Low Mach Flows Research Articles

A compressible flow solver for turbomachinery of the real gases with strongly variable properties

Accurate prediction of real gas flows with strongly variable properties is an essential prerequisite for turbomachinery performance analysis. This paper presents a density-based solver for real gas flows in turbomachinery. The solver employs a third-order discretization scheme to improve computational accuracy. Real gas equations of state and look-up table are utilized in the solver to account for the strong nonlinear variations of thermophysical properties. The preconditioning method is adopted for simulations, including low-Mach flow regions, to address convergence difficulties. The implicit Time Consistent Preconditioned Gauss-Seidel Scheme (TCPGS) is employed for the time-stepping. The solver is validated by transonic compressor cascade wind tunnel experiments. Numerical test cases are adopted to evaluate the solver performance, including NASA Rotor 67, NASA Rotor 37, real gas flows in the Laval nozzle, and compressor seal. It has been proved that the numerical test results are consistent with published technical data. The advantages of this solver include numerical stability, computational efficiency, and physical accuracy, which indicate its applicability in the turbomachinery design process for real gases.

A simple HLLE-type scheme for all Mach number flows

A simple HLLE-type scheme is proposed for all Mach number flows. In the proposed scheme, no extra wave structure is added in the HLLE scheme to resolve the shear wave while the contact wave is resolved by adding a wave structure similar to the HLLEM scheme. The resolution of the shear layers and the flow features at low Mach numbers is achieved by a velocity reconstruction method based on the face normal Mach number. Robustness against the numerical instabilities is achieved by scaling the velocity reconstruction function in the vicinity of shock with a multi-dimensional pressure sensor. The ability of the proposed scheme to resolve low Mach flow features is demonstrated through asymptotic analysis while the stability of the proposed scheme for strong shock is demonstrated through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems at high speeds and is capable of resolving the flow features at very low Mach numbers.

Modified advection upstream splitting method: Revolutionizing accuracy and convergence speed in low-Mach flows

The vital role of the numerical scheme is becoming increasingly critical as the use of computational fluid dynamics grows. To address the unfavorable effects experienced in low-speed flows when using the AUSM+M scheme (Improved Advection Upstream Splitting Method), the present paper presents an improved approach known as Modified-AUSM+M (M-AUSM+M). This novel method offers enhanced reliability in simulating low-Mach number flows, effectively mitigating the challenges associated with low-speed symptoms encountered in the original AUSM+M scheme. The novel scheme is facilitated by the parameter-free form of the pressure diffusion term in the mass flux and the low-dissipative form of the velocity diffusion term in the pressure flux. The impacts of these critical ingredients are then thoroughly evaluated, and the different characteristics are explored in terms of robustness and accuracy using a wide range of low-Mach test cases. The proposed scheme maintains a consistent correlation between accuracy and convergence speed. In addition, the recently devised technique demonstrates superior accuracy compared to AUSM+M and AUSM+UP schemes when dealing with low-Mach flows. Furthermore, the findings indicate an incredible reduction in iteration numbers, ranging from 30% to 80%, by employing the enhanced scheme in low-Mach domains. In the investigation of high-Mach test cases, the newly developed method preserves the accuracy achieved by AUSM+M in high-Mach flows.

Toward the use of a reduced‐order and stochastic turbulence model for assessment of far‐field sound radiation: Low Mach number jet flows

AbstractThis work presents a novel framework for the evaluation of far‐field sound radiation, specializing to a low Mach number jet flow. The framework comprises an analytical and a numerical part. In the analytical part, a low Mach number asymptotic analysis is presented to obtain the spectral sources of sound radiation starting from a pressure wave equation that is directly obtained from the Navier–Stokes equations. The derivation procedure is based on the fundamental premise of Lighthill's acoustic analogy. In the numerical part, a reduced‐order model for turbulent flow, the one‐dimensional turbulence model, is used to simulate the velocity field of a low Mach number turbulent round jet, assumed fully developed and statistically steady, hence homogeneous in the azimuthal direction and for a cross‐sectional slab assumed locally homogeneous in axial direction, too. The generated velocity field is used for the calculation of the spectral pressure sources, and consequently, to estimate the far‐field sound pressure level (SPL) of the jet. The results of the analysis are compared against available experimental SPL measurements from a subsonic jet. A reasonable agreement is obtained for the SPL. Furthermore, the analysis sheds light into the different contributions of the subsonic flow to sound radiation. The framework is readily extendable for any kind of low Mach number flow, including variable density flows and jet flames.

