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The transition of the boundary layer is an important issue that must be considered in the design of hypersonic vehicles. During the ascent phase of the vehicle, both the Mach number and the flight altitude increase simultaneously and affect the location of transition jointly. This paper investigated the plate boundary layer and employed linear stability theory and eN method to study the influence of Mach number and flight altitude on the stability of boundary layer and the transition process during the ascent stage of hypersonic vehicles (Mach number ranges from 4 to 6, and flight altitude ranges from 14 km to 25 km). The research findings indicate that the second mode, which dominates the transition in the boundary layer, becomes more unstable with increasing Mach number. However, it tends to be more stable with increasing flight altitude. Furthermore, the stability of the boundary layer at typical trajectory points during the ascent phase of HIFiRE-1 was analyzed. It is observed that under the combined influence of Mach number and flight altitude, the growth rate of the second mode initially increases and then decreases in ascent stage, resulting in a non-monotonic phenomenon where the transition location shifts forward initially and then moves backward.

Flow stability plays a key role in transition to turbulence in various systems. This transition initiates with disturbances appearing in the laminar base flow, potentially amplifying over time based on flow and fluid parameters. In response to these amplified disturbances, the flow undergoes successive stages of different laminar flows, ultimately transitioning to turbulence. One influential parameter affecting flow stability is the nanoparticle volume fraction (ϕ) in nanofluids, extensively employed in thermofluid systems like cooling devices to enhance fluid thermal conductivity and the heat transfer coefficient. Focusing on the impact of nanoparticles on Jeffery–Hamel flow stability, this study assumes fluid properties are temperature- and pressure-independent, exclusively examining the momentum transfer aspect. The analysis commences by deriving the base laminar flow solution. Subsequently, linear temporal stability analysis is employed, imposing infinitesimally-small perturbations on the base flow as a modified form of normal modes. A generalized Orr–Sommerfeld equation is derived and solved using a spectral method. Results indicate that, assuming nanofluid viscosity as μ nf = μ f / (1 − ϕ) 2. 5 , nanoparticle effects on momentum transfer and flow stability hinge on the ratio of nano-solid particle density to base fluid density ( R ρ = ρ s / ρ f ). For ϕ ∈ (0 , 0. 1 ] , flow stabilization occurs with ϕ when R ρ < 3. 5000 , while destabilization is observed when R ρ > 4. 0135. Notably, nanoparticles exhibit a negligible impact on flow stability when 3. 5000 ≤ R ρ ≤ 4. 0135. • Effect of nanoparticle volume fraction on Jeffery–Hamel flow stability is investigated. • Influence of density ratio on Jeffery–Hamel flow stability is investigated. • Stability results are presented for Reynolds number based on centerline velocity and flow rate. • Results indicate that density ratio plays a decisive role in stability of Jeffery–Hamel flow. [ABSTRACT FROM AUTHOR]

The family of velocity profiles of a submerged jet, which are absolutely unstable in the plane-parallel approximation, is considered. The profiles are specified by two parameters: the first of them is responsible for the location of the only inflection point in the velocity profile, and the second is responsible for the shear layer thickness. An algorithm for determining the length of the region of local absolute instability of the jet with a given input velocity profile, that is, the distance at which absolute instability gives way to convective instability, has been implemented. The dependence of this length on the parameters defining the input profile is obtained. A connection between the characteristics of local absolute instability calculated in the plane-parallel approximation and global instability of the jet evolving in space is analytically obtained. The input velocity profile that corresponds to sufficiently large length of the zone of local absolute instability, at which global instability of spatially developing jet occurs, is demonstrated. Thus, the possibility of existence of global instability of plane submerged jets with special velocity distributions is demonstrated. [ABSTRACT FROM AUTHOR]

Under the low-noise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminar-turbulent transition is due to amplification of the first mode. Stability of a local self-similar boundary layer over such a wing is investigated both using the e N method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed. [ABSTRACT FROM AUTHOR]

Transition delaying is of great importance for the drag and heat flux reduction of hypersonic flight vehicles. The first mode, with low frequency, and the second mode, with high frequency, exist simultaneously during the transition through the hypersonic boundary layer. This paper proposes a novel bi-frequency synthetic jet to suppress low- and high-frequency disturbances at the same time. Orthogonal table and variance analyses were used to compare the control effects of jets with different positions (USJ or DSJ), low frequencies (f1), high frequencies (f2), and amplitudes (a). Linear stability analysis results show that, in terms of the growth rate varying with the frequency of disturbance, an upstream synthetic jet (USJ) with a specific frequency and amplitude can hinder the growth of both the first and second modes, thereby delaying the transition. On the other hand, a downstream synthetic jet (DSJ), regardless of other parameters, increases flow instability and accelerates the transition, with higher frequencies and amplitudes resulting in greater growth rates for both modes. Low frequencies had a significant effect on the first mode, but a weak effect on the second mode, whereas high frequencies demonstrated a favorable impact on both the first and second modes. In terms of the growth rate varying with the spanwise wave number, the control rule of the same parameter under different spanwise wave numbers was different, resulting in a complex pattern. In order to obtain the optimal delay effect upon transition and improve the stability of the flow, the parameters of the bi-synthetic jet should be selected as follows: position it upstream, with f1 = 3.56 kHz, f2 = 89.9 kHz, a = 0.009, so that the maximum growth rate of the first mode is reduced by 9.06% and that of the second mode is reduced by 1.28% compared with the uncontrolled state, where flow field analysis revealed a weakening of the twin lattice structure of pressure pulsation. [ABSTRACT FROM AUTHOR]

