Inviscid Jet Research Articles

Inviscid jets driven by pressure maxima

Inviscid jets driven by pressure maxima

Swirling instability of coaxial liquid jet in gas surroundings

Linear instability analysis of an inviscid coaxial swirling jet is carried out by deriving an analytical dispersion relation of perturbation growth. The azimuthal Rankine vortex and the axial discontinuous velocity distribution are utilized as the jet basic flow. Due to the existence of double interfaces, the instability mechanisms of the coaxial swirling jet are much more complex than those of the single-layered swirling jet. The effects of control parameters (including the swirling ratio, the Weber number, the jet radius ratio, the velocity ratios between different fluids, and the azimuthal velocity jump at the inner interface) on the temporal instability of coaxial swirling jet with different azimuthal modes are studied. By comparing the growth rate of different azimuthal modes, the predominant mode that determines the jet breakup is identified. The results indicate that an increase in the swirling ratio, the Weber number, and the radius ratio can lead to predominant mode transition to larger azimuthal wavenumbers. The velocity ratio between the inner jet and the annular jet and that between the surrounding fluid and the annular jet mainly affect the axial Kelvin–Helmholtz (KH) instability. An enhancement of the KH instability leads to the jet breakup with smaller azimuthal wavenumbers. The azimuthal velocity jump affects the azimuthal KH instability, the centrifugal instability, and the Coriolis instability simultaneously, thus leading to a multiple influence on modes transition. The phase-diagram of the predominant modes is further given, showing that the relative importance between the centrifugal force and the interfacial tension plays a significant role on the transition of predominant modes.

Orbital stability of solitary waves on a ferrofluid jet

We prove the orbital stability of small-amplitude axisymmetric solitary waves on the surface of an incompressible, inviscid ferrofluid jet. The ferrofluid surrounds a current-carrying rod and is subject to the azimuthal magnetic field generated by the rod. We show that under appropriate assumptions on the magnitude of the magnetic intensity in the ferrofluid, both the trivial flow and the solitary waves with strong surface tension are conditionally orbitally stable, while the conditional orbital stability of solitary waves with near-critical surface tension can be deduced from properties of the corresponding dispersive PDE model equation. The arguments are based on the recent orbital stability results for internal waves by Chen and Walsh (2022) and an improved version of the Grillakis–Shatah–Strauss method introduced by Varholm et al. (2020).

Prediction of Mach stem height in compressible open jets. Part 1. Overexpanded jets

The flow from a supersonic nozzle when operated at off-design conditions exhibits a wide variety of complex flow structures. The prominent ones are the shock reflections inside the jet. The two main types of shock interactions are the regular reflection (RR) and Mach reflection (MR). The prominent characteristic change in the shock pattern when an RR transforms into an MR is the appearance of the Mach stem with a subsonic region downstream of it. The estimation of the Mach stem height gives the size of the subsonic domain and is a direct method to predict the transition from RR to MR or vice versa. The present study is carried out to estimate the size of the Mach stem in an inviscid jet in the overexpanded regime. The analytical methods employed here are the extension of the techniques developed to estimate the Mach stem size in the wedge flows by Li & Ben-Dor (J. Fluid Mech., vol. 341, 1997a, pp. 101–125), Mouton & Hornung (AIAA J., vol. 45, issue 8, 2007, pp. 1977–1987) and Bai & Wu (J. Fluid Mech., vol. 818, 2017, pp. 116–140). The results from the analytical formulation have been compared with the high resolution computational and experimental results. The analytical method reveals that the open jet has a unique, stable MR configuration and forms an upper limit for achievable Mach stem height for the wedge flows. Apart from the estimation of Mach stem height, the growth rates of Mach stem where the RR–MR transition takes place are also calculated and compared with the ones corresponding to wedge flows.

Aerodynamic Modelling of the Airfoil Immersed in Two-Dimensional Jet Flow

In order to study the aerodynamic interaction of the airfoil and jet flow, the free streamline model and the panel method are combined to develop a fast calculation method for the airfoil in two-dimensional inviscid jet flow. The vortex strength and position of the jet boundary are determined by using the free streamline model and the constant total pressure difference assumption, the circulation of the airfoil is solved by the vortex panel method, and the whole process is coupled by relaxation iteration. Firstly, the convergence and effectiveness of the present method are verified. Next, the influence of the length ratio of jet height to airfoil chord, the velocity ratio of jet velocity to freestream velocity, and the ground effect on airfoil aerodynamics are studied. The results show that the aerodynamic characteristics of the airfoil in finite width jet flow and in freestream have a large difference, and it is important to consider the jet deflection for jet/airfoil interaction. In jet flow, the velocity ratio can be regarded as an aerodynamic similarity parameter for the airfoil. When the jet flow is deflected, the airfoil will not only generate lift but also drag, and the ground effect can be used to decrease drag. The developed method in this paper can not only capture the jet deflection but also has higher calculation efficiency than Computational Fluid Dynamic (CFD), which is beneficial for the preliminary design of a powered-lift device.

