Entropy Waves Research Articles

The effect of mean flow on the intrinsic thermoacoustic instabilities in the duct and annular combustion chambers

Thermoacoustic instability in the combustion chamber of gas turbines, aero and rocket engines has become a topic concern. In this paper, a new instability phenomenon in the field of the thermoacoustic instability - Intrinsic ThermoAcoustic instabilities (ITA) is studied. The classic thermoacoustic instability is caused by the coupling among acoustic disturbances, flow fluctuations and heat release pulsations. When the influence of acoustic disturbance is removed, there is still a thermoacoustic instability phenomenon in the combustion chamber, which is known as ITA. In the previous research on ITA, the scholars found that the ITA is mainly determined by the flame response, but many scholars neglected the influence of the mean flow and entropy waves. In this paper, the influence of the mean flow on the ITA mode in the duct and annular combustion chambers is studied by constructing a low-order acoustic network model. At the same time, it also explores the influence of other parameters on the ITA mode. The mean flow greatly affects the growth rate of the ITA mode, and has little effect on its frequency in the duct combustion chamber model. This is also the main reason for neglecting the effect of mean flow on the ITA mode in previous studies. In addition, the influence of other parameters on the ITA mode is also reflected in the growth rate. In the annular combustion chamber, a new ITA mode, which does not meet the −π criterion, is found. And the increase of Mach number makes all ITA modes more unstable. The circumferential mode number has a great influence on the high frequency ITA mode. In addition, the ITA mode has a significant effect on the thermoacoustic mode of the system in the annular combustion chamber.

First and Second Sound in a Compressible 3D Bose Fluid.

The two-fluid model is fundamental for the description of superfluidity. In the nearly incompressible liquid regime, it successfully describes first and second sound, corresponding, respectively, to density and entropy waves, in both liquid helium and unitary Fermi gases. Here, we study the two sounds in the opposite regime of a highly compressible fluid, using an ultracold ^{39}K Bose gas in a three-dimensional box trap. We excite the longest-wavelength mode of our homogeneous gas, and observe two distinct resonant oscillations below the critical temperature, of which only one persists above it. In a microscopic mode-structure analysis, we find agreement with the hydrodynamic theory, where first and second sound involve density oscillations dominated by, respectively, thermal and condensed atoms. Varying the interaction strength, we explore the crossover from hydrodynamic to collisionless behavior in a normal gas.

Shock Formation and Vorticity Creation for 3d Euler

AbstractWe analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Development of a Shock-Stable and Contact-Preserving Scheme for Multidimensional Euler Equations

The shock instability, notably the disastrous carbuncle phenomenon, has plagued many low-dissipation Godunov-type numerical schemes in calculations of high Mach flows. In the current work, two popular stability analysis tools and corresponding numerical experiments are used to investigate the root cause of shock instability of the low-dissipation Harten, Lax, and van Leer with contact (HLLC) scheme. The local linear stability analysis reveals that the HLLC flux could attenuate all perturbations in the streamwise direction but not perturbations of density and shear velocity in the transverse direction. Numerical results also indicate that the shock instability of the HLLC scheme is only related to the transverse flux. The viscosity terms of entropy wave and shear wave are introduced into the transverse flux, and the stability analysis shows that with the help of additional viscosities the shock instability of the HLLC scheme is cured. To preserve the capability of resolving contact discontinuities and shear waves, a pressure-based switching function is incorporated into the expressions of viscosity terms so that the additional viscosities are activated only when calculating the transverse flux in the shock layer. A series of numerical experiments give evidence of the robustness and accuracy of the proposed scheme, and the strategy adopted here can be easily applied to cure shock instabilities of other low-dissipation numerical schemes, e.g., the Roe scheme and the AUSM+ scheme.