The eN method predicts transition based on the level of the linear amplitude amplification of the disturbances in the boundary layer. Boundary layers over cones at Mach 6 were investigated with different nose bluntness and under different wall temperature conditions. Combined with direct numerical simulation (DNS) and parabolized stability equations (PSE), from the viewpoint whether the eN method is able to accurately describe the amplification of the disturbances in the above boundary layers, its reliability for transition prediction was interrogated. Results show that in the cases of small bluntness or high wall temperature, the disturbances undergo the intermodal exchange from the first mode to the second mode when travelling downstream in the boundary layer, so that the eN method based on linear stability theory becomes less reliable. Under the same wall temperature condition, as the nose bluntness increases, the eN method is more reliable. For the same nose bluntness, as the wall temperature decreases, the eN method is more reliable. Since linear stability theory always underestimates the amplification of the disturbances when there is an intermodal exchange, for the given transition criterion NT, which could be calibrated by a certain case, as the bluntness decreases or the wall temperature increases to some extent, the eN method tends to produce a further downstream transition location than reality. To recalibrate the transition criterion, the smaller the nose bluntness or the higher the wall temperature, the larger the modification of NT factor.

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability. [ABSTRACT FROM AUTHOR]

Theoretical assessments of the crossflow (CF) stabilization due to flow slip produced by small grooves on a swept supersonic wing are performed using the linear theory for inviscid flow, the local similar approximation of the boundary layer flow, the slip boundary conditions on the grooved surface and the linear stability theory. The e N computations for stationary CF mode predict that spanwise-invariant grooves with their half-period equal to 0.25 of the boundary-layer displacement thickness can delay the CF-induced transition onset by about 10% on a 30 ∘ swept wing having a parabolic airfoil of 5% thickness ratio, at freestream Mach number 2. It is concluded that the groove laminarization concept deserves further studies. [ABSTRACT FROM AUTHOR]

We present the results of an investigation of the boundary layer stability on a flat plate having a region of gas injection/suction normal to the wall at a large supersonic freestream Mach number. The laminar flow past a flat plate having a region of distributed injection/suction of fixed intensity is modeled numerically using the integration of Navier—Stokes equations. The unstable disturbances in the boundary layer distorted by injection/suction are analyzed within the framework of the linear stability theory and the method for compressible flows. High-frequency disturbances belonging to the plane second mode of the boundary layer, which are the most unstable at high velocities, are considered. It is shown that gas injection/suction leads to a nonmonotonic variation of disturbance growth rates with the appearance of stabilization/destabilization regions, as compared with the case in which injection/suction is absent. [ABSTRACT FROM AUTHOR]

This work is devoted to a numerical study of the influence of foreign-gas injection on the stability of compressible boundary layer on a concave surface. The stability calculation was carried out within the framework of the locally parallel linear stability theory. The results of calculations for the reference case without injection showed that Görtler vortices and the second Mack mode exhibited the highest growth rates at studied parameters. It is found that the injection of a heavy gas (with respect to the oncoming gas) leads to an increase in the growth rate of Görtler vortices and the second Mack mode, whereas the injection of a light gas leads to a decreased growth rate of these disturbances. [ABSTRACT FROM AUTHOR]

In the hypersonic boundary layer, the streamwise instability modes are mainly the Mack first mode and the Mack second mode. After the Mach number exceeds 4.0, the Mack second mode becomes the dominant instability mode for boundary layer transition. Currently, there is no complete analytical method to establish an amplification factor transport equation for the second mode. In order to improve the application of the amplification factor transport (AFT) model in hypersonic boundary layer transition prediction, this paper employs boundary layer similarity solutions to conduct stability analysis on the second mode and introduces a function to calculate the growth rate of disturbances. Additionally, a transport equation for the amplification factor of the second mode is formulated. For the non-local variables appearing in the equation, a local calculation method is provided. Combined with the intermittency factor transport equation, a transition prediction model for the second mode is formed. Hypersonic flat plate, wedge, and flared wedge are selected for model validation. The computed results show good agreement with standard stability analysis or experimental results, demonstrating the rationality of the transition model and its high prediction accuracy and reliability. • Constructs an amplification factor transport (AFT) model for the second mode using analytical method. • Derive the functions in the source term using boundary layer similarity solutions. • Propose a method for determining the maximum value of variables in the boundary layer. [ABSTRACT FROM AUTHOR]

