Compressible Flow Research Articles

Physical description of an isentropic flow in a Laval nozzle

The convergent-divergent nozzles have many industrial uses such as wind turbine, the blades of turbine engines, aircraft wings and screw propeller. The main objective of this study is to identify and evaluate the physical properties of the compressible flow of an ideal gas in a one-dimensional Laval nozzle in terms of its physical and geometrical parameter. This paper will enable us to identify and determine the causes of right shockwave phenomenon. After simplify of the energy balance equations of gas dynamics, Matlab™ was used as a tool for programming. The numerical method for the resolution is based on the iterative method with an error (E=10-5). Numerical results were compared to the modeling results of CFD ‘Fluent’. The results were satisfactory.

A new open-source library based on novel high-resolution structure-preserving convection schemes

This work develops a new finite volume convection scheme and open-source library for convection-dominated problems on unstructured grids. The formulated reconstruction operators can realize high-resolution and structure-preserving properties by adjusting numerical dissipation and anti-dissipation errors in a unified normalized-variable diagram. Then, this work develops a new open-source library based on the devised schemes within one of the most widely used general-purpose open-source software whose solution quality is intrinsically limited by the low accuracy of the conventional total variation diminishing schemes. The performance of the new library is first verified by some fundamental problems including pure advection and inviscid Euler equations. The numerical results of the accuracy tests show that the developed interpolation library can significantly reduce numerical errors with a minor increased computational cost compared with the conventional second-order schemes. The complex profile advection test demonstrates that the new library can offer an improved structure-preserving property that gives essentially oscillation-free solutions and preserves the structures of the passive transported scalar. Furthermore, the robustness of the new library is validated by compressible high-speed flow simulations with irregular geometries. Thus, this work presents a new library of high-resolution structure-preserving schemes for the accurate and efficient discretization of the convection term which plays an essential role in a wide range of computational fluid dynamics. The source code of the new scheme and library are released via DOI:10.5281/zenodo.8399000.

Modelling Air Flow through Pneumatic Valves: A Brief Review with an Experimental Case Study

Compressible flow models are commonly used for describing air flow through pneumatic valves. Because of the difficulties in predicting viscous losses, these models ultimately rely on experimental determination of coefficients. Different equations have been proposed for different fluid speeds, having the sonic fluid velocity as a reference mark. However, one might question whether a much simpler approach, where the fluid is considered as incompressible, would still give good results within the typical range of industrial applications. Moreover, practically all models presuppose that the valve output pressure decreases in time, as in a discharge process. This paper reviews some representative one-dimensional compressible flow models and discusses the appropriateness of using equations based solely on discharging flows. Two experimental circuits, where an air reservoir is pressurized and, subsequently, decompressed, are used for comparison between different flow models. It is shown that a simpler set of equations still produces acceptable results for practical pneumatic applications.

A multi-physics approach for modelling noise mitigation using an air-bubble curtain in impact pile driving

Underwater noise from offshore pile driving has raised significant concerns over its ecological impact on marine life. To protect the marine environment and maintain the sustainable development of wind energy, strict governmental regulations are imposed. Assessment and mitigation of underwater noise are usually required to ensure that sound levels stay within the noise thresholds. The air-bubble curtain system is one of the most widely applied noise mitigation techniques. This paper presents a multi-physics approach for modeling an air-bubble curtain system in application to offshore pile driving. The complete model consists of four modules: (i) a compressible flow model to account for the transport of compressed air from the offshore vessel to the perforated hose located in the seabed; (ii) a hydrodynamic model for capturing the characteristics of bubble clouds in varying development phases through depth; (iii) an acoustic model for predicting the sound insertion loss of the air-bubble curtain; and (iv) a vibroacoustic model for the prediction of underwater noise from pile driving which is coupled to the acoustic model in (iii) through a boundary integral formulation. The waterborne and soilborne noise transmission paths are examined separately, allowing us to explore the amount of energy channeled through the seabed and through the bubble curtain in the water column. A parametric study is performed to examine the optimal configuration of the double bubble curtain system for various soil conditions and pile configurations. Model predictions are compared with measured data. The model allows for a large number of simulations to examine different configurations of a single bubble curtain and a double big bubble curtain.

