Low Mach Number Flows Research Articles

Investigation of the effects of different parameters on the generated pressure waves inside the tunnels

In this research the train movement along the tunnel was simulated numerically, and the time evolution of the flow field in the tunnel was evaluated. The unsteady forms of continuity, Navier–Stokes, and energy equations were applied to solve the compressible viscous flow using the dynamic mesh technique. The importance of using a compressible flow model, even for the low Mach number flow case, was demonstrated. It was shown that even in low train speeds; a compressible model is preferred, as it can predict the pressure fluctuations, while an incompressible model may only be used for predicting the mean pressure. However, in cases where pressure fluctuations are not important, the incompressible model can be used especially for a train with low acceleration. When the trains accelerate, it was found that the initial slope of the pressure curve is proportional to the train acceleration. Therefore, the increase in the train acceleration increases the maximum pressure rise. Also, the first pressure rise depends on the velocity of the train tail as it enters the tunnel. In addition, the earlier equations in the literature for computing the maximum pressure rise, can properly predict the pressure rise of accelerating trains if the train tail velocity, as it enters the tunnel, is used as the velocity scale.

Sound–turbulence interaction model for low mach number flows and its application in natural gas pipeline leak location

When leakage dynamic pressure waves (DPWs) propagate in low Mach number flows, the viscothermal effects are considered the main reason for sound attenuation. However, an experimental analysis conducted in this study shows that the non-equilibrium sound–turbulence interaction process is the main cause. The turbulence effects due to turbulent flows act on the DPWs, and the fluctuations due to the DPWs act on the turbulent flows. Both processes result in the turbulent absorption of the gas to the amplitude of the DPWs, leading to amplitude attenuation at sufficiently low frequencies. To predict the amplitude attenuation, a non-equilibrium sound–turbulence interaction model is established, solved, and verified using analytical and experimental results, which show that attenuation coefficients (ACs) obtained by considering the sound–turbulence interaction effects are 1.6–3.5 times larger than those obtained by only considering the viscothermal effects, even when the Mach number is between 0.0038 and 0.016. The established model can improve leak localization.

An experimental analysis of acoustic input impedance of a narrow pipe with low Mach number flow and thermal gradient.

In this paper, the normalized acoustic input impedance of a narrow pipe with a strong axially non-homogeneous thermal profile subjected to low Mach number flow of up to 0.03 M is studied. The analysis is done experimentally, using the two-microphone three-calibration technique and the results are compared with numerical simulations, using an industrial finite element package. The main application of this study is in the acoustic design of water-cooled charge-air coolers in internal combustion engines. The measurements are done on an effectively semi-infinite narrow pipe. It is shown that neglecting the flow effect in the calibration process of narrow pipes can significantly increase the measurement error. The results show that although the direct modification of the normalized acoustic input impedance due to low Mach number flow is negligible, the flow exerts an indirect but significant effect on this parameter by modifying the thermal gradient profile. Therefore, taking this effect into account can help to achieve an improved acoustical design of engine intake lines.

Preconditioning methods for compressible flow CFD codes: Revisited

The present article aims to implement and investigate a different preconditioning method based in a three-dimensional in-house compressible CFD code that ensures the robustness and numerical stability to determine the flowfield considering low Mach number flow. The present preconditioning method involve two different methodologies developed by references [8, 32]. The CFD solver was developed to calculate the Euler and Navier-Stokes equations, numerically, for steady-state regime based on the cell-centered finite volume method (FVM) using Reynolds Averaged Navier-Stokes equations (RANS). The centered second-order scheme was used for the discretization of convective terms from momentum equations. The explicit second-order five-step Runge-Kutta scheme was employed for the time-marching procedure, using an implicit residual smoothing technique to enhance the numerical stability. A local preconditioning method was implemented due to its robustness in predicting low Mach number flows in a compressible CFD code environment. However, for low Mach number flows, near stagnation points, numerical perturbations were amplified generating a stiffness in the convergence rate, which provided an inaccurate solution and numerical stability degradation. Aiming to improve the preconditioning robustness, a flux function and a new limiter were applied to operate with the preconditioning technique based on a pressure sensor. Those corrections re-scale the eigenvectors and ensure the locality of the algorithm, which improves the numerical stability and guarantees the convergence for low-speed flows. The inviscid flow over a NACA 0012 airfoil for compressible and incompressible cases shown accurate and robust solutions. For a viscous flow over a flat plate case in the compressible and incompressible cases, the preconditioning technique purposed in this work supplied good numerical solution in agreement with the analytical solution.