The generation and development of Görtler vortices in compressible boundary layer on a concave surface has been numerically simulated. The calculation was carried out using the Ansys Fluent software. Stationary and non-stationary disturbances are analyzed at freestream Mach number M ≈ 4. It is shown that when a periodic disturbance in the direction transversal to the flow is generated, it decays on the straight section of the surface, and grows on the concave surface. Comparison of the results of the calculations made with the calculations performed within the framework of the linear stability theory showed that the range of receptivity of the boundary layer to the disturbances on the concave surface amounts approximately to 17 boundary-layer thicknesses. After the receptivity zone, disturbances grow exponentially with small deviations. The flow fluctuation profiles are in good agreement with the data obtained from the linear stability theory. It is shown that the development of a non-stationary disturbance along the surface of the model for the parameters considered in the present study differs little from that of a stationary disturbance. [ABSTRACT FROM AUTHOR]

Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the procedure, such as the truncation errors, the discretization error of the flow solver, the error associated with the nonlinear terms of the Navier–Stokes equations and the error associated with the limited size of the approximation of the Jacobian matrix. This paper develops theoretical equations for the estimation of optimal balance between accuracy and cost for each case. The 2D open cavity flow is used both for explaining the effect of the parameters on the accuracy and the cost of the solution, and for verifying the quality of the predictions. The equations demonstrate the impact of each parameter on the quality of the solution. For example, if higher-order methods are used for approaching a Fréchet derivative in the procedure, it is shown that the solution deteriorates more rapidly for larger grids or less accurate flow solvers. On the other hand, lower-order approximations are more sensitive to the initial disturbance magnitude. Nevertheless, for accurate flow solvers and moderate grid dimensions, first-order Fréchet derivative approximation with optimal computational parameters can provide 5 decimal place accurate eigenvalues. It is further shown that optimal parameters based on accuracy tend to also lead to the most cost-effective solution. The predictive equations, guidelines and conclusions are general, and, in principle, applicable to any flow, including 3D ones. [ABSTRACT FROM AUTHOR]

Transition delaying is of great importance for the drag and heat flux reduction of hypersonic flight vehicles. The first mode, with low frequency, and the second mode, with high frequency, exist simultaneously during the transition through the hypersonic boundary layer. This paper proposes a novel bi-frequency synthetic jet to suppress low- and high-frequency disturbances at the same time. Orthogonal table and variance analyses were used to compare the control effects of jets with different positions (USJ or DSJ), low frequencies (f1), high frequencies (f2), and amplitudes (a). Linear stability analysis results show that, in terms of the growth rate varying with the frequency of disturbance, an upstream synthetic jet (USJ) with a specific frequency and amplitude can hinder the growth of both the first and second modes, thereby delaying the transition. On the other hand, a downstream synthetic jet (DSJ), regardless of other parameters, increases flow instability and accelerates the transition, with higher frequencies and amplitudes resulting in greater growth rates for both modes. Low frequencies had a significant effect on the first mode, but a weak effect on the second mode, whereas high frequencies demonstrated a favorable impact on both the first and second modes. In terms of the growth rate varying with the spanwise wave number, the control rule of the same parameter under different spanwise wave numbers was different, resulting in a complex pattern. In order to obtain the optimal delay effect upon transition and improve the stability of the flow, the parameters of the bi-synthetic jet should be selected as follows: position it upstream, with f1 = 3.56 kHz, f2 = 89.9 kHz, a = 0.009, so that the maximum growth rate of the first mode is reduced by 9.06% and that of the second mode is reduced by 1.28% compared with the uncontrolled state, where flow field analysis revealed a weakening of the twin lattice structure of pressure pulsation.

This study investigates the stability of compressible swirling wake flows including the viscous effects using linear stability theory. A spatial stability analysis is performed to evaluate the influence of the axial velocity deficit and circulation as well as the Reynolds number and Mach number as the main parameters that affect the instability. The growth rates of the unstable modes at several azimuthal wavenumbers are compared. The maximum growth rates and their dependency with respect to each parameter are analyzed. It is confirmed that the instability monotonically increases as the axial velocity deficit increases. For small axial velocity deficit, characteristics that are different from the results reported using inviscid analysis are identified and analyzed. Additionally, a decrease in instability is observed as the viscous and compressibility effects become stronger. In terms of circulation, it is confirmed that there is a certain region of circulation that exhibits maximum instability. The stability analysis is expected to serve as a part of a useful methodology for preliminary design and parametric study for engineering problems such as vortex generators in high-speed flows, owing to both efficiency and accuracy. [ABSTRACT FROM AUTHOR]

The intrinsic instability of three furan derivatives, namely, 2-acetylfuran (AF), 2-ethylfuran (EF), and 2-methylfuran (MF), is experimentally and theoretically investigated and compared. A deep-learning-based end-to-end system is used to segment the cells and measure the crack length on the cellular flame front of the spherically expanding flame to quantitively investigate the flame morphology. Moreover, the flame front radius profile is quantitively investigated to shed light on the correlation between disturbance amplitude and flame radius. With the use of the linear stability model, the theoretical critical flame radius and Peclet number are obtained and compared to their corresponding experimental results to characterize the outset of cellularization and evaluate the flame instability propensity. Our analysis shows that compared with AF and EF, MF is prone to cellularization at a smaller flame radius and has a faster cell proliferation rate and crack length growth rate before reaching the hydrodynamic saturation limit. Meanwhile, the average area of saturated cells tends to be similar for the three furan derivatives. Furthermore, AF premixed flame does not exhibit cellularization before the flame radius is less than 45 mm in low initial pressure. [ABSTRACT FROM AUTHOR]

