Compressible Solver Research Articles

Study on shock wave load characteristics from condensed phase explosive detonations in deep-water explosions

This study investigates shock wave load characteristics from condensed phase explosive detonations in deep-water environments using a high-order compressible multiphase solver. Spatial terms of the solver are discretized by fifth-order weighted essentially non-oscillatory reconstruction in characteristic space, while a third-order total variation diminishing Runge–Kutta method is adopted to deal with the temporal terms. The level-set method captures multiphase interfaces, while a programed burn model describes detonation wave generation. Numerical and experimental validations focus on shock waves in explosives interacting with water. Validations across shallow and deep-water conditions align numerical results with theoretical and experimental values. The solver examines shock wave characteristics across varied charge masses and water depths, revealing peak pressure deviations under identical conditions. The numerical simulation results indicate that the similarity of shock wave loads in underwater explosions is evident not only in peak pressures but also in the pressure–time history curves. Through extensive comparative analysis of results, it has been found that existing formulas for calculating shock wave positive pressure durations are not applicable to deep-water explosions. The research findings and analytical methods presented in this paper can serve as crucial references for further studies on the characteristics of shock wave loads in deep-water explosions.

High-speed turbulent flows towards the exascale: STREAmS-2 porting and performance

Exascale High Performance Computing (HPC) represents a tremendous opportunity to push the boundaries of Computational Fluid Dynamics (CFD), but despite the consolidated trend towards the use of Graphics Processing Units (GPUs), programmability is still an issue. STREAmS-2 (Bernardini et al. Comput. Phys. Commun. 285 (2023) 108644) is a compressible solver for canonical wall-bounded turbulent flows capable of harvesting the potential of NVIDIA GPUs. Here we extend the already available CUDA Fortran backend with a novel HIP backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIP and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analysed focusing on NVIDIA A100 and AMD MI250x cards which are currently at the core of several HPC clusters. The gap between peak GPU performance and STREAmS-2 performance is found to be generally smaller for NVIDIA cards. Roofline analysis allows tracing this behavior to unexpectedly different computational intensities of the same kernel using the two cards. Additional single-GPU comparisons are performed to assess the impact of grid size, number of parallelized loops, thread masking and thread divergence. Parallel performance is measured on the two largest EuroHPC pre-exascale systems, LUMI (AMD GPUs) and Leonardo (NVIDIA GPUs). Strong scalability reveals more than 80% efficiency up to 16 nodes for Leonardo and up to 32 for LUMI. Weak scalability shows an impressive efficiency of over 95% up to the maximum number of nodes tested (256 for LUMI and 512 for Leonardo). This analysis shows that STREAmS-2 is the perfect candidate to fully exploit the power of current pre-exascale HPC systems in Europe, allowing users to simulate flows with over a trillion mesh points, thus reducing the gap between the Reynolds numbers achievable in high-fidelity simulations and those of real engineering applications.

Comparative Performance Assessment between Incompressible and Compressible Solvers to Simulate a Cavitating Wake

To study the effects of fluid compressibility on the dynamics of a cavitating vortex street flow in a regime where the vortex shedding frequency increases as a result of the cavitation increase, the cavitating wake behind a wedge was simulated employing both incompressible and compressible solvers. To do this, a compressible cavitation model was implemented, modifying the Zwart-Gerber-Belamri (ZGB) incompressible solver and including a pressure limit and absorbing boundary conditions to prevent a non-physical pressure field. To validate the performance of the compressible model, preliminary simulations were carried out on a 1D Sod cavitating tube and the cavitating vortex shedding behind a circular body at laminar flow conditions. The results of the cavitating wake behind the wedge with the incompressible and the compressible solvers showed similar predictions in terms of pressure, vortex shedding frequency, and instantaneous and average vapor volume fraction profiles. In spite of this, differences were obtained in the energy content of the fluid force fluctuations on the body at higher frequencies, which appear to be better resolved and amplified when the compressibility model is considered. Overall, both solvers provided comparable results in terms of cavitation phenomena that are well aligned with experimental observations.

