Subsonic Mode Research Articles

Instability of isolator shocks to fuel flow rate modulations in a strut-stabilised scramjet combustor

Abstract Reynolds-Averaged Navier–Stokes (RANS) simulations, both steady and unsteady, are used to investigate supersonic, chemically reacting, flow fields inside a strut-stabilised supersonic combustion ramjet (scramjet) engine operating under different fuel flow rates. Fully supersonic, fully subsonic and mixed modes of operations inside the combustor, obtained at different fuel flow rates, are studied numerically through shock wave visualisations and top-wall static-pressure probing. The effect of changing fuel flow rates, imposed both suddenly and gradually, on the behaviour of shock waves and wall pressure profiles are studied in detail. For certain modes of combustion characterised by the presence of oblique shocks at the strut, shockwaves in the combustor respond predictably to an increase or decrease in fuel flow rate attaining the steady state flow fields as predicted by RANS simulations for those fuel flow rates. For certain other modes of combustion, characterised by the presence of shockwaves in the isolator and the absence of oblique shocks at the leading edge of the strut, shockwaves in the flow field appear unstable to fuel flow rate modulations. For such cases, any change in fuel flow rates, sudden or gradual, increase or decrease, causes the isolator shocks to immediately move upstream and eventually out of the isolator. A plausible physics-based explanation of the observed phenomena is presented.

Wavelet optical flow velocimetry of a scramjet combustor using high-speed frame-straddling focusing schlieren images

Scramjet combustors feature ultra-high-speed turbulent reacting flows with high temperatures and intense luminescence. Measurement of velocity fields under such extreme conditions presents great challenges. The present work demonstrated a seedless velocimetry approach using focusing schlieren images (FSIs) of high spatiotemporal resolution in a scramjet engine. Two fuel mass flow rates (Case1 and Case2) were investigated with corresponding global equivalence ratios of 0.27 and 0.13, respectively. The FSIs enabled by the employment of a high-speed pulsed LED light source are characterized by an effective exposure of 100 ns, and a 500-ns frame-straddling time interval with full resolution of 1280 × 800 pixels recorded at 76 kHz. The 100-ns exposure allows for capturing of transient high-speed flow motion without blurring, and the 500-ns time interval ensures an appropriate spatiotemporal correlation between subsequent schlieren images for high-speed reacting flows. A wavelet-based optical flow velocimetry (wOFV) algorithm was developed and applied to the FSIs. In contrast to the correlation-based algorithms widely employed in PIV for distinct particles, the wOFV algorithm suits better FSIs with continuous variation in brightness. The maximal velocities in the main duct of the scramjet combustor were measured to be approximately 550 m s-1 and 1100 m s-1 for Case 1 and Case2, suggestively corresponding to subsonic and supersonic combustion modes, respectively. The measured velocity inside the cavity is generally below 200 m s-1 for both cases. Recirculation regions and their dynamic motions inside the cavity were well resolved. In summary, the development of the novel velocimetry approach holds great potential for applications in extreme flow conditions. Novelty and Significance Statement: Present work demonstrates a seedless velocimetry approach based on high-speed frame-straddling focusing schlieren imaging coupled with the novel wavelet optical flow velocimetry (wOFV) algorithm. Velocity field measurement realized in a scramjet combustor with high spatiotemporal resolution (1280 × 800 pixels at 38 kHz) for the first time, showing great abilities to accommodate wide velocity range and to resolve dynamic flow characteristics with potentials for broader future applications.

Normal Impact by the Dulled Wedge on the Viscous-Elastic String (A Subsonic Mode)

Normal Impact by the Dulled Wedge on the Viscous-Elastic String (A Subsonic Mode)

Nonlinear wave propagation in homogenized strain gradient 1D and 2D lattice materials: Applications to hexagonal and triangular networks

AbstractThis work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.

Experimental Investigation of Solid Rocket Scramjet Based on Central Strut

Scramjet based on solid propellant has become a potential choice for the development of future hypersonic vehicles. In this paper, a boron-containing solid rocket scramjet based on the central strut injection was proposed, and the ground direct-connect experiment with the equivalence ratios of 0.43 to 2.4 under the flight condition of Mach 6, 25 km was carried out. The pressure and flow rate over time were measured in the experiment. The results show that the engine can realize stable supersonic mode or subsonic mode combustion by changing the gas flow rate. The engine can effectively increase the combustor pressure, reduce the unstable combustion time, and advance the strong combustion position by increasing the gas flow rate. The engine achieved high combustion efficiency when the equivalence ratio was about 1, with a maximum of 88.28%. A numerical simulation analysis was also carried out in this paper. Compared to the experimental results, the pressure error obtained by numerical simulation was less than 4%, and the typical position error was less than 3%, suggesting that the simulation model can be used to predict the behavior of scramjet.