Precisely predicting laminar-turbulence transition locations is essential for improvements in hypersonic vehicle design related to flow control and heat protection. Currently state-of-the-art e N prediction method requires the evaluation of discrete normal modes F and S for the growth rate of instability wave. Meanwhile, in receptivity studies, both the discrete and continuous modes, including acoustic, entropy, and vorticity modes, contribute to the generation of the initial disturbance. The purpose of this paper is to introduce a new very high-order numerical method to accurately compute these normal modes with finite-difference on a non-uniform grid. Currently, numerical methods to obtain these normal modes include two major approaches, the boundary value problem approach and the initial value problem approach. The boundary value approach used by Malik (1990) [17] deploys fourth-order finite difference and spectral collocation methods to solve a boundary value problem for linear stability theory (LST). Nonetheless, Malik's presentation only demonstrated the computation of discrete modes, but not the continuous modes essential for conducting modal analysis on receptivity data. To obtain the continuous spectrum for his multimode decomposition framework, Tumin (2007) [16] relies on an initial value approach based on the Runge Kutta scheme with the Gram-Schmidt orthonormalization. However, the initial value approach is a local method that does not give a global evaluation of the eigenvalue spectra of discrete modes. Furthermore, Gram-Schmidt orthonormalization, which can be error-prone in implementation, is required at every step of the integration to minimize the accumulation of numerical errors. To overcome the drawbacks of these two approaches, this paper improves the boundary value approach by introducing a new general very high-order finite difference method for both discrete and continuous modes eigenfunctions. This general high-order finite difference method is based on a non-uniform grid method proposed by Zhong and Tatineni (2003) [22]. Under the finite difference framework, discrete and continuous modes can be obtained by imposing proper freestream asymptotic boundary conditions based on the freestream fundamental solution behavior. This asymptotic boundary condition is used for obtaining both discrete and continuous modes that have both distinct (acoustic) and similar (vorticity and entropy) eigenvalues. Extensive verification of the new method has been carried out by comparing the computed discrete and continuous modes. Subsequently, the discrete and continuous modes obtained with this finite difference method are essential for the bi-orthogonal decomposition, which holds promising potential in obtaining an accurate evaluation of receptivity coefficients. The result of the bi-orthogonal decomposition for a hypersonic boundary layer flow over a flat plate is verified by comparing with existing results. Ultimately, the bi-orthogonal decomposition using the eigenfunctions has been applied to a case of freestream receptivity simulation for an axis-symmetric hypersonic flow over a blunt nose cone with modal contributions computed as coefficients for receptivity analysis. • General very high-order finite difference method which can be tuned to high-order accuracy with sparsity. • Adaptable numerical method to both global and local eigenvalue problem for discrete modes in linear stability theory. • Unified approach capable of computing discrete and continuous normal modes essential for bi-orthogonal decomposition. • Direct discretization on the non-uniform grid to achieve high-order accuracy while maintaining stencil stability. [ABSTRACT FROM AUTHOR]

2-ethylfuran (2 EF) has potential as a biofuel for combustion devices. To apply it efficiently in combustion devices, it is necessary to study the combustion characteristics such as the intrinsic flame instability of 2 EF. The intrinsic flame instabilities of 2 EF outwardly propagating spherical premixed flames were theoretically and experimentally studied at initial temperatures of 373, 403, and 433 K, pressures of 1, 2, and 4 bar, and equivalence ratios of 0.7–1.4. The flame topography at different stages of flame development was examined. When large cracks appeared on the flame front surface, resulting in small cracks and new cell generation, the flame became unstable. Linear stability theory was used to investigate the effects of hydrodynamic instability and thermal-diffusion instability on the flame. The critical stability curves were plotted, and the theoretical calculations were consistent with the experimental results. The results showed that the best fits for the theoretical and experimental results were n = 2π Pe /48 and n = 2π Pe /80, respectively. The critical radius and Peclet number are calculated and discussed. The critical Peclet number decreased as the equivalence ratio increased. [ABSTRACT FROM AUTHOR]

The results of investigation of the stability of the near-wall flow in a supersonic flow around a flat plate with a section of gas suction from the boundary layer through the wall are presented. The suction system is usually considered as a way for stabilizing the boundary layer and delaying the laminar–turbulent transition, which operates at subsonic and low supersonic speeds. Here, the effect of suction on the development of instabilities in the boundary layer is investigated at high supersonic speeds. The laminar flow around a plate with a section of constant suction of different intensity is modeled numerically by integrating the Navier–Stokes equations. The instabilities in the boundary layer distorted by suction are analyzed within the framework of the linear stability theory using the eN method. High-frequency disturbances related to plane waves of the second Mack mode, which is most unstable at high velocities, are considered. It is found that the instabilities over the suction section can anomalously be amplified more strongly than in the case without suction. [ABSTRACT FROM AUTHOR]

