Unsteady Compressible Flow Research Articles

Propagation Characteristics of Initial Compression Wave Induced by 400 km/h High-Speed Trains Passing through Very Long Tunnels

When high-speed trains enter tunnels, an initial compression wave is generated. As the compression wave propagates at the local speed of sound to the tunnel exit, it radiates into the surrounding environment, forming micro-pressure waves (MPWs). MPWs create sonic booms, resulting in significant environmental issues. The magnitude of the micro-pressure waves is directly proportional to the pressure gradient of the compression wave at the tunnel exit. The nonlinear effects of the initial compression wave during propagation lead to a significant increase in pressure gradient. Therefore, the propagation characteristics of the initial compression wave during the tunnel are the crucial factor affecting the amplitude of MPWs. Based on the one-dimensional compressible unsteady non-isentropic flow model and the improved generalized Riemann variable characteristic method, this paper researched the propagation and evolution characteristics of an initial compression wave generated when 400 km/h high-speed trains enter tunnels with three portal shapes: (no tunnel entrance hood (no hood), an oblique, enlarged tunnel entrance hood (type A), an enlarged equal-section non-uniform opening hole tunnel entrance hood (type B)). The results show that when the initial compression wave propagates inside very long tunnels, the pressure gradient of the compression wave exhibits a trend of initially increasing and then decreasing with the increase in propagation distance. When the pressure gradient of the compression wave reaches its maximum value, the corresponding propagation distance is the steepening critical distance. For no tunnel entrance hoods, type A tunnel entrance hoods, and type B tunnel entrance hoods, the steepening critical distances are 5 km, 6 km, and 16 km, respectively. The steepening critical distance shortens with increasing train speed. Steady friction and unsteady friction effects mainly affect the pressure amplitude and pressure gradient during compression wave propagation, respectively. At lower ambient temperatures, the nonlinear effects in compression wave propagation are significantly enhanced. The mitigation effects of type A tunnel entrance hoods and type B tunnel entrance hoods on pressure gradient reduction are mainly concentrated within 4 km and 12 km, respectively. It is necessary to determine the optimal matching relationship between the tunnel entrance hood and tunnel length based on the characteristics of compression wave propagation to ensure their mitigating performance is maximized.

Improved hybrid approach of monotonic upstream-centered scheme for conservation laws and discontinuity sharpening technique for steady and unsteady flows

In finite-volume methods, monotonic upstream-centered schemes for conservation laws (MUSCL) offer second-order spatial accuracy but tend to produce highly dissipative solutions for density discontinuity and weak shock waves. To address this limitation within a second-order framework, a novel strategy for hybridizing MUSCL with the tangent of the hyperbola interface capturing technique for both steady and unsteady compressible flows is presented. This hybridization optimizes the process based on the degree of nonlinearity and discontinuity around the target cells, providing a novel method to sharply resolve weak shock waves and robustly compute strong shock waves within the hybrid scheme. The proposed scheme sharply captures exceedingly weak shock waves that conventional MUSCL fails to resolve accurately due to excessive numerical dissipation. Furthermore, for resolving small vortices induced by instability at slip lines, computational results demonstrate high-resolution surpassing fifth-order spatial accuracy schemes within this second-order spatial accuracy framework with less computational cost. Moreover, the scheme exhibits commendable convergence and robustness when applied to steady-state problems featuring strong shock waves. This scheme offers a more precise and high-resolution alternative to conventional MUSCL for compressible flow computations, as it requires no additional stencil for reconstruction, unlike conventional fifth-order schemes.

Physics-constrained and flow-field-message-informed graph neural network for solving unsteady compressible flows