Role of cavity in a Mach 8 axisymmetric scramjet combustor: Flame stabilization vs combustion enhancement

The cavity-assisted scramjet has been proven to be the most promising propulsion system for air-breathing hypersonic vehicles. In this paper, numerical simulations of a Mach 8 axisymmetric scramjet combustor are conducted and validated to investigate the effect of the cavity. The results indicate that the combustion state undergoes significant changes as the combustion heat release increases. Detailed analysis reveals that the role of the cavity in flame stabilization and combustion enhancement also changes with combustion heat release. Under weak heat release conditions, the high-speed environment results in reduced combustion efficiency, and the primary role of the cavity is to stabilize the flame. Increasing the cavity size does not yield significant gains but could bring redundant mass. As heat release intensifies, the combustion enhancement effect of the cavity becomes more prominent. The presence of the cavity dramatically improves fuel combustion efficiency. The distribution of supersonic and subsonic combustion modes, as well as that of premixed and diffusion combustion modes, is also affected by cavity size and combustion heat release. In the engineering development of scramjets, it is suggested that the design of the cavity flameholder should involve careful consideration of combustion heat release.

Combustion mode and heat release characteristics of a kerosene-fueled rocket-aided ramjet combustor in ramjet-to-scramjet mode transition

In this study, a rocket-aided ramjet engine (RARE) configuration is proposed that is aimed at improving the thrust gap and enhancing the engine thrust stability in the ramjet-to-scramjet mode transition of dual-mode scramjet (DMSJ) engines. The combustion mode and relevant heat release characteristics in the kerosene-fueled combustor during the mode transition are analyzed in detail through numerical simulations and ground direct-connect tests at the simulated flight condition of Mach 6. In the ramjet mode, the combustion mode distribution is dominated by diffusion and supersonic combustion, whereas the heat release comes mainly from diffusion and subsonic combustion. The subsonic combustion mode is that which has the highest heat release efficiency, accounting for 28.6% of the total combustion volume, and contributing 67.9% of the total heat release. The combustion heat release level in the rocket-aided scramjet mode is higher than the simple sum of the pure rocket and scramjet modes. The RARE combustor effectively maintains the heat release level and stabilizes the distribution of several different combustion modes from the ramjet to the scramjet mode using the embedded rocket. Furthermore, a robust method for a smooth ramjet-to-scramjet mode transition is provided for ramjet engines. Compared with the engine operation without embedded rocket, the engine thrust variation is reduced from 50.77% to 1.33% with the aid of the embedded rocket, which enhances the operational stability of the engine considerably during the mode transition.

Statement and general technique for solving problem of oscillation of a hereditarily deformable aircraft

This article provides a general statement and a technique for solving the problem of oscillations of a hereditarily deformable aircraft in a gas flow with a finite number of degrees of freedom. Using the Lagrange equations and the variational principle of the hereditary theory of viscoelasticity, the equations of motion of the problem under consideration are derived. The generalized forces acting on the aircraft in the subsonic flight mode are determined according to the stationarity hypothesis. As a result, closed interconnected weakly singular integro-differential equations are obtained that describe the mathematical model of the problem with a finite number of degrees of freedom. General schemes for the numerical solution of these equations are outlined. As an example, the flexural-torsional-aileron flutter of the transient process of a hereditarily deformable wing with a finite freedom number is considered.

Multi-regime reaction front and detonation initiation by temperature inhomogeneity

Auto-ignition, reaction front propagation, and detonation development are foundational events in combustion, and are relevant to the occurrence of engine knock. It is generally understood that different auto-ignition modes can be initiated by non-uniform initial temperatures, manifesting the transition from supersonic to subsonic combustion modes with increasing temperature gradients. In this work, we have investigated the auto-ignition and reaction front propagation of syngas/air mixtures initiated by wide-ranging temperature gradients, in both spherical and planar coordinates, and have identified a universal detonation response diagram with multiple, non-monotonic boundaries of auto-ignition modes under engine-relevant conditions. Specifically, it is shown that with increasing gradient steepness, in addition to the conventional three regimes of supersonic auto-ignition deflagration, detonation development, and subsonic auto-ignition deflagration, the reaction front propagation speed would first decrease dramatically and then increase, hence inducing additional detonation regimes. Consequently, two detonation peninsulas are identified, with the first corresponding to the well-established Bradley detonation peninsula and the second manifesting a broader detonation regime. Both detonation peninsulas depend on the hotspot size and they can connect together when the hotspot radius becomes sufficiently large. The transient auto-ignition processes and chemical-gas dynamic interactions agree with the typical characteristics of various auto-ignition modes. Finally, auto-ignition modes are summarized in the detonation diagram, in which the Bradley detonation peninsula is well reproduced and the new detonation peninsula is quantitatively determined. The present study demonstrates that auto-ignition modes are significantly affected by the non-monotonic behavior of reaction front propagation, and the use of actual propagation speed is necessary for steeper temperature gradients in order to determine more accurate dimensionless parameters.

