Compressible Fluid Flow Research Articles

Simple and robust contact-discontinuity capturing central algorithms for high speed compressible flows

The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for this purpose and are typically based on Riemann solvers, which are strongly dependent on the underlying eigen-structure of the governing equations. Objective of the present work is to develop simple algorithms which are not dependent on the eigen-structure and yet can tackle easily the hyperbolic parts. Central schemes with smart diffusion mechanisms are apt for this purpose. For fixing the numerical diffusion, the basic ideas of satisfying the Rankine-Hugoniot (RH) conditions along with generalized Riemann invariants are proposed. Two such interesting algorithms are presented, which capture grid-aligned steady contact discontinuities exactly and yet have sufficient numerical diffusion to avoid numerical shock instabilities. Both the algorithms presented are robust in avoiding shock instabilities, apart from being accurate in capturing contact discontinuities, do not need wave speed corrections and are independent of eigen-struture of the underlying hyperbolic parts of the systems.

Comsolic solution of an elliptic cylindrical compressible fluid flow

In this article, the primary focus is to investigate the heat transfer effects with viscous compressible laminar flow in the permeable elliptic cylinder. The Reynolds number is kept 100 for flow to be laminar. The physics of heat transfer is selected to be coupled with the laminar flow. The results for particular step-size time for Velocity distribution, pressure profile, temperature profile, isothermal temperature contours, and drag coefficient have been analyzed. Mesh has been generated through COMSOL, mesh entities have been elaborated statistically. The maximum and minimum velocity profile is observed at the elliptical cylinder’s walls and upper, lower boundary respectively. The maximum velocity observed is 2.22 m/s. Pressure profile around elliptic corners is found maximum, distinct patterns are observed even under the influence of applied heat. Temperature is observed maximum at walls but it gradually increases as moving from the upper boundary towards the lower boundary. The isothermal contour patterns are observed maximum near the walls, drag coefficient of gradual decrease is observed. COMSOL multi-physics is utilized for mathematical modeling of problems and the Backward-Differentiation-Formula has been exploited to handle problems numerically. The results will help greatly to understand the characterizations of viscous fluids and in industries like air furnaces and automobile cooling systems.

Modelling laser-fluid coupling and cavitation in laser lithotripsy

The absorption of laser by fluid and the resulting vapor bubbles plays a significant role in laser lithotripsy and many other industrial applications. In this talk, we present a coupled photo-thermal-mechanical model of laser interaction in compressible multiphase fluid flows. The model couples the three-dimensional compressible Navier–Stokes equation with a nonlocal laser absorption equation. The computational framework is an extension of the recently developed FIVER (“a Finite Volume method with Exact multi-material Riemann solver”) framework, which features the use of level set and embedded boundary methods for tracking material (fluid–fluid and fluid–solid) interfaces, and the solution of local, one-dimensional multi-material Riemann problems for enforcing interface conditions. We will start with a brief review of the key model equations and numerical algorithms adopted by FIVER, as well as recent efforts on verification and validation. Next, physical models of laser absorption and laser-induced heating will be presented. Numerical models and methods for simulating phase change and tracking the vapor–liquid interface will be introduced and assessed. The performance of this computational framework will be demonstrated using several simplified model problems and a numerical experiment of cavitation in Holmium:YAG laser lithotripsy.