Calculation and analysis of aerodynamic characteristics for airfoils immersed in two-dimensional jet flow

In order to study the aerodynamic interaction of the airfoil and jet flow, the free streamline model and the panel method are combined to establish a calculation method for the aerodynamic characteristics of the airfoil in a two-dimensional inviscid jet flow. Using the assumption of constant total pressure difference and free streamline model to determine the vortex strength and position of the jet boundary, the aerodynamic force of the airfoil is solved by the vortex panel method, and the whole process is calculated by relaxation iteration. Firstly, the relevant theory in this paper is introduced, and the convergence and effectiveness of the present method are also tested. Next, the influence of the position and the ratio of jet height to airfoil chord on airfoil aerodynamics in the jet flow are studied. Finally, the momentum theory is used to analyze the aerodynamic characteristics of the airfoil in the jet flow. The results show that the aerodynamic characteristics of the airfoil in the jet flow is quite different from that in the freestream. When the jet flow is deflected, the airfoil will not only generate lift but also drag. The method in this paper can be used to study the aerodynamic characteristics of the airfoil immersed in the jet flow.

Capillary ionic liquid electrospray: beam compositional analysis by orthogonal time-of-flight mass spectrometry

Orthogonal time-of-flight mass spectrometry has been used to characterize the kinetic energy and charged species distributions from an in vacuo electrospray ion source for four different ionic liquids at volumetric flow rates between 0.3 and 3.3 nanolitres per second. In all cases, the mass spectra revealed charged species consisting of singly charged and multiply charged ions as well as two broad, unresolved droplet distributions occurring in the 104 to 106 atomic mass unit per charge range. The mean jet velocity and mean jet breakup potential were established from analysis of the energy profile of the high mass-to-charge droplets. At the jet breakup point, we find the energy loss and the jet diameter flow rate dependence of the electrospray beam to be similar to that determined by Gamero-Castaño (Phys. Fluids, vol. 20, 2008, 032103; Phys. Rev. Fluids, vol. 8, 2021, 013701) for 1-ethyl-3-methylimidazolium bis(trifluromethylsulfonyl)imide at similar volumetric flow rates. Similar trends are observed for all four liquids over the flow regime. A jet instability analysis revealed that jet electrification and viscous effects drive the jet breakup from the case of an uncharged, inviscid jet; jet breakup occurs at droplet and jet radius ratios that deviate from 1.89. Using the analytically determined ratio and the beam profile, different species are modelled to reconstruct the mass spectra; primary droplets constitute only a fraction of the total species present. The populations of the species are discussed.

Transition from absolute to convective instability in a compound jet

A spatiotemporal analysis is performed for an incompressible and inviscid compound jet moving in an unbounded inviscid static medium in this article. A detailed parametric study is carried out to explore the transition from absolute to convective instability for different operating conditions. The absolute and convective regions are shown through four plots: (i) inner density ratio (Qi) and Weber number (We), (ii) outer density ratio (Qo) and Weber number (We), (iii) surface tension ratio (σ) and Weber number (We) and (iv) radius ratio (λ) and Weber number (We). There exists a critical Weber number below which the compound jet becomes absolutely unstable and above which the compound jet becomes convectively unstable. The present results complement the existing results and give a complete theoretical understanding of the compound jets instability behavior.

Acoustic Wave Generation from Two-Dimensional Supersonic Inviscid Jet Impinging on Inclined Plate

This study numerically analyzes the interaction between a two-dimensional supersonic inviscid jet impinging on an inclined flat plate and the inlet disturbance using a simplified model depicting the rocket launch acoustic noise. The jet is a correctly expanded Mach 1.8 supersonic jet, the plate angle is 45 deg, and the nozzle–plate distance is five times the nozzle height. Three types of acoustic waves, namely, 1) a wave propagating normal to the wall, 2) a wave propagating upstream from the top and bottom of the plate shock, and 3) a wave propagating omnidirectionally from the first tail shock, which are consistent with those in Akamine’s experiment, are observed. The acoustic wave generation mechanisms are 1) a rapid growth of pressure amplitude downstream of the plate shock, 2) a deformation of the plate shock accompanied with the oscillation of the stagnation pressure, and 3) a cyclic pressure fluctuation due to the cyclic change in the shock structure near the first tail shock. Although the flowfield studied is simple compared with the actual rocket launch flow environment, the mechanism revealed in this study will provide a useful insight into understanding the sound generation mechanism in a complicated three-dimensional turbulent impinging jet.