Sustained flight at hypersonic speeds is characterized by high pressure and aerothermal loads imposed on the structure of the aerodynamic vehicle. A consequence of lightening the structural design permits fluid–structure interaction phenomena that can significantly alter the flow and initiate unsteady structural responses. We investigate the coupling between high-speed laminar boundary layer flows over a mechanically compliant panel and analyze the dynamic system response of the coupled system to boundary layer instabilities by means of local convective linear stability analysis. The resulting non-dimensional interaction parameters describing the compliant system are shown to affect the boundary layer instabilities in the infinitely thin panel limit, and the transition from the rigid limit is described by two distinctly different responses: (a) a piston-like, one-dimensional panel deflection, or (b) a synchronization with flexural waves. Compliance is shown to non-monotonically change convective wave growth rates and induce uncertainty in the integrated N-factors. [ABSTRACT FROM AUTHOR]

Based on the database from linear stability theory (LST) analysis, a local amplification factor transport equation for stationary crossflow (CF) waves in low-speed boundary layers was developed in 2019. In this paper, the authors try to extend this transport equation to compressible boundary layers based on local flow variables. The similarity equations for compressible boundary layers are introduced to build the function relations between non-local variables and local flow parameters. Then, compressibility corrections are taken into account to modify the source term of the transport equation. Through verifications of different sweep angles, Reynolds numbers, angles of attack, Mach numbers, and different cross-section geometric shapes, the rationality and correctness of the new transport equation established in this paper are illustrated. [ABSTRACT FROM AUTHOR]

A submerged air jet of circular cross section of 0.12 m in diameter and a long laminar region (~5 jet diameters) is obtained experimentally at the Reynolds number of 5400. Within the linear analysis of stability, two branches of growing perturbations are found, which are generated by three inflection points on the experimental jet profiles. The frequency ranges of perturbations, as well as their growth rates and wavelengths are obtained. Experiments on introducing controlled perturbations into the jet with a long laminar portion are conducted. The characteristics of waves amplified in experiments due to the introduction of perturbations prove to be close to the predictions of the linear theory of stability. Thus, the applicability of the linear stability theory to the submerged jet is validated experimentally. [ABSTRACT FROM AUTHOR]

The paper presents parametric studies of the first and second azimuthal absolute modes in annular non-swirling and swirling jets. The spatio-temporal linear stability analysis is applied to investigate an influence of governing parameters including axial velocity gradients in inner and outer shear layers, back-flow velocity, swirl number and shape of the azimuthal velocity. A new base flow is formulated allowing a flexible variation of the shape of axial and azimuthal velocity profiles. It is shown that the first helical absolute mode is governed mainly by the back-flow velocity and swirl intensity. A steepness of the inner shear layer can control the absolute mode frequency. The velocity gradient in the outer shear layer and the shape of the azimuthal velocity have rather limited impact on the absolute mode characteristics. Finally, it is shown that the second helical absolute mode can dominate the flow with a stronger swirl intensity. [ABSTRACT FROM AUTHOR]

The interaction of a laminar boundary layer with a shock wave at a Mach number M = 1.43 is studied by numerical simulation. The results obtained by direct numerical simulation are compared with the results of calculations using the Reynolds-averaged Navier–Stokes (RANS) equations supplemented with different turbulence models describing laminar–turbulent transition. The possibility of determining the position of the flow turbulence zone based on linear stability theory and the e N -method is estimated. Comparison of the numerical simulation with experimental data shows that engineering RANS methods can be used to study supersonic flows in which transition to turbulence occurs in regions of shock wave–boundary layer interaction. [ABSTRACT FROM AUTHOR]

The influence of a local change in surface temperature of a contoured nozzle corresponding to the Mach number M = 6 on the boundary layer stability and laminar-turbulent transition is numerically studied. The profiles of the laminar boundary layer are obtained by solving the Navier-Stokes equations with the use of the Ansys Fluid software system. N-factors of the growth rates of the Goertler vortices and also disturbances of the first and second Mack modes are calculated in the approximation of the linear stability theory. It is demonstrated that local heating ensures lower growth rates of the amplitudes of the Goertler vortices and the first Mack mode as compared to the base case; the more intense the heating, the more expressed this effect. The growth rate of the amplitude of the second-mode disturbances decreases during local heating of the nozzle to a temperature close to the stagnation temperature and increases at higher temperatures of local heating. It is found that local cooling leads to an increase in the growth rates of the amplitudes of the Goertler vortices and second Mack mode. The amplitude of the first Mack mode in the cooling region is smaller than that in the base case; however, further downstream, it is much greater than that in the base case. It is found that the surface of contoured nozzles should be heated in the region of the maximum growth rates of the amplitudes of the Goertler vortices; the higher the temperature, the more pronounced the expected effect. However, the maximum possible temperature is determined by the growth of the second Mack mode. The optimal option is to use the temperature of local heating of the surface at which the growth rate of the amplitude of the second mode is smaller than that of the Goertler vortices. [ABSTRACT FROM AUTHOR]