Dynamics of a single cavitation bubble near a cylindrical blind hole

Cavitation bubble dynamics, such as microjets and moving shock waves, are strongly influenced by their surroundings. We investigated the complex bubble behavior during the growth and collapse stages near a blind hole. The simultaneous study, which is a combination of experiment and numerical methods, was performed. The single bubble was induced by a laser focus beam near a blind hole in the cuvette and measured by a high-speed camera with an image processing method. Numerical predictions were conducted for a detailed further investigation of the pressure and velocity fields near and inside the bubble. A fully compressible two-phase Navier-Stokes solver based on the homogeneous flow assumption was used. Both experimental and numerical results showed good agreement with each other. Strong deformation of the bottom bubble surface evolution was observed at low standoffs above the hole entrance. An extremely high-velocity microjet with a mushroom cap-shaped bubble was predicted under high standoffs below the hole entrance. Secondary cavitation in the blind hole was observed experimentally, and we discussed the low-pressure region caused by the interaction among the shock wave, bubble, and blind hole. Consequently, the tendencies of maximum microjet velocity and time-dependent surface pressure in the collapse phase are suggested.

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.

An artificial compressibility approach to solve low Mach number flows in closed domains

An artificial compressibility approach is proposed to compute the solution of the compressible equations in the low Mach number limit, in closed domain with moving boundaries. The low Mach number stiffness is reduced by introducing an artificial sound speed, much lower than the physical one. This allows to avoid both the acoustic time step restriction and the loss of accuracy of classical compressible solvers, without solving a Poisson equation for the pressure or using the time-implicit discretization of the Turkel-type preconditioning technique. Moreover the proposed formulation involves the conservative variables plus the dynamic pressure, which facilitates the implementation of the approach in classical CFD codes for compressible flows. The numerical experiments presented show that the approach is both accurate and CPU efficient.

Sidewall influence of varying free stream Mach number in ramp induced shock wave boundary layer interactions

This study investigates the three-dimensional (3D) effects introduced by the end walls for an aspect ratio of 1 in ramp-induced shock wave boundary layer interactions. The simulations are performed using a symmetry boundary condition in the spanwise direction at free-stream Mach numbers in 3D. The simulations are performed using an in-house compressible supersonic solver “OpenSBLIFVM”. Two free stream Mach numbers 2.5, and 3 are used in the current work, and the simulated results are compared with the aspect ratio 1 simulations by Mangalagiri and Jammy. The inflow is initialized with a similarity solution; its Reynolds number based on the boundary layer thickness is adjusted such that the Reynolds number at the start of the ramp is kept at 3×105 for all simulations. From the results, it is evident that the introduction of sidewalls resulted in a shorter centerline separation length when compared with the two-dimensional (2D) simulations. This contradicts the results at Mach 2 by Mangalgiri and Jammy where the vortex observed at Mach 2 in the central separation region disappeared with increasing free-stream Mach number. Additionally, the topology of interaction shifted from owl-like separation of the second kind to the first kind when the freestream Mach number increased from 2 to 2.5. It can be concluded that the interaction topology is crucial to the increase or decrease of the central separation length when compared to 2D simulations.

On the Features of Numerical Simulation of Hydrogen Self-Ignition under High-Pressure Release

The paper is devoted to the comparative analysis of different CFD techniques used to solve the problem of high-pressure hydrogen release into the air. Three variations of a contemporary low-dissipation numerical technique (CABARET) are compared with each other and a conventional first-order numerical scheme. It is shown that low dissipation of the numerical scheme defines better resolution of the contact surface between released hydrogen and ambient air. As a result, the spatial structures of the jet and the reaction wave that arise during self-ignition are better resolved, which is useful for predicting the local effects of high-pressure hydrogen release. At the same time, the dissipation has little effect on the induction delay, so critical conditions of self-ignition can be reliably reproduced even via conventional numerical schemes. The test problem setups formulated in the paper can be used as benchmarks for compressible CFD solvers.

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.

Experimental and numerical study of a hollow droplet impacting on inclined solid surfaces

This study sheds light on the complex dynamics of hollow droplet impacts and highlights the unique behaviors that differentiate them from their dense counterparts. The impact dynamics of hollow droplets on surfaces at varying angles were investigated through a combination of experimental and numerical methods. Two-view imaging technique is used to capture the droplet flattening during the experimental study. A three-dimensional compressible solver is developed to model the droplet impact using the volume of fluid method to capture the liquid and gas interface. The study revealed two distinct behaviors when comparing the flattening of hollow droplets to that of dense droplets. First, a unique counter-jet formation was observed following the collision of a hollow droplet perpendicular to the surface, indicating an inherent characteristic of hollow droplet flattening. The length of this counter-jet was primarily influenced by the droplet velocity and liquid viscosity, with the perpendicular velocity component playing a key role in its size. Second, unlike dense droplets that recoil and form a dome shape upon impact on hydrophobic surfaces, hollow droplets form a donut shape due to disturbances caused by bubble rupture during spreading. These disturbances fragmented the liquid sheet, preventing the droplet from recoiling and resulting in a distinctive donut shape. On surfaces with different orientations, the hollow droplet exhibited two velocity components, where the normal component controls the counter-jet size while the tangential component induces tangential motion. The donut shape splat was also observed on surfaces with different orientations.