Effect of clocking on entropy noise generation within an aeronautical high pressure turbine stage

This article reports a detailed experimental and numerical study of the clocking effect between entropy wave spots and stator leading edges on the evolution of the entropy wave and on indirect noise generation in a high pressure turbine stage. Experimental campaigns considering burner-representative temperature fluctuations injected upstream of an uncooled high-pressure gas turbine stage have been performed in the high-speed closed-loop test rig of the Fluid Machine Laboratory (LFM) of the Politecnico di Milano. Acoustic measurements focused on entropy noise generation have been carried out by the German Aerospace Center, DLR with two flush mounted in-duct microphone arrays. URANS CFD simulations with and without entropy fluctuations imposed at the stage inlet were performed with the TRAF code, developed by the Università degli Studi di Firenze. A numerical post-processing procedure, based on the time and space discrete Fourier transform (DFT) of the conservative variables, has been implemented to extract the low-frequency content connected to the entropy fluctuations and indirect noise emissions. Simulations show an overall good agreement with the experiments, especially at the stage outlet thus confirming the possibility to predict entropy noise by means of URANS simulations with time varying inlet conditions. By exploiting the combination of experiments and simulations, the evolution of the entropy wave, the identification of entropy noise generation areas, and the evaluation of indirect noise emissions, for the different clocking positions were properly assessed. This study also demonstrates that this type of simulations can be used for the geometric design optimization of combustor/turbine coupling performing detailed parametric studies concerning the clocking position of the perturbation source in order to reduce the turbine-combustor interactions and the indirect noise emissions.

Effect of flame motion on longitudinal combustion instabilities

In the analysis of combustion instabilities, especially for the longitudinal modes, the flame typically is regarded as a discontinuity at rest and the flame motion is usually ignored. However, this may lead to errors in the prediction of combustion instabilities for certain conditions. This paper investigates the effect of flame motion on the longitudinal combustion instabilities in a simple ducted combustion chamber. An analytical model considering the flame motion is incorporated into the thermoacoustic system. The dispersion relation is established, and the eigenvalues of thermoacoustic system can be obtained by solving it. The present study considers the cases with and without entropy noise produced at the outlet boundary. The effect of flame motion on longitudinal combustion instabilities is evaluated by consider it and not. When there is no entropy noise, the effect of the flame motion remains small. However, when the entropy noise is considered, the flame motion can have a large effect on different longitudinal modes. Furthermore, the presence of the flame motion can dissipate the entropy wave generated from the flame and further the corresponding combustion instability for the present configuration.

A solution for the quasi-one-dimensional linearised Euler equations with heat transfer

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three variables, namely the dimensionless mass, stagnation temperature and entropy fluctuations, which are invariants of the system at zero frequency and with no heat transfer. The resulting first-order system of differential equations is then solved using the Magnus expansion method, where the perturbation parameters are the normalised frequency and the volumetric heat transfer. In this work, a measure of the flow non-isentropicity (in this case the steady heat transfer) is used for the first time as an expansion parameter. The solution method was applied to a converging–diverging nozzle with constant heat transfer for both subcritical and supercritical flow cases, showing good agreement with numerical predictions. It was observed that the acoustic and entropy transfer functions of the nozzle strongly depend on the frequency and heat transfer.

A physical model for indirect noise in non-isentropic nozzles: transfer functions and stability

We propose a mathematical model from physical principles to predict the sound generated in nozzles with dissipation. The focus is on the sound generated from the acceleration of temperature inhomogeneities (also known as entropy waves), which is referred to as indirect noise. First, we model the dissipation caused by flow recirculation and wall friction with a friction factor, which enables us to derive quasi-one-dimensional equations from conservation laws. The model is valid for both compact nozzles and nozzles with a spatial extent. Second, the predictions from the proposed model are compared against the experimental data available in the literature. Third, we compute the nozzle transfer functions for a range of Helmholtz numbers and friction factors. It is found that the friction and the Helmholtz number have a significant effect on the gain/phase of the reflected and transmitted waves. The analysis is performed from subsonic to supersonic regimes (with and without shock waves). The acoustic transfer functions vary significantly because of non-isentropic effects and the Helmholtz number, in particular, in the subsonic-choked regime. Finally, we calculate the effect that the friction of a nozzle guide vane has on thermoacoustic stability. It is found that the friction and the Helmholtz number can change thermoacoustic stability from a linearly stable regime to a linearly unstable regime. The study opens up new possibilities for the accurate prediction of indirect noise in realistic nozzles with implications on both noise emissions and thermoacoustic stability.