Data-Targeted Prior Distribution for Variational AutoEncoder

Bayesian methods were studied in this paper using deep neural networks. We are interested in variational autoencoders, where an encoder approaches the true posterior and the decoder approaches the direct probability. Specifically, we applied these autoencoders for unsteady and compressible fluid flows in aircraft engines. We used inferential methods to compute a sharp approximation of the posterior probability of these parameters with the transient dynamics of the training velocity fields and to generate plausible velocity fields. An important application is the initialization of transient numerical simulations of unsteady fluid flows and large eddy simulations in fluid dynamics. It is known by the Bayes theorem that the choice of the prior distribution is very important for the computation of the posterior probability, proportional to the product of likelihood with the prior probability. Hence, we propose a new inference model based on a new prior defined by the density estimate with the realizations of the kernel proper orthogonal decomposition coefficients of the available training data. We numerically show that this inference model improves the results obtained with the usual standard normal prior distribution. This inference model was constructed using a new algorithm improving the convergence of the parametric optimization of the encoder probability distribution that approaches the posterior. This latter probability distribution is data-targeted, similarly to the prior distribution. This new generative approach can also be seen as an improvement of the kernel proper orthogonal decomposition method, for which we do not usually have a robust technique for expressing the pre-image in the input physical space of the stochastic reduced field in the feature high-dimensional space with a kernel inner product.

PySPH: A Python-based Framework for Smoothed Particle Hydrodynamics

PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is generated from this high-level Python code and executed on either multiple cores, or on GPUs, seamlessly. It also supports distributed execution using MPI. PySPH supports a wide variety of SPH schemes and formulations. These include, incompressible and compressible fluid flow, elastic dynamics, rigid body dynamics, shallow water equations, and other problems. PySPH supports a variety of boundary conditions including mirror, periodic, solid wall, and inlet/outlet boundary conditions. The package is written to facilitate reuse and reproducibility. This article discusses the overall design of PySPH and demonstrates many of its features. Several example results are shown to demonstrate the range of features that PySPH provides.

Clausius-Duhem inequality for quasi-1D transient flows in variable cross-section area deformable pipes

This paper presents the derivation of the Clausius-Duhem inequality for quasi-1D transient flows of compressible fluids in radially deformable pipes of varying cross-section area. To do so, a decomposition of the normal stress in spherical and deviatoric components was considered, so that the power expended to radially deform the fluid could be properly accounted for in the first law of thermodynamics, generating a coherent Clausius-Duhem inequality. Based on the derived inequality for Newtonian-Fourier fluids, we focus on their implications and applications. As implications we show that the restrictions imposed on the dynamic and bulk viscosities are different from those retrieved from the 1D and 3D contexts. As applications, we present two distinct studies concerning pipe flows. The first shows by appealing to numerical simulations that the weighting-function and local-balance unsteady friction models violate the second law of thermodynamics since they present negative local rate of energy dissipation. The second presents an analysis to estimate upper bounds of the local rate of energy dissipation associated with shear, and volumetric and axial deformations for laminar and turbulent transient regimes, under flow conditions characterized by the Ghidaoui's dimensionless parameter P^, for liquids with different bulk to shear viscosity ratios. Although the dissipation is dominated by shear, that one due to volumetric deformation may become more relevant for laminar flows, when small numbers P^ and high bulk viscosities liquids are considered.

Two-step computational aeroacoustics approach for underhood cooling fan application

Aeroacoustic noise is one of the important characteristics of the fan design. Computational Aeroacoustics (CAA) can provide better design options without relying on physical prototypes and reduce the development time and cost. There are two ways of performing CAA analysis; one-step and two-step approach. In one-step CAA, air flow and acoustic analysis are carried out in a single software. In two-step approach, air flow and acoustic analysis are carried out in separate software. Two-step CAA approach can expedite the calculation process and can be implemented in larger and complex domain problems. For the work presented in this paper, a mockup of an underhood cooling fan was designed. The sound pressure levels were measured for different installation configurations. The sound pressure level for one of the configurations was calculated with two-step approach and compared with test data. The compressible fluid flow field was first computed in a commercially available computational fluid dynamics software. This flow field was imported in a separate software where fan noise sources were computed and further used to predict the sound pressure levels at various microphone locations. The results show an excellent correlation between test and simulation for both tonal and broadband components of the fan noise.

Applying the Swept Rule for Solving Two-Dimensional Partial Differential Equations on Heterogeneous Architectures

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems and three key parameters: problem size, GPU block size, and work distribution. Our solver showed a speedup range of 0.22–2.69 for the heat diffusion equation and 0.52–1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs.

