Secondary Atomization of Droplets at Extreme Conditions

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.

In order to accurately analyze the secondary atomization phenomenon during fire-fighting jets, in this paper, the acceleration, deformation and breakup of droplets after secondary atomization are studied experimentally, and the characteristics of droplets after secondary atomization are studied. The critical flow rate of secondary water atomization was obtained. By analyzing the relationship between the factors affecting the secondary atomization characteristics and the number of atomized particles in the mixed crushing mode, the results show that the breaking angle decreases first and then increases with the increase of the we number; When 45 < we <60; the breaking angle is less than the average level, and the instantaneous breaking velocity decreases; The bag diameter before bag-like breaking generally decreases with the increase of the number of broken particles. The relationship between the characteristic quantity of atomization quality and the we number provides an experimental research basis for improving the fire extinguishing efficiency.

In this paper, laminar flow past a rotating circular cylinder placed in a compressible uniform stream is investigated via a two-dimensional numerical simulation and the compressibility effects due to the combination of the free-stream and cylinder rotation on the flow pattern such as forming, shedding, and removing of vortices and also the lift and drag coefficients are studied. The numerical simulation of the flow is based on the discretization of convective fluxes of the unsteady Navier-Stokes equations by second-order Roe’s scheme and an explicit finite volume method. Because of the importance of the time dependent parameters in the solution, the second-order time accurate is applied by a dual time stepping approach. In order to validate the operation of a computer program, some results are compared with previous experimental and numerical data. The results of this study show that the effects due to flow compressibility such as normal shock wave caused the interesting variations on the flow around the cylinder even at a free-stream with a low Mach number. At incompressible flow around the rotating cylinder, increasing the speed ratio, α (ratio of the surface speed to free-stream velocity), causes the ongoing increase in the lift coefficient, but in compressible flow for each free-stream Mach number, increasing the speed ratio results in obtaining a limited lift coefficient (a maximum mean lift coefficient). In addition, results from the compressible flow indicate that by increasing the free-stream Mach number, the maximum mean lift coefficient is decreased, while the mean drag coefficient is increased. It is also found that by increasing the Reynolds number at low Mach numbers, the maximum mean lift coefficient and critical speed ratio are decreased and the mean drag coefficient and Strouhal number are increased. However at the higher Mach numbers, these parameters become independent of the Reynolds number.

The turbulence in the viscous, compressible flow in a 3D wall-bounded channel, simulated using the direct simulation Monte Carlo (DSMC) method, has been used as a test bed for examining different aspects of transition and turbulence ([1, 2, 3]) at high Mach Ma = U_m / \\sqrt(gamma k_B T_w /m), and Reynolds numbers Re = (rho_m U_m H)/mu_w. Here, H is the channel half-width, U_m is the mean velocity, rho_m is the mean density, T_w is the wall temperature, m is the molecular mass, mu_w is the molecular viscosity based on the temperature at the isothermal wall, and k_B is the Boltzmann constant. The laminar-turbulent transition is accompanied by a discontinuous change in the friction factor even at high Mach number. The transition Reynolds number increases faster than linearly with Mach number, and the Knudsen number at transition (also proportional to the ratio of Mach and Reynolds numbers) passes through a maximum as the Mach number is increased. This maximum value is small, less than 0.009, indicating that transition is a continuum phenomenon even at high Mach numbers. The transition Reynolds number predicted by the linear stability analysis is significantly higher than that observed in the simulations, though its variation with Mach number is qualitatively similar. In a high Mach turbulent channel flow wall slip in the temperature and the velocities ([2]) are found to be significant. Interestingly, we find that the slip in the streamwise fluctuating velocity is higher than that in the mean velocity at high Mach number. We find that the amplitudes of the tangential fluctuating velocities increase between (0.2 - 0.4) power of the distance from the wall. In a compressible turbulent channel flow, we examine the result that the ratio of the mean free path and Kolmogorov scale increases proportional as (Ma/Re^{1/4}), and it increases asymptotically with Mach number in the high Mach number limit. The simulation show that the ratio (mean free path to Kolmogorov scale) does decrease as (Re^{-1/4}), but it does not increase linearly with Mach number. This is due to the decrease in the local Mach number within the channel, due to the increase in the temperature by viscous heating. We have also found that the smallest length scale for the velocity gradients is comparable to, or smaller than, the mean free path. Though this appears unusual, it should be noted that the smallest length for the gradients is the distance between molecules, and not the mean free path. In our simulations, the inter-molecular distance turns out to be much smaller than the mean free path. In fact, the inter-molecular distance is smaller than the cell size (we have 200 simulated molecules per cell), whereas the Kolmogorov scale and the mean free path are larger than the cell size. Even though the distance between molecules is the smallest length scale for gradients, the mean free path is the length scale for molecular transport, since the kinematic viscosity and thermal conductivity are proportional to the product of the mean free path and the fluctuating velocity. The present results suggest that the smallest scale for transport could be much larger than the smallest scale for gradients, thereby suggesting non-local transport in high Mach number turbulent flows at the smallest scales. A modification of the linear velocity profile in the viscous sub-layer near the wall, which takes into account temperature and density variations, is derived. The power law variation of the velocity and temperature is predicted under the assumption that the increase in temperature across the viscous sub-layer is larger than the wall temperature. It is found that the scaling laws do depend on the molecular model, through the dependence of viscosity and thermal conductivity on the temperature. The predicted power law, is found to be in good agreement with simulations, for two different molecular models, the hard-sphere and the variable hard-sphere.