Incompressible versus compressible fluid flow models: A case study on furnace tap-hole lancing

Pyrometallurgical furnaces, essential for metal extraction, operate at temperatures exceeding 1600°C and represent complex multiphase systems that challenge direct industrial research. Multiphysics models play a key role in shedding light on their intricate behaviours, supporting the refinement of design and operational strategies. Integral to the operation are the tap-holes, which facilitate the removal of molten products and are routinely opened by lancing, a process comparable to the use of a cutting torch, where high temperatures result from oxygen reacting with an iron lance. When the lance pierces the clay, oxygen gas enters the furnace, which could influence the behaviour of the molten material inside. In this work, a multiphase fluid flow model was used to investigate bulk flow dynamics, with a focus on the effects of the lancing process on the inside of the furnace, immediately behind the tap-hole. Incompressible and compressible multiphase fluid solvers were used and compared with respect their performance - the intention was to assess whether using a compressible solver would yield a different solution to the incompressible one. It was concluded that there are negligible disparities in bulk fluid flow behaviour between the solvers for the case studies examined, indicating that solver selection might be less consequential for certain aspects of oxygen lancing.

A structure preserving numerical method for the ideal compressible MHD system

We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of the magnetic field to the momentum and total mechanical energy are treated as source terms. Our approach uses the Marchuk-Strang splitting technique and involves three distinct components: a compressible Euler solver, a source-system solver, and an update procedure for the total mechanical energy. The scheme allows for significant freedom on the choice of Euler's equation solver, while the magnetic field is discretized using a curl-conforming finite element space, yielding exact preservation of the involution constraints. We prove that the method preserves invariant domain properties, including positivity of density, positivity of internal energy, and the minimum principle of the specific entropy. If the scheme used to solve Euler's equation conserves total energy, then the resulting MHD scheme can be proven to preserve total energy. Similarly, if the scheme used to solve Euler's equation is entropy-stable, then the resulting MHD scheme is entropy stable as well. In our approach, the CFL condition does not depend on magnetosonic wave-speeds, but only on the usual maximum wavespeed from Euler's system. To validate the effectiveness of our method, we solve a variety of ideal MHD problems, showing that the method is capable of delivering second-order accuracy in space for smooth problems, while also offering unconditional robustness in the shock hydrodynamics regime as well.

Flame-acoustic interactions in high-pressure H2/air diffusion flames

Understanding flame-acoustics interaction (FAI) that can potentially trigger thermoacoustic instabilities is of critical importance to mitigate the serious side effects of pressure oscillations. While FAI has been studied extensively in premixed flames, comparatively less analysis has been conducted to explore FAI mechanisms in non-premixed flames, especially under high-pressure conditions. This study aims to numerically investigate FAI in high-pressure hydrogen/air counterflow diffusion flames, with special attention on the impact of pressure on FAI. To this end, a fully compressible unsteady counterflow solver combined with Navier-Stokes Characteristic Boundary Conditions (NSCBC) is employed to capture the reflection of the acoustic waves at the boundaries. The results show that for all ambient pressures ( 1 ≤ P a ≤ 60 bar) considered here, real-gas effects on flame structures are negligible and that increasing P a would lead to a power-law dependence of density gradient on P a with an exponent of 1.5. Furthermore, all tested cases show acoustic growth with time under fully reflecting boundary conditions, which is found to be pressure dependent. The flames become less resilient to FAI when the pressure (or density gradient) is increased. The results from the spectral analysis show that for all ambient pressures, there is only a single dominant frequency at the low-density fuel side and two dominant frequencies at the high-density oxidiser side. This indicates that the pressure oscillation is more sinusoidal at the H 2 side than that at the air side. Moreover, the phase space portraits of pressure signals indicate that the dynamics of the system are becoming periodic and approaching a limit cycle. It is found that the integrated heat release rate and the pressure fluctuations are partially in phase, which is responsible for the growth of high-frequency acoustic waves at both fuel and oxidiser sides. On the other hand, the significant density gradient contributes to the growth of low-frequency acoustic waves at the oxidiser side due to the high degree of acoustic reflectivity at the density boundary.