With the increasing use of deep neural networks as surrogate models for accelerating computational simulations in mechanics, the application of artificial intelligence in computational fluid dynamics has seen renewed interest in recent years. However, the application of deep neural networks for flow simulations has mainly concentrated on relatively simple cases of incompressible flows. The strongly discontinuous structures that appear in compressible flows dominated by convection, such as shock waves, introduce significant challenges when approximating the nonlinear solutions or governing equations. In this work, we propose a novel physics-constrained, flow-field-message-informed (FFMI) graph neural network for spatiotemporal flow simulations of compressible flows involving strong discontinuities. To enhance the nonlinear approximation capability of strong discontinuities, a shock detector method is leveraged to extract the local flow-field messages. These messages are embedded into the graph representation to resolve the discontinuous solutions accurately. A new FFMI sample-and-aggregate-based message-passing layer, which aggregates the edge-weighted attributes with node features on different hop layers, is then developed to diffuse and process the flow-field messages. Furthermore, an end-to-end paradigm is established within the encoder–decoder framework to transform the extracted information from the flow field into latent knowledge about the underlying fluid mechanics. Finally, a variety of one- and two-dimensional cases involving strong shock waves are considered to demonstrate the effectiveness and generalizability of the proposed FFMI graph neural network.

Aerodynamic force by Lamb vector integrals in unsteady compressible flows

PurposeThis study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.Design/methodology/approachExact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).FindingsTwo total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.Originality/valueNo thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

BE-BDF2 Time Integration Scheme Equipped with Richardson Extrapolation for Unsteady Compressible Flows

In this work we investigate the effectiveness of the Backward Euler-Backward Differentiation Formula (BE-BDF2) in solving unsteady compressible inviscid and viscous flows. Furthermore, to improve its accuracy and its order of convergence, we have equipped this time integration method with the Richardson Extrapolation (RE) technique. The BE-BDF2 scheme is a second-order accurate, A-stable, L-stable and self-starting scheme. It has two stages: the first one is the simple Backward Euler (BE) and the second one is a second-order Backward Differentiation Formula (BDF2) that uses an intermediate and a past solution. The RE is a very simple and powerful technique that can be used to increase the order of accuracy of any approximation process by eliminating the lowest order error term(s) from its asymptotic error expansion. The spatial approximation of the governing Navier–Stokes equations is performed with a high-order accurate discontinuous Galerkin (dG) method. The presented numerical results for canonical test cases, i.e., the isentropic convecting vortex and the unsteady vortex shedding behind a circular cylinder, aim to assess the performance of the BE-BDF2 scheme, in its standard version and equipped with RE, by comparing it with the ones obtained by using more classical methods, like the BDF2, the second-order accurate Crank–Nicolson (CN2) and the explicit third-order accurate Strong Stability Preserving Runge–Kutta scheme (SSP-RK3).

Thermal analysis of an unsteady compressible flow in an asymmetric channel with joule heating: a finite difference approach

Thermal analysis of an unsteady compressible flow in an asymmetric channel with joule heating: a finite difference approach

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

The paper deals with the numerical modeling of two-phase flows while using Baer–Nunziato type models. Focus is given here on the numerical treatment of source terms that involve three (or four) relaxation time scales. A new coupled approach relying on the continuous analysis of the system of ODEs is compared with a more widely used strategy grounded on the fractional step approach. Properties of schemes are given in both cases. Several numerical applications show that the coupled approach should be preferred for both stability and accuracy reasons.

Dynamic Transition of Unsteady Supersonic Flow From Mach to Regular Reflection Over a Moving Wedge

Abstract The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach reflection (MR) and regular reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the x-direction with a velocity, V(t) at a freestream Mach number of 3. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. The Arbitrary Lagrangian–Eulerian (ALE) technique is applied to deform the mesh during the wedge motion. The dynamic transition from MR to RR is defined by two criteria, the sonic and the von Neumann. Moreover, the lag in the dynamic transition from the steady-state condition is studied using various nondimensional angular velocities, κ, in the range of [0.1-2]. The lag effect in the shock system is remarkable at the high values of κ greater than 1.5. Furthermore, the dynamic transition from MR to RR happens below the dual solution domain (DSD) because the shock is upstream curved during the wedge motion.

Numerical Simulation of Centrifugal Pump Cavitation Based on ANSYS

Centrifugal pump is the key equipment in petrochemical, agriculture, shipbuilding and other industries. Its safe, reliable and reliable work is an important guarantee to ensure its normal operation. Cavitation is a kind of unsteady compressible turbulent flow, which has a great influence on its performance and efficiency due to material exchange between gas and liquid phases. The appearance of the impeller internal cavitation phenomenon will reduce the pump head and efficiency, which is caused by the impeller and other flow components of damage, causing greater noise, and thereby the pump work and work performance have been greatly affected. Improving the efficiency of the centrifugal pump will undoubtedly reduce the social requirements for energy, which is consistent with the current goal of energy conservation and emission reduction advocated by society. The performance and efficiency of a centrifugal pump can be improved effectively by numerical simulation and analysis of the cavitation phenomenon.