Simplified Numerical Models of the Unsteady Tip Leakage Flow in Compressor

Simplified Numerical Models of the Unsteady Tip Leakage Flow in Compressor

Advancing high-speed flow simulations: SAUSM – an innovative hybrid numerical scheme for shock stability and accuracy

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM[Formula: see text] scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM[Formula: see text] in smooth regions. The proposed SAUSM method combines AUSM[Formula: see text] and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM[Formula: see text] in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM’s proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM[Formula: see text], including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM[Formula: see text] when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research.

An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

Analysis of the choking condition of one-dimensional diabatic flows with wall friction

The choking condition of a one-dimensional steady-state diabatic flow, with wall friction, of a perfect gas through a constant cross-section pipe has been analysed by applying a recent analytical solution. Such a choking condition can be achieved for an initially subsonic flow and a supersonic one, even when the heat flux goes from the fluid to the wall. Entropy–enthalpy diagrams have been analysed, and a universal choking condition for compressible diabatic flows with wall friction has been determined. The analytical solution of a supersonic flow, in which a normal shock occurs, has been obtained for a diabatic flow with wall friction and compared with the results of a numerical model.

IMPROVING CHARACTERISTICS OF THE IMPELLER OF A HIGH-PRESSURE CENTRIFUGAL COMPRESSOR BY DESIGNING WITH THE HELP OF CAD

High-pressure compressors are among the most common pneumatic machines in industry and transport. Classical methods of designing such machines are based on flow modeling methods in two-dimensional and one-dimensional settings. The specified design methods lead to the creation of sufficiently perfect constructions, but their characteristics can still be improved. To simulate the flow in a high-pressure compressor, it becomes relevant to study the possibilities of optimizing the design using the Ansys Vista CAD system, which can significantly increase the efficiency of the compressor. The goal of the work is to improve the characteristics of the high-pressure centrifugal compressor impeller by designing with the help of CAD. The study was carried out on the basis of the design of the flow part of the impeller of a high-pressure centrifugal compressor using the Ansys VistaCCD automated design system based on the operation parameters of a mass-produced compressor. It was found that the efficiency maxima location of the designed and serial compressor impellers are approximately the same, while the polytropic efficiency of the designed impeller is 6 % more. At the same time, the ratio of total pressures decreases by 18 %. On the other hand, the high-efficiency zone of the impeller is significantly expanded for the designed impeller. This range has increased more than three times. At the same time, in the zone of optimal efficiency, the power consumed for the designed impeller decreases by 20 % to 240 kW. The designed impeller has a more perfect distribution of pressures for the splitter with approximately the same characteristics for the main blades of the impellers. Analyzing the velocity vectors and distributions, it can be derived that the serial compressor has two separation zones: in the blade bending region and at the outlet, unlike the designed one.

Flow irreversibility and heat transfer effects on turbine efficiency

The quantification of the flow irreversibilities is crucial to developing future turbomachinery. Traditionally, design correlations and efficiencies are based on comparisons to isentropic relations to quantify the deviation from an “ideal” case. However, isentropic relations typically assume one-dimensional adiabatic flow, representing a significant departure from the actual situation in turbines operating with large levels of heat transfer. In this paper, the aerothermal losses and power generation in reversible processes are derived for three-dimensional compressible flow considering heat transfer effects. A new definition of the power potential in a reversible process is proposed that can be used to perform detailed budgeting of the losses. The proposed new loss framework can be adopted locally, which enables the precise identification of the loss source. New aerodynamic and aerothermal efficiency expressions are proposed to assess shaft power extraction in combination with heat exchange. The new method enables designers to identify the regions with high loss generation in steady and also in unsteady flow conditions, offering new avenues to evaluate the loss generation mechanisms during the design phase. Therefore, our new tool is essential to developing reduced-order models for the design of future fluid machinery.