A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows

Compressible flows at low Mach numbers are prevalent in various engineering applications, such as combustion, aeroacoustics, heat transfer, and more. In this study, we present a sharp interface immersed boundary method (IBM) tailored for low Mach number viscous compressible flows. The IBM is developed using a robust interpolation scheme, ensuring stability for complex geometries with zero-thickness walls. To satisfy the boundary condition, the interpolation needs to use points from the same side, thus preventing interaction across the zero-thickness wall. Additionally, a simple modification is proposed to fully eliminate interaction between two opposite sides when performing stencil calculations for high order schemes. This is achieved by gradually reducing the order when the stencil is close to the wall. Furthermore, the IBM efficiently addresses the issue of moving objects in compressible flows, specifically the treatment of fresh cells, without necessitating any special treatment. Results showcase the method’s applicability to aerodynamic simulations at low Mach numbers, simulations of compression and expansion processes, and direct numerical simulations of aeroacoustics.

효율적인 저마하수 유동 음향 포착을 위한 OpenFOAM 기반의 압력기반 압축성 해석자 분석

For efficient capturing of low-Mach flow acoustics, a compressible pressure-based semi-implicit algorithm with characteristic splitting is implemented on the OpenFOAM framework. In this paper, detailed descriptions of the OpenFOAM code for SICS algorithms were shown and a comparison study of semi-implicit characteristic splitting (SICS) and compressible PIMPLE algorithm was performed. To validate SICS solver, the aeolian tone of the cylinder was simulated and the corresponding acoustic pressure was compared with the previously reported value. To evaluate pressure-based solver performance, acoustic wave propagation and scattering problems were simulated. It is found that a pressure-based solver with SICS algorithm shows better cost-effective performance on low-Mach flow acoustics than a solver with a compressible PIMPLE algorithm. The present SICS solver was extended to reacting flow and one-dimensional flame structures were resolved correctly. The SICS solver can be used to simulate flame-acoustic coupling of low-Mach flow more efficiently.

A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations

This paper is devoted to the simulation of compressible magnetohydrodynamic (MHD) flows with the Lattice Boltzmann Method (LBM). The usual LBM is limited to low-Mach flows. We propose a robust and accurate numerical method based on the vectorial kinetic construction of [5,25], which allows us to extend the LBM to arbitrary Mach flows. We also explain how to adjust the numerical viscosity in order to obtain stable and accurate results in smooth or discontinuous parts of the flow and reduced divergence errors. The method can handle shock waves and can be made second order in smooth regions. It is also very well adapted to computing with Graphics Processing Unit (GPU). Our GPU implementation in 2D achieves state-of-the-art accuracy, with near-optimal performance. We finally present numerical computations of a tilt instability that demonstrate the capability of the method to handle physically relevant simulations.

Experimental investigation of multimodal noise generation by ducted low Mach number flows through orifice plates

Noise generation by low Mach number air flows through circular orifices in rectangular ducts is investigated. In particular, the influence of the number and position of the orifices maintaining a constant flow area is addressed. A review of the available theories suggests a certain importance of such parameters in the excitation of higher-order acoustic duct modes. A qualitative coefficient is proposed for a first characterization of the ability to enhance or lessen a given higher-order acoustic mode by the plate geometry. An experimental campaign is performed to measure the total emitted acoustic power by different plate geometries as well as its modal composition. It is found that the orifices' numbers and positions greatly influence the acoustic emissions while the flow pressure drop caused by the obstacles is similar. The proposed qualitative coefficient shows good agreement with the experimental results. A particle image velocimetry measurement campaign is performed to visualize the near-field average flow behavior upstream and downstream of the orifice plates. An increase in the turbulent velocity fluctuations in the vicinity of the orifices is observed on both sides, further validating previous studies on the subject.

