Compressible Fluid Research Articles

Equations of state and hysteresis loops in isothermal cavitation

This paper investigates the influence of the use of the cubic equation of state (EOS) in the isothermal cavitation of compressible fluids. To do so, a thermodynamic consistent cavitation model that was recently proposed has been used. This model is derived under the Thermodynamics of Irreversible Processes and considers the irreversible dissipative character of the phase change transformation. Numerical simulations carried out using linear and cubic EOS are presented and compared. Neglecting surface tension effects, the results obtained demonstrate that there is no significant difference between the responses of these two types of EOS for water up to saturation pressures up to about 200 kPa. Hysteresis loops observed in the simulations with both types of EOS are virtually the same. It suggests that linear EOSs can provide good approximations for metastable behaviors (intrinsically present in cubic EOS) as well as for the Gibbs free energy difference (the thermodynamic force associated with irreversible phase change transformation), rendering a great simplification in the analysis.

Natural Vibrations and Stability of Composite Cylindrical Shells Containing a Quiescent Fluid

This paper presents the results of investigation of the natural vibrations and stability of circular vertical multilayered cylindrical shells, fully or partially filled with a quiescent compressible fluid subjected to hydrostatic and external static loads. The behavior of the elastic structure and fluid medium is described based on the classical shell theory and Euler’s equations. The linearized equations of motion of the shell, together with the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is developed using Godunov’s orthogonal sweep method. The dependences of the lowest vibration frequencies and critical external pressure on the ply angle and the filling level of two-layer and three-layer cylindrical shells are analyzed in detail. It is demonstrated that, in contrast to the ply angle and a given combination of boundary conditions, the lay-up scheme of composite materials plays different parts in the problems of maximizing the fundamental frequency of vibrations and extending the stability boundaries.

Applications of partial differential equations to transient heat and mass transfer in MHD flow over a porous medium

The flow problem discussed in this research is an investigation of compressible viscous fluid in an unstable 2D MHD laminar driven vortex and stable boundary layer flow, passing a heated stretched sheet at varying speeds via a porous medium exposed to a magnetic field with viscous dissipation, thermal diffusion, thermal radiation, chemical reaction and Dufour effects. With the aid of similarity transformations, PDEs that come out in governing equations of this formulations are converted into non-linear sets of ODEs. Well-defined bvp4c technique used to numerically solve these converted equations. With use of various graphs, the consequences of different factors on the distributions of velocity, temperature and concentration were examined numerically and graphically. Physical parameters for this issue are also discussed.

1D models of an active magnetic regeneration cycle for cryogenic applications

In investigation of an active magnetic regenerator (AMR) cycle operating at room temperatures, 1D models have been extensively used to accurately computing its performance metrics. However, extending these models to simulate an AMR cycle at cryogenic temperatures introduces inherent complexities and challenges. The broad temperature span and low operating temperatures required for cryogenic applications, such as hydrogen liquefaction, lead to significant density variations of the working fluid within the AMR that cannot be overlooked. In this work, two 1D AMR models assuming a compressible working fluid operating at cryogenic temperatures are demonstrated which address the large density variations and the numerical stiffness of the equations. The models exhibit good agreement with experimental and 2D numerical results of an AMR configuration designed for hydrogen liquefaction. A comparative study is conducted between the developed models and an incompressible AMR model at cryogenic temperatures shows that the incompressible model predicts cooling powers that are higher by a factor of up to 10 at high values of utilization, highlighting the error of assuming an incompressible fluid on estimating the performance metrics.

Low Mach number limit of a diffuse interface model for two‐phase flows of compressible viscous fluids

AbstractIn this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well‐prepared initial data and same densities in the limit.

Electrifying Chemistry: Characterizing TEMPO-Based Electrocatalysts for Isopropanol to Acetone Conversion in Novel Heat Pumps

Heating, ventilation, and air conditioning (HVAC) systems account for more than 40% of the U.S. electricity usage, primarily utilizing vapor compression system (VCS) heat pumps, raising environmental concerns. The phase down of high GWP refrigerants, targeting an 85% reduction by 2035, prompts the exploration of novel heat pump technologies. Electrochemical looping heat pumps (ELHP) show promise by employing redox reactions for fluid compression to replace conventional compression technologies. However, energy-intensive redox interconversion necessitates catalysts to lower activation energy. Inspired by electrosynthesis principles, 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) emerged as a successful homogeneous electrocatalyst for selective isopropanol oxidation to acetone for use in ELHP. HPLC and 13C NMR confirmed remarkable selectivity (~100%) at practical isopropanol concentrations.To enhance TEMPO's catalytic activity, various electron-withdrawing and donating groups were explored. TEMPO-OCH3, among seven derivatives, exhibited superior efficiency with a notable rate constant (6 M-1s-1) and turnover frequency (3.1 s-1). This study innovatively applies concepts from molecular catalysis for the development of efficient catalyst materials.