In the combustor inlet diffuser section of gas turbine engine, high-velocity air from compressor flows into the diffuser, where a considerable portion of the inlet velocity head PT3 − PS3 is converted to static pressure (PS) before the airflow enters the combustor. Modern high through-flow turbine engine compressors are highly loaded and usually have high inlet Mach numbers. With high compressor exit Mach numbers, the velocity head at the compressor exit station may be as high as 10% of the total pressure. The function of the diffuser is to recover a large proportion of this energy. Otherwise, the resulting higher total pressure loss would result in a significantly higher level of engine specific fuel consumption. The diffuser performance must also be sensitive to inlet velocity profiles and geometrical variations of the combustor relative to the location of the pre-diffuser exit flow path. Low diffuser pressure losses with high Mach numbers are more rapidly achieved with increasing length. However, diffuser length must be short to minimize engine length and weight. A good diffuser design should have a well considered balance between the confliction requirements for low pressure losses and short engine lengths. The present paper describes the effect of divergence angle on diffuser performance for gas turbine combustion chamber using Computational Fluid Dynamic Approach. The flow through the diffuser is numerically solved for divergence angles ranging from 5 to 25°. The flow separation and formation of wake regions are studied.

SummaryThe lattice Boltzmann method (LBM) is a powerful technique for the computational modeling of a wide variety of single‐s and multiphase flows involving complex geometries. Although the LBM has been demonstrated to be effective for the solution of incompressible flow problems, there are limitations when this methodology is applied to the solution of compressible flows, especially for flows at high Mach numbers. In this article, we investigate strategies to overcome some of the limitations associated with the application of LBM to compressible flows. To this purpose, one of the key contributions of this study is the synthesis and integration of previous efforts concerning the formulation of LBM for the large‐eddy simulation (LES) of compressible turbulent flows in the subsonic flow regime. It is shown how certain limitations of applying the LBM to compressible flows can be addressed by using either a higher order Taylor series expansion of the Maxwell–Boltzmann equilibrium distribution function or using the Kataoka and Tsutahara (KT) LBM model formulation for compressible flows. The proposed LBM/LES methodology for compressible flows has been combined with the Kirchhoff integral formulation for computational aeroacoustics and used to simulate the flow and acoustic fields of compressible jet flows at high subsonic speeds with practical relevance for providing a better understanding of problems associated with jet noise. In this context, simulations of the physics associated with the jet flow and concomitant noise in the near‐ and far‐field regimes were conducted using the proposed framework of a compressible LBM/LES and Kirchhoff integral method. The results of the subsonic isothermal and nonisothermal jet flow simulations for the flow and acoustic fields have been compared with available numerical and experimental results with generally good to excellent agreement.

Secondary atomization is extensively studied by investigating a droplet subjected to a steady air/gas stream. However, droplets are often subjected to unsteady or pulsating flows, such as in aero-engines or rockets, because of thermo-acoustic instabilities in the combustion chambers. The investigation focuses on the droplet dynamics and breakup in a pulsating flow for a range of density ratios (ρr), 1000 to 10, under sinusoidal airflow of different amplitudes and frequencies as compared to the dynamics in a steady flow. The volume of fluid multiphase model tracks the liquid–gas interface, and the governing equations are solved using the finite volume method. The two-dimensional axisymmetric pulsating simulations demonstrate accuracy comparable to the corresponding three-dimensional simulations at a much lower computational cost and are used for parametric studies. The droplets under the pulsating flow show a wavy surface, and larger vortex structures are observed during the deceleration period. At a high-density ratio (1000), pulsating flow enhances droplet deformation for a faster breakup, with the flow amplitude having more impact than its frequency. For a medium-density ratio (100), where breakup occurs under steady flow, droplet breakup is inhibited in the pulsating flow at low amplitude and high frequency. In the case of a low-density ratio (10), there is no breakup under steady flow, but pulsating flow promotes breakup, except at low amplitude and high frequency. The droplet breakup is always achieved for the highest amplitude, while lower frequencies push the liquid mass from the center of the droplet to the rim.

Investigation of flow phenomena in air–water safety relief valves by means of a discontinuous Galerkin solver

3 - On some basics of compressible fluid flows

This paper deals with the effects of heat release and compressibility on temporally evolving, turbulent mixing layers. Direct Numerical Simulations (DNS) of such layers at two different convective Mach numbers are performed with and without combustion which allows to study the effects of heat release and compressibility separately and combined. It is shown that both, compressibility and heat release, dampen the turbulence activity and lead to a reduced growth of the mixing layer. Alterations in pressure fluctuations are a main reason for the changes. The effects of compressibility are not as strong in the reacting mixing layer as in the inert one. A significant difference between the inert and the reacting mixing layers at high convective Mach number is that entropic density fluctuations prevail over the acoustic ones when reaction takes place while both contribute to nearly equal parts in the non-reacting compressible flow.