Sound generation in the flapping wing flight of insects

Flapping wing flight has been topic of recent interest with respect to the maneuverability and agility of insects. Computational fluid dynamics methods have been used to investigate the aerodynamics though typically for incompressible flow. The underlying sound generation mechanism, though of fundamental biological and physical interest, have much less attention. Experimental acoustical and high speed video studies of the Coconut Rhinoceros Beetle (Oryctes rhinoceros) and the Oriental Flower Beetle (Protaetia orientalis) have motivated large scale simulations accounting for three dimension flow, compressibility, and fluid structure interactions. Computational fluid dynamics simulations were performed using the unsteady compressible flow solver (CAESIM, Adaptive Research, Inc.) using a high resolution (TVD) methodology. Models of the wing flapping motion were accomplished using mesh deformation techniques with the flapping following from rotation with prescribed bending and coupled rotation and translation from the wing’s hinge position. Fluid structure interactions with respect to the wing’s flexibility are investigated in terms of the wing bending and the leading edge vortex formation.

Adaptative finite element simulation of unsteady turbulent compressible flows on unstructured meshes

The simulation of high-speed turbulent compressible flows using Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and a mesh adaptation strategy is presented in this work. A compressible dynamic Smagorinsky model is employed for the compressible LES model and the CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes. An accurate mesh adaptation scheme is frequently applied along the simulation including mesh refinement, mesh coarsening, edge or face swapping and a vertex smoothing technique in order to control the interpolation error and the mesh size. A feature-based error estimation is employed considering multi-scale and multi-metric intersection in order to capture turbulence effects. Two and three-dimensional applications are evaluated in order to investigate the capabilities of the present approach for evaluating external turbulent and compressible aerodynamics problems. The turbulent transonic flow around a circular cylinder in 2D and 3D domains and the turbulent supersonic flow past a blunt cylinder-flare model are investigated. Aerodynamic coefficients, frequency analysis and pressure distributions are compared against experimental data and other numerical simulations.

Unsteady radiative–convective flow of a compressible fluid: a numerical approach

This article is designed to inspect the thermal effects of an unsteady compressible flow of a viscous fluid through a symmetric channel. Combined effects of convective heat transfer, magnetic field, and radiation are also given special attention in this article. Basic laws of mass, momentum, and energy for compressible flow are employed in the modeling of the current problem. In addition, slip boundary conditions are also implemented in the analysis of the above thermal flow problem. Coupled nonlinear differential equations are solved numerically using explicit finite difference technique. Finally, the influence of different sundry parameters on the axial velocity, flow rate, and heat transfer are visualized through graphs. Time variant behavior of flow rate is calculated. Outcomes of the results reveal that the increment of the flow rate is related to the increase of compressibility parameters. Enhancement in the temperature profiles in the presence of radiation number is also reported. This model is the most general version of peristalsis of compressible flow in view of natural convection and radiation impact with extensive applications in aircraft industry, geophysics, and other industrial situations (cooling of electronic equipment, heat exchangers, and so forth).

Numerical analysis of aerodynamic characteristics of multi-pod hyperloop system

The Hyperloop system is a new and innovative mode of transportation in which high-speed pods move through near-vacuum tubes. The multi-pod Hyperloop Systems are essential for increased transportation capacity. In this study, a multi-pod Hyperloop System was analyzed using numerical simulations at different values of the distance between the pods (i.e., 2 L–3.5 L). The pressure and velocity flow fields and the aerodynamic characteristics of the pods were analyzed for four different flow speeds, that is, 100, 200, 300, and 400 m/s, using unsteady compressible flow conditions. The simulation results indicated that the pressure waves generated across the pods play a significant role in the determination of the aerodynamic characteristics of the pods. Increasing the distance between the pods results in the delay of the pressure wave interaction. The aerodynamic drag increases on the first pod with the increase in the distance between the pods due to an increase in the pressure gradient. In contrast, the aerodynamic drag decreases across the second pod with the increase in the distance between them. So, the distance between the pods is a critical factor that should be considered when designing the Hyperloop System with more than one pod.