Application of a New Hybrid Immersed Boundary Method for the Simulation of Viscous Compressible Flows

In this paper, we present a hybrid immersed boundary method (HIBM) for the simulation of two- and three-dimensional compressible viscous flows around stationary and moving obstacles. The proposed approach combines the compressible boundary condition-enforced IBM proposed by Qiu et al. and the Brinkman penalization methods. The boundary condition-enforced IBM uses a fractional step approach alongside a Dirac delta function to satisfy the boundary conditions on the body surface. Although this method works properly in subsonic regimes, it cannot correctly simulate the wake region for a supersonic flow. On the other hand, the penalization method considers the body as a porous media with a low permeability that forces the velocity and energy inside the body to converge to the body velocity and energy. However, unlike the boundary condition-enforced IBM, the streamlines penetrate the body. In the present approach, the positive features of the above-mentioned methods were included and their drawbacks were excluded. The proposed approach was applied using the finite volume method and an E-CUSP scheme. The performance of the proposed method was numerically evaluated in simulating compressible fluid flow around both stationary and moving boundaries, showing a close agreement with other numerical and experimental data available in the literature. Further, the effects of geometry, Reynolds, and Mach numbers were investigated on the supersonic flow field around elliptical cylinders of various aspect ratios. The results revealed that increasing the aspect ratio led to an increase in the shock standoff distance, recirculation zone, and drag coefficient.

About one of the mathematical models of viscous flow incompressible fluid above sandy bottom

In this research we propose a mathematical model for the flows of a viscous incompressible fluid along an inclined plane under the action of gravity over a sandy bottom. The analysis was carried out in the linear instability of the flow and reduced the problem to finding the eigenvalues. Investigated and analyzed the questions of wave formation on the free and bottom surfaces of the liquid. The regions of flow instability are determined for any Froude numbers. Obtained results were compared with experimental data and with the results of other authors on this topic.

Compressible flow simulation with moving geometries using the Brinkman penalization in high-order Discontinuous Galerkin

In this work we investigate the Brinkman volume penalization technique in the context of a high-order Discontinous Galerkin method to model moving wall boundaries for compressible fluid flow simulations. High-order approximations are especially of interest as they require few degrees of freedom to represent smooth solutions accurately. This reduced memory consumption is attractive on modern computing systems where the memory bandwidth is a limiting factor. Due to their low dissipation and dispersion they are also of particular interest for aeroacoustic problems. However, a major problem for the high-order discretization is the appropriate representation of wall geometries. In this work we look at the Brinkman penalization technique, which addresses this problem and allows the representation of geometries without modifying the computational mesh. The geometry is modelled as an artificial porous medium and embedded in the equations. As the mesh is independent of the geometry with this method, it is not only well suited for high-order discretizations but also for problems where the obstacles are moving. We look into the deployment of this strategy by briefly discussing the Brinkman penalization technique and its application in our solver and investigate its behavior in fundamental one-dimensional setups, such as shock reflection at a moving wall and the formation of a shock in front of a piston. This is followed by the application to setups with two and three dimensions, illustrating the method in the presence of curved surfaces.

Ergodic theory for energetically open compressible fluid flows

The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier–Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff–Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel measurable function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any t∈R). In particular, the ergodic averages converge for any trajectory provided its ω-limit set in the trajectory space supports a unique (in law) stationary solution.

A note on the long-time behavior of dissipative solutions to the Euler system

We show that the Reynolds defect measure for a dissipative weak solution of the compressible Euler system vanishes for large time. This may be seen as a piece of evidence that the dissipative solutions are asymptotically close to weak solutions in the turbulent regime, whence suitable for describing compressible fluid flows in the long run.