Scramjet Intake Aerodynamic Studies Using Sharp Interface Immersed Boundary Method

In this present article, the use of a throttling device in the form of movable flap to study scramjet inlet unstart has been investigated numerically. The flap has been employed as an effort to simulate the rise in combustor pressure of the scramjet. Computational analysis for freestream Mach number and freestream pressure of and respectively, have been performed by a two-dimensional compressible CFD in-house Finite volume solver for perfect gas. Convective fluxes have been evaluated using AUSM scheme.Inviscidflow has been assumed for all the simulations. Particular point of interest in these simulations is the application of Immersed Boundary Method along the wall boundaries,enabling the use of structured grid for complex geometries. The results demarcate the starting condition of the inlet based on the flap throttling values. Comparative results in the form of Mach number and pressure contours are presented for different flap positions. The use of Immersed Boundary Method has been successfully displayed bysimulating a movable flap.

A comprehensive CFD investigation of tip vortex trajectory in shrouded wind turbines using compressible RANS solver

It is well known that a shroud placed around a wind turbine can increase its power coefficient, but it brings complex mechanisms by which the shroud alters the flow passing through the rotor. Such mechanisms impose numerical challenges, as the shrouded turbines present nonlinear behavior in the wake. This paper deals with a comprehensive analysis of tip vortex trajectory in shrouded wind turbines using Reynolds Averaged Navier–Stokes numerical solutions. The analysis includes aerodynamic performance and vortex characteristics of the whole wind turbine. The Multiple Reference Frame is used on a high-order unstructured compressible solver to study both, isolated and shrouded rotor. The NREL Phase VI Unsteady Aerodynamic Experiment rotor is used as a test case. The accuracy of results for wind speeds between 7 and 25 ms−1 is discussed. Overall, good agreement is achieved between the computed pressure distributions and the experimental reference values. At stalled blade, more efforts are needed to improve numerical solutions, especially for integrated load quantities. The vortex structure is examined, showing that shroud impacts tip vortex trajectory by the increase of the axial induced velocity at the rotor plane. This result, demonstrates that the classical Prandtl tip loss is not accurate for shrouded turbine analysis, and modern finite blade functions are needed. The influence of the flow conditions on the tip vortex trajectory, flow separation and shroud interaction are also discussed.

High-order space–time parallel computing of the Navier–Stokes equations

Space–time parallel methods can leverage modern parallel computing architectures to further accelerate numerical simulations where parallelizing only in space limits concurrency. In this paper, we develop a high-order space–time parallel computing method for solving the Navier–Stokes equations. The method is based on revisionist integral deferred correction (RIDC) algorithm proposed by Christlieb, Macdonald and Ong [SIAM J. Sci. Comput., 32 (2010), pp. 818-835]. This parallel-in-time algorithm yields high-order accurate results within a wall-clock time comparable to that of a forward or backward Euler simulation. We extend the RIDC algorithm to a space–time parallel method and apply the method to a compressible fluid solver using the message passing interface (MPI) framework. The global communicator is split into space and time communicators to manage parallel computing in spatial and temporal domains, respectively. Accuracy tests show that the method is high-order accurate. Numerical results encompassing both smooth flows and flows with discontinuities demonstrate that the proposed method can accelerate the computation robustly. Additionally, a three-dimensional space–time parallel computation of flow around a sphere is performed. The results indicate that RIDC has the potential to be used in the field of computational fluid dynamics.

A compressible solver for two phase-flows with phase change for bubble cavitation

The present work describes the development of a novel fully compressible solver for two-phase flows with liquid-vapour phase change. Phase change phenomena in compressible two-phase flows are driving mechanisms for a multitude of phenomena including cavitation, droplet evaporation in acoustic fields, phase change in closed environments. Those are fundamental for a large number of technological applications including combustion chambers, propellant management in space and submarine engine design. The accurate simulation of phase change phenomena in compressible flows requires a direct numerical solver thermodynamically consistent and able to describe the smallest driving scales and to handle capillary effects. The present solver has these characteristics. It solves the full system of conservation equations for real fluid compressible flows of single species written in primitive variables using a semi-implicit pressure based solver. It leads to the energy equation being a Screened Poisson equation for the pressure that can be solved as a linear system. For the sake of thermodynamic consistency, several cubic equations of state are proposed to describe liquid and vapour phases as well as evolving saturation conditions at the interface. The proposed solver can be considered as an extension of classical incompressible solvers for nucleate boiling based on sharp interface approaches towards configurations with temporally and spatially evolving saturation conditions at the interface. It enables a complete coupling between local liquid-vapour phase change at the interface and pressure variations due to local flow features or time evolving thermodynamic conditions. Its interest is demonstrated with several benchmarks of increasing complexity with an ultimate configuration involving bubble cavitation due to the pressure drop in a convergent pipe.