Spherically symmetric stationary flows of a rarefied two-phase fluid

The spherically symmetric stationary flows of isothermal rarefied two-phase fluid are studied. The results of the research give a qualitative description such flows for arbitrary positive initial data. Namely, for arbitrary positive initial velocities and densities of the first and the second phase, which are set at the initial sphere of arbitrary radius, the obtained phase portrait gives a qualitative description of the distribution of characteristics at the spheres of other radii. A classification of all possible types of spherically symmetric stationary flows of isothermal two-phase fluid in a case of the spread of a substance has been carried out. In the work it is also described a bifurcation of a dynamical system. As a result of this bifurcation, some attracting set appears at the curve of singular points. The emergence of this set greatly changes a quantity of the types of two-phase flows. Another result of the study is a description of all types of continuous transonic spherically symmetric stationary flows at the investigating model of two-phase fluid. The study showed that if the ratio of the flows of the first and second phases through an initial sphere is bigger than 8, then there is a non-zero probability of a realization in two-phase fluid dynamics a continuous transition from supersonic mode to subsonic mode. There have been carried out different numerical experiments, which are illustrated the obtained results.

A unifying theory of jet screech

This paper describes the mechanism underpinning modal staging behaviour in screeching jets. An upstream-propagating subsonic guided-jet mode is shown to be active in all stages of screech. Axial variation of shock-cell spacing manifests in the spectral domain as a series of suboptimal peaks. It is demonstrated that the guided-jet mode may be energized by interactions of the Kelvin–Helmholtz wavepacket with not only the primary shock wavenumber peak, but also suboptimal peaks; interaction with suboptimals is shown to be responsible for closing the resonance loop in multiple stages of jet screech. A consideration of the full spectral representation of the shocks reconciles several of the classical models and results for jet screech that had heretofore been paradoxical. It is demonstrated that there are multiple standing waves present in the near field of screeching jets, corresponding to the superposition of the various waves active in these jets. Multimodal behaviour is explored for jets in a range of conditions, demonstrating that multiple peaks in the frequency spectra can be due to either changes in which peak of the shock spectra the Kelvin–Helmholtz wavepacket is interacting with, or a change in azimuthal mode, or both. The absence of modal staging in high-aspect-ratio non-axisymmetric jets is also explained in the context of the aforementioned mechanism. The paper closes with a new proposed theory for frequency selection in screeching jets, based on the observation that these triadic interactions appear to underpin selection of the guided-jet mode wavelength in all measured cases.

Simulation of the pulsed outflow of air and fine powder mixture, partially filling the discharge channel

The paper studies the regularities of the pulsed outflow of air and fine powder mixture, which partially fills the ejection cylindrical channel, in both one-dimensional and two-dimensional formulations. The dynamics of a gas-dispersed medium are described in the framework of the Eulerian continuum approach with different velocities and temperatures of gas and powder particles. Analytical self-similar solutions are constructed in the equilibrium approximation. For the numerical solution of the problem, a hybrid large-particle method of the second order of accuracy in space and time is used. Comparison of exact self-similar and numerical solutions confirmed the reliability of the method. The outflow of the mixture of high-pressure gas and powder particles has a pronounced wave character, which is associated with the decomposition of the initial discontinuity, the movement, and refraction of waves at the interface of media inside the channel, as well as the reflection of waves from its bottom. The characteristic time intervals of the wave process and the corresponding distributions of gas-dynamics quantities are established. Depending on the generalized self-similar variable, the pressure, density, and velocity of the mixture are monotonic functions, and the profile of the specific (per unit cross-section) mass flow has a maximum in the critical section. Dimensionless parameters and specific mass flow of a two-phase medium in the outlet section of the discharge channel are determined. In the case of a channel limited by the size of the high-pressure chamber, a two-dimensional physical picture of the formation and evolution of a gas-dispersed mixture was studied. At the initial stage of the outflow, an “anomalous” grouping of powder particles is observed with the formation of a shock-wave structure in the subsonic mode of the carrier gas flow. After the powder layer leaves the channel, the pure gas flowing out of it accelerates to supersonic speed and an intense vortex motion develops in the wake of the gas-dispersed jet. The calculated values of the parameters allow us to justify the achievable level of technical characteristics (speed, mass flow rate) of the flow of the working gas-dispersed medium of pulsed powder devices. The proposed methodology and the results obtained are the basis for making rational decisions at the early stages of design and preparation of initial data on design and operating parameters for testing prototypes of pulsed powder technical devices.