The Effect of Compressibility and Outer Boundaries on Incipient Viscous Fingering

SummaryThe knowledge of the effects of instability and heterogeneity on displacements, primarily enhanced oil recovery, and carbon dioxide storage are well known, although they remain difficult to predict. The usual recourse to modeling these effects is through numerical simulation. Simulation remains the gold standard for prediction; however, its results lack generality, being case-specific. There are also several analytic models for displacements that are usually more informative than simulation results. However, these methods apply to steady-state, incompressible flow.Carbon dioxide injection for storage uses compressible fluids and, in the absence of producers, will not approach steady-state flow (Wu et al. 2017). Consequently, it is unlikely that storage will be in reservoirs of open boundaries (steady-state flow). Flow of compressible fluid necessitates the use of closed or partially sealed boundaries, a factor that is consistent with compressible flow.This work deals with the conditions that cause the onset of incipient viscous fingering or Saffman-Taylor (ST) instability. The actual growth and propagation of fingers, a subject of much recent literature, is not discussed here. The original ST formalism of M > 1 for gravity-free flow is highly restrictive: it is for linear flow of nonmixing incompressible fluids in steady-state flow. In this work, we relax the incompressible flow restriction and thereby broaden the ST criterion to media that have sealing and/or partially sealing outer boundaries. We use the nonlinear partial differential equation for linear flow and developed analytic solutions for a tracer flow analog and also for a two-fluid compressible flow. The analysis is restricted to stabilized flow and to constant compressibility fluids, but we are not restricted to small compressibility fluids.There is no transition (mixing) zone between displacing and displaced fluids; the displacement is piston-like. The absence of a transition zone means that the results apply to both miscible and immiscible displacements, absent dispersion, or local capillary pressure. The assumption of a sharp interface is to focus on the combined effect of mobility ratio and compressibility. We use the product of the fluid compressibility and pressure drop (cfΔP) to differentiate the compressibility groups (Dake 1978; Dranchuk and Quon 1967), where ΔP is defined as the pressure drop within the specific fluid region.The results will be based on proposed analytical solutions compared to numerical simulation. The proposed formulation is less restrictive than the original ST formalism of M > 1 and allows evaluation of viscous fingering initiation or ST stability criterion in the presence of different boundary conditions (open vs. closed boundaries) with compressible fluids under the stated assumptions, which is the scope of this work.The key contribution here is the effect of external boundaries, which consequently makes necessary the use of compressible fluids. Absent compressibility, the necessary condition for the growth of a viscous finger is simply the mobility ratio, M > 1. It is the objective of this work to study how the ST criterion is affected by the presence of sealing and partially sealing outer boundaries with the consequent inclusion of compressible flows as in carbon dioxide storage and enhanced oil recovery by gas injection.The results show that adding compressibility always makes displacements more unstable for stabilized background flow, even for a favorable mobility ratio (M < 1) at extremely large compressibility (e.g., cf > 5×10−3 1/psi). For a sealed external boundary (no production or leakage), displacements will become more stable as a front approaches an external boundary for all mobility ratios (M) investigated.

RETRACTED ARTICLE: Numerical and experimental evaluation of cavitation flow around axisymmetric cavitators

The primary objective of this research is to study the cavitating effects of fluid flow past different axisymmetric cavitator in the upper sub-critical flow regime, which corresponds to the Reynolds number (2 × 104 to 2 × 105). Experiments are conducted in a water tunnel with a fluid flow velocity of 30 to 60 m/s at a constant rate of injection. The commercial software tool, ANSYS Fluent 18.1, is used to simplify three dimensional Reynolds averaged Navier Stokes equation with the compressible fluid flow by considering the pressure-based solver with standard K- ω turbulence model. The transport equation-based Schnerr and Sauer cavitation model is employed to study the cavitation phenomena. The finite volume discretisation method is implemented to evaluate the cavity length and diameter, respectively. A comparison of the numerical and experimental results shows that the numerical method can predict accurately the shape parameters of the natural cavitation phenomena such as cavity length, cavity diameter, and cavity shape. Results reported that with an increase in velocity, the cavity length and diameter increased to 250 and 20%, respectively. With a decrease in the cavitator angle at constant Reynolds number, the drag coefficient decreases up to 40%. Also, for the 30° cavitator, the drag coefficient rises by 28% when cavitation number is increased from 0.25 to 0.32.

