Compressible Flow Theory Research Articles

Numerical study of chain-reaction implosions in a spatial array of ceramic pressure hulls in the deep sea using a compressible multiphase flow model

Ceramic pressure hull arrays, which are core components in providing buoyancy to underwater vehicles, are at risk of chain-reaction implosions in deep-sea environments. This study establishes a numerical model for the chain-reaction implosions of ceramic pressure hull arrays. The model is based on the theory of compressible multiphase flow. The structural finite element method combined with the ceramic material failure criterion is used to determine the cause of chain-reaction implosions. Adaptive mesh refinement is adopted to capture the gas–liquid interface accurately. The accuracy of the numerical simulation method for compressible multiphase flow is verified through an implosion experiment involving a single ceramic pressure hull. Subsequently, the simultaneous implosions of an array of ceramic pressure hulls are calculated and investigated. Finally, the chain-reaction implosions of an array of ceramic pressure hulls are calculated using the proposed model. The propagation of the implosion shockwaves and the implosion flow field distribution are analyzed and compared with those of the simultaneous implosion case. The pressure reduction in the flow field caused by the expansion waves of the implosion is found to cause the chain-reaction implosion of neighboring ceramic pressure hulls. In the chain-reaction process, the air converges at the array center, and the implosion shockwaves converge toward the center and overlap, resulting in the largest-amplitude implosion shockwave occurring near the center of the array. This phenomenon is named the converging effect of chain-reaction implosions.

Acceptance Testing of Used Cascade Impactor Stages Based on Pressure Drop Measurements in a Flow System Managed with a Critical Flow Venturi: Part I-Laboratory Proof-of-Principle.

Background: Cascade impactors are essential for measuring the aerodynamic particle size distribution delivered by metered dose, dry powder, and similar inhalable drug products. For quality control of used impactors, periodic optical inspection of the nozzles of each impactor stage (stage mensuration) is currently the only method sufficiently precise to test whether used impactors are suitable for continued use, in accord with pharmacopeial standards. Here, we demonstrate a new method for quality control of used impactors. The method combines stage-wise pressure-drop measurement with a critical flow venturi (CFV) for air flow management. This technique avoids the unacceptably large uncertainty in conventional air flow rate measurements and instead relies on pressure and temperature measurement upstream of the CFV. These measurements can be made precisely with affordable equipment. Methods: We placed a toroidally shaped CFV downstream of a Next Generation Impactor™** (NGI) and precisely measured the stagnation pressure (±0.02%) and temperature (±0.03%) upstream of this CFV at impactor inlet flow rates close to 60 L/min. Pressure-drop measurements (±0.25%) at stages 3-7 and the micro-orifice collector were made with capacitive diaphragm transducers and with a special lid to the NGI that allowed pneumatic connection to the interstage passageways before and after each impactor stage. Results: The measured pressure drop values matched, to fractional percentage precision, those predicted by the incompressible flow theory through the nozzles and the compressible flow theory through the CFV. Conclusions: Practical equipment has been assembled that measures, to fractional percentage precision, the pressure drop through impactor nozzles at precisely managed flow conditions. The experimental results support the relevant flow principles. The results, thereby, support the use of this method for quantifying whether used impactor stages are suitable for continued use in the testing of registered inhalable drug products, in accord with pharmacopeial standards.

Numerical simulation and analysis of the chain-reaction implosions of multi-spherical hollow ceramic pressure hulls in deep-sea environment

Thin-walled hollow ceramic pressure hulls on deep-sea underwater vehicles are at risk for highly destructive chain-reaction implosions. A numerical method of simulating the chain-reaction implosions of multiple ceramic pressure hulls in deep-sea environment was developed. The fluid solver used for this method adopted the compressible multiphase flow model and adaptive mesh refinement, combining the finite element method and the failure criteria of brittle materials to determine the conditions that trigger an implosion. An implosion experiment was conducted for a single ceramic pressure hull, and the experimental results verified the accuracy of the fluid solver based on compressible multiphase flow theory. The chain-reaction implosions of two ceramic pressure hulls were also computed. The computation results showed that the air cavity in a spherical pressure hull diffused the expansion wave during the compression stage. The pressure drop in the flow field initiated by the expansion wave caused the ceramic spherical shell to reach its ultimate strength, thus triggering chain-reaction implosions. The two implosion shockwaves were superimposed during the diffusion process. The peak pressure at the superposition position of the two shockwaves is related to the spacing between the two pressure hulls.