A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem

A novel notion for constructing a well-balanced scheme – a gradient-robust scheme – is introduced and a showcase application for the steady compressible, isothermal Stokes equations in a nearly-hydrostatic situation is presented. Gradient-robustness means that gradient fields in the momentum balance are well-balanced by the discrete pressure gradient — which is possible on arbitrary, unstructured grids. The scheme is asymptotic-preserving in the sense that it reduces for low Mach numbers to a recent inf–sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM–FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straightforward extension to barotropic situations with nonlinear equations of state is feasible.

A Multistate Low-dissipation Advection Upstream Splitting Method for Ideal Magnetohydrodynamics

Abstract We develop a new numerical scheme for ideal magnetohydrodynamic (MHD) simulations, which is robust against one- and multidimensional shocks, and is accurate for low Mach number flows and discontinuities. The scheme belongs to a family of the advection upstream splitting method employed in computational aerodynamics, and it splits the inviscid flux in MHD equations into advection, pressure, and magnetic tension parts, and then individually evaluates mass, pressure, and magnetic tension fluxes at the interface of a computational cell. The mass flux is designed to avoid numerical shock instability in multidimensions, while preserving contact discontinuity. The pressure flux possesses a proper scaling for low Mach number flows, allowing reliable simulations of nearly incompressible flows. The magnetic tension flux is built to be consistent with the HLLD approximate Riemann solver to preserve rotational discontinuity. We demonstrate various benchmark tests to verify the novel performance of the scheme. Our results indicate that the scheme must be a promising tool to tackle astrophysical systems that include both low and high Mach number flows, as well as magnetic field inhomogeneities.

Analysis of Rayleigh–Taylor instability at high Atwood numbers using fully implicit, non-dissipative, energy-conserving large eddy simulation algorithm

Large eddy simulation of three-dimensional, multi-mode Rayleigh–Taylor instability at high Atwood numbers is performed using a recently developed, kinetic energy-conserving, non-dissipative, fully implicit, finite volume algorithm. The algorithm was especially designed for simulating low-Mach number, variable density/viscosity, transitional, and turbulent flows. No interface capturing mechanism is required. Buoyancy and heat transfer effects can be handled without relying on the Boussinesq assumption. Because of this feature, unlike the pure incompressible ones, it does not suffer from the loss of physical accuracy at high Atwood and Rayleigh numbers. In this study, the mixing phenomenon in Rayleigh–Taylor instability and the effects of high Atwood numbers on the development of the flow are investigated using various diagnostics such as local mole fractions, bubble and spike penetration lengths and growth rates, mixing efficiencies, Taylor micro-scales, and corresponding Reynolds numbers and energy ratios. Additionally, some important terms of the Reynolds stress transport equation are also introduced, such as Reynolds stresses (and their anisotropies) and turbulent production. Results show that Rayleigh–Taylor instability at high Atwood numbers is characterized by rapid development of instability due to the increasing growth rates and higher velocities of spike fronts, larger asymmetry in the mixing region, denser interactions in the non-linear phase, and changes in bubble and spike morphologies. It is also found that interactions of spike-fronts with their surroundings are the primary mechanisms of turbulent production and transition to turbulence. However, late time mean flow measures such as energy ratio and mixedness are not significantly affected. A scaling relation between the spike to bubble penetration ratio and the heavy to light density ratio is also provided.

Diffusion and dissipation in acoustic propagation simulation by convection-pressure split algorithms in all Mach number form

The topic of the paper is accuracy analysis of acoustic propagation simulation in low Mach number flows, by finite volume co-located discretisation methods of the time-dependent compressible fluid Euler equations that use the concept of convection-pressure splitting (CPS). These are algorithms that split the flux vectors into a part associated to the convection by the fluid particles, and a part associated to the propagation of the pressure waves. For the convection part, the appropriate space discretisation is the upwind one. For the pressure part, there are alternatives. We discern five types of algorithms that all are adapted for use in low Mach number flows, and thus are considered as all Mach number algorithms. We study the behaviour of the different types for the propagation of small pressure perturbations, of discontinuous or smooth shape, in low Mach number flows. We demonstrate that four of the proposed algorithms of convection-pressure split type are dissipative for such applications, although they are designed for low Mach number flows. The objective of the paper is to analyse why some algorithms are appropriate for acoustic propagation simulation and why some are not appropriate.