Manifold-informed state vector subset for reduced-order modeling

Reduced-order models (ROMs) for turbulent combustion rely on identifying a small number of parameters that can effectively describe the complexity of reacting flows. With the advent of data-driven approaches, ROMs can be trained on datasets representing the thermo-chemical state-space in simple reacting systems. For low-Mach flows, the full state vector that serves as a training dataset is typically composed of temperature and chemical composition. The dataset is projected onto a lower-dimensional basis and the evolution of the complex system is tracked on a lower-dimensional manifold. This approach allows for substantial reduction of the number of transport equations to solve in combustion simulations, but the quality of the manifold topology is a decisive aspect in successful modeling. To mitigate manifold challenges, several authors advocate reducing the state vector to only a subset of major variables when training ROMs. However, this reduction is often done ad hoc and without giving detailed insights into the effect of removing certain variables on the resulting low-dimensional data projection. In this work, we present a quantitative manifold-informed method for selecting the subset of state variables that minimizes unwanted behaviors in manifold topologies. While many authors in the past have focused on selecting major species, we show that a mixture of major and minor species can be beneficial to improving the quality of low-dimensional data representations. The desired effects include reducing non-uniqueness and spatial gradients in the dependent variable space. Finally, we demonstrate improvements in regressibility of manifolds built from the optimal state vector subset as opposed to the full state vector.

Numerical optimizing noise damping performances of Helmholtz resonators with a rigid baffle implemented at neck in presence of a grazing flow

As an applicable noise attenuator, Helmholtz resonator is mainly used to dampen acoustic noise at low- and medium-frequency ranges. It is typically implemented in combustion-engines and gas turbines to dampen thermoacoustic instabilities. However, it has a narrow effective frequency range and does not work effectively at off-design conditions. In this work, we consider a modified structured Helmholtz resonator (HR) at its neck by applying a rigid baffle in order to maximize its’ noise damping effect and to broaden its frequency bands. The resonator is attached to a cylindrical duct/pipe in presence of a mean flow (grazing flow), aiming to simulate the practical engines flow configuration. For this, a two-dimensional frequency domain numerical model is developed by using COMSOL V5.3. The numerical simulations are carried out by solving the linearized Navier–Stokes equation in frequency domain with low computational cost and time. In order to obtain an optimum design in terms of the maximum noise damping performances, 10 new different configurations/designs are proposed. The effects of 1) the single baffle attached to the upstream or downstream sidewall of the neck ends, that is, Design A, B, C, and D or double baffles, that is, Design E, F, G, and H), 2) the baffle implementation location, 3) the length of the rigid baffle, and 4) the grazing flow low Mach number are evaluated and compared. It is found that Design C is associated with improved TL by 50% and decreased resonant frequency by 20% comparing with the conventional HR. The present preliminary study shows that Design C is the better design. Further experimental and optimization researches are needed to sheds light on the optimum design of a Helmholtz resonator with neck structure being modified, as there is a low Mach number grazing flow.

High Order Semi-implicit WENO Schemes for All-Mach Full Euler System of Gas Dynamics

In this paper, we propose high order semi-implicit schemes for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions for low Mach flows. High order accuracy in time is obtained by semi-implicit temporal integrator based on the IMEX Runge-Kutta (IMEX-RK) framework. High order in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions adapted to the semi-implicit IMEX-RK time discretization. The schemes are proven to be asymptotic preserving and asymptotically accurate as the Mach number vanishes. Besides, they can well capture discontinuous solutions in the compressible regime, especially for two dimensional Riemann problems. Numerical tests in one and two space dimensions will illustrate the effectiveness of the proposed schemes.

A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

A fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.

A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids

This article presents a massively parallel and robust strategy to perform the simulation of turbulent incompressible two-phase flows on unstructured grids in complex geometries. This strategy relies on a combination of a narrow-band accurate conservative level set (ACLS)/ghost-fluid framework with isotropic adaptive mesh refinement. This combination enables to accurately capture interface dynamics and topology, and the small physical scales at the liquid-gas interface are resolved at an affordable cost. The ACLS method, even if not strictly mass-conserving, ensures the exact conservation of a smoothed phase indicator, which minimizes the liquid mass conservation errors. In the accurate conservative level set framework, presented first in Desjardins et al. (2008) [25], the interface is defined as the iso-contour of a hyperbolic tangent function, which is advected by the fluid, and then reshaped using a reinitialization equation. Several forms of this reinitialization exist: the original ACLS form proposed by Desjardins et al. involves numerical estimation of the hyperbolic tangent gradient, which is difficult to compute accurately on unstructured meshes. It is thus susceptible to induce artificial deformation of the interface. A new form has been recently proposed in Chiodi and Desjardins (2017) [29], which takes advantage of a mapping onto a classical distance level set while much better preserving the interface shape. Nevertheless, the implementation of this new form on unstructured grids requires special care. In this work, a robust implementation of this new form on unstructured meshes is proposed and implemented in the YALES2 low-Mach flow solver. In order to compute interface normals and curvature, the signed-distance function is reconstructed in parallel at nodes in the narrow band around the interface using a Geometric-Projection Marker Method (GPMM). This method relies on the triangulation of the level set iso-contour and exact geometric projection to the closest surface elements. Spatial convergence, robustness and efficiency of the overall procedure are firstly demonstrated through classical interface transport test cases and two-phase flow examples. Eventually, to emphasize the significant computational gain using adaptive mesh refinement and the ability to compute complex turbulent flows with large density ratios, two Large-Eddy Simulations (LES) of atomizing liquid jets in air are presented, each one at various resolutions. The first one is a low-pressure water jet in quiescent air from a compound nozzle with full computation of the internal injector flow, while the latter is a high-pressure kerosene jet in crossflow. Both simulations are validated against experiments, demonstrating the potential of the method to access a deep numerical insight into jet instabilities and internal flow dynamics with 3D unstructured meshes.