Holographic turbulence from a random gravitational potential

We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid placed in a stochastic gravitational potential. We demonstrate that the dynamics of the fluid can be obtained using a dual holographic description realized by an asymptotically Anti-de Sitter black brane driven by a random boundary metric. Using the holographic duality we study the energy power spectrum of a fluid with an inverse energy cascade and show that it is compatible with that of a compressible fluid flow. We calculate the local energy dissipation and the local fluid velocity distribution which provide other measures of the holographic fluid turbulence.

Pressure-Sensitive-Paint-Driven Hybrid Unsteady Compressible Flow Simulation

A hybrid unsteady compressible computational fluid dynamics simulation (CFD) driven by pressure-sensitive paint (PSP) data is proposed, and the concept is demonstrated in two dimensions. By imposing the wall pressure acquired with PSP as the Dirichlet boundary condition, an unsteady compressible Euler equation solver is marched together with integral boundary-layer equations in time. As a result, an entire flowfield that fits the PSP measurement is created in the CFD domain. This concept is tested by taking PSP data from a past article of a wind-tunnel test using the NASA CRM65 airfoil and the steady and unsteady capabilities of this data-driven hybrid simulation are demonstrated for transonic flows in two dimensions, and the convergence characteristics are also investigated. It is found that a steady shock position, which cannot be accurately predicted by the Euler equation solver with a boundary layer, can be rectified by the hybrid simulation. Moreover, unsteady shock motion due to buffeting can also be captured well by the hybrid simulation.

Artificial neural network aided vapor–liquid equilibrium model for multi-component high-pressure transcritical flows with phase change

In this work, an artificial neural network (ANN) aided vapor–liquid equilibrium (VLE) model is developed and coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained in Python using TensorFlow, optimized for inference using Open Neural Network Exchange Runtime, and coupled with a C++ based CFD solver. This plug-and-play model/methodology can be used to convert any multi-component CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE model development. The solver is then used to study high-pressure transcritical shock-droplet interaction in both two- and four-component systems and a turbulent temporal mixing layer (TML), where both qualitative and quantitative agreement (maximum relative error less than 5%) is shown with respect to results based on both direct evaluation and the state-of-the-art in situ adaptive tabulation (ISAT) method. The ANN method showed a 6 times speed-up over the direct evaluation and a 2.2-time speed-up over the ISAT method for the two-component shock-droplet interaction case. The ANN method is faster than the ISAT method by 12 times for the four-component shock-droplet interaction. A 7 times speed-up is observed for the TML case for the ANN method compared to the ISAT method while achieving a data compression factor of 2881. The ANN method also shows intrinsic load balancing, unlike traditional VLE solvers. A strong parallel scalability of this ANN method with the number of processors was observed for all the three test cases. Code repository for 0D VLE solvers, and C++ ANN interface—https://github.com/UMN-CRFEL/ANN_VLE.git.

Internal waves and Rayleigh–Taylor instability in magnetized compressible strongly coupled dusty plasmas

This paper investigates the influence of compressibility on the internal wave modes and the density gradient-driven Rayleigh–Taylor (R–T) instability in magnetized strongly coupled dusty plasmas. The dusty magnetohydrodynamic model is formulated for compressible fluids, accounting for the effects of weakly coupled electrons/ions and strongly coupled dust particles under the influence of the gravitational field. The effect of the magnetic field on the dust dynamics has been incorporated through the magnetic force on the electrons and ions in quasineutral dusty plasmas. A dispersion relation of the R–T instability has been derived which has been modified because of the compressibility effect, dust acoustic wave speed and viscoelastic coefficients. The shear Alfvén and compressional viscoelastic wave modes become coupled in the dispersion characteristics. The modified R–T instability criterion is derived in terms of the Alfvén speed, viscoelastic effects and dust grain parameters. The graphical illustrations show that the growth rate of R–T instability has been suppressed due to compressibility, viscoelastic coefficients and dust acoustic speed. The results are useful to discuss the development of R–T instability in magnetized astrophysical dusty plasmas.