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers.

The aerodynamic characteristics of droplet-laden flows past a circular cylinder are investigated using a compressible multiphase flow solver based on the six-equation model. The numerical framework is validated against benchmark cases for both multiphase and single-phase flows. Unlike prior studies that have primarily examined compressibility effects in single-phase flows or multiphase interactions at higher Reynolds numbers, this work is the first to systematically analyze the combined influence of compressibility and droplet–gas coupling in the low-Mach, laminar regime. The study explores the effects of droplet size, volume fraction, and Mach number on flow unsteadiness, droplet distribution, and aerodynamic forces. Results reveal that increasing the droplet volume fraction suppresses vortex shedding and promotes a transition to steady flow, primarily through enhanced interphase drag. Droplets preferentially accumulate in the front stagnation region, with minimal penetration into the wake, particularly under high inertial loading. The mean drag increases with droplet concentration, while the lift initially rises and then diminishes as unsteady behavior is suppressed, accompanied by a corresponding decrease in Strouhal number. At higher Mach numbers, smaller droplets contribute more significantly to drag due to stronger coupling with the compressible gas phase. Overall, the study provides new physical insights into the interplay between compressibility and multiphase dynamics in laminar flows, a regime that has remained largely unexplored.

Self-sustained, low-frequency, coherent flow unsteadiness over rigid, stationary aerofoils in the transonic regime is referred to as transonic buffet. This study examines the role of shock waves in sustaining this transonic phenomenon and its relation to low-frequency oscillations (LFO) that occur in flow over aerofoils in the incompressible regime (Zaman et al., J. Fluid Mech., vol. 202, 1989, pp. 403–442). This is investigated by performing large-eddy simulations of the flow over a NACA0012 profile for a wide range of flow conditions under free-transition conditions. At low Reynolds numbers, zero incidence angle and sufficiently high free-stream Mach numbers, $M$ , transonic buffet occurs with shock waves present in the flow. However, when $M$ alone is lowered, self-sustained, periodic oscillations at a low frequency are observed even though shock waves are absent and the entire flow field remains subsonic at all times. At higher incidence angles, the oscillations are sustained at progressively lower $M$ and are present even at $M=0.3$ , where compressibility effects are low. A spectral proper orthogonal decomposition (SPOD) shows that the spatial structure of these oscillations is consistent for all cases. The SPOD modes are topologically similar, suggesting a connection between transonic buffet and LFO in the incompressible regime. Comparisons with other studies examining transonic buffet on various aerofoils, under forced-transition and fully turbulent conditions support this hypothesis. Future studies using tools of global linear stability analysis, especially at high free-stream Reynolds numbers are required to examine whether the underlying mechanisms of transonic buffet and incompressible LFO are the same.

In this work, we carry out direct numerical simulations of particle suspensions in the compressible turbulent vertical channel (TVC) flows with Mach number Ma = 1.5 and particle Stokes number St = 1–100. The compressibility effect is considered in the particle dynamic model for the first time in the study of compressible particle-laden wall turbulence. We find that in both incompressible and compressible flow, gravity weakens the wall-normal and spanwise fluctuations of particle velocities as the Stokes number increases. However, compared to the incompressible flow case, the compressible effect amplifies the mean velocity, fluctuations of velocity, and slip velocity of particle in the streamwise direction. The wall-normal and spanwise fluctuations of particle velocities are augmented by the compressible effect in the channel core region. Moreover, in the core region, the effect of fluid compressibility on the wall-normal and spanwise fluctuations of particle velocities attenuates as the Stokes number increases, indicating a competition between the compressible effect and the particle inertia effect. We, furthermore, conduct the quadrant analysis of the local fluctuation velocities of fluid at particle positions and observe preferential distributions in the second and the fourth quadrants at y+ = 12.5–13.5. For compressible TVC flows, the pattern of probability distributions is more elongated, and the percentage is slightly higher in the second and fourth quadrants than that of incompressible flows. This observation implies that more particles locate in the ejection and sweep events in compressible flows than that in incompressible flows, which is anticipated to influence the particle wall-normal transport.

To elucidate the characteristics of droplet breakup induced by a shock wave and vortex ring behind the shock, experiments were conducted with water and various glycerol mixtures under different shock Mach numbers. High-speed visualization system, pressure testing system, and laser particle analyzer were applied to record the interaction process between droplets and a vortex ring after a shock wave. The results show that two stages of interaction are identified, including droplet-shock wave interaction and droplet-vortex ring interaction. Small clusters of droplets separated from the mother droplet will exhibit “white dot” and “swing arms” structures when subjected to vortical flow. At high shock Mach numbers, which generate strong circulation, the centrifugal force from rotation will cause droplet deformation and fragmentation. However, droplets with higher viscosity impede the stretching effect of the vortical flow, resulting in less deformation and fragmentation. Our data could provide valuable insights into droplet breakup in internal combustion engines and other industrial operations.