Aeroacoustic Instability Analysis of Helmholtz Resonators Through High-Order Unsteady Reynolds-Averaged Navier–Stokes Simulations

This paper presents a numerical analysis of the aeroacoustic instabilities in a slit-type Helmholtz resonator subjected to a low Mach number grazing flow. This configuration can be susceptible to nonlinear feedback phenomena due to the mutual coupling between the aerodynamic and acoustic fields in the proximity of the slit. The aeroacoustic flowfield is simulated through a direct approach by solving the unsteady compressible Reynolds-averaged Navier–Stokes equations using a high-order discontinuous Galerkin discretization. The response of the Helmholtz resonator to an incident acoustic field is analyzed using a two-port characterization technique. The onset of the aeroacoustic instabilities is investigated by applying an acoustic energy criterion based on the scattering matrix formulation. The Nyquist stability diagram is studied to determine the system stability and identify the whistling occurrence. The two- and three-dimensional numerical results are compared to experimental data obtained from a dedicated measurement campaign. The comparison between the numerical and experimental data demonstrates a very good agreement, highlighting the potential of the applied numerical approach for the investigation of the aeroacoustic instabilities. This allows a deep description of the aeroacoustic feedback mechanisms leading to the whistling onset, proposing a valid engineering tool for the early design stage.

Analiza flatera kompozitnih trapeznih repnih površina - analiza i eksperiment

In the present work, the aeroelastic stability of tapered composite plates is investigated. Existing flutter models, based on the typical section approach, are reviewed for quasi-steady and unsteady low Mach number axial flows and modified for the thin composite tapered plates. The numerical approach, based on panel vortex methods for flutter analysis, is presented, and results are compared to typical section flutter methods for the tapered composite fins. Experimental work is performed in the subsonic wind tunnel at flow speeds of 20 - 30 m/s range. Good agreement between experimental, analytical, and numerical results is obtained, and it was concluded that the presented methodology could be used for estimating the flutter boundary velocities for the composite thin flat plates.

Numerical simulation of flame acceleration and DDT(deflagration to detonation transition) in hydrogen-air mixtures with concentration gradients

ABSTRACT In this paper, a coupled new solver is used to simulate the acceleration and deflagration to detonation transition (DDT) of inhomogeneous mixtures flame under obstacle conditions. Analyzed the variations of flame front, pressure and density with time. The experimental results show that the vertical concentration gradient affects the chemical reaction rate in the combustion reaction zone, resulting in the flame front stretching along the “front up-back down.” At the same time, the flame propagation velocity is affected by obstacles. After multi-stage “acceleration-deceleration,” it reaches 2700 m/s at 1.23 m from the ignition center, and the pressure jumps to 5.0 MPa. Finally, the transition from detonation to detonation is completed. It is worth noting that the local explosion point is in the corner of the obstacle or pipe wall. This simulation method is compatible with low Mach number laminar flow, turbulent flow, and compressible reaction flow problems under high Mach number. It provides prospective prediction for flame acceleration and detonation formation during hydrogen combustion and detonation engine operation.