The vacuum-core vortex in relativistic perfect fluids

The governing equations in non-relativistic (conventional) compressible fluid flows are derived as a low-energy limit in relativistic flows. This suggests that exact solutions obtained in non-relativistic fluid dynamics possess their relativistic counterparts. As an example of such solutions, we consider a stationary potential flow and examine the relativistic effect on a vacuum-core (hollow-core) vortex solution in compressible fluid flows. The vacuum-core vortex solution is an exact solution in stationary potential flows, which is also true in relativistic flows. We construct the vacuum-core vortex solution in relativistic fluid flows and discuss the differences and similarities between non-relativistic and relativistic flows. We show that the vacuum-core radius in relativistic flows is larger than the one in non-relativistic flows for a fixed polytropic exponent and depends on the transonic speed (local sound speed) in the flow field. We also calculate various physical quantities such as density, pressure, and sound speed as functions of radius r from the center of the core and compare them with those in non-relativistic flows.

On the Cauchy problem of 2D compressible fluid model with the horizontal thermal gradient effect

This article mainly investigates the existence of local strong solution to the Cauchy problem of the 2D compressible fluid model with the horizontal thermal gradient effect. By using delicate weighted energy estimates, the existence of a local strong solution is obtained with the initial density and the initial temperature decay not too slowly at infinity.

EFFACEMENT OF BASAL CISTERNS AS A SINGLE PROGNOSTIC FACTOR IN TRAUMATIC BRAIN INJURY

Effacement of basal cisterns, a condition characterized by the compression or obliteration of the cerebrospinal fluid (CSF)-filled spaces around the brainstem, is an essential radiological finding in the context of traumatic brain injury (TBI). Objectives: The study's primary purpose is to find the effacement of basal cisterns as a single prognostic factor in traumatic brain injury (TBI). Methods: This prospective observational study was conducted at the Pakistan Institute of Medical Sciences, Islamabad, from 2023 to 2023. Data were collected from 250 patients suffering from TBI. For each patient, comprehensive demographic information, including age and gender, was recorded. Additional data included the mechanism of injury, the Glasgow Coma Scale (GCS) score at admission, and the presence of basal cistern effacement as observed on the initial CT scan. Radiological findings, such as midline shift and hematomas, were also documented. Results: The mean age of the patients was 35.6±5.65 years. There were 160 (64%) male and 90 (36%) female patients. Motor vehicle accidents were the most present form of injury 104 (41.6%). The mean GCS score at admission was 7.5 ± 2.1 in the basal cistern group and 12.3 ± 2.8 in the no basal cistern group. The study results revealed a significant association between basal cistern effacement and midline shift, with 61.5% of patients with effacement showing midline shift compared to only 14.8% without effacement (p < 0.01). Conclusion: Basal cistern effacement on initial CT scans is a significant prognostic indicator in traumatic brain injury. Its presence is associated with more severe injury, higher necessity for surgical intervention, and poorer long-term outcomes.

Compressible fluid limit for smooth solutions to the Landau equation

Although the compressible fluid limit of the Boltzmann equation with cutoff has been extensively investigated in Caflisch [Comm. Pure Appl. Math. 33 (1980), 651–666] and Guo, Jang, and Jiang [Comm. Pure Appl. Math. 63 (2010), 337–361], obtaining analogous results in the case of the angular non-cutoff or even in the grazing limit which gives the Landau equation, still remains largely open, essentially due to the velocity diffusion effect of the collision operator such that L^{\infty} estimates are hard to obtain without using Sobolev embeddings. In this paper, we are concerned with the compressible Euler and acoustic limits of the Landau equation for Coulomb potentials in the whole space. Specifically, over any finite time interval where the full compressible Euler system admits a smooth solution around constant states, we construct a unique solution in a high-order weighted Sobolev space for the Landau equation with suitable initial data and also show the uniform estimates independent of the small Knudsen number \varepsilon>0 , yielding the O(\varepsilon) convergence of the Landau solution to the local Maxwellian whose fluid quantities are the given Euler solution. Moreover, the acoustic limit for smooth solutions to the Landau equation in an optimal scaling is also established. For the proof, by using the macro-micro decomposition around local Maxwellians, together with techniques for viscous compressible fluid and properties of Burnett functions, we design an \varepsilon -dependent energy functional to capture the dissipation in the compressible fluid limit with the feature that only the highest-order derivatives are most singular.