In vitro prediction of the lower/upper-critical biofluid flow choking index and in vivo demonstration of flow choking in the stenosis artery of the animal with air embolism

<i>In vitro</i> prediction of the lower/upper-critical biofluid flow choking index and <i>in vivo</i> demonstration of flow choking in the stenosis artery of the animal with air embolism

Numerical simulation and analysis of the underwater implosion of spherical hollow ceramic pressure hulls in 11000 m depth

Pressure hulls play an important role in deep-sea underwater vehicles. However, in the ultra-high pressure environment, a highly destructive phenomenon could occur to them which is called implosion. To study the characteristics of the flow field of the underwater implosion of hollow ceramic pressure hulls, the compressible multiphase flow theory, direct numerical simulation, and adaptive mesh refinement are used to numerically simulate the underwater implosion of a single ceramic pressure hull and multiple linearly arranged ceramic pressure hulls. Firstly, the feasibility of the numerical simulation method is verified. Then, the results of the flow field of the underwater implosion of hollow ceramic pressure hulls in 11000 m depth is analyzed. There are the compression-rebound processes of the internal air cavity in the implosion. In the rebound stage, a shock wave that is several times the ambient pressure is generated outside the pressure hull, and the propagation speed is close to the speed of sound. The pressure peak of the shock wave has a negative exponential power function relationship with the distance to the center of the sphere. Finally, it is found that the obvious superimposed effect between spheres exists in the chain-reaction implosion which enhances the implosion shock wave.

Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow

In a recent paper, Liu et al. [“Lift and drag in three-dimensional steady viscous and compressible flow”, Phys. Fluids 29, 116105 (2017)] obtained a universal theory for the aerodynamic force on a body in three-dimensional steady flow, effective from incompressible all the way to supersonic regimes. In this theory, the total aerodynamic force can be determined solely with the vorticity distribution on a single wake plane locating in the steady linear far field. Despite the vital importance of this result, its validity and performance in practice has not been investigated yet. In this paper, we performed Reynolds-averaged Navier–Stokes simulations of subsonic, transonic, and supersonic flows over a three-dimensional wing. The aerodynamic forces obtained from the universal force theory are compared with those from the standard wall-stress integrals. The agreement between these two formulas confirms for the first time the validity of the theory in three-dimensional steady viscous and compressible flow. The good performance of the universal formula is mainly due to the fact that the turbulent viscosity in the wake is much larger than the molecular viscosity therein, which can reduce significantly the distance of the steady linear far field from the body. To further confirm the correctness of the theory, comparisons are made for the flow structures on the wake plane obtained from the analytical results and numerical simulations. The underlying physics relevant to the universality of the theory is explained by identifying different sources of vorticity in the wake.

Compressible flow in a Noble–Abel stiffened gas fluid

While the compressible flow theory has relied on the perfect gas model as its workhorse for the past century, compressible dynamics in dense gases, solids, and liquids have relied on many complex equations of state, yielding limited insight into the hydrodynamic aspect of the problems solved. Recently, Le Métayer and Saurel studied a simple yet promising equation of state owing to its ability to model both the thermal and compressibility aspects of the medium. It is a hybrid of the Noble–Abel equation of state and the stiffened gas model, labeled the Noble–Able Stiffened Gas (NASG) equation of state. In the present work, we derive the closed form analytical framework for modeling compressible flow in a medium approximated by the NASG equations of state. We derive the expressions for the isentrope, sound speed, isentropic exponent, Riemann variables in the characteristic description, and jump conditions for shocks, deflagrations, and detonations. We also illustrate the usefulness by addressing the Riemann problem. The closed form solutions generalize in a transparent way the well-established models for a perfect gas, highlighting the role of the medium’s compressibility.

Academician CAIUS IACOB – a Brilliant Mathematician Fascinated by Mechanics

The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912–1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about “Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics”. Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the “Mathematical introduction to the mechanics of fluids”. This book, providing original ways to work with classical hydrodynamics and compressible-flow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the “Romanian Academy Institute of Applied Mathematics”. In 2001 the institute merged with the “Centre for Mathematical Statistics”, which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the “Gheorghe Mihoc – Caius Iacob Institute of Mathematical Statistics and Applied Mathematics” of the Romanian Academy.