Active acoustic cloaking of cylindrical shells in low Mach number flow

The vibro-acoustic response of a two-dimensional cylindrical shell in low Mach number flow is herein derived. The analytical model takes into account the structural elasticity and coupling of the shell vibration with its interior and exterior acoustic fields in the presence of a moving fluid. The cylindrical shell is modelled using Donnell-Mushtari theory. Taylor transformations are employed to transfer the convected wave equation into the ordinary wave equation which was then solved using scattering theory. Three excitation cases corresponding to a plane wave, an external monopole source and a radial point force applied directly to the shell are considered. Shell circumferential resonances and interior acoustic resonances are identified. Two active control strategies are then applied to acoustically cloak the cylindrical shell at its acoustic and structural resonances. The first control approach employs acoustic control sources in the exterior fluid domain. In the second approach, control forces are applied to directly excite the elastic shell, whereby the structural response is actively modified to manipulate the scattered and radiated acoustic fields arising from plane wave excitation of the shell. Results show that the second approach is superior in terms of both reduced control effort and cloaking of the global exterior domain. For both control approaches, the performance of the active cloak is shown to deteriorate if the convected flow field is not accounted for in the control process.

Aeroacoustic noise generated by flow around circular cyinder with permeable boundary

A new integral computational formulation is presented to evaluate the noncompact noise induced by low Mach number flows. Based on Howe’s Vortex Sound Theory and wave equation of Green’s function in free space, we obtain a new integral equation by choosing a permeable boundary as the integral boundary. The flow calculation is developed with second-order CFD solvers, and noise calculation is executed with a two-step method to solve scattered sources and far field pressure. Two- and three-dimensional circular cylinders are chosen as test examples. The pressure amplitude obtained with permeable boundary agrees well with that obtained with body-fitted high-order method. Numerical results indicate that the present method is valid and efficient to calculate noncompact noise, and the permeable boundary can replace the body surface as the integral boundary.

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows

In the first part of this work, we introduce a new relaxation system in order to approximate the solutions to the barotropic Euler equations. We show that the solutions to this two-speed relaxation model can be understood as viscous approximations of the solutions to the barotropic Euler equations under appropriate sub-characteristic conditions. Our relaxation system is a generalization of the well-known Suliciu relaxation system, and it is entropy satisfying. A Godunov-type finite volume scheme based on the exact resolution of the Riemann problem associated with the relaxation system is deduced, as well as its stability properties. In the second part of this work, we show how the new relaxation approach can be successfully applied to the numerical approximation of low Mach number flows. We prove that the underlying scheme satisfies the well-known asymptotic-preserving property in the sense that it is uniformly (first-order) accurate with respect to the Mach number, and at the same time it satisfies a fully discrete entropy inequality. This discrete entropy inequality allows us to prove strong stability properties in the low Mach regime. At last, numerical experiments are given to illustrate the behaviour of our scheme.

Acoustic Behavior Prediction and Analysis of Resonators in the Presence of Low Mach Number Flow

The frequency-domain linearized Navier–Stokes equations (LNSEs) are used to describe the sound field of Helmholtz resonators and concentric perforated tube resonators in the presence of low Mach number flow. The numerical procedure of LNSEs method is performed in three steps, computational fluid dynamics (CFD) calculation, data transfer and acoustics calculation. The transmission loss predictions of the resonators exhibit good agreement with measurements published in the literature. The results show that the low Mach number flow shifts the resonance frequencies of resonators and changes the acoustic attenuation behavior, which may be attributed to the change of acoustic impedance of the opening and orifices. In order to weaken the effect of flow on the resonance frequency, the modified configurations of resonators are proposed by using the conical tubes to reduce the flow velocity passing the opening and orifices. Numerical results demonstrated that the influence of flow velocity on the resonance frequency of the modified resonators is less sensitive than the original configurations.

