complete bottom-hole cleaning, essential increase of oil recovery and overhaul period. Elaborated equipment is simple and easy to use. Other comparatively advantageous application of the technology provides increase of efficiency of a gas-lift well operation, expressed in considerable reduction of a specific gas consumption associated with essential increase of oil recovery and overhaul period. The design of the equipment is reliable and simple to service. There are different modifications of the equipment for single-row, double-row lifts in packer and packerless designs. The introduced technologies have passed broad test in field conditions. The operative and complete cleaning of numerous oil wells was carried out, where the altitude of sand plugs varied from 20m to 180m; oil output of wells and their overhaul period have been increased and specific gas discharge reduced significantly.

A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier-Stokes equations for the liquid phase with an additional vapor transport equation for the vapor phase. The model tracks regions of liquid vaporization and applies compressibility effects to compute the local variation in speed of sound using the Homogeneous Equilibrium Model (HEM) assumptions. The variation of local cell density as a function of local pressure is used to construct the source term in the vapor fraction transport equation. The novel Cavitation-Induced-Momentum-Defect (CIMD) correction methodology developed in this study serves to account for cavitation inception and collapse events as relevant momentum source terms in the liquid phase momentum equations. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG K-ε model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Turbulent kinetic energy and dissipation contributions from the vapor regions are integrated with the liquid phase turbulence using relevant source terms. Numerical simulations are carried out using a Finite Volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the supplemented vapor transport equation. Our results concur with previously established theories concerning sheet and cloud cavitation such as the re-entrant jet motion, cavity closure and the impact of adverse pressure gradients on cavitation dynamics.

Noise generated from large-scale wave-like eddies in a Mach 0.9 hot axisymmetric jet is studied. The mean jet flow is computed using a Reynolds-Averaged Navier-Stokes solver with the k-ω turbulence model. Spatial development of near-field pressure perturbations is computed using a 3D Parabolized Stability Equation (PSE) method, and the far-field noise radiated from these convective instabilities is obtained by solving the wave equation. The 3D PSE method developed here allows the effects of strong azimuthal mean-flow variations to be captured and analyzed. Results show that large-scale wave-like eddies, or instability waves, travel slightly above sonic speed for the first few jet diameters, and that the dominant noise sources are concentrated near the edge of the time-averaged potential core. Good agreement between computed results and experiment are found for relative sound pressure levels and directivity. Also, at the low frequencies considered, the sound field associated with azimuthal wave-number m = 0 shows better agreement with experimental data than with (the most amplified) m = 1.

Staff at Pacific Northwest National Laboratory has developed a compact, non-invasive, ultrasonic interrogation technique to characterize fluid or dense slurry during pipeline transport or in process vessels during mixing or settling. The ultrasonic transducers are mounted directly on the outside of the process container or pipe spool piece so the pipe or vessel wall becomes part of the measurement system. The transducers are pulsed to measure the density, speed of sound, and attenuation of the signal which penetrates the pipe wall and through the slurry. These signals are analyzed to determine fluid density, solids concentration, and track changes in particle size. Analysis of multiple signal reflections provides increased measurement sensitivity.

An axisymmetric numerical simulation approach to the holetone feedback problem is developed. It is based on the discrete vortex method and an ‘acoustic analogy’ representation of flow noise sources. The shear layer of the jet is represented by ‘free’ discrete vortex rings, and the jet nozzle and the end plate by bound vortex rings. A vortex ring is released from the nozzle at each time step in the simulation. The newly released vortex rings are disturbed by acoustic feedback. The simulated frequencies f follow the criterion L/u c + L/c 0 = n/f where L is the gap length, u c is the shear layer convection velocity, c 0 is the speed of sound, and n is a mode number ( n = 1/2, 1, 3/2, ...). This is in agreement with experimental observations. The numerical model also display mode shifts (jumps in the chosen value of n ), as seen in experiments.