Compressible subsonic jet flows issuing from a nozzle of arbitrary cross-section

We are concerned with the well-posedness theory of two-dimensional compressible subsonic jet flow issuing from a semi-infinitely long nozzle of arbitrary cross-section. Given any atmospheric pressure p0, we show that there exists a critical mass flux mcr depending on p0 and Ω, such that if the incoming mass flux m0 is less than the critical value, then there exists a unique smooth subsonic jet flow, issuing from the given nozzle. The jet boundary is a free streamline, which initiates from the end point of the nozzle smoothly and extends to the infinity. One of the key observations in this paper is that the restriction of the incoming mass flux guarantees completely the subsonicity of the compressible jet in the whole flow field, which coincides with the observation on the compressible subsonic flows in an infinitely long nozzle without free boundary in [8].

Spatially Sampled Pressure Profile Measurements in Externally Pressurized Gas Journal Bearings

Externally pressurized gas journal bearings (EPGJBs) are widely adopted to support high-speed rotors. This article presents novel experimental benchmark test data that enable EPGJB model validation. Axial and circumferential pressure profile measurements are presented for a 40-mm-diameter annular restrictor EPGJB operating at speeds up to 25 krpm. The corresponding rotor position, air mass flow rate, and load capacity are also measured. The effects of supply pressure, rotational speed, and load on the measured variables are presented. The measurements are in good agreement with numerical model computations. The cases in which the model deviates from the measured data are discussed in terms of compressible flow theory.

Numerical modelling of Fanno flows in micro channels: a quasi-static application to air vents for plastic moulding

The flow in micro air vents, as those used in the plastic moulding industry, can be assimilated to a Fanno flow. Even though Fanno theory is well-established, its outcome strongly depends on the correct assessment of the friction factor term. Yet, friction factor evaluation is not straightforward since traditional fluid-dynamics formulas fail to account for the compressibility effects and are only valid when low Mach numbers are attained, which is often not the case. A numerical model implementing the non-isoentropic compressible Fanno flow theory is presented. A friction factor correlation is proposed, based on the results of a large set of CFD simulations used for calibrating the numerical model. The model is then used for characterizing micro air vent geometries under different operating stagnation pressures and temperatures. The vents characterization is finally employed for the quasi-static assessment of the mass flow rate through the vents, and of the air pressure in the mould during a typical moulding process.

An approach for the numerical prediction of the compressible supercavitating flows over ultrahigh-speed underwater object

Purpose Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows. Design/methodology/approach An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow. Findings The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity. Originality/value A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

Global existence of weak solutions to an angiogenesis model

The aim of this paper is to prove global existence of weak solutions to the angiogenesis model proposed by Tosin et al. (Bull Math Biol 68(7):1819–1836, 2006). The model consists of compressible Navier–Stokes equations coupled with a reaction–diffusion equation describing the concentration of a chemical solution responsible of endothelial cells migration and blood vessels formation. Proofs are based on the control of the entropy term associated with the entropy solution of the hyperbolic mass conservation equation and the adaptation of the results of Feireisl (Dynamics of viscous compressible fluids, Oxford University Press, 2003), Lions (Mathematical topics in fluid mechanics, vol 2, compressible models. Oxford Lecture Series in Mathematics and its Applications, 1998) and Novotny and Straskhaba (Introduction to the theory of compressible flow, Oxford University Press, 2004), are inevitable for all models dealing with compressible Navier–Stokes equations. We use the vanishing artificial viscosity method to prove existence of a solution; the main difficulty for passing to the limit is the lack of compactness due to hyperbolic equation, which usually induces resonance phenomenon. This is overcome by using the concept of the compactness of effective viscous pressure combined with suitable renormalized solutions to the hyperbolic mass conservation equation.

Influence of Plasma Pressure Fluctuation on RF Wave Propagation**supported by the National Basic Research Program of China (No. 2014CB340205) and National Natural Science Foundation of China (No. 61301173)

Pressure fluctuations in the plasma sheath from spacecraft reentry affect radio-frequency (RF) wave propagation. The influence of these fluctuations on wave propagation and wave properties is studied using methods derived by synthesizing the compressible turbulent flow theory, plasma theory, and electromagnetic wave theory. We study these influences on wave propagation at GPS and Ka frequencies during typical reentry by adopting stratified modeling. We analyzed the variations in reflection and transmission properties induced by pressure fluctuations. Our results show that, at the GPS frequency, if the waves are not totally reflected then the pressure fluctuations can remarkably affect reflection, transmission, and absorption properties. In extreme situations, the fluctuations can even cause blackout. At the Ka frequency, the influences are obvious when the waves are not totally transmitted. The influences are more pronounced at the GPS frequency than at the Ka frequency. This suggests that the latter can mitigate blackout by reducing both the reflection and the absorption of waves, as well as the influences of plasma fluctuations on wave propagation. Given that communication links with the reentry vehicles are susceptible to plasma pressure fluctuations, the influences on link budgets should be taken into consideration.