Application of functional coatings by supersonic thermal plasma flows

Development of modern high-speed technologies for thermal spraying proves that deposition of high-quality dense coatings requires velocity of sprayed particles to be 600 m/s and above. Plasma spraying is the most versatile and highly productive deposition method of various functional coatings without any limitations on the melting points of the sprayed materials. Present work describes a DC plasma torch designed for operation in a supersonic mode. The supersonic plasma torch features de Laval nozzle, utilization of air as a plasma-forming gas, and annular injection unit for delivery of the powder to the plasma jet. The comparison of NiCr and NiAl coatings deposited both in subsonic and supersonic modes are presented. Methods for further increasing the sprayed particles’velocity and the requirements for their heating temperature are proposed.

Study on scramjet engines with complex inlet flow conditions

Scramjet engine is one of the key technologies to realize hypersonic flight. It has great research value for its performance under complex inlet flow conditions. In this paper, the free jet test model of RBCC aircraft is established, and the numerical simulation is carried out with Japanese NAL direct connected hydrogen fuel combustion chamber test. Aiming at the problems of coupling analysis accuracy and long calculation period, a one-dimensional internal flow coupling analysis method based on one-dimensional flow is proposed to solve the backpressure problem in the subsonic combustion state. The experimental results show that this method can predict the flow separation point in the isolation section well in the subsonic combustion mode, and the error is less than 10%, the prediction results of the peak pressure and the mean pressure along the passage are less than 23% and 10.4%, respectively. In the supersonic combustion mode, the accuracy of one-dimensional flow is higher, and the prediction error for the peak pressure in the combustion chamber is less than 3.79%, and the prediction error for the location of the peak pressure is less than 2.3%.

Research progress in numerical simulation of Laval nozzle

The Laval nozzle is a very widely used device that has made great contributions due to its invention in aerospace, mechanical engineering, applied chemistry etc. The development of many modern technologies relies on the establishment of nozzles. In this paper, the current research advances on the numerical simulation methods of the nozzle flow and nozzle-related investigation or applications in different fields are reviewed. For example, the analytical and numerical simulation of nozzles in subsonic and supersonic modes are mentioned in this article. In summary, although the applications for various fields of nozzles are now very mature, the solution of the Navier-Stokes equation for nozzles is still a future direction where science and mathematics need to be strongly developed.

On the mass exchange mode controlled by high-speed compressive mainstream/cavity interaction in a laboratory dual-mode scramjet combustor

Stable and efficient mass exchange is crucial to the combustion stability of a dual-mode scramjet. In subsonic mode, the progression of mass exchange between the cavity fluid and the mainstream, which is controlled by the cavity shear layer, is different from the scramjet mode due to the weak compressibility effects. However, mass exchange mode studies in the subsonic mode are rare. In this study, experimental research has been conducted to obtain the flow structure of Mach 0.3 and 0.5 inflow over a rectangular cavity and reveal the properties of mass exchange using particle image velocimetry technology. The results reveal the weak compressibility effects and geometry effects on the mass exchange by analyzing the growth rate and turbulence characteristics of the cavity shear layer. The mass exchange between the cavity fluid and mainstream is determined based on the vertical velocity along the cavity lip line. When the flow Mach number increased from 0.3 to 0.5, the growth rate of the cavity shear layer decreases due to the weak compressibility effects. Also, the growth rate of the cavity shear layer is smaller than that of the compressible free shear layer due to the effects of recirculation within the cavity. For length-to-depth (L/D) ratios ranging from 0.8 to 1.2, the cavity shear-layer growth rate decreases with increasing L/D. However, at an L/D of 1.5, the shear-layer growth rate increases, which changes the mass exchange mode. Finally, the effects of increasing the Mach number (Mach = 0.3 versus 0.5) show that the L/D ratio at the “crossover” point of the mass exchange mode transition is reduced (L/D = 1.5 versus 1.2) due to the weak compressibility at a higher Mach number.