Linear Instability of Inviscid Jets with Thermo-Capillarity

Linear Instability of Inviscid Jets with Thermo-Capillarity

A moving particle semi‐implicit method for free surface flow: Improvement in inter‐particle force stabilization and consistency restoring

AbstractThe moving particle semi‐implicit (MPS) method has been widely applied in free surface flows. However, the implementation of MPS remains limited because of compressive instability occurred when the particles are under compressive stress states. This study proposed an inter‐particle force stabilization and consistency restoring MPS (IFS‐CR‐MPS) method to overcome this numerical instability. For inter‐particle force stabilization, a hyperbolic‐shaped quintic kernel function is developed with a non‐negative and smooth second order derivative to satisfy the stability criterion under compressive stress state. Then, a contrastive study is conducted on the contradiction between the common understanding of the conventional MPS hyperbolic‐shaped kernel function and its performance. The result shows that the conventional MPS hyperbolic‐shaped kernel function can easily cause violent repulsive inter‐particle force and then lead to the compressive instability. Therefore, the first order derivative of the modified hyperbolic‐shaped quintic kernel function is recommended as the form of the contribution of the neighbor particles to achieve a more stable inter‐particle repulsive force. For consistency restoring, the Taylor series expansion and the hyperbolic‐shaped quintic kernel are combined to improve the accuracy of the viscosity and pressure calculation. The IFS‐CR‐MPS algorithm is subsequently verified by the inviscid hydrostatic pressure, jet impacting, and viscous droplet impacting problems. These results can be used for choosing kernel function and the contribution of neighbor particles in particle methods. Copyright © 2016 John Wiley & Sons, Ltd.

Effect of surfactant on the break-up of a liquid thread: Modeling, computations and experiments

The effect of insoluble surfactant on the breakup of an inviscid jet surrounded by a viscous fluid at low Reynolds number is studied both theoretically and experimentally. Equations governing the evolution of the interface and surfactant concentration are derived using long wavelength approximations. Numerical simulations of this long-wave asymptotic model show that the presence of surfactant at the interface retards the pinch-off and a slender quasi-steady thread is formed. After the formation of the thread, the diffusion of surfactant plays an important role and causes the jet to pinch. Experiments are performed and the results are presented which show that the presence of surfactant slows down the breakup of the bubble. We used high speed digital imaging to capture details of the pinching bubble in a glycerol/water mixture in the absence or presence of surfactants. Digitized video images of bubble elongation are captured sequentially in time and analyzed using image analysis software. It is found that the presence of surfactant slows down the breakup of a jet in a highly viscous exterior fluid. Experimental findings are in agreement with the theoretical and computational results.

Modeling the atomization of high-pressure fuel spray by using a new breakup model

The main objective of this research is to develop a new breakup model and investigate the influence of cavitation, turbulence on processes of high-pressure diesel sprays. The model distinguishes between jet primary atomization and droplet secondary atomization. The primary atomization was simulated based on a modified turbulence induced atomization model taken into account the coupling effects of the relaxation of the velocity profile, cavitation and turbulent fluctuation based on the principle of conservation of energy. The growth time scale of surface waves was provided by Kelvin–Helmholtz (K–H) instability theory on an infinite length cylinder for an inviscid liquid jet. The time scale of initial surface waves based on K–H instability theory on an infinite plane jet is much larger than that based on infinite length cylindrical jet. Based on the present modified model, the weighting coefficients of turbulence and cavitation on the overall atomization can be distinguished clearly. There was remarkable variation in simulated spray shape with present models. It could be seen that the original turbulence induced atomization model results in a shorter spray penetration and smaller drops near the spray core than the modified model. When applying the turbulent weighting coefficient Ct in the determination of the spray angle, the resultant value of spray angle gradually drops due to the reduction of Ct. However, the spray angle increases with increasing the cavitation weighting coefficient Ccav. Comparing the experimental results (such as spray angle, tip penetration and spray shape) with the theoretical ones for different injection pressure, gives a reasonable agreement.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Electro-viscous instability of a swirling compound jet