Generalizations of incompressible and compressible Navier–Stokes equations to fractional time and multi-fractional space

This study develops the governing equations of unsteady multi-dimensional incompressible and compressible flow in fractional time and multi-fractional space. When their fractional powers in time and in multi-fractional space are specified to unit integer values, the developed fractional equations of continuity and momentum for incompressible and compressible fluid flow reduce to the classical Navier–Stokes equations. As such, these fractional governing equations for fluid flow may be interpreted as generalizations of the classical Navier–Stokes equations. The derived governing equations of fluid flow in fractional differentiation framework herein are nonlocal in time and space. Therefore, they can quantify the effects of initial and boundary conditions better than the classical Navier–Stokes equations. For the frictionless flow conditions, the corresponding fractional governing equations were also developed as a special case of the fractional governing equations of incompressible flow. When their derivative fractional powers are specified to unit integers, these equations are shown to reduce to the classical Euler equations. The numerical simulations are also performed to investigate the merits of the proposed fractional governing equations. It is shown that the developed equations are capable of simulating anomalous sub- and super-diffusion due to their nonlocal behavior in time and space.

Compressible unsteady steam flow and heat transport analysis: a numerical investigation

The unsteady compressible steam laminar flow associated with heat transfer in fluids in a squared cylinder is examined in this work. The current challenge was created utilizing the CFD approach. The laminar flow is chosen with a low Mach number. With the geometric wall, the flow has a no-slip condition. The pressure on the flow is kept at 0 pas, and the temperature in the flow regime is 305.13. A 0.5 m/s velocity is used to start the flow. With the use of graphics, the effects of time on velocity and pressure distributions are discussed. Different outcomes are also mentioned, such as drag coefficients, lift coefficients, and heat distributions. The velocity drops from 2.5 to 1.6 m/s at t = 7 s in the absence of anybody's force and temperature 305.13 K. Pressure increases from 0.00098 to 0.001 Pas in the flow interval of 10 s. Surface temperature increases from 360 to 375 K in time intervals of 10 s keeping pressure constant. And contour temperature increases from 371.56 to 374.2 K in time intervals of 10 s keeping the pressure constant. This information provides us with caution about the emission of steam from the chimneys of furnaces. It implies that when steam flows from a cylindrical geometry like chimneys of furnaces it heats the upper inner and outer parts which may destroy the material. So for safety, that emission should be taken for a short interval of time otherwise it will result in a havoc process. The lift coefficient remains constant and the drag coefficient increases from 0.0005 to 0.065. Under that condition, fluid has to face more resistance. To overcome that difficulty fluid should be provided with high velocity to continue it for a long time. The technique used to solve modeled problems is the Backward Difference Formula.

Advances in aero-acoustics of flying beetles

An understanding of the acoustics of invasive species of beetles is needed for potential detection and tracking methods in agricultural monitoring. However, the underlying mechanisms of sound generation are not well understood, especially with respect to the higher harmonic sounds. The Coconut Rhinoceros Beetle (Oryctes rhinoceros) and the Oriental Flower Beetle (Protaetia orientalis) have been studied during tethered flight with synchronized microphone array measurements and high speed video (1000–10,000 fps). The larger Coconut Rhinoceros Beetles have fundamental ∼50 Hz with distinctive torsional wing rotation compared to Oriental Flower Beetle (∼100 Hz). Computational fluid dynamics simulations were performed using the unsteady compressible flow solver (CAESIM, Adaptive Research, Inc.) using a highresolution (TVD) methodology. Models of the wing flapping motion were accomplished using mesh deformation techniques with the flapping following from rotation with prescribed bending and coupled rotation and translation from the wing’s hinge position. Fluid structure interactions with respect to the wing’s flexibility are investigated in terms of the wing bending and the leading edge vortex formation.