Estimation of vitiation effects on flameholding and mode transition in a dual-mode supersonic combustor

To estimate the vitiation effects of test air on flameholding and mode transition in a direct-connected dual mode combustor, an experimental study was conducted with two types of air heater (electric heater and methane combustion heater) at various kerosene equivalence ratios. Total temperature, total pressure and Mach number of combustor entrance were matched in comparative tests. The lean blowout limits, wall pressures and mode transitions were compared. For clean air heater, the lean blowout limit occurred at the equivalence ratio of 0.105, while for methane combustion heater, it occurred at 0.135. Considering mode transition, the combustor operated in subsonic combustion mode at kerosene equivalence ratio above 0.30 with clean air; while for methane combustion heater, mode transition from supersonic to subsonic combustion occurred at equivalence ratio of 0.33. This indicated that the test data should be fully evaluated when using a combustion heater, especially in lean blowout limit and mode transition.

Experimental study of ignition and combustion characteristics of ethylene in cavity-based supersonic combustor at low stagnation temperature and pressure

At low inflow Mach number without throttling, since low static temperature the ignition and flame holding is still a big challenge in supersonic combustor. In this paper, the ignition and flame transient development in ethylene fueled cavity-based supersonic combustor are experimentally investigated at low conditions of stagnation temperature 950 K, pressure 0.82 MPa, and the isolator entrance Mach number 2.0. The results show ethylene can achieve successful ignition and stable combustion at low inflow Mach number with global equivalence ratios (ER) varying from 0.12 to 0.3. The combustion mode could be either supersonic or subsonic which depends on the ER. The combustion mode is supersonic stable combustion mode at ER = 0.12, 0.18 and 0.24 while the mode is subsonic stable combustion mode at ER = 0.27, 0.3. Owing to the better fuel/air mixing, ethylene injected from upstream position burns more intensively than that of downstream position at the same ER. It is also found that combustion and shockwaves are strengthened with each other until the balance between the pressure of shockwaves and the backpressure of combustion. This balance makes the flow structures and combustion keep stable. Comparing the combustion and shockwaves of different ER and injector position, the mutual promotion between combustion and shock wave is further demonstrated.

Development of Ultrasonic Techniques for Measurement of Spatially Non-Uniform Elastic Properties of Thin Plates by Means of a Guided Sub-Sonic A0 Mode

Air-coupled ultrasonic guided A0 mode is already used for material characterization. By measuring the phase velocity of the A0 mode the elastic properties, such as the Young’s modulus, can be determined. The objective of this work was the development of measurement methods and corresponding signal processing procedures enabling the acquisition of spatial distributions of non-uniform elastic properties of thin films and plates. Those methods are based on the excitation of a slow sub-sonic A0 Lamb wave mode in a plate, the measurement of normal displacements at different distances from the source, the formation of the B-scan, and processing the collected signals. Two different signal processing methods were proposed and investigated. In the first method the all zero-crossing instants of the ultrasonic signals at different distances are found and from them spatial distributions of the A0 mode velocity are determined. According to the second method 2D spatial-temporal spectrum of the B-scan is calculated and propagating A0 modes with different velocities are identified. Efficiency of the proposed methods was evaluated theoretically and experimentally using thin mineral MICA paper samples, which is used in the electrical and aerospace industries as an insulating material. The zones with different A0 mode phase velocities (95 ± ∆3 m/s and (106 ± ∆6 m/s) at the frequency 47 kHz were identified.

Air-Coupled Reception of a Slow Ultrasonic A0 Mode Wave Propagating in Thin Plastic Film.

At low frequencies, in thin plates the phase velocity of the guided A0 mode can become slower than that of the ultrasound velocity in air. Such waves do not excite leaky waves in the surrounding air, and therefore, it is impossible to excite and receive them by conventional air-coupled methods. The objective of this research was the development of an air-coupled technique for the reception of slow A0 mode in thin plastic films. This study demonstrates the feasibility of picking up a subsonic A0 mode in plastic films by air-coupled ultrasonic arrays. The air-coupled reception was based on an evanescent wave in air accompanying the propagating A0 mode in a film. The efficiency of the reception was enhanced by using a virtual array which was arranged from the data collected by a single air-coupled receiver. The signals measured at the points corresponding to the positions of the phase-matched array were recorded and processed. The transmitting array excited not only the A0 mode in the film, but also a direct wave in air. This wave propagated at ultrasound velocity in air and was faster than the evanescent wave. For efficient reception of the A0 mode, the additional signal-processing procedure based on the application of the 2D Fourier transform in a spatial–temporal domain. The obtained results can be useful for the development of novel air-coupled ultrasonic non-destructive testing techniques.