Compressible Flow Research Articles

Stability analysis of a uniform viscous transonic flow past a rotating circular cylinder

This work analyzes the transonic flow around a rotating circular cylinder. The combination of a uniform freestream flow and the flow due to the rotation of the cylinder (assuming clockwise rotation) generates a lift force (Robins-Magnus effect) that, for transonic flows, is conditioned by the presence of a shock wave on the upper side of the cylinder.Previous studies have focused primarily on incompressible flows, compressible flows at low Mach numbers, and hypersonic flows with detached shock waves. These works have barely considered the effect of the presence of the shock wave, its interaction with the wake of the cylinder and its impact in the aerodynamic coefficients.Two-dimensional numerical simulations have been carried out using the SU2 code. From these simulations, the value of the aerodynamic coefficients as a function of time and a set of snapshots of the fluid field have been obtained and analyzed using the POD and DMD techniques. This has allowed the identification of the dominant modes that characterize the time variations in the lift and drag coefficients acting on the circular cylinder for different values of the characteristic parameters of the problem.

An Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Scheme for Compressible Multi-Material Flows on Adaptive Quadrilateral Meshes

An Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Scheme for Compressible Multi-Material Flows on Adaptive Quadrilateral Meshes

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

A study of streamline geometries in subsonic and supersonic regions of compressible flow fields

The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.

Implication of injection angle and jet-to-cross flow ratio on the combustion characteristics of a scramjet combustor

The present work deals with the implication of injection angle and jet-to-cross flow ratio on the combustor performance of a cavity-based scramjet combustor. Unsteady, two-dimensional compressible flow through the scramjet combustor is considered to comprehend the effects of Mach number (Ma), jet-to-cross flow ratio ([Formula: see text]) and injection angle (α) on the combustion characteristics. Results are presented for the following range of parameters: 2.0 ≤ Ma ≤ 2.7; 15° ≤ α ≤ 60° and 0.5 ≤ [Formula: see text] ≤ 1.2. Intense recirculation zone is observed at θ = 45° irrespective of inlet Mach number which are quintessential for proper mixing. Further, the size of the recirculation zone is the largest when jet-to-cross flow ratio is equal to 0.8 acting as a precursor for enhanced mixing performance. Moreover, static pressure reaches an optimum value at injection angle of 45° beyond which further increase would result in thermal choking. Our study reveals that mixing is improved with an increase in Mach number (Ma). It is observed that the size of the recirculation zone is strongly dependent on the jet-to-cross flow pressure ratio along with the injection angle. To put it in a nutshell, the injection angle of 45° along with a jet-to-cross flow pressure ratio of 0.8 is conducive the optimal performance in scramjet combustor.

The role of annular 2-lobe nozzle in a strut injection system on the mechanism of fuel distribution at a scramjet engine

The strut injection system is a conventional technique for the injection of the fuel in combustor in hypersonic vehicles. The present article investigates the usage of the annular 2-lobe injector to improve the fuel jet behind the strut. Computational studies have been employed for the modeling of fuel jets released from 2-lobe injectors at the supersonic free stream of the combustion chamber. Simulation of the compressible flow is done by solving Reynolds-Averaged Navier-Stokes (RANS) equations with the turbulence model of SST. The roles of the proposed injection configuration on the flow and fuel jet penetration are disclosed in this work. The shape of fuel jet plume behind the injector is also investigated to explain the mechanism of fuel jet distribution in this technique. Presented data disclosed that the usage of the annular 2-lobe nozzle instead of a single circular jet improves fuel mixing by about 50 % behind the strut model.

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

Implementation and Validation of an Original OpenFOAM Code for Fluid–Structure Interaction Problems in Compressible Flow

An improved Baldwin–Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

A general multi-objective Bayesian optimization framework for the design of hybrid schemes towards adaptive complex flow simulations

Achieving accuracy with underresolved simulation of complex compressible flows with multiscale flow structures is a challenge. Either the numerical dissipation or the resolution and thereby the numerical cost is impractically high. Also, in the design of numerical solvers, the application of a solver for specific flow classes is balanced by robustness allowing the study of a broad range of flows. In this study, we propose a hybrid fifth-order targeted essentially non-oscillatory (TENO5)-based scheme tailored to optimally simulate compressible flows with underresolved dilatational and vortical multiscale structures. For optimal design, three data-driven objectives are defined. A novel objective that derives from the numerical dissipation rate analysis is a key element to deal with underresolved complex flows in practical applications. The optimization process employs a multi-objective Bayesian optimization framework with an expected hypervolume improvement and three flow configurations representative for a broad range of two- and three-dimensional flows with genuine and non-genuine subgrid scales. The optimized hybrid scheme is validated by comparing with shock-capturing schemes of the weighted essentially non-oscillatory (WENO)- and TENO- families with flows of complex shock interactions, Kelvin-Helmholtz instabilities, shock-vortex interactions, vortical and turbulent flows