Surface instability of a swirling liquid sheet emanating from a centrifugal injector in presence of external and internal gas flows is studied in this paper. A three-dimensional flow for the liquid sheet and two-dimensional flows for external and internal gas flows are considered. The set of equations involved in this analysis differs from the earlier analyzes. In previous studies, a cylindrical liquid sheet has been considered to implement the linear theory but in this study, the linear stability theory is implemented on a coneshaped liquid sheet for different cone angles. Actually more over than axial and tangential movements, the radial movements of liquid sheet and gas flows are considered in the present model. Due to complexity of the derived governing equations, semi-analytical and numerical methods were applied to solve them. The case study is oxidizer injector of rocket engines. Implementation of linear stability theory on a hollow cone-shaped liquid sheet better can predict instability phenomenon than the general linear stability analysis for this type of liquid sheets. The results show very close agreement with available experimental data. [ABSTRACT FROM AUTHOR]

Featured Application: This work can be used in autonomous driving control systems to alleviate traffic congestion. Although the difference between the velocity of two successive vehicles is considered in the full velocity difference model (FVDM), more status information from preceding vehicles affecting the behavior of car-following has not been effectively utilized. For improving the performance of the FVDM, an extended modified car-following model taking into account traffic density and the acceleration of a leading vehicle (DAVD, density and acceleration velocity difference model) is presented under the condition of vehicle-to-vehicle (V2V) communications. Stability in the developed model is derived through applying linear stability theory. The curves of neutral stability for the improved model indicate that when the driver pays more attention to the traffic status in front, the traffic flow stability region is larger. Numerical simulation illustrates that traffic flow disturbance could be suppressed by gaining more information on preceding vehicles. [ABSTRACT FROM AUTHOR]

A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline functions with polynomial augmentation (PHS+poly) are used to construct the discrete linearized incompressible and compressible Navier-Stokes operators on scattered nodes. Rigorous global and local eigenvalue stability studies of these global operators and their constituent RBF stencils provide a set of parameters that guarantee stability without the need for hyperviscosity or other ad hoc regularizations, while balancing accuracy and computational efficiency. Specialized elliptical stencils to compute boundary-normal derivatives are introduced, and the treatment of reflectional and rotational symmetries is discussed. In particular, treating the pole singularity in cylindrical coordinates permits dimensionality reduction from 3D to 2D in rotational flows like jets. The numerical framework is demonstrated and validated on several hydrodynamic stability methods ranging from classical linear theory of laminar flows to state-of-the-art non-modal approaches that are applicable to turbulent mean flows. The examples include linear stability, resolvent, and wavemaker analyses of cylinder flow at Reynolds numbers ranging from 47 to 180, and resolvent and wavemaker analyses of the self-similar flat-plate boundary layer at a Reynolds number as well as the turbulent mean of a high-Reynolds-number transonic jet at Mach number 0.9. All previously-known results are found in close agreement with the literature. Finally, the resolvent-based wavemaker analyses of the Blasius boundary layer and turbulent jet flows offer new physical insight into the modal and non-modal growth in these flows. • Radial basis function framework for hydrodynamic stability analysis. • Accurate, stable, and efficient discretizations of large eigenvalue problems. • Treatment of boundary conditions and pole singularity for scattered nodes. • Validated for various stability theoretical methods and three benchmark problems. • Resolvent-based wavemaker analysis for Blasius boundary layers and turbulent jets. [ABSTRACT FROM AUTHOR]

Inelastic time-dependent fluids display continuous and reversible changes in viscosity when subjected to a constant shear-rate. These alterations arise from the gradual modification of the material's microstructure due to shear-induced effects, known as shear rejuvenation. When this process generates smaller structural units, it is termed thixotropy; conversely, if it produces larger units, it is labeled anti-thixotropy. Aging is another characteristic of such fluids, denoting the capacity of the material to regain its original structure in the absence of shear, thus reversing the initial time-dependent change. This phenomenon often results from thermally activated Brownian motion prompting the reorganization of the material's microconstituents. Consequently, attractive forces between these components can instigate the reconstruction of a network-like structure within the material. This study centers on investigating how variations in fluid microstructure impact the onset of transition to turbulence in a flat plate boundary-layer flow. Specifically, the focus is on cases where larger structural units emerge during the breakdown process (anti-thixotropy). To represent such fluids, the Quemada model, an inelastic structural-kinetic model, is employed. This model effectively captures thixotropy and anti-thixotropy by appropriately configuring model parameters. The analysis begins with obtaining a local similarity solution for the generalized Blasius equation, representing the base flow. Subsequently, the stability of this flow is assessed using linear temporal stability theory. This involves introducing infinitesimally-small normal-mode perturbations to the base flow, yielding the generalized Orr–Sommerfeld equation. Solving this equation using the spectral method provides insights into stability. Results from this study indicate that for low Deborah numbers, the shear-thickening behavior prevails, causing destabilization. In contrast, higher Deborah numbers lead to stability. This implies that anti-thixotropy effectively delays the onset of transition to turbulence and could hold practical applications for flow control. • Stability of anti-thixotropic boundary-layer over a flat plate is investigated. • Quemada model, a structural-kinetic model, is adopted as the rheological model. • Generalized Blasius and Orr–Sommerfeld equations for a Quemada fluid are derived. • Results show that anti-thixotropy can delay onset of transition to turbulence. [ABSTRACT FROM AUTHOR]