Key features and highly effective prediction of complete startup from frozen state for high-temperature heat pipe in heat pipe reactor

High-temperature heat pipe is an efficient phase change heat transfer device, widely applied in the space nuclear reactors, the China Fusion Engineering Test Reactor, solar collectors, and the thermal protection of hypersonic vehicles. In order to understand the startup characteristics of the heat pipe and to predict its transient behavior with high accuracy, this paper first experimentally investigated the startup performance of a sodium heat pipe from the frozen state under different heating powers from 534 W to 1897 W. Then, a new compressible flow model for startup from the frozen state was developed and verified, solved the independence problems of mesh number and time-step used in the numerical treatments of most traditional heat pipe codes. Finally, based on the assessed model and experimental data, the startup procedure and the influences of heating power on the working temperature, kick-in time, and temperature difference were analyzed respectively. The comparisons indicated that the new model is extremely informative and effective, and the results provided knowledge for understanding the safe and optimum working regime of a high-temperature heat pipe using in heat pipe reactor.

Numerical simulation of compressible gas flow in flat channels in the narrow channel approximation

In this paper, numerical simulation of a compressible gas in plane channels of constant and variable cross-section is performed within the framework of two-dimensional parabolized Navier-Stokes equations. The "narrow channel approximation" model is used for the numerical solution of the uranation system.A number of transformations are described in detail, such as de-dimensioning the equation system, reducing the considered area to a square, as well as thickening the calculated points in large gradients of gas dynamic parameters. Flow conservation conditions are used to determine the pressure gradient.An effective method is given for simultaneously determining the pressure gradient and the longitudinal velocity, then other gas dynamic parameters stable for subsonic and supersonic flows, as well as a method for determining the critical flow rate for solving Laval nozzle problems.The results of methodical calculations are presented, with the aim of verifying the effectiveness of the developed calculation methodology, as well as confirming the reliability of the results obtained by comparing them with data from other authors

A new high-fidelity Total Variation Diminishing scheme based on the Boundary Variation Diminishing principle for compressible flows

High-accuracy and stable simulations of compressible flows have been highly demanded in many engineering situations. However, it remains a challenging task due to the complicated fluid structures in compressible flows, which include both continuous and discontinuous solutions. The total variation diminishing (TVD) scheme is a mainstream numerical method because it has second-order accuracy for the smooth solution and suppresses numerical oscillations near the discontinuous solution. The properties of the TVD scheme depend on the design of the second-order slope-limiter function, Φ(r), for which minmod, superbee, and van Leer types are commonly adopted. However, the limiter function that provides both superior numerical accuracy and stability has not yet been established. In this paper, we provide an adaptive model for determining the suitable limiter function in the second-order TVD range, unlike the conventional methods, which use one type of limiter function for the entire calculation region. To designate the suitable limiter value, we use the boundary variation diminishing (BVD) principle, which suggests the most appropriate reconstruction method within the specific candidates. The numerical results of benchmark tests show that the proposed scheme has fewer numerical dissipation errors and provides a suitable limiter value that ensures both accuracy and stability.

Convergence of the CEM-GMsFEM for compressible flow in highly heterogeneous media

This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM hinges on two crucial steps: First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. Then the basis functions are obtained by solving local energy minimization problems over the oversampling domains using the auxiliary space. The basis functions have exponential decay outside the corresponding local oversampling regions. The convergence of the proposed method is provided, and we show that this convergence only depends on the coarse grid size and is independent of the heterogeneities. An online enrichment guided by a posteriori error estimator is developed to enhance computational efficiency. Several numerical experiments on a three-dimensional case to confirm the theoretical findings are presented, illustrating the performance of the method and giving efficient and accurate numerical solutions.

On the unsteady cavitation characteristics of compressible liquid nitrogen flows through a venturi tube