A comparative analysis of the evolution of compositional and entropy waves in turbulent channel flows

Indirect combustion noise, as an important source of noise in gas turbines, was traditionally attributed solely to entropy waves. In recent years, compositional waves were introduced as another contributor to indirect combustion noise. Nonetheless, unlike that of entropy waves, the annihilation of compositional waves by the mean flow has remained largely unexplored. Hence, the current numerical study analyzes the spatiotemporal evolution of different components of compositional waves and compares them with the decay of entropy waves. A convecting wave, including a mixture of combustion products at elevated temperature, is introduced at the inlet of a simple channel. This allows simultaneous analysis of entropy and compositional waves. The passage of these along the channel is modeled using a large eddy simulation, and the annihilation of the waves' components is examined in the frequency domain. It is shown that the turbulence level of the mean flow and convective heat transfer on the walls can both result in a considerable wave deterioration. However, the effects of heat losses from the channel walls are found to be stronger than that of turbulence intensity. Importantly, as the wave is convected, the chemical potential function remains coherent for most of the channel length, and deterioration of the compositional wave majorly ensues from the mixture fraction gradient. The results indicate that, overall, the compositional sources feature 10%–20% more dissipation in comparison with the entropic sources. Therefore, compositional waves are less likely to survive the flow and generate noise.

Heliospheric effects caused by Sun-originating versus LISM-advected fluctuations

Context. We investigate the response of the heliosphere to fluctuations in the local interstellar medium (LISM) as compared to the influence of solar-cycle fluctuations. Aims. We discuss the differences between effects coming from the two types of drivers of time-dependent effects in the heliosphere in the context of the shape of the heliosphere, the thickness of the inner heliosheath, and the position of the ribbon of enhanced energetic neutral particle emission, as observed by the IBEX mission. Methods. Our study is based on a comparison of fully time-dependent simulations obtained with a three-dimensional (3D) model of the heliosphere. Results. We show that density fluctuations, taking the form of entropy waves and originating from the LISM, may reduce the thickness of the inner heliosheath to a similar extent as the solar-cycle effects. However, the relative motions of the termination shock and the heliopause in the two types of simulations are different. The amplitude of variation of the heliopause position is greater for the LISM fluctuation. The IBEX ribbon position is shown to be not significantly affected by the two types of drivers, although the effect of LISM fluctuation is stronger than that of the solar cycle. In this context, slight systematic changes of the position of the IBEX ribbon in its different sectors (i.e., changes in the heliospheric nose followed by variations in the heliospheric flanks) may serve as an indicator of the passage of a density fluctuation in the LISM, as suggested by our study. We also discuss the difficulties in fitting the LISM parameters in the presence of time-dependent effects.

Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid

Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.

Neurological Disorder Detection of Brain Abnormal Activities Using a New Enhanced Computer-aided Model

In the field of neurodevelopmental disorders, Autism Spectrum Disorders (ASD) are recognized as one of the dramatically increased etiologically and clinically heterogeneous diseases. Although, increasing the number of children who have difficulties in communication or suffer from sudden malfunction of the brain, the current diagnostic approaches for those kind of disease are time-consuming and are mainly based on clinical interviews. In this paper, a new enhanced diagnostic model is introduced addressing many of the challenges which threats the analysis of Electroencephalography (EEG) signals. A preprocessing stage is proposed to choose the key segment of EEG channel and remove the artifacts in the EEG signals to enhance their quality. The proposed model uses a set of discriminative features based on discrete wavelet transform (DWT) such as skewness, standard division, shannon entropy and relative wave energy. Also, extracting cross correction between brain regions to detect abnormal connectivity and synchronization. Two EEG datasets are used to verify the accuracy of the proposed model. The fusion of two EEG dataset helps in building a more generalized mode to diagnose epilepsy and ASD. In the fused dataset, the combination of the mentioned features and Random Forest have produced a very promising diagnosis result with minimum diagnostic time, with an average accuracy equals to 96.78%. The proposed model obtained better classification accuracy compared to the existing methods.