Multiscale modeling of chemical vapor infiltration process for manufacturing of carbon-carbon composite

Abstract Producing large parts by chemical vapour infiltration (CVI) process is quite challenging due to non-uniform nature of temperature and gas precursor distribution. Many a times repeated experiments are required to optimize the process parameters for manufacturing composites with isotropic properties. This is not only cumbersome but also cost intensive. To address this critical issue, we develop a multiscale mathematical model for thermal gradient forced chemical vapour infiltration (TG-FCVI) process considering only heterogeneous decomposition of propylene on carbon preform. The model takes account of the flow field, mass transport, reaction kinetics and the transient nature of porosity to identify the optimum process parameters. As the time taken in deposition is very large, the flow in free channel is much faster than the pores and therefore the flow equations are solved coupling both the domains in steady state (low Mach number flow). The effect of various process parameters on composites homogeneity like temperature, temperature gradient, inlet precursor concentration and inlet gas flow rate were studied. The model was validated with the available experimental data. It has been observed that high temperature gradient and inlet concentration favours homogeneous C-C composite with high final bulk density. However, increasing temperature of reactor and reducing inlet reagent concentration causes surface pore blockage and resulting in inhomogeneity in direction of axial flow

Reduction of Aeroacoustic Sound and Aerodynamic Drag Using Porous Cover

The application of a porous media on square cylinders to reduce drag in cross-flow is an active research area. Be that as it may, the related stream incited sound in the encompassing flow likewise experiences decrease, an angle which has gotten less consideration. This paper exhibits a numerical strategy for coupled streamlined and aero acoustic estimations for low Mach number flow current pass a square cylinder with permeable cover. Computations are performed at a subcritical Re of 54,800 using URANS technique and FW-H acoustic analogy. The cylinder without porous cover is subjected to an incoming flow is considered for validation against measurements. A significant drag reduction and sound reduction is observed with the presence of the porous layer. Comparisons are made among the modified cylinder and its unmodified counterpart.

Vortex Induced Aerodynamic Noise Generation from Wind Turbine Blades

An important aerodynamic noise source from lifting surface occurs from trailing edge of an aerofoil as found in wind turbine blades. In this work, semi-empirical method proposed by Brookes, Pope, Marcolini is applied to evaluate trailing edge bluntness vortex shedding noise source. For low Mach number flows (0.1884) and moderate to high chord Reynolds number, 4.73 × 105 - 3.35 × 106, change in sound power level was assessed for trailing edge thicknesses in terms of 0.1%, 0.5% and 1% chord lengths at wind speeds of 8 m/s, 10 m/s. For overall change of trailing edge thickness from 0.1% to 1% chord, an increase in noise levels up to 50 dB was found at low frequencies, while a decrease up to 30 dB was found between mid-band to high frequencies of spectra.

AUSM‐like expression of HLLC and its all‐speed extension

SummaryAdvection upstream splitting method (AUSM) and Harten‐Lax‐van Leer with contact (HLLC) are two popular families of flux functions. The AUSM is simple and requires no eigenstructure, which facilitates its extensions to general equations of state. Furthermore, one of its variants, simple low‐dissipation AUSM (SLAU), is applicable to all speeds and features removal of parameter setting by the user. HLLC, on the other hand, clearly defines three distinct waves in Riemann problem, namely, left‐running and right‐running acoustic waves, and entropy wave. This paper demonstrates that HLLC can be written in a very similar form with the AUSM family and that the similar manner in extending AUSM family to all speeds is easily incorporated into HLLC in this AUSM‐like form. Then, we combine the strengths of the both flux functions and offer a new inviscid numerical flux function within the framework of monotone upwind scheme for conservation laws (MUSCL) in computational fluid dynamics (CFD) for Euler and Navier‐Stokes equations. The resultant HLLC with low dissipation (HLLCL) numerical flux can compute low Mach number flows and sound propagations at the same time with high accuracy, as demonstrated by one‐dimensional and two‐dimensional numerical examples. Furthermore, the results indicate that its extensions to general fluids such as supercritical fluids are encouraging.