Improvement of aerodynamic characteristics of air propellers of wind power plants using jet mechanization of blades

The paper considers the possibility of increasing the efficiency of wind power plants through the use of jet mechanization of propeller blades. The study of jet mechanization of the blade was carried out for the aerodynamic profile of NACA 0012 by numerical simulation in the Flow Vision software. The calculations were carried out by solving the plane problem of a completely compressible fluid or gas flow around the blade profile. The results of numerical simulation confirmed the change in the profile characteristics when additional air is supplied to the profile suction surface. The results obtained have been verified with the results of other authors. The data obtained as a result of modeling can be used both in the creation of new wind stations and in the capital improvement of the existing ones.

Effect of vortex and entropy sources in sound generation for compressible cavity flow

The present study reports the effect of different source terms on the near and far-field acoustic characteristics of compressible flow over a rectangular cavity using hybrid computational aeroacoustics methodology. We use a low dispersive and dissipative compressible fluid flow solver in conjunction with an acoustic perturbation equation solver based on the spectral/hp element method. The hybrid approach involves calculating the base fields and the acoustic sources from a fluid simulation in the first step. In the next step, the acoustic solver utilizes the variables to predict the acoustic propagation due to the given sources. The validation of the methodology against benchmark cases provides quite accurate results while compared against the existing literature. The study is then extended to assess the importance of the entropy source term for the flow over a rectangular cavity. The predictions of hybrid simulations with vortex and entropy source terms reproduce the perturbation pressure values very close to the existing direct numerical simulation results. Moreover, the results suggest that the use of just the vortex source terms over-predicts the perturbation pressure near the source region. Finally, we have carried out detailed simulations with all the source terms to investigate the noise sources for compressible flow over the cavity for different Mach number ranges (M=0.4,0.5,0.6,0.7,1.5). The obtained acoustic spectra and the sound directivity are in close agreement with the reference experiment.

Numerical and experimental evaluation of near-wake cavitation flow around axisymmetric cavitators

ABSTRACT The primary objective of this research is to study the cavitating effects of fluid flow past different axisymmetric cavitator in the upper sub-critical flow regime, which corresponds to the Reynolds number (2 × 104 to 2 × 105). Experiments are conducted in a water tunnel with a fluid flow velocity of 30 to 60 m/s at a constant rate of injection. The commercial software tool, ANSYS Fluent 18.1, is used to simplify three dimensional Reynolds averaged Navier Stokes equation with the compressible fluid flow by considering the pressure-based solver with standard k–ϵ turbulence model. A comparison of the numerical and experimental results shows that the numerical method can predict accurately the shape parameters of the natural cavitation phenomena such as cavity length, cavity diameter, and cavity shape. Results reported that with an increase in velocity, the cavity length and diameter increased to 250% and 20% respectively.

The role of fluid flow in the dynamics of active nematic defects

We adapt the Halperin–Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that ±1/2 defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it is not possible to eliminate the fluid velocity in favor of the local defect polarization alone. For the case of two defects with opposite charge, the non-local hydrodynamic interaction is mediated by non-reciprocal pressure-gradient forces. Finally, we derive continuum equations for a defect gas coupled to an arbitrary (compressible or incompressible) fluid flow.

Key influence factors on suspension compressible fluid through pore induced by SAW (motion of black powder in pipeline)

The flow of compressible fluid with suspended particles in circular tube under the effect of surface acoustic wave (SAW) is investigated. The system of differential equations for both the fluid and particles phases is solved using the perturbation method to simplify the system of equations. The time average of flow rate is calculated, and the effect of Reynolds number, wave number, concentration and density ratio is studied. Comparison between our study and the previous is discussed. The effect of SAW on the flow of suspended natural gas is taken as an application. Real data are used to introduce this application. The SAW on pipeline may avoid accumulation of black powder.