Transport of Swirling Entropy Waves through an Axial Turbine Stator

The transport of entropy waves and their impact on the stage aerodynamics are still open questions. This paper shows the results of an experimental campaign that focuses on the swirling entropy waves advection through an axial turbine stator. The research aims at quantifying the aerodynamic impact of the swirling entropy waves on the first nozzle and characterizing their transport. The disturbance is generated by a novel entropy wave generator that ensures a wide set of different injection parameters. The device injects the disturbance axially, four different clocking positions are investigated. Measurements show a severe temperature attenuation of the swirling entropy wave at stator outlet. The high temperature location changes with the injection position as a result of the different interaction with the stator secondary flows. Depending on the injection position, the aerodynamic flow field is strongly perturbed by the injected swirl profile, instead the entropy wave effect is negligible.

On boundary-layer receptivity to entropy waves

In this paper, we consider the generation of the Tollmien–Schlichting waves in the boundary layer on the surface of a wing exposed to entropy waves. It is well known that the free-stream turbulence is composed of two perturbation modes: the vorticity waves and the entropy waves. The receptivity of the boundary layer to the vorticity waves has been studied extensively by various authors. The entropy waves have not attracted such attention. We show that, in high speed subsonic flows, the entropy waves are as important for the receptivity as the vorticity waves. Methodologically, our work relies on the asymptotic analysis of the Navier–Stokes equations at large values of the Reynolds number, which results in the formulation of a suitably modified triple-deck theory. The entropy waves produce oscillations of the gas temperature and density, but the velocity and the pressure remain unperturbed to the leading order. This precludes the entropy waves from penetrating the boundary layer, as happens, for example, with the acoustic waves. Our analysis reveals that the entropy waves decay rapidly in the transition layer that forms near the outer edge of the boundary layer. We find that an entropy wave alone cannot generate the Tollmien–Schlichting waves. However, when the boundary layer encounters a wall roughness, the flow near the roughness appears to be perturbed not only inside the boundary layer but also in the inviscid region outside the boundary layer. The latter comes into the interaction with the density perturbations in the entropy wave. As a result, a localised ‘forcing’ is created that produces the Tollmien–Schlichting waves. In this paper we present the results of a linear and nonlinear receptivity analysis. We find that the nonlinearity enhances the receptivity significantly, especially when a local separation region forms on the roughness.

Entropy Wave Instability in Dirac and Weyl Semimetals.

Hydrodynamic instabilities driven by a direct current are analyzed in 2D and 3D relativisticlike systems with the Dyakonov-Shur boundary conditions supplemented by a boundary condition for temperature. Besides the conventional Dyakonov-Shur instability for plasmons, we find an entropy wave instability in both 2D and 3D systems. The entropy wave instability is a manifestation of the relativisticlike nature of electron quasiparticles and a nontrivial role of the energy current in such systems. These two instabilities occur for the opposite directions of fluid flow. While the Dyakonov-Shur instability is characterized by the plasma frequency in 3D and the system size in 2D, the frequency of the entropy wave instability is tunable by the system size and the flow velocity.

Impact of Swirling Entropy Waves on a High Pressure Turbine

AbstractThe harsh environment exiting modern gas turbine combustion chamber is characterized by vorticity and temperature perturbations, the latter commonly referred as entropy waves. The interaction of these unsteadiness with the first turbine stage causes non-negligible effects on the aerodynamic performance, blade cooling, and noise production. The first of these drawbacks is addressed in this paper by means of an experimental campaign: entropy waves and swirl profile are injected upstream of an axial turbine stage through a novel combustor simulator. Two injection positions and different inlet conditions are considered. Steady and unsteady experimental measurements are carried out through the stage to address the combustor-turbine interaction characterizing the injected disturbance, the nozzle, and rotor outlet aerothermal field. The experimental outcomes show a severe reduction of the temperature perturbation already at stator outlet. The generated swirl profile influences significantly the aerodynamic, as it interacts with the stator and rotor secondary flows and wakes. Furthermore, the clocking position changes the region most affected by the disturbance, showing a potential modifying the injection position to minimize the entropy wave and swirl profile impact on the stage. Finally, this work shows that in order to proficiently study entropy waves, the unsteady aerodynamic flow field stator downstream has to be addressed.