This paper describes the application of a finite volume procedure for a fluid network to predict fluid transients following a rapid valve closure in a long cryogenic pipeline. The conservation equations of mass, momentum, energy, and the equation of state for real fluids are solved in the fluid network consisting of nodes and branches. In the present formulation, the speed of sound does not appear explicitly in the governing equations. Instead, the equation of state for a real fluid is solved in conjunction with the conservation equations to calculate the compressibility factor for modeling the wave propagation phenomenon. The numerical procedure is also capable of modeling the wave propagation due to phase change and gas-liquid mixture. The predicted history of pressure and velocity variation in a single pipe has been compared to the solution by the method of characteristics (MOC) for liquid oxygen (LO 2 ), liquid hydrogen (LH 2 ), and water (H 2 O). The paper also presents the numerical solution of pressure surges for a gas-liquid mixture, condensation of vapor, and flow circuit with parallel branches and tailpipe.

The instantaneous measurement of transient flow rates is an important problem in many fluid power applications such as the investigation of the flow ripple generated by hydraulic pumps or the measurement of flow rate changes at the ports of fast switching valves. This paper deals with the utilization of the dynamic characteristics of laminar flow in circular pipes for the indirect measurement of flow rates. A discrete time state space realization of the transmission line dynamics is computed via inverse Laplace transform and an identification and model reduction method based on the singular value decomposition. This dynamic system is used for the computation of the flow rate at one end of a pipe section. Special attention is paid to the identification of the speed of sound and the dimensionless dissipation number of the pipe section, since exact knowledge of these parameters is crucial for the reliabilty of the measurement results.

A real time multi-functional ultrasonic sensor system is proposed to provide automated drilling fluid monitoring that can improve the capability and development of slimhole and microhole drilling. This type of reliable, accurate, and affordable drilling fluid monitoring will reduce the overall costs in exploration and production. It will also allow more effective drilling process automation while providing rig personnel a safer and more efficient work environment. Accurate and timely measurements of drilling fluid properties such as flow rate, density, viscosity, and solid loading are key components for characterizing rate of drill penetration, providing early warning of lost circulation, and for use in real-time well control. Continuous drilling fluid monitoring enhances drilling economics by reducing the risk of costly drilling downtime, increasing production performance, and improving well control. Investigations conducted to characterize physical properties of drilling mud indicate that ultrasound can be used to provide real-time, in-situ process monitoring and control. Three types of ultrasonic measurements were evaluated which include analysis of in wall, through wall and direct contact signals. In wall measurements provide acoustic impedance (the slurry density and speed of sound product). Through wall and direct contact measurements provide speed of sound and attenuation. This information is combined to determine physical properties such as slurry density, solids concentration and can be used to detect particle size changes and the presence of low levels of gas. The measurements showed that for the frequency range investigated in-wall measurements were obtained over the slurry density range from 1500 to 2200 kg/m 3 (10 to 17 pounds solids per gallon of drilling fluid). Other measurements were obtained at densities in the 1500 to 1800 kg/m 3 range. These promising measurement results show that ultrasound can be used for real-time in-situ characterization of the drilling process by monitoring drilling mud characteristics.

Propagation of pressure waves caused by a thermal shock in liquid metals containing gas bubbles is performed by a numerical simulation. The present study examined the influences of bubble radius and void fraction on the absorption of thermal expansion of liquid metals and attenuation of pressure waves. As the result of the calculation, since the large bubbles which have a lower natural frequency than the small bubbles cannot respond to the heat input, the peak pressure at the heated region increases with increasing bubble radius. Especially, when the bubble radii are around 500 μm, the pressure wave propagates through the mixture not with the sonic speed of the mixture but with that of liquid mercury. On the other hand, decreasing the void fraction makes behavior of bubbles nonlinear and a collapse of bubble produces a high pressure wave. However, the calculation shows that the method of introducing micro gas bubbles into liquid metals is effective to prevent cavitation erosion on the wall.