In this paper, the unsteady cavitating flows of liquid nitrogen (LN2) through a three-dimensional (3D) venturi tube in different thermal cavitation modes are modeled based on the mixture multiphase model with the LES method and Sauer-Schnerr cavitation model. A numerical framework considering compressibility and the thermal effects of cryogenic fluids is developed, and the modified temperature-dependent Tait equations of state provide the mathematical closure. The numerical results are compared with those from previous experiments that we have conducted, and it is indicated that the simulations and experiments agree well. Condensation shock wave propagation is observed to be initiated by the impingement of the collapse-induced pressure waves from the previously shedding cloud, and details of the process are presented. The impacts of the thermal effect on the cavitation dynamics, especially the evolution of cavitation patterns and dynamic interactions between cavitation and vortex, are analyzed. The numerical results show that the formulation of condensation shock generated at the rear of the cavity varies with temperature. In addition to the pressure waves caused by shed vapor collapse, the violent mass transfer process at the closure region of the cavity releases a substantial quantity of latent heat, initiating further condensation towards the cavity as liquid temperature decreases. The entropy production theory is derived and implemented, and different entropy production terms are established in unsteady LN2 cavitating flow with different thermal effects to understand the interactions between cavitation and entropy production. The present study provides insight into the interactions of cavitation-condensation shock in the LN2 cavitating flow and contributes to a better understanding of the influences of thermal effects on cryogenic cavitation dynamics.

A kinetic energy and entropy preserving (KEEP) finite volume scheme on unstructured meshes for compressible flows

A kinetic energy and entropy preserving (KEEP) finite-volume scheme on unstructured meshes is proposed for non-dissipative and stable compressible flow computations. The KEEP finite volume scheme proposed in the present study is based on the existing KEEP schemes developed for finite difference methods. The KEEP schemes have shown superior numerical robustness without numerical dissipation in previous studies. The KEEP schemes are discretized such that the numerical fluxes discretely replicate the key analytical relations that the governing equations hold, leading to preservation of kinetic energy and a superior entropy preservation property in the incompressible and inviscid limits. This study proposes using cell-vertex discretization for the proposed KEEP finite volume scheme in order to maintain this characteristic property of the KEEP scheme and achieve second-order accuracy in space on simplex meshes and arbitrary meshes that are not highly irregular. In the numerical tests performed in this study, the proposed KEEP finite volume scheme successfully performs long-time stable computations on various unstructured meshes. Also, the proposed KEEP scheme shows much better numerical stability and spatial accuracy than the KEEP scheme with cell-centered discretization.

Parametric optimisation of entropy using sensitivity analysis and response surface methodology for the compressed flow of hybrid nanoliquid in a stretchable channel

Parametric optimisation of entropy using sensitivity analysis and response surface methodology for the compressed flow of hybrid nanoliquid in a stretchable channel

Lagrangian Voronoï meshes and particle dynamics with shocks

We present a new first order particle method on lagrangian and moving Voronoï meshes for the numerical simulation of compressible flows with shocks and internal interfaces between different gas. The method is based on the closed form formula of the partial derivative of the volume of Voronoï cells with respect to the generators. The mathematical proof of the formula seems original with respect to the literature. A corollary is that the volume of Voronoï cells is generically of class C1 with respect to the generators. The final scheme is conservative in local mass, total momentum and total energy, and it is endowed with an entropy inequality which insures the correctness of shocks calculations. Numerical illustrations in dimension d=2 are displayed for basic problems on coarse meshes. The implementation developed to obtain the numerical illustrations uses a freely available library for the generation of the Voronoï cells at all time steps.

Gas–Particle Dynamics in High-Speed Flows

High-speed disperse multiphase flows are present in numerous environmental and engineering applications with complex interactions between turbulence, shock waves, and particles. Compared with its incompressible counterpart, compressible two-phase flows introduce new scales of motion that challenge simulations and experiments. This review focuses on gas–particle interactions spanning subsonic to supersonic flow conditions. An overview of existing Mach-number-dependent drag laws is presented, with origins from eighteenth-century cannon firings and new insights from particle-resolved numerical simulations. The equations of motion and phenomenology for a single particle are first reviewed. Multiparticle systems spanning dusty gases to dense suspensions are then discussed from numerical and experimental perspectives.

Compressible turbulent convection in highly stratified adiabatic background

Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure change very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux$J_c(z)$at the top of the convection zone is reported here by a series of highly resolved three-dimensional direct numerical simulations beyond the Oberbeck–Boussinesq and anelastic limits for dimensionless dissipation numbers,$0.1 \le D\le 0.8$, at fixed Rayleigh number$Ra=10^6$and superadiabaticity$\epsilon =0.1$. The highly stratified compressible convection regime appears for$D > D_{crit}\approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50 % reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top sublayer deep into the bulk.