Modeling the Transport of Fuel Mixture Perturbations and Entropy Waves in the Linearized Framework

Abstract In this paper, a new method is introduced to model the transport of entropy waves and equivalence ratio fluctuations in turbulent flows. The model is based on the Navier–Stokes equations and includes a transport equation for a passive scalar, which may stand for entropy or equivalence ratio fluctuations. The equations are linearized around the mean turbulent fields. These serve as the input to the model in addition to a turbulent eddy viscosity, which accounts for turbulent diffusion of the perturbations. Based on these inputs, the framework is able to predict the linear response of the flow velocity and passive scalar to harmonic perturbations that are imposed at the boundaries of the computational domain. These, in this study, are fluctuations in the passive scalar and/or velocities at the inlet of a channel flow. The code is first validated against analytic results, showing very good agreement. Then, the method is applied to predict the convection, mean flow dispersion, and turbulent mixing of passive scalar fluctuations in a turbulent channel flow, which has been studied in previous work with direct numerical simulations (DNS). Results show that our code reproduces the dynamics of coherent passive scalar transport in the DNS with very high accuracy and low numerical costs. Furthermore, we demonstrate that turbulent mixing has a significant effect on the transport of the passive scalar fluctuations. Finally, we apply the method to explain experimental observations of transport of equivalence ratio fluctuations in the mixing duct of a model burner.

On the generation of entropy noise in a shock containing nozzle of high-performance aircraft at afterburner

High performance aircraft operate at high jet temperature and velocity. Measured noise data indicate that at afterburner condition their noise contain components not found in high temperature supersonic laboratory model jets. The combustion process inside an afterburner is highly unsteady and incomplete. Residual combustion takes place in the jet plume. This suggests that the flow from the afterburner into the jet nozzle would contain significant amount of hot and cold temperature blobs, generally referred to as entropy waves. It is known that when entropy waves move through a non-uniform mean flow, indirect combustion noise (also called entropy noise) would be generated. Military styled nozzles have a rather abrupt area change at and near the throat. This induces the formation of internal shocks inside the nozzle. This paper investigates the generation of entropy noise when strong entropy blobs or waves are convected through the internal shocks. It is found that the result of entropy blobs-shock interaction could lead to the radiation of intense entropy noise out of the nozzle exit into the jet plume as fast waves with a speed equal to sound speed plus jet flow speed. These fast waves create highly supersonic flow disturbances in the jet flow leading to strong Mach wave radiation. It is proposed that this Mach wave radiation is the source of a new noise component observed in the spectra of the F-22A aircraft. Detailed analysis of the F-22A noise data provides support for the proposal.

Numerical study of shock-disturbances interaction in hypersonic inviscid flows with real gas effects using high-order WENO scheme

In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The solution methodology adopted based on the high-order WENO scheme with the shock capturing technique can reasonably simulate the strong discontinuities in the solution domain without needing any numerical artifact and this feature makes the solution method suitable for the shock-disturbances interaction in hypersonic flows in which real gas effects are to be considered. To study the physical phenomenon of the shock-disturbances interaction problem in high-speed inviscid equilibrium airflows, two test cases are simulated by applying the solution methodology adopted. In the first test case, the interaction between the incoming fast acoustic wave with the bow shock formed around a cylinder with the nose radius of RN=0.0381 m at M∞=8.03 and T∞=182.333 K is simulated. In the second test case, the cylinder radius is taken RN=2.54×10−2 m and the upstream velocity and temperature are u∞=5590m/s and T∞=1833 K, respectively, and all kinds of free stream disturbances, including the entropy wave and the fast and slow acoustic waves, for different wave numbers are considered. The computations are carried out for both the perfect gas and equilibrium air models and the effects of real gas on both the mean and disturbances fields are also studied. The present study introduces the first-known numerical investigation of the shock-disturbances interaction in hypersonic flow over blunt noses with real gas effects in which the numerical results obtained are thoroughly validated by the analytical/theoretical ones and good agreement is found.

Scattering of entropy waves into sound by isolated aerofoils

Abstract