Lattice-Boltzmann modeling of centrifugal buoyancy-induced flows in rotating compressor cavities

Turbofan compressor cooling circuits exhibit inherent unsteadiness within their cavities due to the interplay of forced and natural convection phenomena. This dynamic is fueled by axial cooling throughflow, centrifugal forces, and large temperature gradients. This paper introduces an extended compressible lattice-Boltzmann approach tailored for accurately modeling centrifugal buoyancy-driven flows in such cavities. The approach integrates a local rotating reference frame model into a hybrid thermal lattice Boltzmann method, facilitating the simulation of rotating flows of perfect gases. Moreover, a new mass-conserving boundary treatment, based on the reconstruction of distribution functions, enhances precision in predicting rotor disk heat transfer. Finally, an adapted direct-coupling mesh-refinement strategy, accounting for source terms at grid transitions, enables efficient high buoyancy flow simulations. The proposed approach effectively recovers flow and heat transfer mechanisms on sealed and open rotating compressor cavity rigs, spanning a large range of Rayleigh numbers (up to 109). Through an analysis of the compressibility effects, adjustments to the adiabatic exponent and Eckert number allow for a significant boost in computational speed without undermining the reliability of the flow and heat transfer dynamics, aligning well with established theoretical models and numerical studies. With computational efficiency that outperforms conventional compressible finite volume solvers, the proposed approach stands as a promising method for industrial-scale modeling of turbomachinery cooling circuits.

Statistical assessment of the wave loads at walls through two-phase CFD modeling of the effects of air compressibility

The modeling of wave impacts against coastal structures requires the analysis of hundreds or thousands of waves to be statistically meaningful. Long irregular wave attacks, when affordable, can be performed experimentally, but may be inadequate to track the air entrapment and account for air compressibility, which, instead, plays a key role in the wave impacts. On the other hand, long simulations are generally avoided in numerical modeling for computational effort and numerical stability reasons, even more so when two-phase flows and air compressibility are involved. In such a context, this paper presents, for the first time, the application of a plug-in suite developed in the OpenFOAM® environment to the representation of long time series of irregular waves impacting against coastal defenses while solving two compressible fluids. To this purpose, such a plug-in compressible suite was applied to reproduce recent 2D experiments of wave overtopping and wave impacts at smooth dikes with crown walls. The numerical stability of the compressible solver and its adequacy to accurately reproduce the wave reflection and the wave overtopping are first verified by comparing the numerical results with the laboratory tests. Second, the improved representation of the wave pressures and wave forces at the walls obtained with the plug-in compressible suite is shown by comparing its results with the corresponding ones obtained with the incompressible solver. Specifically, the plug-in suite—accounting for the effects of the air compressibility during the impact events—outperforms the incompressible native solver in the capture of the pressure peaks, in the reproduction of the time–pressure trace, and in the statistical analysis of the pressure distribution along the crown wall.

Numerical investigation of combustion instability in a liquid rocket engine: Interaction effect between hydrodynamics and acoustic mode

In this paper, we present the numerical evidence of multiple bifurcations in thermoacoustic instability as we decrease the equivalence ratio (ϕ) from fuel-rich (ϕ = 1.5) to fuel-lean (ϕ =0.59) within a single-element coaxial liquid rocket engine burning hydrogen peroxide and methane. An axisymmetric compressible Large Eddy Simulation solver in an open-source platform OpenFOAM combined with a global methane chemical kinetical mechanism was used to model the turbulent mixing and combustion process. After the validation of grid independence and simulation results, the synchronization phenomenon between hydrodynamic instability, acoustics and combustion is the main focus of this paper. The results here first revealed that in a direction of decreasing equivalence ratios, the first transition to limit cycle state from combustion noise state was observed via intermittency. A second bifurcation was also observed, leading to quasi-period thermoacoustic instability from the limit cycle state. Intrinsic vorticity modes and natural acoustic modes could be regarded as oscillators. The competition and cooperation between the two modes led to a phenomenon beyond limit cycle states. The vortex dynamics of thermoacoustic systems are dominated by the interaction of intrinsic vorticity modes and natural acoustic modes and exhibit an adjustment of vortex shedding frequencies, resulting in different stability regions. Herein, the flame index was performed in more detail to distinguish between the premixed flame and diffusion flame. Results indicated that the burning mode was an important driver in promoting instability whilst it also served as a medium for competition and cooperation between the natural acoustic modes and intrinsic vorticity modes.