The joint effect of pulsating throughflow and external electric field on the outset of convective instability in a horizontal porous medium layer saturated by a dielectric nanofluid is investigated. Pulsating throughflow alters the basic profiles for temperature and the volumetric fraction of nanoparticle from linear to nonlinear with layer height, which marks the stability expressively. To treat this problem, the Buongiorno’s two-phase mathematical model is used taking the flux of volumetric fraction of nanoparticle is vanish on the horizontal boundaries. Using the framework of linear stability theory and frozen profile approach, the stability equations are derived and solved analytically applying the Galerkin weighted residuals method with thermal Rayleigh-Darcy number as the eigenvalue. The effect of increasing the external AC electric Rayleigh-Darcy number , the modified diffusivity ratio and the nanoparticle Rayleigh number is to favorable for the convective motion, while the Lewis number and porosity parameter have dual influence on the stability scheme in the existence of pulsating throughflow. The frozen profile method shows that the result of pulsating throughflow in both directions is stabilizing. An enlarged amplitude of throughflow fluctuations offers to increased stability by an amount that vary on frequency. It is also found that the oscillatory mode of convection is not favorable for nanofluids if the vertical nanoparticle flux is vanish on the boundaries.

Stability of detonation waves (DWs) propagating in a plane or rectangular channel with respect to two-dimensional and three-dimensional disturbances is considered. Accepting a simple hypothesis that the most unstable mode of the linear theory continues to dominate even in the nonlinear regime, one can derive a number of fairly definite predictions of the developed DW structure from the linear stability theory. In particular, the theory predicts the number of detonation cells formed in a channel of a specified size and the cell size, the minimum size of the channel in which the multifront DW structure can still exist, and the parameters at which the number of cells changes in a jump-like manner. All these predictions are qualitatively consistent with available experimental data and numerical results. [ABSTRACT FROM AUTHOR]

Stability of the laminar boundary layer on the surface of a hypersonic nozzle for the Mach number M = 6 of the Transit-M wind tunnel is calculated. The laminar boundary-layer profiles are obtained by solving the Navier-Stokes equations numerically within the framework of the Ansys Fluent software. N-factors of the Goertler vortices and of the first and second Mack modes are obtained in the approximation of the linear stability theory. It is demonstrated that the Goertler vortices are the most unstable disturbances for the nozzle under consideration. Empirical dependences of the local Reynolds number of the laminar-turbulent transition on the N-factor and unit Reynolds number are determined. [ABSTRACT FROM AUTHOR]

Laminar-turbulent transition caused by modal disturbance growth in the wake flow of isolated roughness elements on blunt re-entry capsules is studied numerically at typical cold hypersonic wind-tunnel conditions. Two fundamentally different heat shield shapes are considered. On the sphere-cone forebody the wake flow of the roughness is exposed to an adverse pressure gradient, whereas the spherical heat shield exhibits a strongly favorable pressure gradient. The pressure gradient effects on the development of the stationary wake flow and its modal instability characteristics are discussed for various heights and diameters of the cylindrical roughness element. Regions of increased shear develop in its wake, which persist longer in the adverse pressure gradient case. Consequently, the results of spatial two-dimensional eigenvalue analyses reveal that the unstable wake-flow region extends much further downstream and the wake-mode instabilities are considerably more amplified. The disturbance kinetic energy production terms are used to assess the contributions of the different shear-layer regions to the mode growth and its dependence on the pressure gradient. [ABSTRACT FROM AUTHOR]

In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number H S , the modified diffusive ratio N A and the nanoparticle Rayleigh number R N is to quicken the convective motion, while the Lewis number L e has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number P m is not greater than unity. [ABSTRACT FROM AUTHOR]

Exceptional megaflood-scale bedforms on Earth are commonly associated with the catastrophic draining of glacial lakes in the late Pleistocene. The widest studied events have been the Missoula and Altai floods with 300–700 m flow depth, 1–20 m bedform height and 10–300 m wavelength. Nowadays, the Saint-Venant equations have succeeded at simulating the catastrophic glacial-lake drainage process numerically, but we still lack a depth-averaged morphodynamic theory able to predict the growth of dunes and antidunes. The disparity of spatial scales in megafloods prevents the use of non-depth-averaged rotational flow equations, motivating the present shallow-water theory for the formation of megaflood-scale bedforms. We adopt a non-equilibrium sediment transport equation rooted in Einstein's pioneering work. Here we prove that the bed instability triggers to form dunes and antidunes simply by lagging the entrainment term for sediment mass conservation, or the bottom shear stress, with respect to the depth-averaged flow velocity. We formalise this result using a linear stability theory that captures the existence regions of dune and antidune in addition to the roll wave instability. Furthermore, in the spirit of Kennedy (Annu. Rev. Fluid Mech. , vol. 1, 1969, pp. 147–168), we derive a closed-form solution of growth rate and wave speed of the bedform. The nondimensional groups controlling the linear instabilities are the Froude number, ℱ r , the Shields parameter, Sh , and the grain roughness relative to flow depth, d. Subsequently, we simulate the drainage of the largest Missoula flood numerically to explain the formation of giant antidunes in the Camas Prairie (Montana, US) during the late stage of the megaflood. Also considered are large fields of gravel dunes in the Kuray-Chuja Lake Basin (Altai Mountains, Siberia). The simulated hydraulic conditions over bedforms in both basins yield values of the nondimensional parameters that lie in the theoretical region of dunes and antidunes according to the proposed theory and in situ measurements in sandy rivers and flume experiments. [ABSTRACT FROM AUTHOR]