One-dimensional turbulence investigation of variable density effects due to heat transfer in a low Mach number internal air flow

A novel spatial formulation of the One-Dimensional Turbulence (ODT) model is applied to a vertical pipe-flow with heat transfer, analogous to the Direct Numerical Simulation (DNS) performed by Bae et al. [Phys. Fluids 18, (075102) (2006)]. The framework presented here is an extension for radially confined domains of the cylindrical ODT spatial formulation for low Mach number flows with variable density. The variable density simulations for air (Prandtl number Pr=0.71) are performed at an initial bulk Reynolds number Reb,0,DNS=6000 and Grashof number Gr0,DNS=6.78×106. ODT results are presented for both the spatial formulation introduced in this work and the standard temporal formulation for cylindrical flows introduced by Lignell et al. [Theor. Comput. Fluid Dyn. 32, 4 (2018), pp. 495–20]. Streamwise bulk profiles and radial profiles at specific streamwise positions for the temporal and spatial formulations are in good agreement with the DNS results from Bae et al. For the present application, the spatial formulation yields physically better results in comparison to the temporal formulation. Overall, the findings in the original work of Bae et al. were corroborated with ODT. Although the framework proposed in this work is not a compressible framework and has some clear limitations regarding conservation properties, we suggest its use for future studies in the low Mach number variable density regime.

Diffuse interface immersed boundary method for low Mach number flows with heat transfer in enclosures

A novel diffuse interface immersed boundary (IB) approach in the finite volume framework is developed for non-Boussinesq flows with heat transfer. These flows are characterized by variable density, large temperature differences, nonzero velocity divergence, and low Mach numbers. The present IB methodology assumes that the solid body immersed in the domain is filled with a “virtual” fluid and constructs a unified momentum equation that is solved everywhere in the domain. The unified momentum equation is obtained as a convex combination of the Navier-Stokes equation and the no-slip boundary condition employing the solid volume fraction. The hydrodynamic pressure (p) that drives the flow is obtained by the solution of a variable density Poisson equation that is constructed by assuming that the velocity field inside the solid always remains solenoidal although the velocity divergence is nonzero in the fluid domain. The unified Poisson equation is also solved everywhere in the domain and has source terms that depend on the solid volume fraction, temperature gradients, and the spatially invariant thermodynamic pressure (P) that vanish in the Boussinesq limit. The thermodynamic pressure in closed domains follows from the principle of global mass conservation and is used to determine the density field everywhere in the domain except inside the solid where the density remains constant. Numerical simulations are carried out for natural and mixed convective flows in enclosures with stationary and moving heated bodies encompassing both Boussinesq and strongly non-Boussinesq flow regimes. The results of these investigations show that the local Nusselt number distribution over the body surface is oscillatory particularly when grid lines are not aligned with the surface of the body. However, the proposed approach can reasonably accurately compute the average heat transfer in both Boussinesq and non-Boussinesq flows. Investigations show that the heat transfer is significantly enhanced in the non-Boussinesq regime as compared to the Boussinesq regime. A comparison of results from the present approach with those obtained using a body-fitted finite volume solver for stationary bodies demonstrates that the proposed IB approach can compute the flow dynamics quite accurately even on Cartesian meshes that do not conform to the geometry. The IB approach presented herein is a generic approach for quasi-incompressible flows and may be applied to other low Mach number flows such as mixing and reacting flows.

Direct noise computation of a generic vehicle model using a finite volume method

This paper demonstrates the applicability of a finite volume method for the direct noise computation of road vehicles. For this purpose, a generic vehicle model consisting of major aeroacoustic components of a production car is considered. Such components are the A-pillar and the side mirror. The flow past the vehicle model is calculated using a compressible flow solver for low Mach number flows, accompanied with an approach based on detached eddy simulation for turbulence modelling. Two variants of the vehicle model are calculated, namely with and without side mirror. Validation of aerodynamic results is performed by comparing simulated surface pressure spectra on the side window to wind tunnel measurements. Thereafter, acoustic waves generation and propagation are examined. The propagation of acoustic waves from the sources to the windows surface is calculated directly using the compressible solver, as well as indirectly using a surface integral method. The results of both methods are then used as an input for a vibroacoustic model and surface acceleration spectra are compared between both approaches and wind tunnel measurements. A general assessment of both numerical approaches is given and the aeroacoustic impact of the A-pillar as well as the side mirror regarding their contribution to the overall acoustic level is presented.