Large eddy simulations of sheet-to-cloud cavitation transitions with special emphasis on the simultaneous existence of the re-entrant jet and shock waves

Sheet-to-cloud cavitation transitions are very complex owing to the simultaneous appearance of the re-entrant jet and shock waves. The objective of this paper is to investigate the physics of compressible cavitating flows with emphasis on the simultaneous existence of the re-entrant jet and shock waves. A compressible cavitating solver, which considers the compressibility effects of both the liquid and the vapour, was used to account for the different shedding characteristics induced by the re-entrant jet mechanism (RJM), the shock wave mechanism (SWM), and both the re-entrant jet and the shock waves (RJM-SMW). The solver used Large Eddy Simulations (LES) and the Schnerr-Sauer cavitation model. The numerical results are first compared with available experimental data [1] which showed satisfactory agreement for various aspects of the flow, including the pressure distribution, cavity shapes, condensation front speed, and shedding frequency. The results first show three different cavity shedding processes induced by the re-entrant jet and the shock waves. Frequency analyses show that the shock waves produce a wider frequency distribution which indicates that shock waves induce more shedding than the re-entrant jet. The quasi-periodic characteristics of the transitions between the various cavity shedding characteristics are mainly induced by the variations of the pressure, residual cavity volume and medium compressibility. Further analyses show that the different pressure, residual cavity volume and medium compressibility amplitudes determine the cavity shedding characteristics in the subsequent shedding cycle. When the conditions favour both the re-entrant jets and the shock wave effects, both the re-entrant jet and the shock waves impact the cavity shedding.

A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate

AbstractUnderstanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogeneous multiscale method (HMM) to describe the flow fields accurately. The multiscale approach combines a hyperbolic system of balance laws on the continuum scale with molecular-dynamics (MD) simulations on the microscale level. Notably, the multiscale approach is necessary to compute the interface dynamics because there is—at present—no closed continuum-scale model. The basic HMM relies on a moving-mesh finite-volume method and has been introduced recently for the compressible one-component flow with phase transitions by Magiera and Rohde in (J Comput Phys 469: 111551, 2022). To overcome the numerical complexity of the MD microscale model, a deep neural network is employed as an efficient surrogate model. The entire approach is finally applied to simulate droplet dynamics for argon-methane mixtures in several space dimensions. To our knowledge, such compressible two-phase dynamics accounting for microscale phase-change transfer rates have not yet been computed.

Performance Comparison of CFD Microbenchmarks on Diverse HPC Architectures

OpenFOAM is a CFD software widely used in both industry and academia. The exaFOAM project aims at enhancing the HPC scalability of OpenFOAM, while identifying its current bottlenecks and proposing ways to overcome them. For the assessment of the software components and the code profiling during the code development, lightweight but significant benchmarks should be used. The answer was to develop microbenchmarks, with a small memory footprint and short runtime. The name microbenchmark does not mean that they have been prepared to be the smallest possible test cases, as they have been developed to fit in a compute node, which usually has dozens of compute cores. The microbenchmarks cover a broad band of applications: incompressible and compressible flow, combustion, viscoelastic flow and adjoint optimization. All benchmarks are part of the OpenFOAM HPC Technical Committee repository and are fully accessible. The performance using HPC systems with Intel and AMD processors (x86_64 architecture) and Arm processors (aarch64 architecture) have been benchmarked. For the workloads in this study, the mean performance with the AMD CPU is 62% higher than with Arm and 42% higher than with Intel. The AMD processor seems particularly suited resulting in an overall shorter time-to-solution.

A Large Time Step Wave-Adding Simple Scheme for Unsteady Compressible Flows

In this paper, we construct a large time step wave-adding scheme (LTS-WA) for unsteady Euler equations in compressible flows with a much simpler strategy in the wave-adding procedure, named LTS-WAS. The new method does not need to calculate coefficients of contribution and also add the waves according to their types and families, which makes the scheme easy for coding and optimisation. The new scheme has a high speedup ratio, and its formulation is the same in scalar and system cases. The scheme is extended to 3D compressible flows using the dimension split method. Numerical experiments show that the new scheme maintains the advantages of the original LTS-WA scheme at large CFL numbers, and has a higher efficiency.

Predicting compressor mass flow rate using various machine learning approaches

Abstract A major focus of the present study is to construct high-fidelity models for predicting corrected mass flow rates based on the collected compressor map data. Both traditional machine learning research and modern deep learning techniques have been employed to obtain well-fitted regression models of compressor mass flow rate. As traditional machine learning methods, Multiple Linear Regression and Random Forest, are conducted on compressor maps for prediction of corrected mass flow rate. The time series-based deep learning models are able to capture the overall trend of a given input for specific map data. Therefore, a time series-based deep learning technique, namely Gated Recurrent Unit has been employed to improve regression results. Besides, the prediction capabilities of the models, results also show that the proposed models can be used for the development of dynamic aero-thermal mathematical models of gas turbine engines and mass flow rate models created for dynamic compressors in other disciplines.