Temperature and high pressure effects on choked flow in the microchannel

We studied the choked flow behavior of gas flow in a single microchannel at inlet pressures of up to 2.2 MPa. Fair agreement was obtained between the basic compressible flow theory, known as Fanno flow, numerical simulations, and experiments for the mass flow rate dependency on the inlet pressure. Investigation of the effect of varying the inlet temperature on the choked flow behavior revealed that the power law scaling of the maximum flow rate on the temperature varies with inlet pressure. This was suggested, using numerical simulations, to be a result of heat loss to the environment.

H2O beams for zinc oxide film growth produced by a Pt-catalyzed H2–O2 reaction at various divergent aperture angles of a de Laval nozzle

High-energy H2O beams generated by a de Laval nozzle, meant for the growth of zinc oxide thin films through chemical vapor deposition, were assessed based on compressible flow theory at various divergent aperture angles. In this process, high temperature H2O was generated by a catalytic reaction between H2 and O2 on Pt nanoparticles and effused through the nozzle into the reaction zone. The theoretical beam temperature distributions, reduced scaling parameters and mean cluster sizes of the H2O beams generated at angles between 50 and 90° were evaluated. The reduced scaling parameters of the H2O beams for all angles were calculated to be less than 200 and the mean cluster sizes were estimated to be less than one irrespective of the divergent aperture angle of the nozzle, suggesting that clusters are not formed in the H2O beam in our apparatus. The crystallinity and electrical properties of the zinc oxide films grown using various divergent aperture angles were also evaluated.

Effects of Pressure Variation on Polarization Properties of Obliquely Incident RF Waves in Re-Entry Plasma Sheath

Synthesizing the compressible turbulent flow theory and plasma electromagnetic (EM) theory together, a novel method connecting pressure variation and relative permittivity of re-entry plasma sheath is developed. Using this method and transmission line analogy, effects of pressure variation on polarization properties of obliquely incident EM waves at GPS frequency and Ka frequency is studied. Numerical results indicate that effects in different conditions are various. When electron density is lower than $10^{18}~\text{m}^{\mathrm {-3}}$ , influences of pressure variation are obvious at GPS frequency, while Ka frequency is feeble. For GPS frequency, effects enlarge with the increase in incident angle, but reduce with the increase in collision frequency and electron density. Ka frequency has more advantages on mitigating the disturbances of pressure variations in this situation. While in the opposite situation, influences are more remarkable at Ka frequency. Considering that GPS wave rapidly attenuates in the sheath when electron density is higher than $10^{18}~\text{m}^{\mathrm {-3}}$ and Ka wave does not, Ka frequency is an effective way to mitigate the blackout during the re-entry process after its shortcomings on polarization alteration have been carefully considered.

Comments on “A Semihydrostatic Theory of Gravity-Dominated Compressible Flow”

Comments on “A Semihydrostatic Theory of Gravity-Dominated Compressible Flow”

Study of the Fluid Flow on Proportional Valve in Spool Displacement using CFD

The main objective of this work is to estimate the fluid flow of a proportional valve. The study is based on the classical compressible flow theory and the computations with the help of CFD based commercial software ? ANSYS CFX. The fluid flow with the movement of spool along the sleeve is simulated. To change the spool moving from 0.4mm to 2.0mm, the moving mesh method with different condition of orifice is considered here. The results show that it is the highest at the 80 % (1.6mm) opening and at the 20 % (0.4mm) opening, is the lowest.

Tuning PID Controller Using Genetic Algorithms for Electro-Hydraulic System with Tracking Force Control

The aim of this paper is design a controller for force control of an Electro-Hydraulic System and selection of a PID gains are using genetic algorithm. The mathematical model is considered as the Newton second law and compressible fluid flow theory. This paper compares two kinds of tuning methods for PID controller. One is the controller design by the genetic algorithm, second is the controller design by the Ziegler and Nichols method. Each PID gains are tested with step input function, square signal, half-sine signal and half-saw signal. And results show performance index with rise time, settling time and Maximum %OS. It was found that the proposed PID gains tuning by the genetic algorithm is better than the Ziegler &amp; Nichols method.