• Critical Reynolds analysis for different polymer concentration and elastic forces; • Influence of Polymer concentration (covering a wide range) on the stability; • Direct Numerical Simulation of non-stationary Non-Newtonian fluid flow; • Visualization of the disturbances distribution of each variable; • Disturbance structure changes with low beta parameter and high Weissenberg numbers. Several flows of practical interest are of viscoelastic fluids and it is desirable to know if these flows are in a laminar or turbulent state. In this paper, the laminar-turbulent transition is studied in which the convection of Tollmien–Schlichting waves is investigated for the incompressible two-dimensional flow between two parallel plates. The viscoelastic fluid adopted is modeled by the Oldroyd-B constitutive equation. Direct Numerical Simulation (DNS) and Linear Stability Theory (LST) were used to verify the stability of the viscoelastic fluid flow to unsteady disturbances. In the DNS formulation, the governing equations are discretized by high-order compact finite difference schemes for the spatial derivatives, while time integrations are carried out by a fourth order Runge–Kutta method. For the LST analysis, the Orr–Sommerfeld equation is modified to include viscoelastic effects and solved by a shooting method. In order to evaluate the flow stability when submitted to unsteady disturbances and to find the neutral stability curves, a range of numerical simulations was performed with different dimensionless parameters for the viscoelastic fluid flow and the results were compared with the Newtonian fluid flow. The influence of the elastic forces and the amount of the polymer concentration in the fluid were investigated. A wide range of polymer concentration was studied. The results show that the variation of the critical Reynolds number may be monotonic for certain conditions. The DNS simulations were carried out, and the amplification rates obtained were compared with the LST results, with a very good agreement. The DNS results allow also the visualization of the disturbances variation in streamwise and wall-normal directions, showing the behavior of the velocity components, vorticity and the non-Newtonian extra-stress tensor components. The DNS results show a significant change in flow structure for certain combinations of the polymer concentration and elastic forces parameters. [ABSTRACT FROM AUTHOR]

Abstract A transonic wind tunnel transition test is implemented on a fuselage-wing configuration with the sweep angle 35 ∘ for commercial aircraft. The wide range of angle of attack from − 3.69 ∘ to 3.07 ∘ assures that with increasing angle of attack, the laminar to turbulent transition dominant factor varies from cross-flow (CF) vortices to Tollmien-Schlichting (TS) waves. With linear stability theory, the limiting N-factors are calibrated based on the pressure distribution by experiment or the Reynolds Averaged Navier-Stokes (RANS) solver using the fixed experimental transition location. The pressure distribution of the RANS solver agrees well with the experiment in general except some small discrepancies, which causes deviation by 0.6 for the limiting TS N-factor. The RANS solver and the stability analysis provide the limiting N-factors of 7.0 and 8.7 for CF-vortices and TS-waves at the two sides, respectively. In the between, the TS value decays with the CF value due to their interaction. Thus, the transition criterion for limiting N-factors is established for the laminar prediction tool of e N method at similar transonic wind tunnel. With the transition criterion, the transition location difference for 95% cases between the simulation and the experimental data is lower than 5% chord. The good match illustrates that the transition tool is accurate and robust for engineering applications, and also verifies the reasonability of the limiting N-factors. Therefore, the transition criteria at similar transonic conditions and well-performed e N transition tool can be applied for the future laminar wing design. [ABSTRACT FROM AUTHOR]

Highlights • The initial stage of annular gas-liquid flow is studied using two optical techniques. • Just below the inlet, thick film covered with two-dimensional quasi-regular initial waves is observed. • Break-up into 3D-waves which coalesce into quasi-2D disturbance waves occurs further downstream. • The characteristics of the initial waves are measured at the linear growth stage. • Linear stability theory gives reasonable agreement with the measured frequency and velocity of the waves. Abstract The initial stage of downward co-current annular flow was studied using two optical techniques: brightness-based laser-induced fluorescence technique and shadow technique. The experiments were conducted in a circular pipe and in a rectangular duct. The working area was represented by the first few centimetres from liquid inlet; the latter was organised as a tangential slot. The process of formation of disturbance waves was found to consist of three stages: formation of regular initial two-dimensional high-frequency waves; fragmentation into localised irregular three-dimensional waves and formation of large-scale quasi-two-dimensional disturbance waves. All the stages occur closer to the inlet at higher gas velocities and lower liquid flow rates. It was found that the initial two-dimensional waves appear at the initial area of thick film in the vicinity of the inlet. Spatiotemporal measurements were conducted and spectral and statistical approaches were applied to study the characteristics of the initial waves at the linear growth stage. The obtained characteristics were compared to the linear stability calculations; the comparison showed satisfactory agreement for the frequencies and velocities of the initial waves after taking into account non-equilibrium film thickness at the inlet. [ABSTRACT FROM AUTHOR]