The aim of this work is to study the effects of a combination of axial and swirl velocity on the instability of an annular liquid jet. A linear instability analysis yields an analytical dispersion relation, which governs the temporal growth of perturbations to an electrified streaming annular viscous liquid jet coated by two cylindrical shells of streaming swirling inviscid gases. The three-layer system is subjected to an electric field normal to the interfaces. In our study, the electric body force vanishes, and the electric field and fluid dynamics are coupled only at the interfaces through the tangential and normal interfacial stress balance equations. The governing electrohydrodynamic equations, along with the hydrodynamic and electrical boundary conditions, are solved, and then the corresponding dispersion relation is obtained. The instability analysis of a inviscid jet is discussed as a special case. Numerical results on the effect of the various problem parameters on the instability and breakup of a liquid jet are presented. It is observed, for instance, that the swirling ratio of the outer gas layer always enhances the stability of flow in the case of axisymmetric disturbances, whereas it has a dual effect (destabilizing effect) corresponding to the case of asymmetric disturbances. It has been found that the higher electrical potential, the larger the maximum growth rate and critical wave number of the disturbances and, consequently, the initial applied electric potential tends the instability and breakup of the liquid jet.

Turned trochoidal disturbance on a liquid jet surface

This paper shows that a turned trochoidal function disturbance may lead to peripheral drops production. The resulting model is used to describe that a turned trochoidal disturbance leads to peripheral drops production on the liquid jet surface without the necessity for superimposed disturbances. The trochoid is a non-unique parametric function. Only non-unique parametric functions disturbances may lead to peripheral drops production. The trochoidal function disturbance is decomposed to Fourier series. Every Fourier element receives an amplification factor in accordance to the Rayleigh inviscid jet model. Peripheral drops are received on the jet surface. The paper shows that all trochoidal disturbance functions, prolate cycloid, cycloid and curtate cycloid have a capability of peripheral drops producing. A limited capability of peripheral drops production is introduced for the trochoidal curtate cycloid. Produced drops size are reduced for increasing the jet velocity and wave number. Smaller drops are also received by transition from the prolate cycloid to curtate cycloid disturbance.

Turned trochoidal disturbance on a liquid jet surface

This paper shows that a turned trochoidal function disturbance may lead to peripheral drops production. The resulting model is used to describe that a turned trochoidal disturbance leads to peripheral drops production on the liquid jet surface without the necessity for superimposed disturbances. The trochoid is a non-unique parametric function. Only non-unique parametric functions disturbances may lead to peripheral drops production. The trochoidal function disturbance is decomposed to Fourier series. Every Fourier element receives an amplification factor in accordance to the Rayleigh inviscid jet model. Peripheral drops are received on the jet surface. The paper shows that all trochoidal disturbance functions, prolate cycloid, cycloid and curtate cycloid have a capability of peripheral drops producing. A limited capability of peripheral drops production is introduced for the trochoidal curtate cycloid. Produced drops size are reduced for increasing the jet velocity and wave number. Smaller drops are also received by transition from the prolate cycloid to curtate cycloid disturbance.

Critical Layer Analysis of Stuart Vortices in a Plane Jet

Asymptotic techniques are used to model quasi-steady-state vortices in the plane (Bickley) inviscid jet. A nonlinear critical layer analysis is used to find a family of steady-state finite amplitude two-dimensional vortices which are based on the Stuart vortex.

Temporal instability analysis of inviscid compound jets falling under gravity

Compound liquid jets can be used in a variety of industrial applications ranging from capsule production in pharmaceutics to enhance printing methods in ink-jet printing. An appreciation of how instability along compound jets can lead to breakup and droplet formation is thus critical in many fields in science and engineering. In this paper, we perform a theoretical analysis to examine the instability of an axisymmetric inviscid compound liquid jet which falls vertically under the influence of gravity. We use a long-wavelength, slender-jet asymptotic expansion to reduce the governing equations of the problem into a set of one-dimensional partial differential equations, which describe the evolution of the leading-order axial velocity of the jet as well as the radii of both the inner and the outer interfaces. We first determine the steady-state solutions of the one-dimensional model equations and then we perform a linear temporal instability analysis to obtain a dispersion relation, which gives us useful information about the maximum growth rate and the maximum wavenumber of the imposed wave-like disturbance. We use our results to estimate the location and qualitative nature of breakup and then compare our results with numerical simulations.

A note on the stability of inviscid zonal jet flows on a rotating sphere

AbstractThe linear stability of inviscid zonal jet flows on a rotating sphere is re-examined. A semi-circle theorem for inviscid zonal flows on a rotating sphere is proved. It is also shown that numerically obtained eigenvalues of the linear stability problem do not converge well with a spectral method which was adopted in previous studies, due to an emergence of critical layers near the poles. By using a shooting method where the integral path bypasses the critical layers in the complex plane, the eigenvalues are successfully obtained with ${\ensuremath{\sim} }10\hspace{0.167em} \% $ correction of the critical rotation rates compared to those obtained in Baines (J. Fluid Mech., vol. 73, 1976, pp. 193–213).