Computational Analysis of MHD Nonlinear Radiation Casson Hybrid Nanofluid Flow at Vertical Stretching Sheet

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The effect of nonlinear radiation was studied. We considered the SWCNT (signal wall carbon nanotube) and MWCNT (multi-wall carbon nanotube) with base liquid (water). Under the flow suppositions, a mathematical model was settled by means of boundary layer approximations in terms of partial differential equations. The suitable transformation was developed by using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique named bvp4c. The impacts of pertinent flow parameters on skin friction, Nusselt number, and temperature and velocity distributions were depicted through tabular form as well as graphical form. In this study, the Yamada Ota model achieved a higher heat transfer rate compared to the Tiwari Das and Xue hybrid nanofluid models. The skin friction (CfxRe−1/2) increased and temperature gradient (NuxRe−1/2) declined due to the increment of solid nanoparticle concentration (ϕ2). Physically, skin friction increased because the higher values of the solid nanoparticles increased resistance to the fluid motion.

Numerical study of unsteady compressible flow induced by multiple pods operating in the Hyperloop system

This study investigated the variations in aerodynamic drag and the pressure wave effects caused by more than two pods operating in a Hyperloop tube. Three speeds, i.e., 100, 200, and 300 m/s, and two distances between two separate pods, i.e., 43 and 86 m, were simulated using SST k-ω turbulence model. The results indicate that drag of single- and multi-pod systems have similar tendencies that increase with increasing pod speed. For pod speed exceeding the critical Mach number, irrespective of the connectedness or separation of the pods, the last pod always experiences the highest drag. Otherwise, at lower speeds, the differences between the drag acting on each of the pods is negligible. The distance between two pods has a minor influence of less than 4% on the drag. The effects of two different pod shapes, i.e. rectangular and semicircular, on the drag of three connected pods are also small. The average drag per pod was calculated, and it was observed that when more pods were operated, the average drag reduced significantly. The operation of the connected-pod system creates a slightly lower drag than that of a separate-pod system.

Optimizing an acoustic liner by automatic differentiation of a compressible flow solver

The attenuation power of an acoustic liner is optimized by unsteady compressible flow simulations that model the presence of the liner with a time-domain impedance boundary condition (TDIBC). Two test cases are considered: a one-dimensional impedance tube and a two-dimensional grazing incidence tube. The impact of the liner on the pressure field is tuned through various TDIBC parameters imposed at the boundary where the liner surface is located. Automatic differentiation of the direct numerical simulation (DNS) code yields the gradients of the time-integrated pressure perturbations with respect to the TDIBC parameters. The gradients are subsequently used in an iterative process that minimizes the perturbations at a given location. In both test cases considered, TDIBC parameters are found which are more effective at attenuating perturbation frequencies other than those the initial TDIBC is designed to cancel. Finally, a sensitivity analysis reveals the importance of the choice of the initial TDIBC parameters for finding optimized settings. Our results pave the way to a wider application of the presented procedure in more complex problems with bulk flow motion and larger perturbation amplitudes.

Numerical analysis of shock wave train in single-expansion ramp nozzle under harmonic inlet and outlet conditions

The single-expansion ramp nozzle (SERN) is intensely over-expanded and leads to a large separation zone. The flow separation is the central phenomenon causing a reduction in thrust, and shock waves lead to a drop in the flow stagnation pressure and increase the energy loss. In this study, the unsteady compressible flow in a SERN was studied by employing the k-kl-ω transition turbulence model with high ability in separation flow prediction. In this regard, the finite volume code with the pressure-implicit with the splitting of operators algorithm and the adaptive mesh refinement technique were applied. Firstly, the results were compared with published data and it is revealed that the numerical methodology was capable of detecting the exact structure of lambda shock and wall pressure. Then, the influences of harmonic inlet and outlet conditions were evaluated on the flow behavior. The results showed that for harmonic inlet pressure conditions the value of friction coefficient in the case with wavelength of 0.3 is greater than the cases with the wavelength of 0.15 and 0.6. Also, it is found that the shock train did not form for the case with wavelength of 0.6. Furthermore, for the harmonic condition in outlet pressure, the minimum wall shear stress was obtained for the case with the wavelength of 015, and the shock strength, in this case, is more than the cases with wavelength of 0.6 and 0.3.