Subsonic Flow Research Articles

Nonlinear vibration analysis of thin plate with periodically distributed tunable-stiffness nonlinear oscillators in subsonic flow

This paper provides a new passive control method for nonlinear vibration of subsonic thin plates. The control method uses periodically distributed tunable-stiffness nonlinear oscillators (NLO). By using von Karman’s nonlinear plate theory and subsonic aerodynamic model, the nonlinear dynamic model of thin plate is established based on Hamilton’s principle. Through analyzing the system’s nonlinear dynamics bifurcation, the impact of periodic distribution on the stability is discussed. The amplitude-frequency responses are discussed under different NLO installation modes and design parameters by using Matcont software. The results show that the periodically distributed tunable-stiffness nonlinear oscillators can improve the stability of the system and have a remarkable suppression effect. The optimal control scheme for vibration suppression by periodically distributed tunable-stiffness nonlinear oscillators is obtained. The results obtained from this research can offer a valuable understanding of nonlinear vibration control, thereby enabling the identification of various control approaches that can be implemented in practical applications during future design endeavors.

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10−3 to 10−1, which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

Accelerating aeroelastic UVLM simulations by inexact Newton algorithms

AbstractWe consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

Turbulent drag reduction with streamwise-travelling waves in the compressible regime

The ability of streamwise-travelling waves of spanwise velocity to reduce the turbulent skin-friction drag is assessed in the compressible regime. Direct numerical simulations are carried out to compare drag reduction in subsonic, transonic and supersonic channel flows. Compressibility improves the benefits of the travelling waves, in a way that depends on the control parameters: drag reduction becomes larger than the incompressible one for small frequencies and wavenumbers. However, the improvement depends on the specific procedure employed for comparison. When the Mach number is varied and, at the same time, wall friction is changed by the control, the bulk temperature in the flow can either evolve freely in time until the aerodynamic heating balances the heat flux at the walls, or be constrained such that a fixed percentage of kinetic energy is transformed into thermal energy. Physical arguments suggest that, in the present context, the latter approach should be preferred. This provides a test condition in which the wall-normal temperature profile more realistically mimics that in an external flow, and also leads to a much better scaling of the results, over both the Mach number and the control parameters. Under this comparison, drag reduction is only marginally improved by compressibility.

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.

Numerical modeling of air ejectors covering supersonic, subsonic and closed-port operations

The physics and modeling of air ejectors in on- and off-design conditions have been extensively addressed in the past, reaching a good level of maturity. However, to achieve a robust model at system scale integrating an ejector, there is a need for developing 0D models suitable to tackle abnormal functioning modes, such as cases where the ejector works in subsonic conditions, reverse flows, or closed ports. Based on state-of-the-art models, a new 0D model has been built in the current work, where proper subroutine implementations allow covering normal and abnormal operations of convergent nozzle ejectors. The current research also focuses on understanding the physical behavior of air ejectors for aeronautical applications. In this regard, CFD-RANS simulations are used to perform model verification and calibration as well as to gain knowledge of the whole operational envelope. The regimes reproduced by the 0D model, and validated by CFD, cover the normal operating mode with different choking regimes, the occurrence of a subsonic primary flow, and the closed secondary port case. Additional cases are run to assess other features of the ejector behavior, such as the influence of geometrical properties on the choking mechanism and the impact of thermal effects.

Suppression effect of the leading-edge groove on deep cavity noise at low speeds: Groove length