A pressure-based diffuse interface method for low-Mach multiphase flows with mass transfer

This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In contrast to the classical conservative four-equation model formulation, the adopted set of equations features volume fraction, temperature, velocity and pressure as the primary variables. The model includes the effects of viscosity, surface tension, thermal conductivity and gravity, and has the ability to incorporate complex equations of state. Additionally, a Gibbs free energy relaxation procedure is used to model mass transfer. A key characteristic of the proposed methodology is the use of high performance and scalable solvers for the solution of the Helmholtz equation for the pressure, which drastically reduces the computational cost compared to analogous density-based approaches. We demonstrate the capabilities of the methodology to simulate flows with large density and viscosity ratios through extended verification against a range of different test cases. Finally, the potential of the methodology to tackle challenging phase change flows is demonstrated with the simulation of three-dimensional nucleate boiling.

Gas-liquid two-phase flows simulation based on weakly compressible scheme with interface-adapted AMR method

A weakly compressible scheme using the interface-adapted adaptive mesh refinement (AMR) method is proposed for simulating low Mach number gas-liquid two-phase flows in large-scale and high-resolution simulations. A pressure evolution equation is derived from the iso-thermal process and low-Mach-number assumptions. We solve the Navier-Stokes equation and the pressure equation explicitly including acoustic waves. In the conventional semi-implicit method to solve incompressible two-phase flows, the computational cost of the linear solver increases as the problem size becomes larger. The conservative phase-field equation was solved using the finite volume method (FVM) to capture the gas-liquid interface while conserving the total mass of each phase. We developed GPU code for a tree-based AMR that greatly reduces the computational cost of assigning a high-resolution mesh around the moving interface region. The data structure of the memory pool has extra space allocated to prevent frequent memory allocations and deallocations. Results for the two-phase flow benchmark problems, 2D rising-bubble and dam-breaking onto dry floor problem, are in good agreement with the results of incompressible solvers. The two-phase flow simulation of the dam-breaking onto a wet floor problem maintained the shape interface regardless of whether the AMR method was used or not. We have computed a two-dimensional soap bubble growing from 16mm to 120mm in diameter with about 0.9 million total cells. The final thickness of the liquid film was about 0.1mm with the finest cell size being 0.0195mm, equivalent to 8,192×8,192 uniform cells. This computation showed that high-resolution two-phase flow simulation with the explicit scheme and AMR method reproduced the behavior of the thin liquid film.

A hybrid AUSM scheme (HAUS) for multi-phase flows with all Mach numbers

A new numerical flux scheme is proposed for compressible multi-phase flows at all Mach numbers. The hybrid AUSM-family scheme (HAUS) combines various AUSM-type schemes. HAUS is facilitated by reconstructing the mass flux term present in AUSM-family schemes such as AUSMPW, SLAU-type, and AUSM+ up, and subsequently rebuilding the pressure flux term. Numerical validations are performed under various conditions from hypersonic compressible to low Mach incompressible flow regimes using the homogeneous mixture model equation with the proposed scheme. Various numerical validation problems demonstrate that the HAUS is both accurate and stable for all speed ranges of single and multi-phase flows.

Turbulent Flow Characteristics in a Model of a Solid Rocket Motor Chamber with Sidewall Mass Injection and End-Wall Disturbance

The present analytical, numerical, and experimental investigations are performed to study the flow field in acoustically simulated solid rocket motor (SRM) chamber geometry. The computational solution is carried out for a high Reynolds number and low Mach number internal flows driven by sidewall mass addition in a long chamber with end-wall disturbances. This kind of flow (transient, weakly viscous, and contains vorticity) have several features in common with a turbulent flow field. The numerical study is performed by solving the unsteady Reynolds-averaged Navier–Stokes equations along with the energy equation using the control volume approach based on a staggered grid system. The v2-f turbulence model has been implemented in the current study. A comparison of the SIMPLE and PISO algorithms showed that both algorithms provide identical results, and the computational time using the PISO algorithm is higher by about 6% than the corresponding value of the SIMPLE algorithm. A fair agreement has been obtained between the numerical, analytical, and experimental results. Moreover, the results showed that the complex turbulent internal flow patterns are induced inside the chamber due to the strong interaction of the sidewall injection with the traveling acoustic waves. Such a complex internal structure is shown to be dependent on the piston frequency and sidewall mass flux. The current study, for the first time, emphasizes the acoustic-fluid dynamics interaction mechanism and the accompanying unsteady rotational fields along with the effect of the generated turbulence on the unsteady vorticity and its impact on the real burning rate.