On the discrepancy between crossovers of solubility in supercritical carbon dioxide and retention in supercritical fluid chromatography

Various crossover phenomena are immanent to supercritical fluids due to multidirectional temperature effects in highly compressible supercritical fluid media. Solubility crossover, i.e. controversial effect of temperature on solubility at different pressures, is probably the most well-known among them. A curious discrepancy in upper crossover pressure values between solubility in supercritical carbon dioxide and retention in supercritical fluid chromatography with pure CO2 as an eluent was unexpectedly observed for several non-polar compounds on different stationary phases. In some cases, retention crossover was found to happen at pressures almost twice as high as pressures for solubility crossover for the same compound. Retention data for three solutes with known solubility crossovers: anthracene, benzoic acid and vanillin, were collected at different pressures and temperatures for several stationary phases. The existence of upper retention crossovers, i.e. such pressure values beyond which temperature increase starts decreasing retention, were registered for all solute-sorbent combinations.Using known thermodynamic models of temperature effect on retention in supercritical fluid chromatography and on solubility in supercritical carbon dioxide, possible reasoning for the observed discrepancies is discussed. Major contribution of the balance between adsorption and partition retention mechanisms in defining retention crossover values is hypothesized.

Spectral Properties of Operators in the Problem on Normal Oscillations of a Mixture of Viscous Compressible Fluids

Spectral Properties of Operators in the Problem on Normal Oscillations of a Mixture of Viscous Compressible Fluids

Dissipative solutions to the model of a general compressible viscous fluid with the Coulomb friction law boundary condition

We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this result consists of a three level approximation method: A Galerkin approximation, the classical parabolic regularization of the continuity equation as well as convex regularizations of the potential generating the viscouss stress and the boundary terms incorporating the Coulomb friction law into the dissipative formulation. This approach combines the techniques already known from the proof of the existence of dissipative solutions to a model of general compressible viscous fluids under inflow-outflow boundary conditions as well as the proof of the existence of weak solution to the incompressible Navier-Stokes equations under the Coulomb friction law boundary condition. It is the first time that this type of boundary condition is considered in the case of compressible flow.

Decay of higher order derivatives for Lp solutions to the compressible fluid model of Korteweg type

As a follow-up study of [31], we present a derivation of upper bounds for the decay of arbitrary higher order derivatives of solutions to the compressible Navier-Stokes-Korteweg system in the Lp critical Besov space. The approach, based on Gevrey regularizing estimates, is to establish uniform bounds on the growth of the radius of analyticity of the solution in negative Besov norms, which may be applicable to a wide range of dissipative systems.

Spatiotemporal Evolution of Gas in Transmission Fluid under Acoustic Cavitation Conditions

The presence of gas in transmission fluid can disrupt the flow continuity, induce cavitation, and affect the transmission characteristics of the system. In this work, a gas void fraction model of gas–liquid two-phase flow in a transmission tube is established by taking ISO 4113 test oil, air, and vapor to accurately predict the occurrence, development, and end process of the cavitation zone as well as the transient change in gas void fraction. This model is based on the conservative homogeneous flow model, considering the temperature change caused by transmission fluid compression, and cavitation effects including air cavitation, vapor cavitation, and pseudo-cavitation. In this model, the pressure term is connected by the state equation of the gas–liquid mixture and can be applied to the closed hydrodynamic equations. The results show that in the pseudo-cavitation zone, the air void fraction decreases rapidly with pressure increasing, while in the transition zone from pseudo-cavitation to air cavitation, the air void fraction grows extremely faster and then increases slowly with decreasing pressure. However, in the vapor cavitation zone, the vapor void fraction rises slowly, grows rapidly, and then decreases, which is consistent with the explanation that rarefaction waves induce cavitation and compression waves reduce cavitation.

Nonuniqueness of Weak Solutions to the Dissipative Aw–Rascle Model

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.