Detached Eddy Simulations combined with Ffowcs Williams–Hawkings acoustic analogy of subsonic flows over a deep cavity preceded by deep grooves with different lengths were conducted to investigate the effects of groove length on the flow characteristics and the noise suppression in the vicinity of the deep cavity. The length-to-depth ratio of the deep cavity is 2/3, and the length-to-depth ratios of the grooves are 1/2. The distance between the grooves and the cavity remains constant at twice the groove length. The groove length ranges from 5 mm to 30 mm. The Reynolds number based on the cavity length is 8 × 10−5. The analysis results indicate that all grooves studied in this paper have some effect on the distribution of sound energy of near-field noise and near-/far-field noise amplitude, but have no effect on the characteristic frequencies of cavity noise and far-field noise directivity. When the groove length is 15 mm and 20 mm, the deep grooves are most effective in suppressing deep cavity noise. The time-averaged velocities in the incoming boundary layer, shear layer, and wake region decrease, and the height of the boundary layer downstream of the cavity increases, which reduces the intensity of the interaction between the flow structure and solid wall downstream of the cavity, resulting in a reduction in flow-acoustic feedback noise. Meanwhile, the suppression effect of the groove flow on the cavity flow effectively alters the flow characteristics of the entire cavity mouth, the rear edge wall, and part of the bottom surface region, reducing the energy at these locations. This is the primary reason for the reduction in broadband noise and acoustic resonance noise.

Influence of bleeding positions in self-recirculating casing treatments on the stability of a subsonic axial compressor

Influence of bleeding positions in self-recirculating casing treatments on the stability of a subsonic axial compressor

Accretion flows around spinning compact objects in the post-Newtonian regime

We present the structure of a low angular momentum accretion flows around rotating compact objects incorporating relativistic corrections up to the leading post-Newtonian order. To begin with, we formulate the governing post-Newtonian hydrodynamic equations for the mass and energy-momentum flux without imposing any symmetries. However, for the sake of simplicity, we consider the flow to be stationary, axisymmetric, and inviscid. Toward this, we adapt the polytropic equation of state (EoS) and analyze the vertically integrated accretion flow confined to the equatorial plane. It is shown that the spin-orbit effects manifest themselves in the accretion dynamics. In the present analysis, we focus on global transonic accretion solutions, where a subsonic flow enters far away from the compact object and gradually gains radial velocity as it moves inwards. Thus, the flow becomes supersonic after reaching a certain radius, known as the critical point. To better understand the transonic solutions and examine the effect of post-Newtonian corrections, we classify the post-Newtonian equations into semi-relativistic (SR), semi-Newtonian (SN), and non-relativistic (NR) limits and compare the accretion solutions and their corresponding flow variables. With these, we find that SR and SN flow are in good agreement all throughout, although they deviate largely from the NR ones. Interestingly, the density profile seems to follow the profile ρ ∝ r -3/2 in the post-Newtonian regime. The present study has the potential to connect Newtonian and GR descriptions of accretion dynamics.

Dynamic-mode-decomposition-based gradient prediction for adjoint-based aerodynamic shape optimization

Accurate and efficient gradient computation is the key to aerodynamic shape optimization. In this paper, dynamic mode decomposition (DMD) is employed to analyze the dynamic characteristics of the early pseudo-time marching of adjoint equations and to predict the gradient. Besides the first-order zero-frequency mode, other zero-frequency modes also contribute to the pseudo iterations of the adjoint equations in the early iterations. Hence, different from existing methods, all zero-frequency modes are retained to reconstruct adjoint fields for gradient prediction. Moreover, to further improve the modeling accuracy, an improved DMD (IDMD) is proposed by omitting the initial snapshots in early iterations. The effect of pseudo-time step on modeling accuracy is also studied. By solving the adjoint equations of the transonic and subsonic flows, the accuracy of the proposed method is verified. Results indicate that the proposed method still works despite the conventional solution process diverges. Through aerodynamic shape optimization examples of transonic flow over an airfoil, the number of adjoint pseudo-time steps is remarkably reduced by 83%, which indicates the proposed IDMD-based gradient prediction method has great potential for improving the efficiency of aerodynamic shape optimization.

A Novel Cell-Based Adaptive Cartesian Grid Approach for Complex Flow Simulations

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR’s efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations.