Implementation of IDEAL algorithm based on Delaunay triangular mesh for 2D-compressible flows

PurposeTo present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.Design/methodology/approachProgramming completely in C++.FindingsFive compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.Originality/valueThe detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

Rigorous justification of the hydrostatic approximation limit of viscous compressible flows

This paper considers the asymptotic limit of small aspect ratio between vertical and horizontal spatial scales for viscous isothermal compressible flows. In particular, it is observed that fast vertical acoustic waves arise and induce an averaging mechanism of the density in the vertical variable, which at the limit leads to the hydrostatic approximation of compressible flows, i.e., the compressible primitive equations of atmospheric dynamics. We justify the hydrostatic approximation for general as well as “well-prepared” initial data. The initial data is called well-prepared when it is close to the hydrostatic balance in a strong topology. Moreover, the convergence rate is calculated in the well-prepared initial data case in terms of the aspect ratio, as the latter goes to zero.

Fundamental heat and entropy transfer mechanisms of convection underlying the first and second laws for an unsteady multiport system and their applications in parallel flow heat exchangers

Although thermal convection is ubiquitous in nature and technology, it has long been argued whether convection can be considered as an independent mode of heat transfer. Here, we show that pure convection mode is generally recognized from the classical first and second laws via mass flow by rooting the unsteady mass conservation relation through an equivalent multiport system. The fundamental distinction is made between convection driven by the thermal and entropy potential differences and mass flow accompanied by zero potential difference. The constitutive relations of the convective heat and entropy fluxes and their thermodynamic relationship are developed in terms of their potential differences with the exponential distribution of temperature difference in a compressible flow. In the absence of work transfer, the first and second laws are simply expressed by the standard Maxwell’s electromagnetic type equations via the total heat and entropy flux vectors. The pure convection theory is applied to a parallel-flow heat exchanger and the linear temperature difference distribution is obtained for both streams via the first-law definitions of the convective and overall heat transfer coefficients in an internal flow. The entropy generation rate inside a heat exchanger is recalculated and indicated to be driven by the difference between the reciprocal of outlet temperatures of two streams, from which the entropy generation number between outlets is developed to eliminate the entropy generation paradox. The present linear temperature difference profiles agree well with the experimental data, and the outlet entropy generation number is also justified by comparing with the previous nondimensionalizing entropy generation numbers.

A Bound-Preserving and Positivity-Preserving High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Compressible Multi-Medium Flows

A Bound-Preserving and Positivity-Preserving High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Compressible Multi-Medium Flows

Simulation of a two-phase loop thermosyphon using a new interface-resolved phase change model

The remarkable progress made in power electronics has been coupled with the miniaturization of systems, requiring high-performance cooling. A solution that has garnered significant interest involves the use of two-phase loops, in which heat transfer is associated with the phase change of the working-fluid. This paper aims at modeling two-phase flow with separated phases in a gravity-driven two-phase loop. The Volume-of-Fluid method is employed to capture the moving interface. Amid the variety of the phase change models available in the literature, we have chosen to employ a hybrid model: a subgrid-scale model to generate phase change at the wall in the absence of an interface, and a interface-resolved model for phase change at pre-existing liquid-vapor interfaces. These models have been implemented in the OpenFOAM computational code. The developed solver makes possible the simulation of compressible laminar two-phase flow with diabatic liquid-vapor phase change. Conjugate heat transfer between the wall and the fluid is also taken into account. Two-dimensional numerical simulations demonstrate that the developed solver is capable of reproducing flow regimes obtained from experiments, including the formation of Taylor bubbles and the propulsion of liquid from the evaporator to the condenser during geyser boiling. Furthermore, this study examines how the filling ratio affects flow regimes and performance.

A third-order compact finite volume scheme on unstructured grid for fluid flows

The large reconstruction stencil is one of the biggest obstacles in design and implementation of high-order finite volume schemes on unstructured grid. To tackle this problem, a third-order compact reconstruction scheme on unstructured grid is developed on the basis of compact least-squares (CLS) finite volume method. In building the reconstruction polynomial, the general boundary condition is adopted to ensure the unified third-order accuracy in both the internal and boundary cells. The reconstruction polynomial is solved in a semi-implicit sense to ensure high computational efficiency without solving the global linear algebraic equations. The theoretical accuracy order and stability limit are firstly verified by the Fourier analysis. The numerical accuracy and efficiency are then verified and validated with several incompressible and compressible flow cases. This work provides a reference to design and analysis of high-order compact finite volume schemes on unstructured grid with unified accuracy.