Experimental investigation of a Y-shaped engine inlet at subsonic flow conditions

Abstract In this paper, the results of an experimental investigation for a Y-shaped engine inlet are presented. The experiment is performed at subsonic flow conditions. The main focus is given to time-dependent total pressures measured at the aerodynamic interface plane. Distinctive frequencies carrying high energy contents of the fluctuating total pressures are given and the relation between time-dependent and time-average performance parameters is presented. The cross-correlation coefficients of the high frequency probe readings distributed through the aerodynamic interface plane are also investigated.

Using Fluid Curtains to Improve Sealing Performance in Turbomachinery Applications

Abstract The results from an investigation into the physics of how fluid curtains can be applied to improve the aerodynamic performance of conventional turbomachinery shaft and rotor seals are described in this paper. Computational fluid dynamics and testing on two experimental facilities are used in the study. In the first part of the work, computational fluid dynamics simulations validated against experimental test data demonstrate the fundamental mechanism by which the presence of the curtain can act to reduce leakage flow through conventional seals. These results are consolidated into a single performance carpet map, showing how the leakage reduction performance and the curtain supply pressure needed to achieve it vary with changes in values of key geometrical parameters. In the second part of the work the effect of swirl in the seal inlet flow, as is often encountered in turbomachinery applications, on the performance of the fluid curtain is investigated experimentally. Test results show that if the swirl momentum in the inlet flow is greater than the momentum of the curtain flow, the performance benefit from applying the curtain is greatly diminished. Overall, the results provide some fundamental design rules for applying fluid curtains to enhance turbomachinery sealing performance for the general type of leakage path geometry (cylindrical channel, 45-deg jet angle, curtain upstream of a conventional seal) and working fluid type and conditions (air, ambient temperature, subsonic leakage channel flow) used in the study.

Shock-capturing PID controller for high-order methods with data-driven gain optimization

We present a novel shock-capturing strategy for high-order methods including discontinuous Galerkin (DG) method with data-driven gain optimization. Inspired by the classical control theory, we utilize a proportional–integral–derivative (PID) controller for capturing shock waves with monotonic subcell distributions. The proposed closed-loop control system for shock-capturing, named shock-capturing PID controller (SPID), consists of two key elements: error estimation based on the multi-dimensional limiting strategies (hMLP and hMLP_BD) and shock stabilization using the Laplacian artificial viscosity (LAV). The two elements are combined in a complementary manner to maximize the advantages of limiting strategy and artificial viscosity while overcoming each weakness. First, based on the multi-dimensional limiting process (MLP) condition and the troubled-boundary detector, the estimated error gives a signal to the SPID how much flow variables stray out of monotonic shock profiles. Second, the SPID estimates the amount of artificial viscosity to stabilize the target shock wave and superimposes numerical diffusion to the governing equations in the form of LAV. Each control action of the SPID (i.e., proportional, integral, and derivative) has a distinct role in capturing and stabilizing shock waves. The proportional action determines a minimal amount of background artificial viscosity. The integral action reinforces a shock-stabilizing numerical diffusion where the artificial viscosity by the proportional action alone is insufficient. The derivative action damps out sudden rises of error and spurious oscillations. The SPID incorporates the gain parameters that regulate the impact of each control action, and each gain parameter is determined via a surrogate-based optimization approach utilizing artificial neural networks (ANN). The SPID with the data-driven gain parameters is verified and validated by conducting extensive numerical tests and by comparing the results to other shock-capturing methods (hMLP, hMLP_BD, and Laplacian artificial viscosity). The numerical results demonstrate the excellent performance of SPID in terms of capturing shock waves and stabilizing shock-induced oscillations. Moreover, the SPID successfully preserves unsteady turbulent eddies for large-eddy simulations (LES) of subsonic and supersonic flows and improves convergence characteristics of steady transonic/supersonic flows.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

Influence of the shape of the anode assembly inner channel on plasma flow velocity

This article considers how the shape of the inner channel in the anode assembly affects plasma flow velocity in a plasma torch. Three different shapes of the anode assembly were analyzed, all with a conical confusor part of 50 mm in length: with a diameter transition from 12 to 6 mm, from 12 to 8 mm, and from 12 to 10 mm. A computer experiment was performed using the finite element method and then validated by the subsequent full-scale experiment on a laboratory plasma unit. The obtained results were verified. The verification outcomes showed a satisfactory convergence and were consistent with the published data. A review of the existing plasma unit designs for powder production, application of functional coatings, and surface modification was carried out. The software packages implementing the finite element method to solve these problems were examined. The study yielded practical recommendations for consumers and developers of plasma equipment and identified the shapes of the anode assembly enabling both supersonic and subsonic plasma flow regimes.

Subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli’s quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math. 49 (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity.

Flow Analyses of Integrated Liquid Fuel RAMJET Propulsion System

A CFD study is performed to check the seamless flow behaviour of the Liquid Fuel Ramjet Propulsion system which includes, air intakes, combustor and nozzle. Resolving both supersonic and subsonic flow scales in the same domain makes the simulations complex. Addition of combustion with stiff chemistry makes the simulations more difficult. CFD simulations are carried out using commercially available CFD software. Liquid fuel is injected as discrete phase and the flow turbulence is modelled using Realizable k-ε turbulence model. Jet-A + air combustion has been simulated using combined finite rate / eddy dissipation model. Finite rate chemistry was modelled using three step chemistry which was obtained from the published literature. Flow structures such as oblique shocks, normal shocks and combustion are observed.

The nonlinear instability of transverse vibration behavior of functionally graded materials sandwich rectangular plates of under a harmonic loading and subsonic flow

This work is devoted to studying the combined action of periodic in-plane load and tangential subsonic flow on the nonlinear mechanism of the out-plane deformation of the functionally graded composite plate. Three distribution functions are proposed to investigate the distribution of the transverse shear strains and stresses across the thickness of the plates. By using Hamilton’s variational principle, the equations governing the plate instability boundaries are formulated. A nonlinear differential equation describing the first mode of the plate dynamic instability behavior by employing Galerkin’s method. The method of multiple time scales is used to obtain a periodic one-mode solution, which directly leads to the solvability condition. The different resonance cases for the interaction between the frequency of out- plane deformation and the external forces are discussed to discover the extent of the sandwich functionally graded material (FGM) rectangular plate resistance in the presence of external influences. Various bifurcation diagrams for different cases of resonance are obtained versus the basic parameters. In view of this study, we could get a deeper look at the complexity of frequency components in resonance responses of the sandwich FGM rectangular plate. The results could provide some suggestions for the sandwich plate’s vibration reduction design or fault diagnosis field or design fault diagnosis.

Experimental and numerical investigation of porous bleed control for supersonic/subsonic flows, and shock-wave/boundary-layer interactions

This paper presents a comprehensive experimental and numerical investigation into the control of boundary layers using porous bleed systems. The study focuses on both supersonic and subsonic flow regimes, as well as on the control of shock-wave/boundary-layer interactions. By simplifying this complex problem into two separate scenarios, the research establishes the necessity of individually characterizing bleed systems for both supersonic and subsonic flow regimes due to variations in the flow topology within the bleed holes. In supersonic conditions, a strong agreement between experimental and numerical results validates the effectiveness of porous bleed in controlling boundary layers. Notably, three-dimensional effects are experimentally demonstrated, and variations of the boundary-layer profiles along the span are the first time experimentally proven. The study extends its scope to subsonic flows, revealing that while boundary-layer bleeding enhances flow momentum near the wall, mass removal induces a decrease in momentum in the outer boundary layer and external flow. The research also explores shock-wave/boundary-layer interaction control, achieving a remarkable alignment between simulations and experiments. The findings endorse the use of Reynolds-Averaged Navier-Stokes simulations for studying porous bleed systems in various flow conditions, providing valuable insights to enhance bleed models, especially in the context of shock-wave/boundary-layer interaction control.